Time, Magic and the Self (I/III)

January 24, 2013 § Leave a comment

There is.

Isn’t it? Would you agree? Well, I would not. In other words, to say ‘There is.’ is infinitesimally close to a misunderstanding. Or a neglect, if you prefer. It is not the missing of a referent, though, at least not in first instance. The problem would be almost the same if we would have said ‘There is x’. It is the temporal aspect that is missing. Without considering the various aspects of temporality of the things that build up our world, we could neither understand the things nor the world.

Nowadays, the probability for finding some agreement for such a claim is somewhat higher than it once was, in the high tides of modernism. For most urbanists and architects, time was nothing but a somewhat cumbrous parameter, yet nothing of any deeper structural significance. The modern city was a city without time, after breaking the traditions, even not creating new ones. Such was the claim, which is properly demonstrated by Simon Sadler [1] citing Ron Herron, group member of Archigram.

“Living City”1 curator Ron Herron described his appreciation of “Parallel of Life and Art”: It was most extraordinary because it was primarily photographic and with apparently no sequence; it jumped around like anything.

Unfortunately, and beyond the mere “functioning,” the well-organized disorg-anization itself became a tradition. Koolhaas called it Junkspace [2]. Astonishingly, and not quite compatible to the admiration of dust-like scatterings that negate relationality, Archigram claims to be interested in, if not focused to life and behavior. Sadler summarizes (p.55)

“Living City” and its catalogue were not about traditional architectural form, but its opposite: the formlessness of space, behavior, life.

Obviously, Sadler himself is not quite aware about the fact that behavior is predominantly a choreography, that is, it is about form and time as well as form in time. The concepts of form and behavior as implied by Archigram’s utopias are indeed very strange.

Basically, the neglect of time beyond historicity is typical for modern/modernist architects, urbanists and theorists up to our days, including Venturi [2], Tschumi [4] or Oswald [5]. Even Koolhaas does not refer expressis verbis to it, albeit he is constantly in a close orbit of it. This is astonishing since key concepts in the immediate neighborhood of time such as semiotics, narration or complexity are indeed mentioned by these authors. Yet, without a proper image of time one remains on the level of mere phenomena. We will discuss this topic of time on the one side and architects and architecture on the other later in more detail.

Authors like Sigfried Giedion [6] or Aldo Rossi [7] didn’t change much concerning the awareness for time in the practice of architecture and urbanism. Maybe, partly because their positions have been more self-contradictive than consistent. On the one hand they demanded for a serious consideration of time, on the other hand they still stuck to rather strong rationalism. Rationalist time, however, is much less than just half of the story. Another salient reason is certainly given by the fact that time is a subject that is notoriously difficult to deal with. As Mike Sandbothe cites Paul Ricoeur [8]:

Ultimately, for Ricoeur time marks the „mystery“ of our thinking, which resists representation by encompassing our Dasein in a way that is ineluctable for our thinking.2

This Essay

One of the large hypotheses that I have been following across the last essays is that we will not be able to understand the Urban3 and architecture without a proper image of differentiation. Both parts of this notion, the “image” and the “differentiation” need some explication.

Despite “differentiation” seems to be similar to change, they are quite different from each other. The main reason being that differentiation comprises an activity, which, according to Aristotle has serious consequences. Mary Louise Gill [9] summarizes his distinction as follows:

Whereas a change is brought about by something other than the object or by the object itself considered as other (as when a doctor cures himself), an activity is brought about by the object itself considered as itself. This single modification yields an important difference: whereas a change leads to a state other than the one an object was previously in, an activity maintains or develops what an object already is.4

In other terms, in case of change it is proposed that it is relatively unconstrained, hence with less memory and historicity implied, while activity, or active differentiation implies a greater weight of historicity, less contingency, increased persistence and thus an increased intensity of being in time.

Besides this fundamental distinction we may discern several modes of differentiation. The question then is, how to construct a proper “whole” of that. Obviously we can think of different such compound “wholes,” which is the reason for our claim that we need a proper image of differentiation.

Now to the other part of the notion of the “image of differentiation,” the image. An “image” is much more than a “concept.” It is more like a diagram about the possibility to apply the concept, the structure of its use. The aspect of usage is, of course, a crucial one. Actually, with respect to the relation between concepts and actions we identified the so-called “binding problem”. The binding problem claims that there is no direct, unmediated way from concepts to actions, or the reverse. Models are needed, both formalizable structural models, being more close to concepts, and anticipatory models, being more close to the implementation of concepts. The operationalization of concepts may be difficult. Yet, action without heading to get contact to concepts is simply meaningless. (The reason for the emptiness of ‘single case’-studies.) Our overall conclusion regarding the binding problem was that it is the main source for frictions and even failure in the control and management of society, if it is not properly handled, if concepts and actions are not mediated by a layer of “Generic Differentiation.” Only the layer of “Generic Differentiation” with its possibility for different kinds of models can provide the basic conditions to speak about and to conceive any of the mechanisms potentially relevant for the context at hand. Such, the binding problem is probably one of the most frequent causes for many, many difficulties concerning the understanding, designing and dealing with the Urban, or its instances, the concrete city, the concrete settlement or building, the concrete neighborhood.

This transition between concept and action (or vice versa) can’t be fully comprised by language alone. For a certain reasons we need a diagram. “Generic Differentiation”, comprising various species of probabilistic, generalized networks, is conceived as part of a larger compound—we may call it “critical pragmatics”—, as it mediates between concepts and actions. Finally we ended up with the following diagram.

Figure 1: “Critical Pragmatics for active Subjects.” The position of Generic Differentiation is conceived as a necessary layer between the domains of concepts and actions, respectively. See text below for details and the situs where we developed it.

basic module of the fractal relation between concept/conceptual, generic differentiation and operation/operational comprising logistics and politics that describes the active subject urban reason 4t

Note, that this diagram just shows the basic module of a more complete diagram, which in the end would form a moebioid fractal due to self-affine mapping: this module appears in any of the three layers in a nested fashion. Hence, a more complete image would show this module as part of a fractal image, which however could not be conceived as a flat fractal, such like a leaf of fern.5 The image of pragmatics as it is shown above is first a fractal due to the self-affine mapping. Second, however, the instances of the module within the compound are not independent, as in case of the fern. Important traces of the same concepts appear at various levels of the fractal mapping, leading to dimensional braids, in other words to a moebioid.

So, as we are now enabled for approaching it, let us return to the necessity of considering the various aspects of temporality. What are they in general, and what in case of architecture, the city, the Urban, or Urban Reason? Giedion, for instance, related to time with regard to the historicity and with regard to an adaptation of the concept of space-time from physics, which at that time was abundantly discussed in science and society. This adaptation, according to Giedion, can be found in simultaneity and movement. A pretty clear statement, one might think. Yet, as we will see, he conceived of these two temporal forms of simultaneity and movement in a quite unusual way that is not really aligned to the meaning that it bears in physics.

Rossi, focusing more on urban aspects, denotes quite divergent concepts of time. He did not however clearly distinguish or label them. He as well refers to history, but he also says that a city has “many times” (p.61 in [7]), a formulation that reminds to Bergson’s durée. Given the cultural “sediments” of a city within itself, its multiply folded traces of historical times, such a proposal is easy to understand, everybody could agree upon it.

Besides the multiplicity of referential historical time—we will make the meaning of this more clear below—, Rossi also proposes implicitly a locality of time through the acceleration of urbanization through primary elements such as “monuments”, or building that own a “monumental” flavor. Unfortunately, he neither does refer to an operationalization of his time concept nor does he provide his own. In other words, he still refers to time only implicitly, by describing the respective changes and differentiations on an observational level.

These author’s proposals provide important hints, no doubt. Yet, we certainly have to clarify them from the perspective of time itself. This equals firstly an inversion of the perspective from architectural or urbanismic vantage point taken by Giedion and Rossi, who in both cases started from built matter. Before turning to architecture, we have to be clear about time. As a second consequence, we have to be cautious when talking about time. We have to uncover and disclose the well-hidden snares before we are going to push the investigation of the relation between temporality and architecture further down.

For instance, both Giedion and Rossi delivered an analysis. This analyticity results in a pair of consequences. Either it is, firstly, just useful for sorting out the past, but not for deriving schemes for synthesis and production, or, secondly, it requires an instantiation that would allow to utilize the abstract content of their analysis for taking action. Such an instantiation could produce hints for a design process that is directed to the future. Yet, neither Giedion [6] nor Rossi [7] did provide such schemes. Most likely precisely due to the fact that they did not refer to a proper image of time!

This essay is the first of two in a row about the “Time of Architecture”. As Yeonkyung Lee and Sungwoo Kim [10] put it, there is much need for its investigation. In order to do so, however, one has to be clear about time and its conception(s). Insofar we will attempt to trace time as a property of architecture and less as an accessory, we also have to try to liberate time from its distinctive link to human consciousness without sacrificing the applicability of the respective conception to the realm of the human.

Hence, the layout of this essay is straightforward.

(a) First we will introduce a synopsis on various conceptions of time as brief as possible, taking into account a few, and probably the most salient sources. This will equip us with possible distinctions about modes or aspects of time as well as the differences between and interdependencies of time and space.

In architecture and urbanism, almost no reference can be found to philosophical discourses about time. Things are handled intuitively, leading to interesting but not quite valuable and usable approaches. We will see that the topic of “time” raises some quite fundamental issues, reaching at least into the field of hermeneutics, semiotics, narratology, and of course philosophy as well. The result will be a more or less ranked list of images of time as it is possible from a philosophical vantage point.

(b) Before the background of this explication and the awareness for all the possible misunderstandings around the issue of time, we will introduce a radically different perspective. We will ask how nature “creates time”. More precisely, we will ask about the abstract elements and mechanisms that are suitable for “creating time.” As weird this may seem at first, I think it is even a necessary question. And for sure nobody else posed this question ever before (outside of esoterics, perhaps, nut we do not engage in esoterics here!).

The particularity of that approach is that the proposed structure would work as a basis for deriving an operationalization for the interpretation of material systems as well as an abstract structure for a foundation of philosophical arguments about time. Of course, we have to be very careful here in order to avoid falling back into naturalist or phenomenological naiveties. Yet, carefulness will allow us to blend the several perspectives onto time into a single one, without—and that’s pretty significant—reducing time to either space or formal exercises like geometry. Such, the reward will be a completely new image of time, one that is much more general than any other and which overcomes the traditional separations, for instance that which pulls apart physical time and time of experience. Another effect will be that the question about the origin of time will vanish, a question which is continuously being discussed in cosmology (and theology, perhaps, as well).

(c) From the new perspective then we will revisit architecture and the Urban (in the next essay). We will not only return to Giedion, Rossi, or Koolhaas but we also will revisit the “Behavioral Turn that we have been introducing some essays ago.

Displayed in condensed form, our program comprises the following three sections:

  • (a) Time itself as a subject of philosophy.
  • (b) The creation of time.
  • (c) Time of Architecture.

Before we start a few small remark shall be in order. First, it may well appear as somewhat presumptuous to try to handle time in sufficient depth within just one or two sections of a single essay. I am fully aware about this. Yet, the pressure to condense the subject matter also helps to focus, to achieve a structural picture on the large scale. Second, it should be nevertheless clear that we can’t provide a comprehensive overview or summary about the various conceptions of time in philosophy and science, as interesting this would have been. It would exceed even the possibilities of a sumptuous book. Instead, I will lay out my arguments by means of a purposeful selection, enriched with some annotations.

On the other hand this will provide one of the very rare comprehensive inquiries about time, and the first one that synthesizes a perspective that is backward compatible to those authors to whom it should.

Somewhat surprising, this could even include (theoretical) physics. Yet, the issue is quite complex and very different from mainstream, versions of which you may find in [27, 28]. Even as there are highly interesting and quite direct links to philosophy, I decided to put this into a separate essay, which hopefully will happen soon. Just to give you a tiny glimpse on it: Once Richard Feynman called his mentor and adviser John Wheeler in the middle of the night, asking him, “How many electrons are there in the universe?” According to the transmission Wheeler answered: “There is exactly one.” Sounds odd, doesn’t it? Nevertheless it may be that there are indeed only a few of them, according to Robbert Dijkgraaf, who also proposes that space-time is an emergent “property,” while information could be conceived as more fundamental than those. This, however, has a rather direct counterpart in the metaphysics of Spinoza, who claimed that there is only 1 single attribute. Or (that’s not an unhumbleness), take our conception of information that we described earlier. Anyway, you may have got the point.

The sections in the remainder of this essay are the following. Note that in this piece we will provide only chapter 1 and 2. The other chapters from “Synthesis” onwards will follow as a separate piece.

1. Time in Philosophy—A Selection

Since antiquity people have been distinguishing two aspects of time. It was only in the course of the success of modern physics and engineering that this distinction has been gone forgotten in the Western world’s common sense. The belief set of modernism with its main pillar of metaphysical independence may have been contributing as well. Anyway, the ancient Greeks assigned them the two gods of chronos and kairos. While the former was referring to measurable clock-time, the second denoted the opportune time. The opportune time is a certain period of time that is preferential to accomplish an action, argument, or proof, which includes all parts and parties of the setting. The kairos clearly exceeds experience and points to the entirety of consummation. The advantage of taking into account means and ends is accompanied by the disadvantage of a significant inseparability.

Aristotle

Aristotle, of course, developed an image of time that is much richer, more detailed and much less mystical. For him, change and motion are apriori to time [11]. Aristotle is careful in conceiving change and motion without reference to time, which then gets determined as “a number of change with respect to the before and after” (Physics 219 b 1-2). Hence, it is possible for him to conceive of time as essentially countable, whereas change is not. Here, it is also important to understand Aristotle’s general approach of hylemorphism, which states that—in a quite abstract sense—substance always consists of a matter-aspect and a form-aspect [11]. So also for time. For him, the matter-aspect is given by its kinetic, which includes change, while the form aspect shows up in a kind of order6. Time is a kind of order is not, as is commonly supposed, a kind of measure, as Ursula Coope argues [13]. Aristotle’s use of “number” (arithmos) is more a potential for extending operations, as opposed to “measure” (metron), which is imposed to the measured. Hence, “order” does not mean that this order is necessarily monotone. It is an universal order within which all changes are related to each other. Of course, we could reconstruct a monotone order from that, but as said, it is not a necessity. Another of the remarkable consequences of Aristotle’s conception is that without an counting instance—call it observer or interpretant —there is no time.

This role of the interpreter is further explicated by Aristotle with respect to the form of the “now”. Roark summarizes that we have understand that

[…] phantasia (“imagination”) plays a crucial role in perception, as Aristotle understands it, and therefore also in his account of time. Briefly, phantasia serves as the basis for both memory and anticipation, thereby making possible the possession of mental states about the past and the future. (p.7)

Actually, the most remarkable property of Aristotle’s conception is that he is able to overcome the duality between experience and physical time by means of the interpretant.

Pseudo-Paradoxes

It is not by chance alone that Augustine denied the Aristotelian conception by raising his infamous paradox about time. He does so from within Christian cosmogony. First he argues that the present time vanishes, if we try to take close look. Then he claims that both past and future are only available in the present. The result is that time is illusory. Many centuries later, Einstein would pose the same claim. Augustine transposed the problem of time into one of the relation between the soul and God. For him, no other “solution” would have been reasonable. Augustine instrumentalises a misunderstanding of references, established by mixing incompatible concepts (or language games). Unfortunately, Augustine inaugurated a whole tradition of nonsense, finally made persistent by McTaggart’s purported proof of the illusion of time [14] where he extended Augustine’s already malformed argument into deep nonsense, creating on the way the distinction between A-series (past, present and future) and B-series (earlier, later) of time. It is perpetuated until our days by author’s like Oaklander [15][16] or Power [17]. Actually, the position is so nonsensical and misplaced—Bergson called it a wrong problem, Wittgenstein a grammatical mistake—that we will not deal with it further7.

Heidegger

Heidegger explicitly refers to phenomenology as it has been shaped by Edmund Husserl. Yet, Heidegger recognized that phenomenology—as well as the implied ontology of Being—suffers from serious defects. Thus, we have to take a brief look onto it.

With the rise of phenomenology towards the end of the 19th century, the dualistic mapping of the notion of time has been reintroduced and reworked. Usually, a distinction has been made between clock-time on the one hand and experiential time on the other. This may be regarded indeed as quite similar to the ancient position. Yet, philosophically it is not interesting to state such. Instead we have to ask about the relation between the two. The same applies to the distinction of time and space.

There are two main positions dealing with this dualism. On the one side we find Bergson, on the other Brentano and Husserl as founders of phenomenology. Both refer to consciousness as an essential element of time. Of course, we should not forget that this is one of the limitations we have to overcome, if we want to achieve a generalized image of time.

Phenomenology suffers from a serious defect, which is given by the assumption of subjects and objects as apriori entities. The object is implied as a consequence of the consciousness of the subject, yet this did not result in a constructivism à la Maturana. Phenomenology, as an offspring of 19th century modernism and a close relative of logicism, continued and radicalized the tendency of German Idealism to think that the world could be accessed “directly”. In the words of Thomas Sheehan [19]:

And finally phenomenology argued that the being of entities is known not by some after-the-fact reflection or transcendental construction but directly and immediately by way of a categorical intuition.

There are two important consequences of that. Firstly, it violates the primacy of interpretation8 and has to assume a world-as-such, which in other words translates into a fundamentally static world. Secondly, there is no relation between to appearances of an object across time.

Heidegger, in “Being and Time” [21] (original “Sein und Zeit” [22]), tried to correct this defect of phenomenology and ontology by a hermeneutic transformation of phenomenology. This would remove the central role of consciousness, which is replaced by the concept of the “Being-there” (Dasein) and so by the “Analysis of Subduity.” He clearly states (end of §3 in “Being and time”) that any ontology has to be fundamental ontology. The Being-there (Dasein) however needs— in order to be able to see its Being—temporality.

The fundamental ontological task of the interpretation of being as such, therefore, includes working out the Temporality of being. The concrete answer to the question of the sense of being is given for the first time in the exposition of the problematic of Temporality. ([22], p.19)

How is temporality described? In §65 Heidegger writes:

Coming back to itself futurally, resoluteness brings itself into the Situation by making present. The character of “having been” arises from the future, and in such a way that the future which “has been” (or better, which “is in the process of having been”) releases from itself the Present. This phenomenon has the unity of a future which makes present in the process of having been; we designate it as “temporality”.9

Time clearly “delimits” Being as a conditioning horizon:

[…] we require an originary explication of time as the horizon of the understanding of being in terms of temporality as the being of Dasein who understands being. ([22], p.17)

Heidegger examines thoroughly the embedding of Being-there into time and the conditioning role of “time.” For instance, we can understand a tool only with respect to its future use. Temporality itself is seen as the structure of “care”, a major constitutive of the being of Dasein, which similarly to anticipation carries a strong reference to the future:

The originary unity of the structure of care lies in temporality” ([22], p.327).

Temporality is the meaning and the foundation of Being.10 Temporality is an Existential. Existential analysis claims that Being-there does not fill space, it is not within spatiality (towards the end of §70):

Only on the basis of its ecstatico-horizontal temporality is it possible for Dasein to break into space. The world is not present-at-hand in space; yet, only within a world does space let itself be discovered. The ecstatical temporality of the spatiality that is characteristic of Dasein, makes it intelligible that space is independent of time; but on the other hand, this same temporality also makes intelligible Dasein’s ‘dependence’ on space—a ‘dependence’ which manifests itself in the well-known phenomenon that both Dasein’s interpretation of itself and the whole stock of significations which belong to language in general are dominated through and through by ‘spatial representations’. This priority of the spatial in the Articulation of concepts and significations has its basis not in some specific power which space possesses, but in Dasein’s kind of Being. Temporality is essentially deterioriating11, and it loses itself in making present; […]

This concept of temporality could have been used to overcome the difference between “vulgar time” (chronos) and experiential time, to which he clearly sub-ordinated the former. Well, “could have been” if Heidegger’s program would have been completable. But Heidegger finally failed, “Being and Time” remained fragmentary. There are several closely related aspects for this failure. Ultimately, perhaps, as Cristina Lafont [24] argues, it is impossible to engage in a radical program of detranscendentalization and at the same time to try to achieve a fundamental foundation. This pairs with the inherited phenomenological habit to disregard the primacy of interpretation. The problem for Heidegger now is that the sign in the language is already in the world which has to be subdued. As Lafont brilliantly revealed, Heidegger still adheres to the concept of language as an “ontic” instrument, as something that is found in the outer world. Yet, this must count simply as a highly inappropriate reduction. Language constantly and refracted points towards the inwardly settled translation between body and thought and the outward directed translation between thought and community (of speakers), while translation is also kind of a rooting. Such we can conclude that ultimately Heidegger therefore still follows the phenomenological subject-object scheme. His attempt for a fundamental foundation while avoiding any reference to transcendent horizons must fail, even if this orientation towards the fundamental pretends to just serve as an indirect “foundation” (see below).

There is a striking similarity between Augustine and Heidegger. We could call it metaphysical linearity as a cosmological element. In case of Augustine it is induced by the believe in Salvation, in case of Heidegger by the believe into an absolute beginning paired with a (implicit) believe to step out of language. In a lecture held in 1963, that is 36 years after Being and Time, titled “Time and Being”, Heidegger revisits the issue of time. Yet, he simply capitulated from the problem of foundations, referring to “intuitional insight” as a foundation. In the speech “Time and Being” hold in 1962 [25], he said

To think the Being in its own right requires to dismiss Being as the originating reason of being-Being (des Seienden), in favor of the Giving that is coveredly playing in its Decovering (Entbergen), i.e. of the “There is as giving fateness.”12 (p.10)13

Here, Heidegger refutes foundational ontology in favour of the communal and external world by he concept of the Giving14. Yet, the step towards the communal still remains a very small step, since now not only the Other gets depersonalized as far as possible. The real serious issue here is that Heidegger now replaces the ontological conception of “ontic” language by the “ontic” communal. He still does not understand the double-articulation of the communal through language. We may say that Heidegger is struck by blindness (on his right eye).

Inga Römer [47] detects a certain kind of archaism throughout the philosophy of Heidegger, which comes along as a still not defeated thinking about origins.

Finally, in „Being and Time“ Heidegger detects the origin of time in the event, which he dedicatedly determines as the provider [m: the Giving] of Being and time. This Giving is seen as being divested from itself. The event, determined by Heidegger elsewhere as a singular tantum, is eliminated from itself—and nevertheless the event is conceived as the origin of time.15 (p.289)

Many years after the publication of “Being and Time”, in the context of the seminar “Time and Being” Heidegger claimed that he did not conceive fundamental ontology as kind of a foundation. He described the role of the Daseins-analytics as proposed in “Being and Time” in the following way [23]:

Being and Time is in fact on the way to find, taking the route through the timeness of Dasein in the interpretation of Being as temporality, a conception of time, that Owned of “time”, whence “Being” reveals itself as Presenting. Such however it is said that the fundamental mentioned in the fundamental ontology can’t take reference and synthesis. Instead, the whole analytics of Dasein ought to be repeated, subsequent of possibly having thrown light upon the sense of Being, in a more pristinely and completely different manner.16

Indeed, “Being and Time” remained fragmentary, Heidegger recognized the inherent incompatibility of the still transcendental alignment with the conception of the Dasein and was hence forced to shift the target of the Daseins-analytics [26](p.99). Being is not addressed from the vantage point of being-Being (Seiendes) anymore. It resulted in a replacement of the sense of Being by the question about the historical truth of Being as fateness. In the course of that shift, however, temporality lost its role, too, and was replaced by a thinking of a historized event. This event is conceived as kind of a non-spatial endurance [25]:

Time-Space (m: endurance) now denotes the open that in the mutually-serving-one-another of arrival, having been (Gewesenheit) and present clears itself. Only this open spacingly allows (räumt ein) the ordinarily known space its propagation. (p.19)17

As far as this move could be taken as a cure of the methodological problems in “Being and Time,” it turned out, however, to be far detrimental for Heidegger’s whole philosophy. He was forced to determine man by his ecstatic exposition and being-thrown (tossed?) into nothingness. Care as kind of cautious anticipation was replaced first by angst, then by incurable disgust through Sartre. While the early Heidegger precisely tried to cure the missing of primal relationality in phenomenology, the later Heidegger got trapped by an even more aggressive form of singularization and denial of relationality at all. This whole enterprise of existential philosophy suffers from this same deep disrespect if not abhorrence of the communal, of the practice of sharing joyfully a common language that turns into the Archimedic Point of being human. Well, how could he think differently given his particular political aberrancy?

Anyway, Heidegger’s shift to endurance brings us directly to the next candidate.

Bergson

Politically, in real life, Heidegger and Bergson could not be more different. The former more than sympathizing (up to open admiration) with totalitarianism in the form of Hitlerism and fascism, thereby matching his performative rejection of relationality, the latter engaging internationally in forming the precursor of the UN.

But, how does Bergson’s approach to time look like? For Bergson, logicism and the subject-object dichotomy are thoughts that are alien to him. Both actually have to assume a sequential order that yet have to be demonstrated in its genesis.18 The starting point for Bergson is the diagnosis that measurable time, or likewise measuring time, as it is done in physics as well by any clock-time introduces homogeneity, which in turn translates into quantificability [31]. As such, time is converted into a spatial concept, as these properties are also properties of space as physics conceives it. The consequence is that we create pseudo-paradoxes like that which has been explicated by Augustine. To this factum of quantificability Bergson then opposes qualitability. For him, quality and quantity remain incommensurable throughout his works.

At any rate, we cannot finally admit two forms of the homogeneous, Time and Space, without first seeking whether one of them cannot be reduced to the other […] Time, conceived under the form of an unbounded and homogeneous medium, is nothing but the ghost of space, haunting the reflective consciousness. ([32] p. 232)

So we can fix that time is essential a qualitative entity, or in other words, an intensity that is, according to Bergson, opposed to the extensity of spatial entities. Spatial entities are always external to each other, while for intensive entities—such as time—such an externalization is not possible. They can be thought only as a mutually interpenetrating beside-one-another, which however should be thought as an aterritorial “beside”. As Friedrich Kuemmel puts it, intensity, for Bergson, can be detached from extensity.19 Intensity then is being equipped by Bergson with a manifoldness or multiplicity that consequently establishes a reality apart from physical spatiality with its measurable time. This reality is the reality of consciousness and the soul. Bergson calls it “durée”, which of course must not be translated into “duration” (or into the German “Dauer”). Durée is more like the potential for communicable time, or in Deleuze’s words, a “potential number” ([33] p.45), to which we can refer in language literally as “referential time.”

Bergson’s notion of durée is quite easily determined (p.37)

It [durée] is a case of “transition,” of a “change,” a becoming, but it is a becoming that endures, a change that is substance itself. […] Bergson has no difficulty in reconciling the two fundamental characteristics of duration; continuity and heterogeneity. However, defined in this way, duration is not merely lived experience; […] it is already a condition of experience.

As a qualitative multiplicity, durée is opposed to quantitative multiplicity. For Bergson, this duality is a strict and unresolvable one, yet it does not set up an opposition, it is not subject of dialectic. It does, however, follow the leitmotif of Bergson, according to Deleuze ([33] p.23): People see quantitative differences where actually are differences in kind. (RRR)

Deleuze emphasizes that the two multiplicities have to be strictly distinguished ([33] p.38).

[…] the decomposition of the composite reveals to us two types of multiplicity. One is represented by space […]: it is a multiplicity of exteriority, of simultaneity, of juxtaposition, of order, of quantitative differentiation, of difference in degree; it is a numerical multiplicity, discontinuous and actual. The other type of multiplicity appears in pure duration: It is an internal multiplicity of succession, of fusion, of organization, of heterogeneity, of qualitative discrimination, or of difference in kind; it is a virtual and continuous multiplicity that cannot be reduced to numbers.

Here we may recall Aristotle’s notion of time as kind of order. This poses the question whether duration itself is a multiplicity. As Deleuze carves it out ([33] p.85):

At the heart of the question “Is duration one or multiple?” we find a completely different problem: Duration is a multiplicity, but of what type? Only the hypothesis of a single Time can, according to Bergson, account for the nature of virtual multiplicities. By confusing the two types – actual spatial multiplicity and virtual temporal multiplicity- Einstein has merely invented a new way of spatializing time.

Pushing Bergson’s architecture of time further, Deleuze develops his first accounts on virtuality. It becomes clear, that durée is a virtual entity. As such, it is outside of the realm of numbers, even outside of quantificability or quantitability. Speaking in Aristotelian terms we could say that time is a smooth manifold of kinds of orders. Again Deleuze (p.85):

Being, or Time, is a multiplicity. But it is precisely not “multiple”; it is One, in conformity with its type of multiplicity.

For Bergson, tenses are already actualizations of durée. The past is conceived as being different from the present in kind, and could not be compared to it. There is also possibility for a transition from a “past” to a “present.” It is the work of memory (as an abstract entity) that creates the link. Memory extends completely into present, though. Its main effect is to recollect the past. In this sense, memory is stepping forward. Durée and memory are co-extensive.

As we have seen, Bergson’s conception of time is strongly linked to consciousness and its particular memory. We also have seen that he considers physical time as a kind of a secondary phenomenon. He thinks that things surely have no endurance in the sense of a capability to actualize durée into an extended present.

This poses a problem: What is time in our outside? In Time and Free Will he writes [32],

Although things do not endure as we do ourselves, nevertheless, there must be some incomprehensible reason why phenomena are seen to succeed one another instead of being set out all at once. (p.227)

Well, what does this claim “things do not endure as we do ourselves” refer to? Is there endurance of things at all? And what about animals, thinking animals, or epistemic machines? As Deleuze explains, Bergson is able to solve this puzzle only by extending his durée into a cosmic principle ([33], pp.51). Yet, I think that in this case he mixes immaterial and material aspects in a quite inappropriate manner.

Bergson’s conception of time certainly has some appealing properties. But just as its much less potent rival phenomenology it is strongly anthropocentric. It can’t be generalized enough for our purposes that follow the question of time in architecture. Of course, we could conceive of architecture as a thing that is completely passive if nobody looks onto it or thinks about it. But what is then about cities? The perspective of passive things has been largely refuted, first by Heidegger through his hermeneutic perspective, and in a much more developed manner, by Bruno Latour and his Agent-Network-Theory.

In still other terms, we could say that Bergson’s philosophy suffers from a certain binding problem. I think it was precisely the binding problem that caused the hefty dispute between Einstein and Bergson. Just to be clear, in my opinion both of them failed.

Thus we need a perspective that allows to overcome the binding problem without sacrificing either the experiential time, or durée or the measurability of referential time. This perspective is provided by the semiotics of Charles Sanders Peirce.

Peirce

Peirce was an engineer, his formal accounts thus always pragmatic. This sets him apart from Bergson and his early devotion to mathematics. Where the former sees processes in which various parts engage, the latter sees abstract structures.

Being an engineer, Peirce looked at thought and time in a completely different manner. He starts with referential time, with clock-time. He does not criticize it at first hand as Bergson would later do.

The first step in our reconstruction of Peircean time is his move to show that neither thought nor, of course, consciousness can take place in an instant. Consciousness must be a process. Else, thought is a sign. One has to know that for Peirce, a sign is not to be mistaken as a symbol. For him it is an enduring situation. We will return to this point later.

In MS23720 (chapter IV in Writings 3) his primary concern is to explain how thinking could take place

A succession in time among ideas is thus presupposed in time-conception of a logical mind; but need this time progress by a continuous flow rather than by discrete steps?

Of course, he concludes that a “continuous time” is needed. Yet, at this point, Peirce starts to depart from a single, univoke time. He continues

Not only does it take time for an idea to grow but after that process is completed the idea cannot exist in an instant. During the time of its existence it will not be always the same but will undergo changes. […] It thus appears that as all ideas occupy time so all ideas are more or less general and indeterminate, the wider conceptions occupying longer intervals.

This way he arrives at a time conception that could be characterized as a multiplicity of continua. Even if it would be possible to determine a starting time and a time of completion for any of those intervals, it still remains that all those overlapping thoughts form a single consciousness.

Chapter 5 in “Writings 3” (MS239), titled “That the significance of thought lies in reference to the future” [35], starts in the following way.

In every logical mind there must be 1st, ideas; 2nd, general rules according to which one idea determines another, or habits of mind which connect ideas; and, 3rd, processes whereby such habitual connections are established.

The second aspect strongly reminds to our orthoregulation and the underlying “paradox of rule-following” first clearly stated by Ludwig Wittgenstein in the 1930ies [36]. The section ends with the following reasoning:

It appears then that the intellectual significance of all thought ultimately lies in its effect upon our actions. Now in what does the intellectual character of conduct consist? Clearly in its harmony to the eye of reason; that is in the fact that the mind in contemplating it shall find a harmony of purposes in it. In other words it must be capable of rational interpretation to a future thought. Thus thought is rational only so far as it recommends itself to a possible future thought. Or in other words the rationality of thought lies in its reference to a possible future.

In this brief paragraph we may find several resemblances to what we have said earlier, and elsewhere. First, Peirce’s conception of time within his semiotics provide us a means for referring to the binding problem. More precisely, thought as sign process is itself the mechanism to relate ideas and actions, where actions are always preceded, but never succeeded by their respective ideas.

Second, Peirce rejects the idea that a single purpose could be considered as reasonable. Instead, in order to justify reasonability, a whole population of remindable purposes, present and past, is required; all of them overlapping, at least potentially, all of them once pointing to the future. This multiplicity of overlapping and unmeasurable intervals creates a multiplicity of continuations. Even more important, this continuation is known before it happens. Hence, the present extends into the past as well as into the future. Given the fact that firstly the immediate effect of an action is rarely the same as the ultimate effect, and secondly the ultimate effect is often quite different to the expectation related to the purpose, we often do even not know “what” happened in the past. So, by applying ordinary referential time, our ignorance stretches to both sides of present, though not in the same way. It even exceeds the period of time of what could be called event.

Yet, by applying Peirce’s continuity, we find a possibility to simplify the description. For we then are faced by a single kind of ignorance that results in the attitude that Heidegger called “care” (Sorge).

The mentioned extension of the experienced ignorance as an ignorance within the present into the past and the future does not mean, of course, to propose a symmetry between the past and the future with respect to present, as we will see in a moment. Wittgenstein [40] is completely right in his diagnosis that

[…] in the grammar of future tense the conception of “memory” does not occur, even not with inverted sign.21 (p. 159)

The third issue, finally, concerns the way re relates rationality to the notion of “possible future.” This rationality is not claiming absolute objectivity, since it creates its own conditions as well as itself. Peirce’s rationality is a local one, at least at first sight. It is just this creating of the possible future that provides the conditions for the possibility of the experiencibility of future affairs.

The most important (methodological) feature of Peircean semiotics is, however, the possibility to jump out of consciousness, so to speak. Sign situations occur not only within the mind, they are also ubiquitous in interpersonal exchange, and even in the absorption of energy by different kinds of matter. Semiotics provides a cross-medial continuity. This argument has been extended later by John Dewey [37][38], Peirce’s pragmatist disciple .

Such we could say that, if (1) thought comprises signs, and (2) signs are sign situations, then it does not make sense to speak about “instantaneous” time regarding thought and consciousness in particular, but also regarding any interpretation in general, as interpretation is always part of a sign (-situation). Then, we also can say that presence lasts as long as a particular interpretation is “running”. Yet, signs refer to signs only. Interpretations are fundamentally open in its beginning as well as in its end. They are nested and occur in parallel, and are more broken than finished just contingently. Once the time string, or the interpretive chain, respectively, has been broken, past and future appear literally in their own right, i.e. de iure, and only by a formal act.22

The consequence of all that the probabilistic network of interpretations gives rise to a cloud of time strings, any of them with indeterminable ends. It is clear that signs and thus thinking would be absolutely impossible if there would be just one referential clock-time. But even more important, without the inner multiplicity of “sign time” there would be only the cold world of a single strictly causal process. There would be no life and no information. Only a single, frozen black hole.

Given the primacy of the cloud of time strings, it is easy to construct referential time as a clock-time. One just needs to enumerate the overlapping time strings in such a way that enumeration and counting coincide. Once this is done it is possible to refer to a clock. Yet, the clock would be without any meaning without such a enumerative counting. The clock the is suitably actualized in a more simple way by a perfectly repetitive process, that is, a process that actually is outside of time, much as Aristotle thought it is the case for celestial bodies. And once we have established clock time we can engage in interpersonal synchronization of our individual time string populations.

Peircean sign time thus not only allows to reconcile the two modi of time, the experiential time and referential time. It is also possible to extend the same process into historical time, rooting historicity in an alternative and much more appealing manner than it was proposed by Heidegger.

Wittgenstein

All the positions we met so far can be split into two sets. In the first part we find fundamental ontology and existential philosophy (Heidegger), analytic ontology (Oaklander), “folk approaches” (Augustine), idealistic conceptions (McTaggart) and physics with its reductionist perspective . In the second subset we find Aristotle, Bergson and Peirce.

The difference between the two parties lies in the way they root the concept of time. The former party roots it in reality; hence they ask about the inner structure of time, much like one would ask about the inner structure of wood. For the proponents of the second class time is primary experiential time and such always rooted in the interpretant, i.e. some kind of active observer, whether this refers to observers with or without consciousness. For all of them, though in different ways, the present is primary. For Aristotle it is kind of a substance, for Bergson durée, for Peirce the sign as process.

Wittgenstein does not say much time, since he seems to be convinced that there is not so much to say. He simply accepts the distinction between referential time of physics and experiential time and considers them to be incommensurable. [39]

Both ways of expressing it are okay and equitable, yet not blendable.23 ([40], p.81-82)

Already in the Tractatus, Wittgenstein wrote

We cannot compare any process with the “passage of time”—there is no such thing—but only with another process (say, with the movement of the chronometer).24 (TLP 6.3611)

Here it becomes clear that clock-time is nothing “built into matter”, but rather a communally negotiated reference, or in short, referential time. We all refer to the same particular process, whether this is length of a day or the number of state changes in Cs-133.25 Experiential time, on the other hand, can’t be considered as a geometrical entity, hence there is no such thing as a “point” in present. In experience, there is nothing to measure. The main reason for this being that experience is tightly linked to (abstract) modeling, and thus to the choreosteme. In short, experience is a self-generating process without an Archimedean Point.

“Now” does not denote a point in time. It is not a “name of a moment in time.”26 ([43], 157)

[…] yet it is nonsense to say ‚This is this‘, or ‚This is now‘.27 ([43], 159)

„Now“ is an indexical term, just as „I“, „this“ or „here“. Indexical terms do not refer to an index. Quite in contrast, sometimes, in more simple cases, they are setting an index, in more complicated cases indexical terms just denote the possibility for imposing an index onto a largely indeterminate context. Hence, it is for grammatical reasons that we can’t say “this is now.” Time is not an object. Time is nothing of which we could say that it does exist. Thus we also can not ask “What is time?” as this implies the existentialist perspective. The question about the reality of time is ungrammatical, it is like trying to play Chinese checkers28 on a chess board, or chess on a soccer field.

More precisely, there is no possibility to speak about “time as an object” in meaningful terms. For language is (i) a process itself, (ii) a process that intrinsically relates to the communal (there is no private language), and (iii) language is a strongly singular term. Thus we can conclude that there is no such thing as the objectification of time, or objective time.

Examples for such an objectification are easy to find. For instance, it is included in the question posed by Augustine “What is time?”  (Wittgenstein’s starting point for the Philosophical Investigations.) It is also included in the misunderstanding of an objective referential time. Or in the claim that time itself is flowing (like a river). Or in the attempt to proof that time itself is continuous.29

Instead, “now” is used as an indication of—or a pointer to—the present and the presence of the speaker. Its duration in terms of clock-time is irrelevant. It would be nonsense to attempt to measure this duration, because it would mean to measure the speaker and his act itself.

Accordingly, the temporal modi in language, the tenses, such as past, present time, future, reflect to the temporal modi of actions—including speech acts—, which take place in the “now” and are anchored in the future through their purpose ([42] p.142).

Confusing and mixing the two conceptions of time—referential time and experiential time—is the main reason, according to Wittgenstein, for enigmas and paradoxes regarding time (such as the distinction of A-series and B-series by McTaggart and in ontology).

For there is no such thing as the objectification of time, time is intrinsically a relational “entity”. As Deleuze brilliantly demonstrates in his reflections about Bergson [33], time can be thought only as durée, or in my words, as a manifold of anobjected time strings, that directly points to the virtual, which in turn is not isolated, but rather an intensity within the choreosteme.

The idealistic, phenomenological and existential approaches to temporality are deeply flawed, because it is not possible to take time apart, or to take time out of the game. Wittgenstein considers such attempts as a misuse of language. Expressions like „time itself“ or questions like “What is time?” are outside of any possible language.

In the ‘Philosophical Remarks’ he says

What belongs to the essence of the world could not be expressed by language. Only what we could imagine as being different language is able to tell.30 ([40] p.84).

Everything which we are able to describe at all, could also be different.31 ([45],p .173).

In order to play the game of “questioning reality of X” in a meaningful manner it has to be possible that it is not real, or partially. An alternative is needed, which however is missing in existential questions or attempts to find the essence. Thus it is meaningless (free of sense) to doubt (even implicitly) the reality of time, whether as present, as past or as future. It is similar to Moore’s paradox of doubting of having an arm. In the end, at least after Wittgenstein, one always have to begin with language. It is nonsense to begin with existence, or likewise essence.

Wittgenstein rejects the traditional philosophical reflection that always tried to find the eternal, necessary and general truth, essence or “true nature” as opposed to empirical—and pragmatical—impressions. The attempt to determine the reality of X as a being-X-as-such is a misuse of language, it is outside of the logic of language.

For Wittgenstein, the more interesting part of time points to memory, as clock-time is a mere convention. For him, memory is the sourcing wellspring (“Quelle”) of time, since the past is experienceable just as a recall of the past ([40] p.81f). Bergson called it recollection.

I think that there are one major consequence of Wittgenstein’s considerations. Time can be comprehended only as a transcendent structural condition of establishing a relation, hence also acting, speaking and thinking. Without such conditioning it is simply not possible to establish a relation. This extends, of course, also to the realm of the social [46]. Here we could even point to physics, particularly to the maximum speed of light, that is the maximum speed of exchanging information, which translates to the “establishment of time” as soon as a relation has been built. This includes that this building of a relation is irreversible. Within reversibility it does not make sense to speak about time. Even shorter, we could be tempted to say that within information there is no time, if it would be meaningful to think something like “within information”. Information itself is strictly bound to interpretation, which brings us back to Peircean semiotics.

Such we could say that we as humans “create” time mainly by means of language, albeit it is not the only possibility to “create” time. Yet, for us humans (as a collective individual beings32) there is hardly another possibility, for we can’t step out of language. Different languages and different uses of language “create” different times. It is this what Helga Nowotny calls “Eigenzeit” [46] (“self-owned time”).

It is rather important to understand that by means of these argument we don’t refer any more to something like “historical time” or “natural time”. Our argument is much more general.

Secondarily, then, we may conclude that we have to ask about the different ways we use the language game “time”.

Ricoeur

As other authors Paul Ricoeur proposes a strict discontinuity between historical time (“historicality”) and physical time. The former he also calls “time with present”, the latter “time without present.” Yet, unlike other authors he also proposes that this discontinuity can’t be reconciled or bridged. This hypothesis he proceeds to formulate by means of three aporias [47].

  • – Aporia 1, duality: Subjective time and objective time can’t be thought together in a single conception, and even more, they obscure them mutually.
  • – Aporia 2, false unity: Despite we take it for granted that there is one single time, we can’t justify it. We even contradict the insight—which appears as trivial—that there is subjective and objective time.
  • – Aporia 3, inscrutability: Thought can not comprehend time, since its origin can’t be grasped. Conceptually, time is ineluctable. Whenever philosophical thought starts to think about time, this thinking is already too late.

Ricoeur is the second author in our selection who takes a phenomenological stance. Heidegger’s “Being and Time” serves as his point of reference. Yet, Ricoeur is neither interested in the analysis of Being nor of the having-Been. The topic to which he refers in Heidegger, and at the same time his vantage point, is historicality, which he approaches in a very different manner. For Ricoeur, history and historicality can not only be understood just through narrativity; there is even a mutual structural determination. Experience of time as the source of historicality as well as the soil of it gets refigurated through narration. In the essay “On Narrative” [49] that he published while his major work “Time and Narration” [48] was in the making we can find his main hypothesis:

My […] working hypothesis is that narrativity and temporality are closely related—as closely as, in Wittgenstein’s terms, a language game and a form of life. Indeed, I take temporality to be that structure of existence that reaches language in narrativity and narrativity to be the language structure that has temporality as its ultimate referent. Their relationship is therefore reciprocal. (p.169)

Concerning narrativity, Ricoeur draws a lot, of course, on the structure of language and the structure of stories. On both levels various degrees of temporality and nonchronological proportions appear. On the level of language, we find short-range and long-range indicators of temporality, beyond mere grammar. Long-range indicators such as “while” or adverbs of time (“earlier”) do not have a clear boundary, neither structurally nor semantically. The same can be found on the level of the story, the plot as Ricoeur calls it. Here he distinguishes a episodic from a configurational dimension, the former presupposing ordinary, i.e. referential time. Taking into account that

To tell and to follow a story is already to reflect upon events in order to encompass them in successive wholes. (p.178)

it follows that any story comprises a

[…] twofold characteristic of confronting and combining both sequence and pattern in various ways.

In other words, a story creates a multiplicity of possible sequences and times, thereby opening a multiplicity of “planes of manifestation,” or in other words, a web of metaphors33.

[…] the narrative function provides a transition from within-time-ness to historicality.

Yet, according to Ricoeur the configurational dimension of the story has a particular effect on the ordinary temporality of a story as it is transported by the episodics. Through the triggered reflective act, the whole story may condense into a single “thought”.

Finally, the recollection of the story governed as a whole by its way of ending constitutes an alternative to the representation of time as moving from the past forward into the future, according to the well-known metaphor of the arrow of time. It is as though recollection inverted the so-called natural order of time. […] A story is made out of events to the extent that plot makes events into a story. The plot, therefore, places us at the crossing point of temporality and narrativity.

This single thought, the plot of a story as whole now is confronted particularly with the third aporia of inscrutability. Basically, for Ricoeur “not really thinking time” when thinking about time is aporetic. (fTR III 467/dZE III, 417) The aporia

[…] emerges right in that moment, where time, which eludes any attempt to be constituted, turns out to be associated to a constitutive order, which in turn always and already is assumed by the work of that constitution.

Any conception that we could propose about time is confronted with the impossibility of integrating this reflexively ineluctable reason. We never can subject time as an object of our reflexions completely. Inga Römer emphasizes (p.284)

Yet, and this is a crucial point for Ricoeur, “what is brought to its failure here is not thinking, in all its meanings, but rather the drive, better the hubris that our thinking seduces to attempt to dominate sense”. For this failure is only a relative one, the inscrutability is not faced with a lapse into silence, but rather with a polymorphy of arrangements and valuations.34

The items of this polymorphy are incommensurable for Ricoeur. Now, for Ricoeur this polymorphy of time experience is situated in a constitutive and reciprocal relationship with narrativity (see his main hypothesis in “On Narrative” that we cited above). Thereby, our experience of time refigurates and reconfigurates itself continuously. In other words, narration represents a practical and poetic mediation of heterogeneous experiences of time. This interplay, so Ricoeur, can overcome the limitations of philosophical inquiries of time.

Interestingly, Ricoeur rejects any systematicity of his arguments, as Römer points out: (p.454)

This association of withdrawal of grounds at the one hand and the challenge for a thinking-more and thinking-different is the strongest argument for Ricoeur’s explicit refusal of a system regarding the three aporias of time as well as their narrative answers.35 (p.454)

The result of this is pretty clear. The Ricoeurean aporetics starts to molt itself into a narration, constantly staggering and oscillating between its claiming, its negation, its negative positivity and its positive negativity, beginning to dazzle and getting incomprehensible.

Temporality tends to get completely merged in narrativity, which in turn becomes synonymous with the experience of time. Such, there are only two possibilities for Ricoeur, neither of which he actually did follow. The first is the denial of temporality that could be thought independent of narration. The second would be that life is equated with narration.

I think, Ricoeur would favour the second alternative. As Römer summarizes:

Historical practice allows us to mediate experienced time with linear time in its own creation, the historical time.36 (p.326)

Such, however, Ricoeur would introduce a secondary re-mystification, which actually is even an autolog one, since Ricoeur has been starting with it as an inscrutability. At this point, all his arguments vanish and turn into a simple pointing to experience.

In the end, the notion of historical practice remains rather questionable. Ricoeur uses the concepts of witness or testimony as well as “trace,” which of course reminds to Derrida’s infamous trace: an uninterpretable remnant of history. Despite Ricoeur emphasizes the importance of the reader as the situs of the completion of text, he never seems to accept interpretation as a primacy. Here, he closely follows the inherited phenomenological misconceptions of the object that exists independent from and outside of the subject. Other difficulties of it is the denial of transcendence and abstraction, which together with its logicism causes the wrong problem of freedom. Phenomenology never understood, whether in Husserl, Heidegger, Derrida, Ricoeur or analytic philosophy, that comparing things can’t take place on the same level as the compared things. Even the most simple comparison implies the Differential, requiring a considerable amount of constructive activity.

Outside phenomenology, Ricoeur’s attempt is only little convincing, albeit he describes many interesting observations around narration and texts. His aporetics of time appears half-baked, through and through, so to speak. Poisoned by phenomenology, and strangely enough forgetting about language in the formulation of his aporias, he commits almost all of the possible mistakes already in his premises. He objectifies time and he treats it as an existential, which could be explained. After all, his main objection that we “can’t really think time”, does not hit a unique. case. Any thinking of any concept is unable to “really think it.”

Our conclusion is not a rejection of Ricoeur’s basic idea of a mutual relationship between “thinking time” and narration. Yet, obviously thinking about narration and phenomenology is an impossibility itself.

One of interesting observations around narration is the distinction between the episodic and the configurational dimension of a plot. This introduces multiplicity, reversibility, and extended present as well as an additional organizational layer. Yet, Ricoeur failed to step out of his affections with narration in order to get aware of the opportunities attached to it.

Kant

Introducing transcendence into our game, we have to refer to Kant, of course, and his conception of time in his “Transzendentale Ästhetik der Kritik der reinen Vernunft”. Kant’s merit is the emancipation of transcendental thinking from the imagined divinity, albeit he did not push this move far enough.

By no means Kant demonstrated the irreality of time, as Einstein as well as McTaggard boldly claim. Kant just demonstrated that time can’t “have” a reality independent from a subject. Accordingly, the idea of an illusionary or irreal time itself is based on a fiction: the fiction of naïve realism. It claims that there is the possibility of an access to “nature” in a way that is independent of subject. Conversely, this does not mean that time as a reality is constructed by human thinking, of course.

The reason for misunderstanding Kant lies in the fact that Kant still argues completely within the realm of the human, while physicists like Einstein talk about the fiction of primarily unrelated entities. It is a major methodological element of the theoretic constitution of physics to assume so, in order to become able, so the fiction, to describe the relations then objectively. Well, actually this does not make much sense, yet physicists usually believe in it.

Far from showing that time is illusionary, Kant tried to secure the objectivity of time under conditions of empirical constitutions, that is, after the explicit and final departure from still scholastic pre-established harmonies that are guaranteed by God. In order to accomplish that he had to invent kind of an intrinsic transcendentality of empirical arrangements. This common basis he found in the transcendent sensual intuition.

For Kant time is a form of intuition (Anschauung), or more precisely, a transcendental and insofar pure form of sensual intuition. It is however of utmost importance, as Mike Sandbothe writes, that Kant himself relativized the universality that is introduced by the transcendentality of time, or in still other words, the intuition of the transcendental subject.

[…] die Form der Anschauung bloss Mannigfaltiges, die formale Anschauung aber Einheit der Vorstellung gibt.” ([47]p.154, B 160f)

The formal account in the intuition now refers to the use of symbols. Thus, it can’t be covered completely as a subject by the pure reason. Here, we find a possible transition to Wittgenstein, since symbols are symbols by convention. Note that this does not refer to a particular symbol, of course, but to the symbolicity that accompanies any instance of talking about time. On the one hand this points towards the element of historicity, which has been developed by Heidegger in a rather limited manner (because he restricted history to the realm of the Dasein, i.e. consciousness).

On the other hand, however, we could extend Kant’s insight of a two-fold constitution of time into more abstract, and this means a-human regions. In a condensed way Kant shows that we need sensual intuitions and symbolicity in order to access temporal aspects of the world. Sensual intuitions, then, require, in the widest sense, kind of match between sensed and the sensing. In human thinking these are the schemata, in particle physics it is the filter built deeply into matter. We could call this transverse excitability. In physics, it is called quantum.

Yet, the important thing is the symbolicity. We can immediately translate this into quantificability and quantitability. And again we are back at Aristotle’s conception.

2. Synopsis

So, after having visited some of the most important contributions to the issue of time we may try to approach a synopsis of those. Again, we have to emphasize that we disregarded many highly interesting ideas, among others those of Platon in his Timaios with his three “transcendental” categories of Being, Space and Becoming, or those of Schelling (cf. in [31]); or those of Deleuze in his cinema books, where he distinguished the “movement image” (presupposing clock time) from the “time image” that is able to provide a grip onto “time itself,” which, for Deleuze, is the virtual to which Bergson’s durée points to; likewise, any of the works by the authors we referred to should have been discussed in much more detail in order to do justice to them. Anyway.

Our intermediate goal was to liberate time from its human influences without sacrificing the applicability of the respective conception to the realm of the human. We need to do so in order to investigate the relation between time and architecture. This liberation, however, still has to obey to the insight of Wittgenstein that we must not expect to find an “essence” of time. Taking all the aspects together, we indeed may ask, as careful as possible,

How should we conceive of time?

The answer is pretty clear, yet, it comes as a compound consisting of three parts. And above all it is also pretty simple.

(1) Time is best conceived as a transcendent condition for the possibility of establishing a relation.

This “transcendent condition” is not possible without a respective plane of immanence, which in turn comprises the unfolding of virtuality. Much could be said about that, of course, with respect to the philosophical implications, its choreostemic references, or its architectonic vicinity. For instance, this determination of time suggests a close relationship to the issue of information and its correlate, causality. Or we could approach other conceptions of time by means of something like a “reverse synthesis.”

It is perhaps at least indicated to emphasize—particularly for all those that are addicted to some kind of science—that this transcendent condition does not, by no means, exclude any consideration of “natural” systems, even not in its material(ist) contraction. On the other hand, this in turn does not mean, of course, that we are doing “Naturphilosophie” here, neither of the ancient nor the scholastic type.

It is clear that we need to instantiate the subjects of this conception in order to achieve a practical relevance of it. It is in this instantiation that different forms of temporality appear, i.e. durée on the one hand and clock-time on the other. Nothing could be less surprising, now, as an incompatibility of the two forms of temporality. Actually, the expectation of a compatibility is already based on the misunderstanding that claims the possibility of a “direct” comparison (which is an illusion). Quite to the contrast, we have to understand that the phenomenal incommensurability just points to a differential of time, which we formulated as a transcendent condition above.

Now, one of the instantiations, clock-time, or referential time, is pretty trivial. We don’t need to deal with it any further. The other branch, where we find Peirce and Bergson, is more interesting.

As we have seen in our discussion about their works, multiplicity is an essential ingredient of relational time. Peirce and Bergson arrived at it on different ways, though. For Peirce it is a consequence of the multiplicity of thoughts about something, naturally derived from his semiotics. For Bergson, it is a multiplicity within experience, or better the experiencing consciousness. So to speak, they take inverse positions regarding the mediality. We already said that we prefer the Peircean perspective due to its more prominent potential for generalization. Yet, I think the two perspectives could be reconciled quite easily. Both conceptions conceive primal time as “experiential” time (in the widest sense).

Our instantiation of time as a transcendent condition is thus:

(2) Transcendent time gets instantiated as a probabilistic, distributed and manifold multiplicity of—topologically spoken—open time strings.

Each time string represents a single and local present, where “local” does not refer to a “spatial place”, but rather to a particular sign process.

This multiplicity is not an external multiplicity, despite it is triggered or filled from the external. It is also not possible to “count” the items in it, without loosing present. If we count, we destroy the coherence between the overlapping strings of present, thus creating countable referential time. This highlights a further step of instantiation, the construction of expressibility.

(3) The pre-specific multiplicity of time strings decoheres by symbolization into a specific space of expressibility.

Symbolization may be actualized by means of numbers, as already mentioned before. This would allow us to comprehend and speak of movement. We also have seen that we could construct a web of proceeding metaphors and their virtual movement. This would put us in midst the narration and into metaphoricology, as I call it, which refers to the perspective that conceives of being human and of human beings as parts of lively metaphors. In other words, culture itself becomes the story and the narrative.

As still another possibility we could address the construction of a space of expressibility of temporality quite directly. Such a space need to be an aspectional space, of course. Just keep in mind that the aspectional space is not a space of quantities, as it is the case for a Cartesian space. The aspectional space is a space that is characterized by a “smooth” blending of intensity and quantity. We may call it intensive quantities, or quantitable intensities. It is a far-reaching generalization of the “ordinary” space conceptions that we know from mathematics. As the aspects —the replacement of dimensions—of that space we could choose the modes of temporality—such as past, present, future—, the durée, the referential time, or implicit time as it occurs and shows up in behavior or choreostemic space. We also could think of an aspection that is built by a Riemannian manifold, allowing to comprise linearity and circularity as just a single aspect.

The tremendous advantage of such a space is manifold, of course, because an infinite amount of particular time practices can be constructed, even as a continuum. This contiguous and continuous plurality is of a completely different kind as the unmediatable items in the plurality of time conceptions that has been proposed by Mike Sandbothe [8].

The aspectional space of transcendent time offers, I mentioned it, the possibility for expressing time, or more precisely, a particular image of time. There are several of those spaces, and each of them is capable to hold an infinite number of different images of time.

It is now easy to understand that collapsing the conditions for building relations with the instantiation into a concrete time form, or even with the action (or the “phenomenon”) results in nothing else than a terrible mess. Actually, it is precisely the mess that physicists or phenomenology create in different ways. “Phenomenal” observables of this mess are pseudo-paradoxes or dualities. We also could say that such mess is created due to a wrong application of the grammar of time.

There is one important aspect of time and temporality, or perspective onto them, that we mentioned only marginally so far, the event. We met it in Heidegger’s “Being and Time” as the provider [m: the Giving] and insofar also the origin of Being and time. We also saw that Ricoeur uses them as building bricks for stories that combine them into successive wholes. For Dewey (“Time and Individuality”, “Context of Thought”) the concept of an event involves both the individual pattern of growth and the environmental conditions. Dewey, as Ricoeur, emphasizes that there is no geometrical sequence, no strict seriality to which events could be arranged. Dewey calls it concurrence, which could not be separated from occurrence of an event.

Yet, for both of them time remains something external to the conception of event, while Heidegger conceives it as the source of time. Considering our conception of time as a proceeding actualization of Differential Time we could say the the concept of event relates to the actualization of the relation within the transcendence of its conditions. Such it could be said to accompany creation of time, integrating transcendent and practical conditions as well as all the more or less contingent choices associated with it. In some way we can see that we have proceduralized (differentiated) Heidegger’s “point of origin”.37. Marc Rölli [52] sharpens this point by referring to Deleuze’s conception as “radically empiricist”, dismissing Heidegger through the concepts of actuality and virtuality. Such we can see that the immediate condition that is embedding the possibility of experience is the “event,” which in turn can be traced back to a proper image of time. Time, as a condition, is mediated towards experience by the event, as a condition. Certainly, however, the “event” could not be thought without an explicitly formulated conception of time. Without it, a multitude of misunderstandings must be expected. If we accept the perspective that insofar time is preceding substance, which resolves of course into a multiplicity in a Deleuzean perspective, we also could say that the trinity of time, event and experience contributes to the foil of immanence, or even builds it up, where experience in turn refers to the choreostemic constitution of being in the world.

In order to summarize our conception as an overview… here is how we propose to conceive of time

  • (1) Time is a transcendent condition for the possibility of establishing a relation, or likewise a quality.
  • (2) It gets instantiated as a probabilistic multiplicity of open time strings that, by the completion of all instantiations, present presence.
  • (3) The pre-specific multiplicity of time strings decoheres by symbolization into a specific, aspectional space of expressibility.
  • (4) Any particular “choice” of a situs in this space of intensive quantities represents the respective image of time, which then may emerge in worldly actualizations.

Particularly regarding this last element we have to avoid the misunderstanding of a seriality of the kind “I choose then I get”. This choice is an implicit one, just as the other instantiations, and can be “observed” only in hindsight, or more precise, they show themselves only within performance. Only in this way we can say that it brings time into a particular Lebenswelt and its contexts as a matter (or subject) of design.

Nevertheless, we now could formulate kind of a recipe for creating a particular “time”, form of temporality, or “time quality.” This would work also in the reverse direction, of course. It is possible to construct a comparative of time qualities across authors, architects or urban neighborhoods. Hopefully, this will help to improve urban practices. In order to make this creational aspect more clear, we now have to investigate the possibilities to create time “itself”.

to be continued …

(The next part will deal with the question whether it could be possible to identify the mechanisms needed to create time…)

Notes

1. “Living City” was Archigram’s first presentation to the public, which has been curated by Ron Herron in 1963. 

2. German orig.: „Zuletzt markiert die Zeit für Ricoeur das “Mysterium” unseres Denkens, das sich der Repräsentation verweigert, indem es unser Dasein auf eine für das Denken uneinholbare Weise umgreift.“

3. As in the preceding essays, we use the capital “U” if we refer to the urban as a particular quality and as a concept in the vicinity of Urban Reason, in order to distinguish it from the ordinary adjective that refers to common sense understanding.

4. remark about state and development.

5. We discussed them in the essay about growth patterns. The fractal is a consequence of self-affine mapping, roughly spoken, a local replacement by a minor version of the original diagram.

6. It is tempting to relate this position to Heisenberg’s uncertainty principle. Yet, we won’t deal with contemporary physics here, even as it would be interesting to investigate the deficiencies of physical conceptions of time.

7. McTaggart paper about time that has been cited over and over again and became unfortunately very influential. Yet, it is nothing but a myth. For a refutation see Tegtmeier [18]. For reasons of its own stupidity and the boldly presented misinterpretation of the work of Kant, McTaggart’s writing deserves the title of a “most developed philanosy” (Grk: anoysia ανοησία, nonsense, or anosia, immunity). It is not even worthwhile, as we will see later through our discussion of Wittgenstein’s work regarding time, to consider it seriously, as for instance Sean Power does .

8. There is a distant resemblance to Georg Berkley’s “esse est percipi.” [20] Yet, in contrast to Berkley, we conceive of interpretation as an activity that additionally is deeply rooted in the communal.

9. German original: SZ: 326: „Zukünftig auf sich zurückkommend, bringt sich die Entschlossenheit gegenwärtigend in die Situation. Die Gewesenheit entspringt der Zukunft, so zwar, dass die gewesene (besser gewesende) Zukunft die Gegenwart aus sich entlässt. Dies dergestalt als gewesend-gegenwärtigende Zukunft einheitliche Phänomen nennen wir die Zeitlichkeit.

10. One has to consider that Heidegger conceives of Being only in relation to the Being-there (“Dasein”), while the “Being-there” is confined to conscious beings.

11. The translators used ”falling”, which however does not match the German “verfallend”. (Actually, I consider it as a mistake.) Hence, I replaced it by a more appropriate verb.

12. Note that Heidegger always used to write in a highly ambigue fashion, which makes it nearly impossible to translate him literally from German to English. In everyday language “Es gibt” is surely well translated by “There is.” Yet, in this text he repeatedly refers to “giving”. Turning perspective to “giving” opens the preceding “Es” away from its being as impersonate corpuscle towards impersonal “fateness”. This interpretation matches the presentation of the affair in [24].

13. German original: “Das Sein eigens denken, verlangt, das Sein als den Grund des Seienden fahren zu lassen zugunsten des im Entbergen verborgen spielenden Gebens, d.h. des „Es gibt“.“

14. see also: Marcel Mauss, Die Gabe. Form und Funktion des Austauschs in archaischen Gesellschaften. Suhrkamp, Frankfurt 2009 [1925].

15. German orig.: „In “Zeit und Sein” schliesslich sieht Heidegger den Ursprung der Zeit im Ereignis, welches er ausdrücklich als den [sich ] selbst entzogenen Geber von Sein und Zeit bestimmt. Das Ereignis, von Heidegger andernorts bestimmt als singulare tantum, ist selbst grundsätzlich entzogen – und dennoch ist das Ereignis der Ursprung der Zeit.“

16. German original (my own translation): “Sein und Zeit ist vielmehr dahin unterwegs, auf dem Wege über die Zeitlichkeit des Daseins in der Interpretation des Seins als Temporalität einen Zeitbegriff, jenes Eigene der “Zeit” zu finden, von woher sich “Sein” als Anwesen er-gibt. Damit ist aber gesagt, daß das in der Fundamentalontologie gemeinte Fundamentale kein Aufbauen darauf verträgt. Stattdessen sollte, nachdem der Sinn von Sein erhellt worden wäre, die ganze Analytik des Daseins ursprünglicher und in ganz anderer Weise wiederholt werden.“ [21]

17. German original (my translation): “Zeit-Raum nennt jetzt das Offene, das im Einander-sich-reichen von Ankunft, Gewesenheit und Gegenwart sich lichtet. Erst dieses Offene und nur es räumt dem uns gewöhnlich bekannten Raum seine mögliche Ausbreitung ein.“

18. This also holds for any of the attempts hat can be found in physics. The following sources may be considered as the most prominent sources, though they are not undisputed: Carroll [22], Price [23][24], Penrose [25]. Physics always and inevitably conceives of time as a measurable “thing”, i.e. as something which already has been negotiated in its relevance for the communal aspects of thinking. See Aristotle’s conception of time.

19. hint to Schelling, for whom intensity is not accessible at all, but could be conceived only as a force that expands into extensity.

20. You will find Peirce’s writings online here: http://www.cspeirce.com/; the parts reference here for instance at http://www.cspeirce.com/menu/library/bycsp/logic/ms237.htm,

21. German original (my transl.): „Denn in der Grammatik der Zukunft tritt der Begriff des ,Gedächtnis’ nicht auf, auch nicht mit umgekehrten Vorzeichen.“

22. In meditational practices one can extend the interpretive chain in various ways. The result is simply the stopping of referential time.

23. German orig.: „Beide Ausdrucksweisen sind in Ordnung und gleichberechtigt, aber nicht miteinander vermischbar“.

24. German orig.: „Wir können keinen Vorgang mit dem ,Ablauf der Zeit’ vergleichen – diesen gibt es nicht – sondern nur mit einem anderen Vorgang (etwa mit dem Gang des Chronometers).“ translation taken from here.

25. 1 second is currently defined as the duration of 9192631770 transitions between two energy levels of the caesium-133 atom. [39] Interestingly, this fits nicely to Aristotle’s conception of time. The reason to take the properties of Cs-133 as a reference is generality. The better the resolution of the referential scale the more general it could be applied.

26. German orig.: „„Jetzt“ bezeichnet keinen Zeitpunkt. Es ist kein „Name eines Zeitmomentes“.“

27. German orig.: „[…] es ist aber Unsinn zu sagen ‘Dies ist dies’, oder ‘Dies ist jetzt’.“

28. In German “Halma”.

29. Much could be said about physics here, regarding the struggling of physicists to “explain” the so-called arrow of time, or regarding the theory of relativity or quantum physics with its Planck time, but it is not close enough to our interests here. Physics always tries to objectify time, which happens through claiming an universally applicable scale, hence they run into paradoxes. In other terms, the fact of the necessity of conceptions like Planck time, or time dilatation, is precisely that without observer there is nothing. The mere possibility of observation (and the observer) vanishes at the light of speed, or at the singularity “within” black holes”. In some way, physics all the time (tries to) proof(s) their own nonsensical foundations.

30. German orig.: „Was zum Wesen der Welt gehört, kann die Sprache nicht ausdrücken. (…) Nur was wir uns auch anders vorstellen können, kann die Sprache sagen.”

31. German orig.: ,,Alles was wir überhaupt beschreiben können, könnte auch anders sein”.

32. Note that in case of a city we meet somewhat the inverse of it. We could conceive of a city as “an individual being made from a collective.”

33. see also Paul Ricoeur (1978), “The Metaphorical Process as Cognition, Imagination, and Feeling,” Critical Inquiry, 1978.

34. German orig.: „Aber, und das ist für Ricoeur entscheidend, “was hier zum Scheitern gebracht wird, ist nicht das Denken, in allen Bedeutungen des Wortes, sondern der Trieb, besser die hybris, die unser Denken dazu verleitet, sich zu Herrn des Sinns zu machen“. Aufgrund dieses nur relativen Scheiterns stehe der Unerforschlichkeit kein Verstummen, sondern vielmehr eine Polymorphie der Gestaltungen und Bewertungen der Zeit gegenüber.“

35. German orig.: „Diese Zusammengehörigkeit von Entzug des Grundes und Herausforderung um Mehr- und Andersdenken ist der stärkste Grund für Ricoeurs explizite Ablehnung eines Systems sowohl der drei Aporien der Zeit selbst wie auch ihrer narrativen Antworten.“

36. German orig.: „Historische Praxis erlaubt uns, die erlebt Zeit mit der linearen Zeit in einer ihr eigenen Schöpfung, der historischen Zeit, zu vermitteln.“

37. Much more would be to say about the event, of course (cf. [51]). Yet, I think that our characterization not only encompasses most conceptions or fits to most of the contribution to the “philosophy of the event,” it also clarifies and sheds light (kind of x-rays?) on them.

References

  • [1] Simon Sadler, Archigram – Architecture without Architecture. MIT Press, Boston 2005.
  • [2] Koolhaas, Junkspace
  • [3] Robert Venturi, Complexity and Contradiction in Architecture. 1977 [1966].
  • [4] Bernard Tschumi, Architecture and Disjunction. MIT Press, Boston 1996.
  • [5] Franz Oswald and Peter Baccini, Netzstadt: Einführung zum Stadtentwerfen. Birkhäuser, Basel 2003.
  • [6] Sigfried Giedion, Space, Time and Architecture: The Growth of a New Tradition. 1941.
  • [7] Aldo Rossi, The Architecture of the City. Oppositions 1984 [1966].
  • [8] Mike Sandbothe, „Die Verzeitlichung der Zeit in der modernen Philosophie.“ in: Antje Gimmler, Mike Sandbothe und Walther Ch. Zimmerli (eds.), Die Wiederentdeckung der Zeit. Primus & Wissenschaftliche Buchgesellschaft, Darmstadt 1997. available online.
  • [9] Mary Louise Gill, Aristotle’s Distinction between Change and Activity. in: Johanna Seibt (ed.), Process Theories: Crossdisciplinary Studies in Dynamic Categories. p.3-22.
  • [10] Yeonkyung Lee and Sungwoo Kim (2008). Reinterpretation of S. Giedion’s Conception of Time in Modern Architecture – Based on his book, Space, Time and Architecture. Journal of Asian Architecture and Building Engineering 7(1):15–22.
  • [11] Tony Roark, Aristotle on Time: A Study of the Physics.
  • [12] Werner Heisenberg, Physics and Philosophy. The Revolution in Modern Science. Harper, New York 1962.
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  • [16] L. Nathan Oaklander (2004). The Ontology of Time (Studies in Analytic Philosophy)
  • [17] Sean Power, The Metaphysics of Temporal Experience. forthcoming.
  • [18] Erwin Tegtmeier (2005). Three Flawed Distinctions in the Philosophy of Time. IWS 2005.
  • [19] Thomas Sheehan, “Heidegger, Martin (1889-1976)” in: Edward Craig (ed.), Routledge Encyclopedia of Philosophy, Routledge, New York 1998, IV, p.307-323.
  • [20] George Berkley, Eine Abhandlung über die Prinzipien der menschlichen Erkenntnis (1710). Vgl. vor allem die ‚Sectionen‘ III-VII und XXV, Übers. F. Überweg, Berlin 1869.
  • [21] Martin Heidegger, Being and Time. transl. John Macquarrie & Edward Robinson (based on 7th edition of “Sein und Zeit”), Basil Blackwell, Oxford 1962. available online.
  • [22] Martin Heidegger, Sein und Zeit. Tübingen 1979 [1927].
  • [23] Martin Heidegger, Protokoll zu einem Seminar über den Vortrag “Zeit und Sein”. in: Zur Sache des Denkens. Gesamtausgabe Band 14, p.34. Klostermann, Frankfurt 2007 [1967].
  • [24] Cristina Lafont (1993). Die Rolle der Sprache in Sein und Zeit. Zeitschrift für philosophische Forschung, Band 47, 1.
  • [25] Martin Heidegger, Zur Sache des Denkens. Gesamtausgabe Band 14. Klostermann, Frankfurt 2007.
  • [26] Christian Bermes, Ulrich Dierse (eds.), Schlüsselbegriffe der Philosophie des 20. Jahrhunderts. Meiner, Hamburg 2010.
  • [27] Sean Carroll, From Eternity to Here: The Quest for the Ultimate Theory of Time. Oneworld, Oxford 2011.
  • [28] Huw Price, Time’s Arrow and Archimedes’ Point: New Directions. Oxford University Press, Oxford 1996.
  • [29] Huw Price (1994). Reinterpreting the Wheeler-Feynman Absorber Theory: Reply to Leeds. The British Journal for the Philosophy of Science 45 (4), pp. 1023-1028.
  • [30] Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage, London 2004.
  • [31] Friedrich Kuemmel, Über den Begriff der Zeit. Niemeyer, Tübingen 1962.
  • [32] Time and Free Will: An Essay on the Immediate Data of Consciousness, transl., F.L. Pogson, Montana: Kessinger Publishing Company, original date, 1910 (orig. 1889).
  • [33] Gilles Deleuze, Bergsonism.
  • [34] Lawlor, Leonard and Moulard, Valentine, “Henri Bergson”, in: Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), available online.
  • [35] Charles Sanders Peirce, Writings 3, 107-108, MS239 (Robin 392, 371), 1873. available online.
  • [36] Ludwig Wittgenstein, Philosophical Investigations. §201
  • [37] John Dewey, “Time and Individuality,” in: Jo Ann Boydston (ed.), Later Works of John Dewey, Vol.14. Southern Illinois University Press, Carbondale 1988.
  • [38] John Dewey, “Experience and Nature,” in: Jo Ann Boydston (ed.), Later Works of John Dewey, Vol.1. Southern Illinois University Press, Carbondale 1981 , p. 92.
  • [39] Rudolf F. Kaspar und Alfred Schmidt (1992). Wittgenstein über Zeit. Zeitschrift für philosophische Forschung, Band 46(4): 569-583.
  • [40] Ludwig Wittgenstein, Philosophische Bemerkungen. in: Werkausgabe Bd. 2. Frankfurt 1984.
  • [41] “International System of Units (SI)”. Bureau International des Poids et Mesures. 2006.
  • [42] Peter Janich (1996). Die Konstitution der Zeit durch Handeln und Reden. Kodikas/Code Ars Semeiotica 19, 133-147.
  • [43] Ludwig Wittgenstein, Eine Philosophische Betrachtung (Das Braune Buch). in: Suhrkamp Werkausgabe Bd. 5. Frankfurt 1984.
  • [44] Andrea A. Reichenberger, „Was ist Zeit?“ Wittgensteins Kritik an Augustinus kritisch betrachtet. in: Friedrich Stadler, Michael Stöltzner (eds.), Papers of the 28th International Wittgenstein Symposium 7-13 August 2005. Zeit und Geschichte – Time and History. ALWS, Kirchberg am Wechsel 2005.
  • [45] Tagebücher 1924-1916. in: Ludwig Wittgenstein, Werkausgabe Bd.1, Frankfurt 1984.
  • [46] Helga Nowotny, Eigenzeit: Entstehung und Strukturierung eines Zeitgefühls. Suhrkamp 1993.
  • [47] Inga Römer, Das Zeitdenken bei Husserl, Heidegger und Ricoeur. Springer, Dordrecht & Heidelberg 2010.
  • [48] Paul Ricoeur, Zeit und Erzählung, Bd. 3: Die erzählte Zeit, München, Fink , München 1991. (zuerst frz.: Paris 1985).
  • [49] Paul Ricoeur (1980). On Narrative. Critical Inquiry, Vol. 7, No. 1, pp. 169-190.
  • [50] Immanuel Kant, Kritik der reinen Vernunft, in: Wolfgang Weischedel (ed.), Immanuel Kant., Werke in sechs Bänden, Bd. 2, Wissenschaftliche Buchgesellschaft, Darmstadt 1983.
  • [51] Marc Rölli, Ereignis auf Französisch. Von Bergson bis Deleuze. Fink, München 2004.
  • [52] Marc Rölli, “Begriffe für das Ereignis: Aktualität und Virtualität. Oder wie der radikale Empirist Gilles Deleuze Heidegger verabschiedet”, in: Marc Rölli (ed.), Ereignis auf Französisch. Von Bergson bis Deleuze. Fink, München 2004

۞

Growth Patterns

November 29, 2012 § Leave a comment

Growing beings and growing things, whether material

or immaterial, accumulate mass or increase their spreading. Plants grow, black holes grow, a software program grows, economies grow, cities grow, patterns grow, a pile of sand grows, a text grows, the mind grows and even things like self-confidence and love are said to grow. On the other hand, we do not expect that things like cars or buildings “grow.”

Despite the above mentioned initial “definition” might sound fairly trivial, the examples demonstrate that growth itself, or more precisely, the respective language game, is by far not a trivial thing. Nevertheless, when people start to talk about growth or if they invoke the concept of growth implicitly, they mostly imagine a smooth and almost geometrical process, a dilation, a more or less smooth stretching. Urbanists and architects are no exception to this undifferentiated and prosy perspective. Additionally, growth is usually not con- sidered seriously beyond its mere wording, probably due to the hasty prejudgment about the value of biological principles. Yet, if one can’t talk appropriately about growth—which includes differentiation—one also can’t talk about change. As a result of a widely (and wildly) applied simplistic image of growth, there is a huge conceptual gap in many, if not almost all works about urban conditions, in urban planning, and about architecture.1  But why talking about change, for in architecture and urbanism is anyway all about planning…

The imprinting by geometry often entails another prejudice: that of globality. Principles, rules, structures are thought to be necessarily applied to the whole, whatever this “wholeness” is about. This is particularly problematic, if these rules refer more or less directly to mere empirical issues. Such it frequently goes unnoticed that maintaining a particular form or keeping position in a desired region of the parameter space of a forming process requires quite intense interconnected local processes, both for building as well as destroying structures.

It was one of the failures in the idea of Japanese Metabolism not to recognize the necessity for deep integration of this locality. Albeit they followed the intention to (re-)introduce the concept of “life cycle” into architecture and urbanism, they kept aligned to cybernetics. Such, Metabolism failed mainly for two reasons. Firstly, they attempted to combine incommensurable mind sets. It is impossible to amalgamate modernism and the idea of bottom-up processes like self-organization or associativity, and the Metabolists always followed the modernist route. Secondly, the movement has been lacking a proper structural setup: the binding problem remained unresolved. They didn’t develop a structural theory of differentiation that would have been suitable to derive appropriate mechanisms.

This Essay

Here in this piece we just would like to show some possibilities to enlarge the conceptual space and the vocabulary that we could use to describe (the) “growing” (of) things. We will take a special reference to architecture and urbanism, albeit the basics would apply to other fields as well, e.g. to the growth and the differentiation of organizations (as “management”) or social forms, but also of more or even “completely” immaterial entities. In some way, this power is even mandatory, if we are going to address the Urban6, for the Urban definitely exceeds the realm of the empirical.
We won’t do much of philosophical reflection and embedding, albeit it should be clear that these descriptions don’t make sense without proper structural, i.e. theoretical references as we have argued in the previous piece. “As such” they would be just kind of a pictorial commentary, mistaking metaphor as allegory. There are two different kinds of important structural references. One is pointing to the mechanisms2, the abstract machinery with its instantiation on the micro-level or with respect to the generative processes. The other points to the theoretico-structural embedment, which we have been discussing in the previous essay. Here, it is mainly the concept of generic differentiation that provides us the required embedding and the power to overcome the binding problem in theoretical work.

The remainder of this essay comprises the following sections (active links):

1. Space

Growth concerns space, both physical and abstract space. Growth concerns even the quality of space. The fact of growth is incompatible with the conception of space as a container. This becomes obvious in case of the fractals, which got their name due to their “broken” dimensionality. A fractal could be 2.846-dimensional. Or 1.2034101 dimensional. The space established by the “inside” of a fractal is very different from the 3-dimensional space. Astonishingly, the dimensionality even need not be constant at all while traveling through a fractal.

Abstract spaces, on the other hand, can be established by any set of criteria, just by interpreting criteria as dimensions. Such, one gets a space for representing and describing items, their relations and their transformations. In mathematics, a space is essentially defined as the possibility to perform a mapping from one set to another, or in other terms, by the abstract (group-theoretic) symmetry properties of the underlying operations on the relations between any entities.

Strangely enough, in mathematics spaces are almost exclusively conceived as consisting from independent dimensions. Remember that “independence” is the at the core of the modernist metaphysical belief set! Yet, they need neither be Euclidean nor Cartesian as the generalization of the former. The independence of descriptive dimensions can be dropped, as we have argued in an earlier essay. The resulting space is not a dimensional space, but rather an aspectional space, which can be conceived as a generalization of dimensional space.

In order to understand growth we should keep in contact with a concept of space that is as general as possible. It would be really stupid for instance, to situate growth restrictively in a flat 2-dimensional Euclidean space. At least since Descartes’ seminal work “Regulae” (AT X 421-424) it should be clear that any aspect may be taken as a contribution to the cognitive space [8].

The Regulae in its method had even allowed wide latitude to the cognitive use of fictions for imagining artificial dimensions along which things could be grasped in the process of problem solving. Natures in the Meditations, however, are no longer aspects or axes along which things can be compared, evaluated, and arrayed, but natures in the sense that Rule 5 had dismissed: natures as the essences of existing things.

At the same time Descartes also makes clear that these aspects should not be taken as essences of existing things. In other words, Descartes has been ahead of 20ieth century realism and existentialism! Aspects do not represent things in their modes of existence, they represent our mode of talking about the relations we establish to those things. Yet, these relations are more like those threads as String Theory describes them: without fixed endings on either side. All we can say about the outer world is that there is something. Of course, that is far to little to put it as a primacy for human affairs.

The consequence of such a dimensional limitation would be a blind spot (if not a population of them), a gap in the potential to perceive, to recognize, to conceive of and to understand. Unfortunately, the gaps themselves, the blind spots are not visible for those who suffer from them. Nevertheless, any further conceptualization would remain in the state of educated nonsense.

Growth is established as a transformation of (abstract) space. Vice versa, we can conceive of it also as the expression of the transformation of space. The core of this transformation is the modulation of the signal intensity length through the generation of compartments, rendering abstract space into a historical, individual space. Vice versa, each transformation of space under whatsoever perspective can be interpreted as some kind of growth.

The question is not any more to be or not to be, as ontologists tried to proof since the first claim of substance and the primacy of logics and identity. What is more, already Shakespeare demonstrated the pen-ultimate consequences of that question. Hamlet, in his mixture of being realist existentialist (by that very question) and his like of myths and (use) of hidden wizards, guided by the famous misplaced question, went straight into his personal disaster, not without causing a global one. Shakespeare’s masterfully wrapped lesson is that the question about Being leads straight to disaster. (One might add that this holds also for ontology and existentialism: it is consequence of ethical corruption.)

Substance has to be thought of being always and already a posteriori to change, to growth. Setting change as a primacy means to base thought philosophically on difference. While this is almost a completely unexplored area, despite Deleuze’s proposal of the plane of immanence, it is also clear that starting with identity instead causes lots of serious troubles. For instance, we would be forced to acknowledge that the claim of the possibility that a particular interpretation indeed could be universalized. The outcome? A chimaera of Hamlet (the figure in the tragedy!) and Stalin.

Instead, the question is one of growth and the modulation of space: Who could reach whom? It is only through this question that we can integrate the transcendence of difference, its primacy, and to secure the manifold of the human in an uncircumventable manner. Life in all of its forms, with all its immanence,  always precedes logic.3 Not only for biological assemblages, but also for human beings and all its produces, including “cities” and other forms of settlements.

Just to be clear: the question of reaching someone else is not dependent on anything given. The given is a myth, as philosophers from Wittgenstein to Quine until Putnam and McDowell have been proofing. Instead, the question about the possibility to reach someone else, to establish a relation between any two (at least) items is one of activity, design, and invention, targeting the transformation of space. This holds even in particle physics.

2. Modes of Talking

Traditionally spoken, the result of growth is formed matter. More exactly, however, it is transformed space. We may distinguish a particular form, morphos, or with regard to psychology also a “Gestalt,” and form as an abstractum. The result of growth is form. Thus, form actually does not only concern matter, it always concerns the potential relationality.

For instance, growing entities never interact “directly”. They, that is, also: we, always interact through their spaces and the mediality that is possible within them.4 Otherwise it would be completely impossible for a human individual to interact with a city. Before any semiotic interpretive relation it is the individual space that enables incommensurable entities to relate.

If we consider the growth of a plant, for instance, we find a particular morphology. There are different kinds of tissues and also a rather typical habitus, i.e. a general appearance. The underlying processes are of biological nature, spanning from physics and bio-chemistry to information and the “biological integration” of those.

Talking about the growth of a building or the growth of a city we have to spot the appropriate level of abstraction. There is no 1:1 transferability. In a cell we do neither find craftsmen nor top-down-implementations of plans. In contrast, rising a building apparently does not know anything about probabilistic mechanisms. Just by calling something intentionally “metabolism” (Kurokawa) or “fractal” (Jencks), invoking thereby associations of organisms and their power to maintain themselves in physically highly unlikely conditions, we certainly do not approach or even acquire any understanding.

The key for any growth model is the identification of mechanisms (cf. [4]). Biology  is the science that draws most on the concept of mechanism (so far), while physics does so for the least. The level of mechanism is already an abstraction, of course. It needs to be completed, however, by the concept of population, i.e. a dedicated probabilistic perspective, in order to prevent falling back to the realm of trivial machines. In a cross-disciplinary setting we have to generalize the mechanisms into principles, such that these provide a shared differential entity.5

Well, we already said that a building is rarely raised by a probabilistic process. Yet, this is only true if we restrict our considerations to the likewise abstract description of the activities of the craftsmen. Else, the building process starts long before any physical matter is touched.

Secondly, from the perspective of abstraction we never should forget—and many people indeed forget about this—that the space of expressibility and the space of transformation also contains the nil-operator. From the realm of numbers we call it the zero. Note that without the zero many things could not be expressed at all. Similarly, the negative is required for completing the catalog of operations. Both, the nil-operator and the inverse element are basic constituents of any mathematical group structure, which is the most general way to think about the conditions for operations in space.

The same is true for our endeavor here. It would be impossible to construct the possibility for graded expressions, i.e. the possibility for a more or less smooth scale, without the nil and the negative. Ultimately, it is the zero and the nil-operation together with the inverse that allows to talk reflexively at all, to create abstraction, in short to think through.

3. Modes of Growth

Let us start with some instances of growth from “nature”. We may distinguish crystals, plants, animals and swarms. In order to compare even those trivial and quite obviously very different “natural” instances with respect to growth, we need a common denominator. Without that we could not accomplish any kind of reasonable comparison.

Well, initially we said that growth could be considered as accumulation of mass or as an increase of spread. After taking one step back we could say that something gets attached. Since crystals, plants and animals are equipped with different capabilities, and hence mechanisms, to attach further matter, we choose the way of organizing the attachment as the required common denominator.

Given that, we can now change the perspective onto our instances. The performance of comparing implies an abstraction, hence we will not talk about crystals etc. as phenomena, as this would inherit the blindness of phenomenology against its conditions. Instead, we conceive of them as models of growth, inspired by observations that can be classified along the mode of attachment.

Morphogenesis, the creation of new instances of formed matter, or even the creation of new forms, is tightly linked to complexity. Turing titled his famous article the “Chemical Basis of Morphogenesis“. This, however, is not exactly what he invented, for we have to distinguish between patterns and forms, or likewise, between order and organization. Turing described the formal conditions for emergence of order from a noisy flow of entropy. Organization, in contrast, also needs the creation of remnants, partial decay, and it is organization that brings in historicity. Nevertheless, the mechanisms of complexity of which the Turing-patterns and -mechanisms are part of, are indispensable ingredients for the “higher” forms of growth, at least, that is, for anything besides crystals (but probably even for for them in same limited sense). Note that morphogenesis, in neither of its aspects, should not be conceived as something “cybernetical”!

3.1. Crystals

Figure 1a: Crystals are geometric entities out of time.

Crystals are geometrical entities. In the 19th century, the study of crystals and the attempt to classify them inspired mathematicians in their development of the concept of symmetry and group theory. Crystals are also entities that are “structurally flat”. There are no levels of integration, their macroscopic appearance is a true image of their constitution on the microscopic level. A crystal looks exactly the same on the level of atoms up to the scale of centimeters. Finally, crystals are outside of time. For their growth is only dependent on the one or two layers of atoms (“elementary cells”) that had been attached before at the respective site.

There are two important conditions in order to grow a 3-dimensional crystal. The site of precipitation and attachment need to be (1) immersed in a non-depletable solution where (2) particles can move through diffusion in three dimensions. If these conditions are not met, mineral depositions look very different. As far as it concerns the global embedding conditions, the rules have changed. More abstractly, the symmetry of the solution is broken, and so the result of the process is a fractal.

Figure 1b. Growth in the realm of minerals under spatial constraints, particularly the reduction of dimensionality. The image does NOT show petrified plants! It is precipitated mineral from a solution seeped into a nearly 2-dimensional gap between  two layers of (lime) rock. The similarity of shapes points to a similarity of mechanisms.

Both examples are about mineralic growth. We can understand now that the variety of resulting shapes is highly dependent on the dimensional conditions embedding the growth process.

Figure 1c. Crystalline buildings. Note that it is precisely and only this type of building that actualizes a “perfect harmony” between the metaphysics of the architect and the design of social conditions. The believe in independence and the primacy of identity  has been quite effectively delivered into the habit of the everyday housing conditions.

Figure 1d. Crystalline urban layout, instantiated as “parametrism”. The “curvy” shape should not be misinterpreted as “organic”. In this case it is just a little dose of artificial “erosion” imposed as a parametric add-on to the crystalline base. We again meet the theme of the geological. Nothing could be more telling than the claim of a “new global style”: Schumacher is an arch-modernist, a living fossil, mistaking design as religion, who benefits from advanced software technology. Who is Schumacher that he could decree a style globally?

The growth of crystals is a very particular transformation of space. It is the annihilation of any active part of it. The relationality of crystals is completely exhausted by resistance and the spread of said annihilation.

Regarding the Urban6, parametrism must be considered as being deeply malignant. As the label says, it takes place within a predefined space. Yet, who the hell Schumacher (and Hadid, the mathematician) thinks s/he is that s/he is allowed, or even being considered as being able, to define the space of the Urban? For the Urban is a growing “thing,” it creates its own space. Consequently all the rest of the world admits not to “understand” the Urban, yet Hadid and her barking Schumacher even claim to be able to define that space, and thus also claim that this space shall be defined. Not surprisingly, Schumacher is addicted to the mayor of all bureaucrats of theory, Niklas Luhman (see our discussion here), as he proudly announces in his book “The Autopoiesis of Architecture” that is full of pseudo- and anti-theory.

The example of the crystal clearly shows that we have to consider the solution and the deposit together as a conditioned system. The forces that rule their formation are a compound setup. The (electro-chemical) properties of the elementary cell on the microscopic level, precisely where it is in contact with the solution, together with the global, macroscopic conditions of the immersing solution determine the instantiation of the basic mechanism. Regardless the global conditions, basic mechanism for the growth of crystals is the attachment of matter is from the outside.

In crystals, we do not find a separated structural process layer that would be used for regulation of the growth. The deep properties of matter determine their growth. Else, only the outer surface is involved.

3.2. Plants

With plants, we find a class of organisms that grow—just as crystals—almost exclusively at their “surface”. With only a few exceptions, matter is almost exclusively attached at the “outside” of their shape. Yet, matter is also attached from their inside, at precisely defined locations, the meristemes. Else, there is a dedicated mechanism to regulate growth, based on a the diffusion of certain chemical compounds, the phyto-hormones, e.g. auxin. This regulation emancipates the plant in its growth from the properties of the matter it is built from.

Figure 2a. Growth in Plants. The growth cone is called apical meristeme. There are just a handful of largely undifferentiated cells that keep dividing almost infinitely. The shape of the plant is largely determined by a reaction-diffusion-system in the meristem, based on phyto-hormones that determine the cells. Higher plants can build secondary meristemes at particular locations, leading to a characteristic branching pattern.

 

Figure 2b. A pinnately compound leaf of a fern, showing its historical genesis as attachment at the outside (the tip of the meristeme)  from the inside. If you apply this principle to roots, you get a rhizome.

Figure 2c. The basic principle of plant growth can be mapped into L-Grammars, n order to create simulations of plant-like shapes. This makes clear that fractal do not belong to geometry! Note that any form creation that is based on formal grammars is subject to the representational fallacy.

Instead of using L-grammars as a formal reference we could also mention self-affine mapping. Actually, self-affine mapping is the formal operation that leads to perfect self-similarity and scale invariance. Self-affine mapping projects a minor version of the original, often primitive graph onto itself. But let us inspect two examples.

Figure 2d.1. Scheme showing the self-affine mapping that would create a graph that looks like a leaf of a fern (image from wiki).

self-affine Fractal fern scheme
Figure 2d.2. Self-affine fractal (a hexagasket) and its  neighboring graph, which encodes its creation [9].
self-affine fractals hexagasket t

Back to real plants! Nowadays, most plants are able to build branches. Formally, they perform a self-affine mapping. Bio-chemically, the cells in their meristeme(s) are able to respond differentially to the concentration of one (or two) plant hormones, in this case auxine. Note, that for establishing a two component system you won’t necessarily need two hormones! The counteracting “force” might be realized by some process just inside the cells of the meristeme as well.

From this relation between the observable fractal form, e.g. the leaf of the fern, or the shape of the surrounding of a city layout, and the formal representation we can draw a rather important conclusion. The empirical analysis of a shape should never stop with the statement that the respective shape shows scale-invariance, self-similarity or the like. Literally nothing is gained by that! It is just a promising starting point. What one has to do subsequently is to identify the mechanisms leading to the homomorphy between the formal representation and the particular observation. If you like, the chemical traces of pedestrians, the tendency to imitate, or whatever else. Even more important, in each particular case these actual mechanisms could be different, though leading to the same visual shape!!!

In earlier paleobiotic ages, most plants haven’t been able to build branches. Think about tree ferns, or the following living fossile.

Figure 2d. A primitive plant that can’t build secondary meristemes (Welwitschia). Unlike in higher plants, where the meristeme is transported by the growth process to the outer regions of the plant (its virtual borders), here it remains fixed; hence, the leaf is growing only in the center.

Figure 2e. The floor plan of Guggenheim Bilbao strongly reminds to the morphology of Welwitschia. Note that this “reminding” represents a naive transfer on the representational level. Quite in contrast, we have to say that the similarity in shape points to a similarity regarding the generating mechanisms. Jencks, for instance, describes the emanations as petals, but without further explanation, just as metaphor. Gehry himself explained the building by referring to the mythology of the “world-snake”, hence the importance of the singularity of the “origin”. Yet, the mythology does not allow to say anything about the growth pattern.

Figure 2f. Another primitive plant that can’t build secondary apical meristems. common horsetail (Equisetum arvense). Yet, in this case the apical meristeme is transported.

Figure 2g. Patrick Schumacher, Hadid Office, for the master plan of the Istanbul project. Primitive concepts lead to primitive forms and primitive habits.

Many, if not all of the characteristics of growth patterns in plants are due to the fact that they are sessile life forms. Most buildings are also “sessile”. In some way, however, we consider them more as geological formations than as plants. It seems to be “natural” that buildings start to look like those in fig.2g above.

Yet, in such a reasoning there are even two fallacies. First, regarding design there is neither some kind of “naturalness”, nor any kind of necessity. Second, buildings are not necessarily sessile. All depends on the level of the argument. If we talk just about matter, then, yes, we can agree that most buildings do not move, like crystals or plants. Buildings could not be appropriately described, however, just on the physical level of their matter. It is therefore very important to understand that we have to argue on the level of structural principles. Later we will provide an impressive example of an “animal” or “animate” building.7 

As we said, plants are sessile, all through, not only regarding their habitus. In plants, there are no moving cells in the inside. Thus, plants have difficulties to regenerate without dropping large parts. They can’t replace matter “somewhere in between”, as animals can do. The cells in the leafs, for instance, mature as cells do in animals, albeit for different reasons. In plants, it is mainly the accumulation of calcium. Such, even in tropical climates trees drop off their leaves at least once a year, some species all of them at once.

The conclusion for architecture as well as for urbanism is clear. It is just not sufficient to claim “metabolism” (see below) as a model. It is also appropriate to take “metabolism” as a model, not even if we would avoid the representational fallacy to which the “Metabolists” fell prey. Instead, the design of the structure of growth should orient itself in the way animals are organized, at the level of macroscopic structures like organs, if we disregard swarms for the moment, as most of them are not able to maintain persistent form.

This, however, brings immediately the problematics of territorialization to the fore. What we would need for our cities is thus a generalization towards the body without organs (Deleuze), which orients towards capabilities, particularly the capability to choose the mode of growth. Yet, the condition for this choosing is the knowledge about the possibilities. So, let us proceed to the next class of growth modes.

3.3. Swarms

In plants, the growth mechanisms are implemented in a rather deterministic manner. The randomness in their shape is restricted to the induction of branches. In swarms, we find a more relaxed regulation, as there is only little persistent organization. There is just transient order. In some way, many swarms are probabilistic crystals, that is, rather primitive entities. Figures 3a thru 3d provide some examples for swarms.

From the investigation of swarms in birds and fishes it is known that any of the “individual” just looks to the movement vector of its neighbors. There is no deep structure, precisely because there is no persistent organization.

Figure 3a. A flock of birds. Birds take the movement of several neighbors into account, sometimes without much consideration of their distance.

Figure 3b. A swarm of fish, a “school”. It has been demonstrated that some fish not only consider the position or the direction of their neighbors, but also the form of the average vector. A strong straight vector seems to be more “convincing” for the neighbors as a basis for their “decision” than one of unstable direction and scalar.

Figure 3c. The Kaaba in Mekka. Each year several persons die due to panic waves. Swarm physics helped to improve the situation.

Figure 3d. Self-ordering in a pedestrians population at Shibuya, Tokyo. In order to not crash into each other, humans employ two strategies. Either just to follow the person ahead, or to consider the second derivative of the vector, if the first is not applicable. Yet, it requires a certain “culture”, an unspoken agreement to do so (see this for what happens otherwise)

A particularly interesting example for highly developed swarms that are able to establish persistent organization is provided by Dictyostelium (Fig 4a), in common language called a slime-mold. In biological taxonomy, they form a group called Mycetozoa, which indicates their strangeness: Partly, they behave like fungi, partly like primitive animals. Yet, they are neither prototypical fungi nor prototypical animals. in both cases the macroscopic appearance is a consequence of (largely) chemically organized collaborative behavior of a swarm of amoeboids. Under good environmental conditions slime-molds split up into single cells, each feeding on their own (mostly on bacteria). Under stressing conditions, they build astonishing macroscopic structures, which are only partially reversible as parts of the population might be “sacrificed” to meet the purpose of non-local distribution.

Figure 4a. Dictyostelium, “fluid” mode; the microscopic individuals are moving freely, creating a pattern that optimizes logistics. Individuals can smoothly switch roles from moving to feeding. It should be clear that the “arrangement” you see is not a leaf, nor a single organism! It is a population of coordinating individuals. Yet, the millions of organisms in this population can switch “phase”… (continue with 4b…)

Figure 4b. Dictyostelium, in “organized” mode, i.e. the “same” population of individuals now behaving “as if” it would be an organism, even with different organs. Here, individuals organize a macroscopic form, as if they were a single organism. There is irreversible division of labor. Such, the example of Dictyostelium shows that the border between swarms and plants or animals can be blurry.

The concept of swarms has also been applied to crowds of humans, e.g. in urban environments [11]. Here, we can observe an amazing re-orientation. Finally, after 10 years or so of research on swarms and crowds, naïve modernist prejudices are going to be corrected. Independence and reductionist physicism have been dropped, instead, researchers get increasingly aware of relations and behavior [14].

Trouble is, the simulations treat people as independent particles—ignoring our love of sticking in groups and blabbing with friends. Small groups of pedestrians change everything, says Mehdi Moussaid, the study’s leader and a behavioral scientist at the University of Toulouse in France. “We have to rebuild our knowledge about crowds.”

Swarms solve a particular class of challenges: logistics. Whether in plants or slime-molds, it is the transport of something as an adaptive response that provides their framing “purpose”. This something could be the members of the swarm itself, as in fish, or something that is transported by the swarm, as it is the case in ants. Yet, the difference is not that large.

Figure 5: Simulation of foraging raid patterns in army ants Eciton. (from [12]) The hive (they haven’t a nest) is at the bottom, while the food source is towards thr top.  The only difference between A and B is the number of food sources.

When compared to crystals, even simple swarms show important differences. Firstly, in contrast to crystals, swarms are immaterial. What we can observe at the global scale, macroscopically, is an image of rules that are independent of matter. Yet, in simple, “prototypical” swarms the implementation of those rules is still global, just like in crystals. Everywhere in the primitive swarm the same basic rules are active. We have seen that in Dictyostelium, much like in social insects, rules begin to be active in a more localized manner.

The separation of immaterial components from matter is very important. It is the birth of information. We may conceive information itself as a morphological element, as a condition for the probabilistic instantiation. Not by chance we assign the label “fluid” to large flocks of birds, say starlings in autumn. On the molecular level, water itself is organized as a swarm.

As a further possibility, the realm of immaterial rules provides allows also for a differentiation of rules. For in crystals the rule is almost synonymic to the properties of the matter, there is no such differentiation for them. They are what they are, eternally. In contrast to that, in swarms we always find a setup that comprises attractive and repellent forces, which is the reason for their capability to build patterns. This capability is often called self-organization, albeit calling it self-ordering would be more exact.

There is last interesting point with swarms. In order to boot a swarm as swarm, that is, to effectuate the rules, a certain, minimal density is required. From this perspective, we can recognize also a link between swarms and mediality. The appropriate concept to describe swarms is thus the wave of density (or of probability).

Not only in urban research the concept of swarms is often used in agent-based models. Unfortunately, however, only the most naive approaches are taken, conceiving of agents as entities almost without any internal structure, i.e. also without memory. Paradoxically, researchers often invoke the myth of “intelligent swarms”, overlooking that intelligence is nothing that is associated to swarms. In order to find appropriate solutions to a given challenge, we simply need an informational n-body system, where we find emergent patterns and evolutionary principles as well. This system can be realized even in a completely immaterial manner, as a pattern of electrical discharges. Such a process we came to call a “brain”… Actually, swarms without an evolutionary embedding can be extremely malignant and detrimental, since in swarms the purpose is not predefined. Fiction authors (M.Crichton, F.Schätzing) recognized this long ago. Engineers seem to still have difficulties with that.

Such, we can also see that swarms actualize the most seriously penetrating form of growth.

3.4. Animals

So far, we have met three models of growth. In plants and swarms we find different variations of the basic crystalline mode of growth. In animals, the regulation of growth acquired even more degrees of freedom.

The major determinant of the differences between the forms of plants and animals is movement. This not only applies to the organism as a whole. We find it also on the cellular level. Plants do not have blood or an immune system, where cells of a particular type are moving around. Once they settled, they are fixed.

The result of this mobility is a greatly diversified space of possibilities for instantiating compartmentalization. Across the compartments, which we find also in the temporal domain, we may even see different modes of growth. The liver of the vertebrates, for instance, grows more like a plant. It is somehow not surprising that the liver is the organ with the best ability for regeneration. We also find interacting populations of swarms in animals, even in the most primitive ones like sponges.

The important aspects of form in animals are in their interior. While for crystals there is no interiority, plants differ in their external organization, their habitus, with swarms somewhere in between. Animals, however, are different due to their internal organization on the level of macroscopic compartments, which includes their behavioral potential. (later: remark about metabolism, as taking the wrong metaphorical anchor) Note that the cells of animals look quite similar, they are highly standardized, even between flies and humans.

Along with the importance of the dynamics and form of interior compartments, the development of animals in their embryological phase8 is strictly choreographed. Time is not an outer parameter any more. Much more than plants, swarms or even crystals, of course, animals are beings in and of time. They have history, as individual and as population, which is independent of matter. In animals, history is a matter of form and rules, of interior, self-generated conditions.

During the development of animal embryos we find some characteristic operations of form creating, based on the principle of mobility, additionally to the principles that we can describe for swarms, plants and crystals. These are

  • – folding, involution and blastulation;
  • – melting, and finally
  • – inflation and gastrulation;

The mathematics for describing these operations is not geometry any more. We need topology and category theory in order to grasp it, that is the formalization of transformation.

Folding brings compartments together that have been produced separately. It breaks the limitations of signal horizons by initiating a further level of integration. Hence, the role of folding can be understood as a way as a means to overcome or to instantiate dimensional constraints and/or modularity. While inflation is the mee accumulation of mass and amorphous enlargement of a given compartment by attachment from the interior, melting may be conceived as a negative attachment. Abstractly taken, it introduces the concept of negativity, which in turn allows for smooth gradation. Finally, involution, gastrulation and blastulation introduce floating compartments, hence swarm-like capabilities in the interior organization. It blurs the boundaries between structure and movement, introducing probabilism and reversibility into the development and the life form of the being.

Figure 6a. Development in Embryos. Left-hand, a very early phase is shown, emphasizing the melting and inflating, which leads to “segments”, called metamers. (red arrows show sites of apoptosis, blue arrows indicate inflation, i.e. ordinary increase of volume)

Figure 6b. Early development phase of a hand. The space between fingers is melted away in order to shape the fingers.

Figure 6c. Rem Koolhaas [16]. Inverting the treatment of the box, thereby finding (“inventing”?) the embryonic principle of melting tissue in order to generate form. Note that Koolhaas himself never referred to “embryonic principles” (so far). This example demonstrates clearly where we have to look for the principles of morphogenesis in architecture!

In the image 6a above we can not only see the processes of melting and attaching, we also can observe another recipe of nature: repetition. In case of the Bauplan of animal organisms the result is metamery.9 While in lower animals such as worms (Annelidae), metamers are easily observed, in higher animals, such as insects or vertebrates, metamers are often only (clearly) visible in the embryonal phase. Yet, in animals metamers are always created through a combination of movement or melting and compartmentalization in the interior of the body. They are not “added” in the sense of attaching—adding—them to the actual border, as it is the case in plants or crystals. In mathematical terms, the operation in animals’ embryonic phase is multiplication, not addition.

Figure 6d. A vertebrate embryo, showing the metameric organization of the spine (left), which then gets replicated by the somites (right). In animals, metamers are a consequence of melting processes, while in plants it is due to attachment. (image found here)

The principles of melting (apoptosis), folding, inflating and repetition can be used to create artificial forms, of course. The approach is called subdivision. Note that the forms shown below have nothing to do with geometry anymore. The frameworks needed to talk about them are, at least, topology and category theory. Additionally, they require an advanced non-Cartesian conception of space, as we have been outlining one above.

Figure 7. Forms created by subdivision (courtesy Michael Hansmeyer). It is based on a family of procedures, called subdivision, that are directed towards the differentiation of the interior of a body. It can’t be described by geometry any more. Such, it is a non-geometrical, procedural form, which expresses time, not matter and its properties. The series of subdivisions are “breaking” the straightness of edges and can be seen also as a series of nested, yet uncompleted folds (See Deleuze’s work on the Fold and Leibniz). Here, in Hansmeyer’s work, each column is a compound of three “tagmata”, that is, sections that have been grown “physically” independently from each other, related just by a similar dynamics in the set of parameters.

subdivision columns

Creating such figurated forms is not fully automatic, though. There is some contingency, represented by the designer’s choices while establishing a particular history of subdivisions.

Animals employ a wide variety of modes in their growing. They can do so due to the highly developed capability of compartmentalization. They gain almost complete independence from matter10 , regarding their development, their form, and particularly regarding their immaterial setup, which we can observe as learning and the use of rules. Learning, on the other hand, is intimately related to perception, in other words, configurable measurement, and data. Perception, as a principle, is in turn mandatory for the evolution of brains and the capability to handle information. Thus, staffing a building with sensors is not a small step. It could take the form of a jump into another universe, particularly if the sensors are conceived as being separate from the being of the house, for instance in order to facilitate or modify mental or social affairs of their inhabitants.

3.5. Urban Morphing

On the level of urban arrangements, we also can observe different forms of differentiation on the level of morphology.

Figure 8. Urban Sprawl, London (from [1]). The layout looks like a slime-mold. We may conclude that cities grow like slime-molds, by attachment from the inside and directed towards the inside and the outside. Early phases of urban sprawl, particularly in developing countries, grow by attachment form the outside, hence they look more like a dimensionally constrained crystal (see fig.1b).

The concept of the fractal and the related one of self-similarity entered, of course, also the domain of urbanism, particularly an area of interest which is called Urban Morphology. This has been born as a sub-discipline of geography. It is characterized by a salient reductionism of the Urban to the physical appearance of a city and its physical layout, which of course is not quite appropriate.

Given the mechanisms of attachment, whether it is due to interior processes or attachment from the outside (through people migrating to the city), it is not really surprising to find similar fractal shapes as in case of (dimensionally) constrained crystalline growth, or in the case of slime-molds with their branching amoeba highways. In order to understand the city, the question is not whether there is a fractal or not, whether there is a dimensionality of 1.718 or one of 1.86.

The question is about the mechanisms that show up as a particular material habitus, and about the actual instantiation of these mechanisms. Or even shorter: the material habitus must be translated into a growth model. In turn, this would provide the means to shape the conditions of the cities own unfolding and evolution. We already know that dedicated planning and dedicated enforcement of plans will not work in most cities. It is of utmost importance here, not to fall back into representationalist patterns, as for instance Michael Batty sometimes falls prey to [1]. Avoiding representationalist fallacies is possible only if we embed the model about abstract growth into a properly bound compound which comprises theory (methodology and philosophy) and politics as well, much like we proposed in the previous essay.

Figure 9a. In former times, or as a matter of geographical facts, attachment is excluded. Any growth is directed towards the inside and shows up as a differentiation. Here, in this figure we see a planned city, which thus looks much like a crystal.

Figure 9b. A normally grown medieval city. While the outer “shell” looks pretty standardized, though not “crystalline”, the interior shows rich differentiation. In order to describe the interior of such cities we have to use the concept of type.

Figure 10a. Manhattan is the paradigmatic example for congestion due to a severe (in this case: geographical) limitation of the possibility to grow horizontally. In parallel, the overwhelming interior differentiation created a strong connectivity and abundant heterotopias. This could be interpreted as the prototype of the internet, built in steel and glass (see Koolhaas’ “Delirious New York” [15]).

Figure 10b. In the case of former Kowloon (now torn down), it wasn’t geological, but political constraints. It was a political enclave/exclave, where actually no legislative regulations could be set active. In some way it is the chaotic brother of Manhattan. This shows Kowloon in 1973…

Figure 10c. And here the same area in 1994.

Figure 10d. Somewhere in the inside. Kowloon developed more and more into an autonomous city that provided any service to its approx. 40’000 inhabitants. On the roof of the buildings they installed the play grounds for the children.

The medieval city, Manhattan and Kowloon share a particular growth pattern. While the outer shape remains largely constant, their interior develops any kind of compartments, any imaginable kind of flow and a rich vertical structure, both physical and logical. This growth pattern is the same as we can observe in animals. Furthermore, those cities, much like animals, start to build an informational autonomy, they start to behave, to build an informational persistence, to initiate an intense mediality.

3.6. Summary of Growth Modes

The following table provides a brief overview about the main structural differences of growth models, as they can be derived from their natural instantiations.

Table 1: Structural differences of the four basic classes of modes of growth. Note that the class labels are indeed just that: labels of models. Any actual instantiation, particularly in case of real animals, may comprise a variety of compounds made from differently weighted classes.

Aspect \ Class crystal plant swarm animal
Mode of Attachment passive positive active positive active positive and negative active positive and negative
Direction from outside from inside from inside  towards outside or inside from & towards the inside
Morphogenetic Force as a fact by matter explicitly produced inhibiting fields implicit and explicit multi-component fields 11 explicitly produced multi-component fields
Status of Form implicitly templated by existing form beginning independence from matter independence from matter independence from matter
Formal Tools geometric scaling, representative reproduction, constrained randomness Fibonacci patterns, fractal habitus, logistics fractal habitus, logistics metamerism, organs, transformation, strictly a-physical
Causa Finalis(main component) actualization of identity space filling logistics mobile logistics short-term adaptivity

4. Effects of Growth

Growth increases mass, spread or both. Saying that doesn’t add anything, it is an almost syntactical replacement of words. In Aristotelian words, we would get stuck with the causa materialis and the causa formalis. The causa finalis of growth, in other words its purpose and general effect, besides the mere increase of mass, is differentiation12, and we have to focus the conditions for that differentiation in terms of information. For the change of something is accessible only upon interpretation by an observing entity. (Note that this again requires relationality as a primacy)

The very possibility of difference and consequently of differentiation is bound to the separation of signals.13 Hence we can say that growth is all about the creation of a whole bouquet of signal intensity lengths, instantiated on a scale that stretches from as morpho-physical compartments through morpho-functional compartments to morpho-symbolic specializations.14

Inversely we may say that abstract growth is a necessary component for differentiation. Formally, we can cover differentiation as an abstract complexity  of positive and negative growth. Without abstract growth—or differentiation—there is no creation or even shaping of space into an individual space with its own dynamical dimensionality, which in turn would preclude the possibility for interaction. Growth regulates the dimensionality of the space of expressibility.

5. Growth, an(d) Urban Matter

5.1. Koolhaas, History, Heritage and Preservation

From his early days as urbanist and architect, Koolhaas has been fascinated by walls and boxes [16], even with boxes inside boxes. While he conceived the concept of separation first in a more representational manner, he developed it also into a mode of operation later. We now can decode it as a play with informational separation, as an interest in compartments, hence with processes of growth and differentiation. This renders his personal fascinosum clearly visible: the theory and the implementation of differentiation, particularly with respect to human forms of life. It is probably his one and only subject.

All of Koolhaas’ projects fit into this interest. New York, Manhattan, Boxes, Lagos, CCTV, story-telling, Singapore, ramps, Lille, empirism, Casa da Musica, bigness, Metabolism. His exploration(s) of bigness can be interpreted as an exploration of the potential of signal intensity length. How much have we to inflate a structure in order to provoke differentiation through the shifting the signal horizon into the inside of the structure? Remember, that the effective limit of signal intensity length manifests as breaking of symmetry, which in turn gives rise to compartmentalization, opposing forces, paving the way for complexity, emergence, that is nothing else than a dynamic generation of patterns. BIG BAG. BIG BANG. Galaxies, stardust, planets, everything in the mind of those crawling across and inside bigness architecture.  Of course, it appears to be more elegant to modulate the signal intensity length through other means than just by bigness, but we should not forget about it. Another way for provoking differentiation is through introducing elements of complexity, such as contradictory elements and volatility. Already in 1994, Koolhaas wrote [17]15

But in fact, only Bigness instigates the regime of complexity that mobilizes the full intelligence of architecture and its related fields. […] The absence of a theory of Bigness–what is the maximum architecture can do?–is architecture’s most debilitating weakness. […] By randomizing circulation, short-circuiting distance, […] stretching dimensions, the elevator, electricity, air-conditioning,[…] and finally, the new infrastructures […] induced another species of architecture. […] Bigness perplexes; Bigness transforms the city from a summation of certainties into an accumulation of mysteries. […] Bigness is no longer part of any urban tissue. It exists; at most, it coexists. Its subtext is fuck context.

The whole first part of this quote is about nothing else than modulating signal intensity length. Consequently, the conclusion in the second part refers directly to complexity that creates novelty. An artifice that is double-creative, that is creative and in each of its instances personalized creative, how should it be perceived other than as a mystery? No wonder, modernists get overcharged…

The only way to get out of (built) context is through dynamically creating novelty., by creating an exhaustively new context outside of built matter, but strongly building on it. Novelty is established just and only by the tandem of complexity and selection (aka interpretation). But, be aware, complexity here is fully defined and not to be mistaken with the crap delivered by cybernetics, systems theory or deconstructivism.

The absence of a theory of Bigness—what is the maximum architecture can do? —is architecture’s most debilitating weakness. Without a theory of Bigness, architects are in the position of Frankenstein’s creators […] Bigness destroys, but it is also a new beginning. It can reassemble what it breaks. […] Because there is no theory of Bigness, we don’t know what to do with it, we don’t know where to put it, we don’t know when to use it, we don’t know how to plan it. Big mistakes are our only connection to Bigness. […] Bigness destroys, but it is also a new beginning. It can reassemble what it breaks. […] programmatic elements react with each other to create new events- Bigness returns to a model of programmatic alchemy.

All this reads like a direct rendering of our conceptualization of complexity. It is, of course, nonsense to think that

[…] ‘old’ architectural principles (composition, scale, proportion, detail) no longer apply when a building acquires Bigness. [18]

Koolhaas sub-contracted Jean Nouvel for caring of large parts of Euro-Lille. Why should he do so, if proportions wouldn’t be important? Bigness and proportions are simply on different levels! Bigness instantiates the conditions for dynamic generation of patterns, and those patters, albeit volatile and completely on the side of the interpreter/observer/user/inhabitant/passer-by, deserve careful thinking about proportions.

Bigness is impersonal: the architect is no longer condemned to stardom.

Here, again, the pass-porting key is the built-in creativity, based on elementarized, positively defined complexity. We thus would like to propose to consider our theory of complexity—at least—as a theory of Bigness. Yet, the role of complexity can be understood only as part of generic differentiation. Koolhaas’ suggestion for Bigness does not only apply for architecture. We already mentioned Euro-Lille. Bigness, and so complexity—positively elementarized—is the key to deal with Urban affairs. What could be BIGGER than the Urban? Koolhaas concludes

Bigness no longer needs the city, it is the city.’ […]

Bigness = urbanism vs. architecture.

Of course, by “architecture” Koolhaas refers to the secretions by the swarm architects’ addiction to points, lines, forms and apriori functions, all these blinkers of modernism. Yet, I think, urbanism and a re-newed architecture (one htat embraces complexity) may be well possible. Yet, probably only if we, architects and their “clients”, contemporary urbanists and their “victims,” start to understand both as parts of a vertical, differential (Deleuzean) Urban Game. Any comprehensive apprehension of {architecture, urbanism} will overcome the antipodic character of the relations between them. Hope is that it also will be a cure for junkspace.

There are many examples from modernism, where architects spent the utmost efforts to prevent the “natural” effect of bigness, though not always successful. Examples include Corbusier as well as Mies van der Rohe.

Koolhaas/OMA not only uses assemblage, bricolage and collage as working techniques, whether as “analytic” tool (Delirious New York) or in projects, they also implement it in actual projects. Think of Euro-Lille, for instance. Implementing the conditions of or for complexity creates a never-ending flux of emergent patterns. Such an architecture not only keeps being interesting, it is also socially sustainable.

Such, it is not really a surprise that Koolhaas started to work on the issue and the role of preservation during the recent decade, culminating in the contribution of OMA/AMO to the Biennale 2010 in Venice.

In an interview given there to Hans Ulrich Obrist [20] (and in a lecture at the American University of Beirut), Koolhaas mentioned some interesting figures about the quantitative consequences of preservation. In 2010, 3-4% of the area of the earths land surface has been declared as heritage site. This amounts to a territory larger than the size of India. The prospects of that have been that soon up to 12% are protected against change. His objection was that this development can lead to kind of a stasis. According to Koolhaas, we need a new vocabulary, a theory that allows to talk about how to get rid of old buildings and to negotiate of which buildings we could get rid of. He says that we can’t talk about preservation without also talking about how to get rid of old stuff.

There is another interesting issue about preservation. The temporal distance marked by the age of the building to be preserved and the attempt to preserve the building constantly decreased across history. In 1800 preservation focused on buildings risen 2000 years before, in 1900 the time distance shrunk to 300 years, and in 2000 it was as little as 30 years. Koolhaas concludes that we obviously are entering a phase of prospective preservation.

There are two interpretations for this tendency. The first one would be, as a pessimistic one, that it will lead to a perfect lock up. As an architect, you couldn’t do anything anymore without being engaged in severely intensified legislation issues and a huge increase in bureaucrazy. The alternative to this pessimistic perspective is, well, let’s call it symbolic (abstract) organicism, based on the concept of (abstract) growth and differentiation as we devised it here. The idea of change as a basis of continuity could be built so deeply into any architectural activity, that the result would not only comprise preservation, it would transcend it. Obviously, the traditional conception of preservation would vanish as well.

This points to an important topic: Developing a theory about a cultural field, such as it is given by the relation between architecture and preservation, can’t be limited to just the “subject”. It inevitably has to include a reflection about the conceptual layer as well. In the case of preservation and heritage, we simply find that the language game is still of an existential character, additionally poisoned by values. Preservation should probably not target the material aspects. Thus, the question whether to get rid of old buildings is inappropriate. Transformation should not be regarded as a question of performing a tabula rasa.

Any well-developed theory of change in architectural or Urban affairs brings a quite important issue to the foreground. The city has to decide what it wants to be. The alternatives are preformed by the modes of growth. It could conceive of itself as an abstract crystal, as a plant, a slime-mold made from amoeboids, or as an abstract animal. Each choice offers particular opportunities and risks. Each of these alternatives will determine the characteristics and the quality of the potential forms of life, which of course have to be supported by the city. Selecting an alternative also selects the appropriate manner of planning, of development. It is not possible to perform the life form of an animal and to plan according to the characteristics of a crystal. The choice will also determine whether the city can enter a regenerative trajectory, whether it will decay to dust, or whether it will be able to maintain its shape, or whether it will behave predatory. All these consequences are, of course, tremendously political. Nevertheless, we should not forget that the political has to be secured against the binding problem as much as conceptual work.

In the cited interview, Koolhaas also gives a hint about that when he refers to the Panopticum project, a commission to renovate a 19th century prison. He mentions that they discovered a rather unexpected property of the building: “a lot of symbolic extra-dimensions”. These symbolic capital allows for “much more and beautiful flexibility” to handle the renovation. Actually, one “can do it in 50 different ways” without exhausting the potential, something, which according to Koolhaas is “not possible for modern architecture”.

Well, again, not really a surprise. Neither function, nor functionalized form, nor functionalized fiction (Hollein) can bear symbolic value except precisely that of the function. Symbolic value can’t be implanted as little as meaning can be defined apriori, something that has not been understood, for instance, by Heinrich Klotz14. Due to the deprivation of the symbolic domain it is hard to re-interpret modernist buildings. Yet, what would be the consequence for preservation? Tearing down all the modernist stuff? Probably not the worst idea, unless the future architects are able to think in terms of growth and differentiation.

Beyond the political aspects the practical question remains, how to decide on which building, or district, or structure to preserve? Koolhaas already recognized that the politicians started to influence or even rule the respective decision-making processes, taking responsibility away from the “professional” city-curators. Since there can’t be a rational answer, his answer is random selection.

Figure 11: Random Selection for Preservation Areas, Bejing. Koolhaas suggested to select preservation areas randomly, since it can’t be decided “which” Bejing should be preserved (there are quite a few very different ones).

Yet, I tend to rate this as a fallback into his former modernist attitudes. I guess, the actual and local way for the design of the decision-making process is a political issue, which in turn is dependent on the type of differentiation that is in charge, either as a matter of fact, or as a subject of political design. For instance, the citizens of the whole city, or just of the respective areas could be asked about their values, as it is a possibility (or a duty) in Switzerland. Actually, there is even a nice and recent example for it. The subject matter is a bus-stop shelter designed by Santiago Calatrava in 1996, making it to one of his first public works.

Figure 12: Santiago Calatrava 1996, bus stop shelter in St.Gallen (CH), at a central place of the city; there are almost no cars, but every 1-2 minutes a bus, thus a lot of people are passing even several times per day. Front view…

…and rear view

In 2011, the city parliament decided to restructure the place and to remove the Calatrava shelter. It was considered by the ‘politicians’ to be too “alien” for the small city, which a few steps away also hosts a medieval district that is a Unesco World Heritage. Yet, many citizen rated the shelter as something that provides a positive differential, a landmark, which could not be found in other cities nearby, not even in whole Northern Switzerland. Thus, a referendum has been enforced by the citizens, and the final result from May 2012 was a clear rejection of the government’s plans. The effect of this recent history is pretty clear: The shelter accumulates even more symbolic capital than before.

Back to the issue of preservation. If it is not the pure matter, what else should be addressed? Again, Koolhaas himself already points to the right direction. The following fig.13 shows a scene from somewhere in Bejing. The materials of the dwelling are bricks, plastic, cardboard. Neither the site nor the matter nor the architecture seems to convey anything worthwhile to be preserved.

Figure 13: When it comes to preservation, the primacy is about the domain of the social, not that of matter.

Yet, what must be preserved mandatorily is the social condition, the rooting of the people in their environment. Koolhaas, however, says that he is not able to provide any answer to solve this challenge. Nevertheless it s pretty clear, that “sustainability” start right here, not in the question of energy consumption (despite the fact that this is an important aspect too).

5.2. Shrinking. Thinning. Growing.

Cities have been performances of congestion. As we have argued repeatedly, densification, or congestion if you like, is mandatory for the emergence of typical Urban mediality. Many kinds of infrastructures are only affordable, let alone be attractive, if there are enough clients for it. Well, the example of China—or Singapore—and its particular practices of implementing plans demonstrate that the question of density can take place also in a plan, in the future, that is, in the domain of time. Else, congestion and densification may actualize more and more in the realm of information, based on the new medially active technologies. Perhaps, our contemporary society does not need the same corporeal density as it was the case in earlier times. There is a certain tendency that the corporeal city and the web amalgamate into something new that could be called the “wurban“. Nevertheless, at the end of the day, some kind of density is needed to ignite the conditions for the Urban.

Such, it seems that the Urban is threatened by the phenomenon of thinning. Thinning is different from shrinking, which appears foremost in some regions of the U.S. (e.g. Detroit) or Europe (Leipzig, Ukrainia) as a consequence of monotonic, or monotopic economic structure. Yet, shrinking can lead to thinning. Thinning describes the fact that there is built matter, which however is inhabited only for a fraction of time. Visually dense, but socially “voided”.

Thinning, according to Koolhaas, considers the form of new cities like Dubai. Yet, as he points out, there is also a tendency in some regions, such as Switzerland, or the Netherlands, that approach the “thinned city” from the other direction. The whole country seems to transform itself into something like an urban garden, neither of rural nor of urban quality. People like Herzog & deMeuron lament about this form, conceiving it as urban sprawl, the loss of distinct structure, i.e. the loss of clearly recognizable rural areas on the one hand, and the surge of “sub-functional” city-fragments on the other. Yet, probably we should turn perspective, away from reactive, negative dialectics, into a positive attitude of design, as it may appear a bit infantile to think that a palmful of sociologists and urbanists could act against a gross cultural tendency.

In his lecture at the American University in Beirut in 2010 [19], Koolhaas asked “What does it [thinning] mean for the ‘Urban Condition’?”

Well, probably nothing interesting, except that it prevents the appearance of the Urban16 or lets it vanish, would it have been present. Probably cities like Dubai are just not yet “urban”, not to speak of the Urban. From the distant, Dubai still looks like a photomontage, a Potemkin village, an absurdity. The layout of the arrangement of the high-rises remembers to the small street villages, just 2 rows of cottages on both sides of  a street, arbitrarily placed somewhere in the nowhere of a grassland plain. The settlement being ruled just by a very basic tendency for social cohesion and a common interest for exploiting the hinterland as a resource. But there is almost no network effect, no commonly organized storage, no deep structure.

Figure 14a: A collage shown by Koolhaas in his Beirut lecture, emphasizing the “absurdity” (his words) of the “international” style. Elsewhere, he called it an element of Junkspace.

The following fig 14b demonstrates the artificiality of Dubai, classifying more as a lined village made from huge buildings than actually as a “city”.

Figure 14b. Photograph “along” Dubai’s  main street taken in late autumn 2012 by Shiva Menon (source). After years of traffic jamming the nomadic Dubai culture finally accepted that something like infrastructure is necessary in a more sessile arrangement. They started to build a metro, which is functional with the first line since Sep 2010.

dubai fog 4 shiva menon

Figure 14c below shows the new “Simplicity ™”. This work of Koolhaas and OMA oscillates between sarcasm, humor pretending to be naive, irony and caricature. Despite a physical reason is given for the ability of the building to turn its orientation such as to minimize insulation, the effect is a quite different one. It is much more a metaphor for the vanity of village people, or maybe the pseudo-religious power of clerks.

Figure 14c-1. A proposal by Koolhaas/OMA for Dubai (not built, and as such, pure fiction). The building, called “Simplicity”, has been thought to be 200m wide, 300m tall and measuring only 21m in depth. It is placed onto a plate that rotates in order to minimize insulation.

Figure 14b-2. The same thing a bit later the same day

Yet, besides the row of high-rises we find the dwellings of the migration workers in a considerable density, forming a multi-national population. However, the layout here remembers more to Los Angeles than to any kind of “city”. Maybe, it simply forms kind of the “rural” hinterland of the high-rise village.

Figure 15. Dubai, “off-town”. Here, the migration workers are housing. In the background the skyscrapers lining the infamous main street.

For they, for instance, also started to invest into a metro, despite the (still) linear, disseminated layout of the city, which means that connectivity, hence network effects are now recognized as a crucial structural element for the success of the city. And this then is not so different anymore from the classical Western conception. Anyway, even the first cities of mankind, risen not in the West, provided certain unique possibilities, which as a bouquet could be considered as urban.

There is still another dimension of thinning, related to the informatization of presence via medially active technologies. Thinning could be considered as an actualization of the very idea of the potentiality of co-presence, much as it is exploited in the so-called “social media”. Of course, the material urban neighborhood, its corporeality, is dependent on physical presence. Certainly, we can expect either strong synchronization effects or negative tipping points, demarcating a threshold towards sub-urbanization. On the other hand, this could give rise to new forms of apartment sharing, supported by urban designers and town officials…

On the other hand, we already mentioned natural structures that show a certain dispersal, such as the blood cells, the immune system in vertebrates, or the slime-molds. These structures are highly developed swarms. Yet, all these swarms are highly dependent on the outer conditions. As such, swarms are hardly persistent. Dubai, the swarm city. Technology, however, particularly in the form of the www and so-called social media could stabilize the swarm-shape.17

From a more formal perspective we may conceive of shrinking and thinning simply as negative growth. By this growth turns, of course, definitely into an abstract concept, leaving the representational and even the metaphorical far behind. Yet, the explication of a formal theory exceeds the indicated size of this text by far. We certainly will do it later, though.

5.3. In Search for Symbols

What turns a building into an entity that may grow into an active source for symbolization processes? At least, we can initially know that symbols can’t be implanted in a direct manner. Of course, one always can draw on exoticism, importing the cliché that already is attached to the entity from abroad. Yet, this is not what we are interested in here.The question is not so dissimilar to the issue of symbolization at large, as it is known from the realm of language. How could a word, a sign, a symbol gain reference, and how could a building get it? We could even take a further step by asking: How could a building acquire generic mediality such that it could be inhabited not only physically, but also in the medial realm? [23] We can’t answer the issues around these questions here, as there is a vast landscape of sources and implications, enough for filling at least a book. Yet, conceiving buildings as agents in story-telling could be a straightforward and not too complicated entry into this landscape.

Probably, story-telling with buildings works like a good joke. If they are too direct, nobody would laugh. Probably, story-telling has a lot to do with behavior and the implied complexities, I mean, the behavior of the building. We interpret pets, not plants. With plants, we interpret just their usage. We laugh about cats, dogs, apes, and elephants, but not about roses and orchids, and even less about crystals. Once you have seen one crystal, you have seen all of them. Being inside a crystal can be frightening, just think about Snow White. While in some way this holds even for plants, that’s certainly not true for animals. Junkspace is made from (medial) crystals. Junkspace is so detrimental due to the fundamental modernist misunderstanding that claims the possibility of implementing meaning and symbols, if these are regarded as relevant at all.

Closely related to the issue of symbols is the issue of identity.

Philosophically, it is definitely highly problematic to refer to identity as a principle. It leads to deep ethical dilemmata. If we are going to drop it, we have to ask immediately about a replacement, since many people indeed feel that they need to “identify” with their neighborhood.

Well, first we could say that identification and “to identify” are probably quite different from the idea of identity. Every citizen in a city could be thought to identify with her or his city, yet, at the same time there need not be such a thing as “identity”. Identity is the abstract idea, imposed by mayors and sociologists, and preferably it should be rejected just for that, while the process of feeling empathy with one’s neighborhood is a private process that respects plurality. It is not too difficult to imagine that there are indeed people that feel so familiar with “their” city, the memories about experiences, the sound, the smell, the way people walk, that they feel so empathic with all of this such that they source a significant part of their personality from it. How to call this inextricable relationship other than “to identify with”?

The example of the Calatrava-bus stop shelter in St.Gallen demonstrates one possible source of identification: Success in collective design decisions. Or more general: successfully finished negotiations about collective design issues, a common history about such successful processes. Even if the collective negotiation happens as a somewhat anonymous process. Yet, the relative preference of participation versus decreed activities depends on the particular distribution of political and ethical values in the population of citizens. Certainly, participatory processes are much more stable than top-down-decrees, not only in the long run, as even the Singaporean government has recognized recently. But anyway, cities have their particular personality, because they behave18 in a particular manner, and any attempt to get clear or to decide about preservation must respect this personality. Of course, it also applies that the decision-making process should be conscious enough to be able to reflect about the metaphysical belief set, the modes of growth and the long-term characteristics of the city.

5.4. The Question of Implementation

This essay tries to provide an explication of the concept of growth in the larger context of a theory of differentiation in architecture and urbanism. There, we positioned growth as one of four principles or schemata that are constitutive for generic differentiation.

In this final section we would like to address the question of implementation, since only little has been said so far about how to deal with the concept of growth. We already described how and why earlier attempts like that of the Metabolists dashed against the binding problem of theoretical work.

If houses do not move physically, how then to make them behaving, say, similar to the way an animal does? How to implement a house that shares structural traits with animals? How to think of a city as a system of plants and animals without falling prey to utter naivity?

We already mentioned that there is no technocratic, or formal, or functionalist solution to the question of growth. At first, the city has to decide what it wants to be, which kind of mix of growth modes should be implemented in which neighborhoods.

Let us first take some visual impressions…

Figure 16a,b,c. The Barcelona Pavilion by Mies van der Rohe (1929 [1986]).

This pavilion is a very special box. It is non-box, or better, it establishes a volatile collection of virtual boxes. In this building, Mies reached the mastery of boxing. Unfortunately, there are not so much more examples. In some way, the Dutch Embassy by Koolhaas is the closest relative to it, if we consider more recent architecture.

Just at the time the Barcelona pavilion has been built, another important architect followed similar concepts. In his Villa Savoye, built 1928-31, LeCorbusier employed and demonstrated several new elements in his so-called “new architecture,” among others the box and the ramp. Probably the most important principle, however, was to completely separate construction and tectonics from form and design. Such, he achieved a similar “mobility” as Mies in his Pavilion.

Figure 17a: La Villa Savoye, mixing interior and exterior on the top-roof “garden”. The other zone of overlapping spaces is beneath the house (see next figure 17b).

corbusier Villa Savoye int-ext

Figure 17b: A 3d model of Villa Savoye, showing the ramps that serve as “entrance” (from the outside) and “extrance” (towards the top-roof garden). The principle of the ramp creates a new location for the creation and experience of duration in the sense of Henri Bergson’s durée. Both the ramp and the overlapping of spaces creates a “zona extima,” which is central to the “behavioral turn”.

Corbusier Villa Savoye 06 small model

Comparing La Villa Savoye with the Barcelona pavilion regarding the mobility of space, it is quite obvious, that LeCorbusier handled the confluence and mutual penetration of interior and exterior in a more schematic and geometric manner.19

The quality of the Barcelona building derives from the fact that its symbolic value is not directly implemented, it just emerges upon interaction with the visitor, or the inhabitant. It actualizes the principle of “emerging symbolicity by induced negotiation” of compartments. The compartments become mobile. Such, it is one of the roots of the ramp that appeared in many works of Koolhaas. Yet, its working requires a strong precondition: a shared catalog of values, beliefs and basic psychological determinants, in short, a shared form of life.

On the other hand, these values and beliefs are not directly symbolized, shifting them into their volatile phase, too. Walking through the building, or simply being inside of it, instantiates differentiation processes in the realm of the immaterial. All the differentiation takes place in the interior of the building, hence it brings forth animal-like growth, transcending the crystal and the swarm.

Thus the power of the pavilion. It is able to transform and to transcend the values of the inhabitant/visitor. The zen of silent story-telling.

This example demonstrates clearly that morphogenesis in architecture not only starts in the immateriality of thought, it also has to target the immaterial.

It is clear that such a volatile dynamics, such a active, if not living building is hard to comprehend. In 2008, the Japanese office SANAA has been invited for contributing the annual installation in the pavilion. They explained their work with the following words [24].

“We decided to make transparent curtains using acrylic material, since we didn’t want the installation to interfere in any way with the existing space of the Barcelona Pavilion,” says Kazuyo Sejima of SANAA.

Figure 18. The installation of Japanese office SANAA in the Barcelona Pavilion. You have to take a careful look in order to see the non-interaction.

Well, it certainly rates as something between bravery and stupidity to try “not to interfere in any way with the existing space“. And doing so by highly transparent curtains is quite to the opposite of the buildings characteristics, as it removes precisely the potentiality, the volatility, virtual mobility. Nothing is left, beside the air, perhaps. SANAA committed the typical representational fault, as they tried to use a representational symbol. Of course, the walls that are not walls at all have a long tradition in Japan. Yet, the provided justification would still be simply wrong.

Instead of trying to implement a symbol, the architect or the urbanist has to care about the conditions for the possibility of symbol processes and sign processes. These processes may be political or not, they always will refer to the (potential) commonality of shared experiences.

Above we mentioned that the growth of a building has its beginning in the immateriality of thought. Even for the primitive form of mineralic growth we found that we can understand the variety of resulting shapes only through the conditions embedding the growth process. The same holds, of course, for the growth of buildings. For crystals the outer conditions belong to them as well, so the way of generating the form of a building belongs to the building.

Where to look for the outer conditions for creating the form? I suppose we have to search for them in the way the form gets concrete, starting from a vague idea, which includes its social and particularly its metaphysical conditions. Do you believe in independence, identity, relationality, difference?

It would be interesting to map the difference between large famous offices, say OMA and HdM.

According to their own words, HdM seems to treat the question of material very differently from OMA, where the question of material comes in at later stage [25]. HdM seems to work much more “crystallinic”, form is determined by the matter, the material and the respective culture around it. There are many examples for this, from the wine-yard in California, the “Schaulager” in Basel (CH), the railway control center (Basel), up to the “Bird’s Nest” in Bejing (which by the way is an attempt for providing symbols that went wrong). HdM seem to try to rely to the innate symbolicity of the material, of corporeality itself. In case of the Schaulager, the excavated material have been used to raise the building, the stones from the underground have been erected into a building, which insides looks like a Kafkaesque crystal. They even treat the symbols of a culture as material, somehow counterclockwise to their own “matérialisme brut”. Think about their praise of simplicity, the declared intention to avoid any reference beside the “basic form of the house” (Rudin House). In this perspective, their acclaimed “sensitivity” to local cultures is little more than the exploitation of a coal mine, which also requires sensitivity to local conditions.

Figure 18: Rudin House by Herzog & deMeuron

HdM practice a representationalist anti-symbolism, leaning strongly to architecture as a crystal science, a rather weird attitude to architecture. Probably it is this weirdness that quite unintentionally produces the interest in their architecture through a secondary dynamics in the symbolic. Is it, after all, Hegel’s tricky reason @ work? At least this would explain the strange mismatch of their modernist talking and the interest in their buildings.

6. Conclusions

In this essay we have closed a gap with respect to the theoretical structure of generic differentiation. Generic Differentiation may be displayed by the following diagram (but don’t miss the complete argument).

Figure 19: Generic Differentiation is the key element for solving the binding problem of theory works. This structure is to be conceived not as a closed formula, but rather as a module of a fractal that is created through mutual self-affine mappings of all of the three parts into the respective others.

basic module of the fractal relation between concept/conceptual, generic differentiation/difference and operation/operational comprising logistics and politics that describes the active subject

In earlier essays, we proposed abstract models for probabilistic networks, for associativity and for complexity. These models represent a perspective from the outside onto the differentiating entity. All of these have been set up in a reflective manner by composing certain elements, which in turn can be conceived as framing a particular space of expressibility. Yet, we also proposed the trinity of development, evolution and learning (chp.10 here) for the perspective from the inside of the differentiation process(es), describing different qualities of differentiation.

Well, the concept of growth20 is now joining the group of compound elements for approaching the subject of differentiation from the outside. In some way, using a traditional and actually an inappropriate wording, we could say that this perspective is more analytical than synthetical, more scientific than historiographical. This does not mean, of course, that the complementary perspective is less scientific, or that talking about growth or complexity is less aware of the temporal domain. It is just a matter of weights. As we have pointed out in the previous essay, the meta-theoretical conception (as a structural description of the dynamics of theoretical work) is more like a fractal field than a series of activities.

Anyway, the question is what can we do with the newly re-formulated concept of growth?

First of all, it completes the concept of generic differentiation, as we already mentioned just before. Probably the most salient influence is the enlarged and improved vocabulary to talk about change as far as it concerns the “size” of the form of a something, even if these something is something immaterial. For many reasons, we definitely should resist the tendency to limit the concept of growth to issues of morphology.

Only through this vocabulary we can start to compare the entities in the space of change. Different things from different domains or even different forms of life can be compared to each other, yet not as those things, but rather as media of change. Comparing things that change means to investigate the actualization of different modes of change as this passes through the something. This move is by no means eclecticist. It is even mandatory in order to keep aligned to the primacy of interpretation, the Linguistic Turn, and the general choreostemic constitution.

By means of the new and generalized vocabulary we may overcome the infamous empiricist particularism. Bristle counting, as it is called in biology, particularly entomology. Yes, there are around 450’000 different species of beetles… but… Well, overcoming particularism means that we can spell out new questions: about regulative factors, e.g. for continuity, melting and apoptosis. Guided by the meta-theoretical structure in fig.19 above we may ask: How would a politics of apoptosis look like? What about recycling of space? How could infrastructure foster associativity, learning and creativity of the city, rather than creativity in the city? What is epi/genetics of the growth and differentiation processes in a particular city?

Such questions may appear as elitary, abstract, of only little use. Yet, the contrary is true, as precisely such questions directly concern the productivity of a city, the speed of circulation of capital, whether symbolic or monetary (which anyway is almost the same). Understanding the conditions of growth may lead to cities that are indeed self-sustaining, because the power of life would be a feature deeply built into them. A little, perhaps even homeopathic dose of dedetroitismix, a kind of drug to cure the disease that infected the city of Detroit as well as the planners of Detroit or also all the urbanists that are pseudo-reasoning about Detroit in particular and sustainability in general. Just as Paracelsus mentioned that there is not just one kind of stomach, instead there are hundreds of kinds of stomach, we may recognize how to deal with the thousands of different kinds of cities that all spread across thousands of plateaus, if we understand of how to speak and think about growth.

Notes

1. This might appear a bit arrogant, perhaps, at first sight. Yet, at this point I must insist on it, even as I take into account the most advanced attempts, such as those of Michael Batty [1], Luca D’Acci or Karl Kropf [2]. The proclaimed “science of cities” is in a bad state. Either it is still infected by positivist or modernist myths, or the applied methodological foundations are utterly naive. Batty for instance embraces full-heartedly complexity. But how could one use complexity other as a mere label, if he is going to write such weird mess [3], mixing wildly concepts and subjects?

“Complexity: what does it mean? How do we define it? This is an impossible task because complex systems are systems that defy definition. Our science that attempts to understand such systems is incomplete in the sense that a complex system behaves in ways that are unpredictable. Unpredictability does not mean that these systems are disordered or chaotic but that defy complete definition.

Of course, it is not an impossible task to conceptualize complexity in a sound manner. This is even a mandatory precondition to use it as a concept. It is a bit ridiculous to claim the impossibility and then writing a book about its usage. And this conceptualization, whatsoever it would look like, has absolutely nothing to do with the fact that complex systems may behave unpredictable. Actually, in some way they are better predictable than complete random processes. It remains unclear which kind of unpredictability Batty is referring to? He didn’t disclose anything about this question, which is a quite important one if one is going to apply “complexity science”. And what about the concept of risk, and modeling, then, which actually can’t be separated at all?

His whole book [1] is nothing else than an accumulation of half-baked formalistic particulars. When he talks about networks, he considers only logistic networks. Bringing in fractals, he misses to mention the underlying mechanisms of growth and the formal aspects (self-affine mapping). In his discussion of the possible role of evolutionary theory [4], following Geddes, Batty resorts again to physicalism and defends it. Despite he emphasizes the importance of the concept of “mechanism”, despite he correctly distinguishes development from evolution, despite he demands an “evolutionary thinking”, he fails to get to the point: A proper attitude to theory under conditions of evolution and complexity, a probabilistic formulation, an awareness for self-referentiality, insight to the incommensurability of emergent traits, the dualism of code and corporeality, the space of evo-devo-cogno. In [4], one can find another nonsensical statement about complexity on p.567:

“The essential criterion for a complex system is a collection of elements that act independently of one another but nevertheless manage to act in concert, often through constraints on their actions and through competition and co-evolution. The physical trace of such complexity, which is seen in aggregate patterns that appear ordered, is the hallmark of self-organisation.” (my emphasis).

The whole issue with complex systems is that there is no independence… they do not manage to act in concert… wildly mixing with concepts like evolution or competition… physics definitely can nothing say about the patterns, and the hallmark of self-organizing systems is not surely not just the physical trace: it is the informational re-configuration.

Not by pure chance therefore he is talking about “tricks” ([5], following Hamdi [7]): “The trick for urban planning is to identify key points where small change can lead spontaneously to massive change for the better.” Without a proper vocabulary of differentiation, that is, without a proper concept of differentiation, one inevitably has to invoke wizards…

But the most serious failures are the following: regarding the cultural domain, there is no awareness about the symbolic/semiotic domain, the disrespect of information, and regarding methodology, throughout his writings, Batty mistakes theory for models and vice versa, following the positivist trail. There is not the slightest evidence in his writing that there is even a small trace of reflection. This however is seriously indicated, because cities are about culture.

This insensitivity is shared by talented people like Luca D’Acci, who is still musing about “ideal cities”. His procedural achievements as a craftsman of empirism are impressive, but without reflection it is just threatening, claiming the status of the demiurg.

Despite all these failures, Batty’s approach and direction is of course by far more advanced than the musings of Conzen, Caniggia or Kropf, which are intellectually simply disastrous.There are numerous examples for a highly uncritical use of structural concepts, for mixing of levels of arguments, crude reductionism, a complete neglect of mechanisms and processes etc. For instance, Kropf in [6]

A morphological critique is necessarily a cultural critique. […] Why, for example, despite volumes of urban design guidance promoting permeability, is it so rare to find new development that fully integrates main routes between settlements or roads directly linking main routes (radials and counter-radials)?” (p.17)

The generic structure of urban form is a hierarchy of levels related part to whole. […] More effective and, in the long run, more successful urbanism and urban design will only come from a better understanding of urban form as a material with a range of handling characteristics.” (p.18)

It is really weird to regard form as matter, isn’t it? The materialist final revenge… So, through the work of Batty there is indeed some reasonable hope for improvement. Batty & Marshall are certainly heading to the right direction when they demand (p.572 [4]):

“The crucial step – still to be made convincingly – is to apply the scientifically inspired understanding of urban morphology and evolution to actual workable design tools and planning approaches on the ground.

But it is equally certain that an adoption of evolutionary theory that seriously considers an “elan vital” will not be able to serve as a proper foundation. What is needed instead is a methodologically sound abstraction of evolutionary theory as we have proposed it some time ago, based on a probabilistic formalization and vocabulary. (…end of the longest footnote I have ever produced…)

2. The concept mechanism should not be mistaken as kind of a “machine”. In stark contrast to machines, mechanisms are inherently probabilistic. While machines are synonymic to their plan, mechanisms imply an additional level of abstraction, the population and its dynamics. .

3. Whenever it is tried to proof or implement the opposite, the primacy of logic, characteristic gaps are created, more often than not of a highly pathological character.

4. see also the essay about “Behavior”, where we described the concept of “Behavioral Coating”.

5. Deleuzean understanding of differential [10], for details see “Miracle of Comparison”.

6. As in the preceding essays, we use the capital “U” if we refer to the urban as a particular quality and as a concept, in order to distinguish it from the ordinary adjective that refers to common sense understanding.

7. Only in embryos or in automated industrial production we find “development”.

8. The definition (from Wiki) is: “In animals, metamery is defined as a mesodermal event resulting in serial repetition of unit subdivisions of ectoderm and mesoderm products.”

9. see our essay about Reaction-Diffusion-Systems.

10. To emancipate from constant and pervasive external “environmental” pressures is the main theme of evolution. This is the deep reason that generalists are favored to the costs of specialists (at least on evolutionary time scales).

11. Aristotle’s idea of the four causes is itself a scheme to talk about change. .

12. This principle is not only important for Urban affairs, but also for a rather different class of arrangements, machines that are able to move in epistemic space.

13. Here we meet the potential of symbols to behave according to a quasi-materiality.

14. Heinrich Klotz‘ credo in [21] is „not only function, but also fiction“, without however taking the mandatory step away from the attitude to predefine symbolic value. Such, Klotz himself remains a fully-fledged modernist. see also Wolfgang Welsch in [22], p.22 .

15. There is of course also Robert Venturi with his  “Complexity and Contradiction in Architecture”, or Bernard Tschumi with his disjunction principle summarized in “Architecture and Disjunction.” (1996). Yet, both went as far as necessary, for “complexity” can be elementarized and generalized even further as he have been proposing it (here), which is, I think a necessary move to combine architecture and urbanism regarding space and time. 

16. see footnote 5.

17. ??? .

18. Remember, that the behavior of cities is also determined by the legal setup, the traditions, etc.

19.The ramp is an important element in contemporary architecture, yet, often used as a logistic solution and mostly just for the disabled or the moving staircase. In Koolhaas’ works, it takes completely different role as an element of story-telling. This aspect of temporality we will investigate in more detail in another essay. Significantly, LeCorbusier used the ramp as a solution for a purely spatial problem.

20. Of course, NOT as a phenomenon!

References

  • [1] Michael Batty, Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals. MIT Press, Boston 2007.
  • [2] Karl Kropf (2009). Aspects of urban form. Urban Morphology 13 (2), p.105-120.
  • [3] Michael Batty’s website.
  • [4] Michael Batty and Stephen Marshall (2009). The evolution of cities: Geddes, Abercrombie and the new physicalism. TPR, 80 (6) 2009 doi:10.3828/tpr.2009.12
  • [5] Michael Batty (2012). Urban Regeneration as Self-Organization. Architectural Design, 215, p.54-59.
  • [6] Karl Kropf (2005). The Handling Characteristics of Urban Form. Urban Design 93, p.17-18.
  • [7] Nabeel Hamdi, Small Change: About the Art of Practice and the Limits of Planning, Earthscan, London 2004.
  • [8] Dennis L. Sepper, Descartes’s Imagination Proportion, Images, and the Activity of Thinking. University of California Press, Berkeley 1996. available online.
  • [9] C. Bandt and M. Mesing (2009). Self-affine fractals of finite type. Banach Center Publications 84, 131-148. available online.
  • [9] Gilles Deleuze, Difference & Repetition. [1967].
  • [10] Moussaïd M, Perozo N, Garnier S, Helbing D, Theraulaz G (2010). The Walking Behaviour of Pedestrian Social Groups and Its Impact on Crowd Dynamics. PLoS ONE 5(4): e10047. doi:10.1371/journal.pone.0010047.
  • [11] Claire Detrain, Jean-Louis Deneubourg (2006). Self-organized structures in a superorganism: do ants “behave” like molecules? Physics of Life Reviews, 3(3)p.162–187.
  • [12] Dave Mosher, Secret of Annoying Crowds Revealed, Science now, 7 April 2010. available online.
  • [13] Charles Jencks, The Architecture of the Jumping Universe. Wiley 2001.
  • [14] Rem Koolhaas. Delirious New York.
  • [15] Markus Heidingsfelder, Rem Koolhaas – A Kind of Architect. DVD 2007.
  • [16] Rem Koolhaas, Bigness – or the problem of Large. in: Rem Koolhaas, Bruce Mau & OMA, S,M,L,XL. p.495-516. available here (mirrored)
  • [17] Wiki entry (english edition) about Rem Koolhaas, http://en.wikipedia.org/wiki/Rem_Koolhaas, last accessed Dec 4th, 2012.
  • [18] Rem Koolhaas (2010?). “On OMA’s Work”. Lecture as part of “The Areen Architecture Series” at the Department of Architecture and Design, American University of Beirut. available online. (the date of the lecture is not clearly identifiable on the Areen AUB website).
  • [19] Hans Ulrich Obrist, Interview with Rem Koolhaas at the Biennale 2010, Venice. Produced by the Institute of the 21st Century with support from ForYourArt, The Kayne Foundation. available online on youtube, last accessed Nov 27th, 2012.
  • [20] Heinrich Klotz, The history of postmodern architecture, 1986.
  • [21] Wolfgang Welsch, Unsere postmoderne Moderne. 6.Auflage, Oldenbourg Akademie Verlag, Berlin 2002 [1986].
  • [22] Vera Bühlmann, inahbiting media. Thesis, University of Basel 2009. (in german, available online)
  • [23] Report in de zeen (2008). available online.
  • [24] Jacques Herzog, Rem Koolhaas, Urs Steiner (2000). Unsere Herzen sind von Nadeln durchbohrt. Ein Gespräch zwischen den Architekten Rem Koolhaas und Jacques Herzog über ihre Zusammenarbeit. Aufgezeichnet von Urs Steiner.in: Marco Meier (Ed.). Tate Modern von Herzog & de Meuron. in: Du. Die Zeitschrift der Kultur. Vol. No. 706, Zurich, TA-Media AG, 05.2000. pp. 62-63. available online.

۞

Urban Strings

November 17, 2012 § Leave a comment

The urban life on this globe forms a vastly diverse and

heterogeneous universe. How could one ever expect to understand it in its entirety ? And isn’t some sort of understanding required to deal with all the challenges offered by the complexity of urban environments that we are faced with? Such, or similar, is the despair of the urbanist. Some say, urbanism is dead, has disappeared, at least as far as urbanism is said to be concerned about kind of a theory about the city or urban life. Whatever happened to urbanism [1], Herzog & deMeuron are convinced [2] that “There are no theories of cities; there are only cities.” No manifestos any more, please!

Should we dismiss the despair of our putative urbanist? Or should we take the expressed concerns serious? Is it reasonable at all to strive for an understanding? And what could “understanding“ mean in light of the complexity of large urban arrangements? The Newton of urban affairs is quite unlikely to appear, the globally unified formula about urban affairs is certainly a delusion. For what purpose should we aim for insights, as most planning initiatives don’t hit their targets anyway? Why not just dropping the distanced attitude that seems to be implied by theory and planning and just act, on the local or even micro-level, to deal with the challenges? At least urbanists of any shade have already many toolboxes for any kind of problem, haven’t they? Well, the outcome of the “just acting,” the collection of works contributed by swarm architects, results, according to Koolhaas, in nothing else than Junkspace.

The matter is not of least relevance, as there have been more than 50% of all humans living in urban environments by 2011, with a projected 75% by 2050, and even today the conditions for inhabitants of cities as well as for cities themselves are often threatening, to say the least. In many urban aggregations in the South, slums are more something common than an exception.

Behind the scenes, and on a quite general level, any discourse about the city and its theory is about the dynamics of urban culture, or simply the concept of change and its political actualization. Upfront it does not matter whether we talk about succeeding whole-sale plans as in the case of Singapore, or similarly perhaps Masdar, failing planning like in case of Mumbai whether we talk about the effects of the mobilization of people, with positive net total as in the case of Shanghai, or a negative net total as in the case of Leipzig (at least up to 2010), whether we talk about self-organized changes or any mixture of those. Given the enormous diversity of the “cultural actual” we have to find a structure for any argument about urban change that is both general enough to include all of those aspects and, most important, that could be bound to the operational level. Otherwise we simply would neither be able to compare them at all, or to “learn” from it. Note that it is not appropriate to “define” change, as this would obscure any theoretical notion. And the generality of this structure should not be burdened by a neglect of the realm of individual personality. The “operational” comprises the political, of course, and thus also issues of ethics and morality.

This Essay

This essay is proposed to be a further step into the direction of Urban Reason. Urban Reason could be circumscribed as human reason that is unfolding, emerging etc. under the condition of the Urban1. In this piece we will try to elucidate the link between some foundational, that is, more conceptual issues and the possibility for active practice.

As one of the pillars of that endeavor we follow the grand or omni-cultural hypotheses of urbanism: Nowadays, human culture is largely identical with urban culture, and through the influence of the cities even in seemingly non-urbanized areas.

The grand cultural hypothesis is b no means a new one. As early as 1966, Aldo Rossi formulated one of its first more complete versions in his “The architecture of the City” (p.51):

In other words, on the most general level, it must be understood that the city represents the progress of human reason, is a human creation par excellence; and this statement has meaning only when the fundamental point is emphasized that the city and every urban artifact are by nature collective.

Yet, Rossi remains largely on the rationalist track (as we will discuss in a later essay about time and architecture). Even as he departs from “classical modernism” in stressing the importance of history, time and (collective) memory with regard to the understanding of the city, the city still remains an artifact, something produced. As a “skeleton,” any existing architecture informs any subsequent architecture, which is beyond mere cause and effect, but for Rossi this influence also remains neutral regarding the possibility of conceptual schemes of thinking. Additionally, the urban remains constructed, there is no autonomy in it.

Despite Rossi’s concepts certainly provide a valuable starting point, it does not push the issue far enough. Even as he realizes that human reason is involved in the subject of the city, as a rationalist he fails to recognize the self-referentiality in such an arrangement.

The grand cultural hypothesis thus not only provokes the serious issue of how to speak about2 the Urban (see footnote 1). With respect to the realms of thoughts and taughts, the Urban takes a role that is quite similar to that of language: everything we (as humans) can think already takes place within language. We can’t step out of it. Likewise we may say that really everything we think and do relates to the Urban, at least nowadays. Thus, the omni-cultural hypotheses also relieves the thinking about the Urban from the monopolistic claims of science(s), relocating the issue of theory from control and pushing it towards design and play. The secondary claim thus is simply that a theory of the Urban is impossible without a strong and serious appropriation of philosophy.3

Such, our grand cultural hypothesis is markedly different from the early and almost classic opening of Henri Lefebvre in his “The Urban Revolution” :

I’ll begin with the following hypothesis: Society has been completely urbanized. This hypothesis implies a definition: An urban society is a society that results from a process of complete urbanization. This urbanization is virtual today, but will become real in the future. (p.1)

Lefebvre still treats the Urban (capital “U”) as something external, from the perspective of a science study, in this case “urbanism” being the target. After all, Lefebvre holds a strong materialist (-marxist) position throughout his work, rejecting even the idea that epistemology could play a role in dealing with the Urban. So, indeed, markedly different from ours.

Another “eternal” issue to be addressed in the context of the Urban is the question about the role of theory. Just throwing around some neologisms, importing exotic concepts from largely unrelated domains, expressing a demand for ethics or morality or doing historical studies does not constitute a theory. Not quite astonishingly, neither modernism in general nor positivism/scientism in particular have been able to develop an appropriate concept of theory. We will also see, for instance, that it is highly unreasonable to conceive “theory” somehow as the antipode of practice or practical concerns.

The refined and appropriately positioned concept of theory directly raises another, almost always overlooked topic. In the “negotiations” about the reasonability of some common ground there is neither a final justification for anything, nor is it reasonable to refer to “values”. Both abolish any possibility for open evolution and lead directly into narrow ideology and dictatorship. Instead, when talking about and engaging e.g. in urban design affairs, we firstly have to make visible our metaphysical stances. Without such exposition any single move or opinion is either rendered into blind—ultimately technocratic—activism or arbitrariness. Secondly, the metaphysics has to rely on a strictly processual approach, which is cleaned from any thinking that refers to origins, centers or axioms.

Both, theory and metaphysics limit effectively what can be expressed, hence what could be recognized, measured and done, both directly limit the achievable ethics, and both constrain the space of possible methods and means that could be applied in any practical case. There are some striking examples for that, as we will see later.

Another important pillar thus is the exploration and adjustment of the conceptual vocabulary. We propose to drop realism and existentialism as the structural basis of urbanism and to switch to a foundation that speaks “informational,” that embraces probabilism in a reflected manner, of course without sliding into the technocratic abyss and also without dropping aspects of empathy. This requires a proper methodological setup that consists of rather clearly identified methodological domains. We will propose a layered structure for that.

The effects of this re-orientation of Urban Theory and its two-sided, bi-lateral binding to both abstract philosophy and practical policy are not limited to the considerations of the Urban. It will also exert a significant force onto philosophy. What (for us) is particularly at stake philosophically is a reconciliation of transcendence with material aspects of the world. Which transposes in less spherical wording to the transitions between concepts and operations, which in turn regards the issue of methods and planning.

The remainder of this essay comprises the following sections (active links):

1. Rendering “Theory”

There are indeed a lot challenges, as even a short visit of the site The Global Urbanist may proof. The variety and scale of the problems is enormous—staggering would be probably a more appropriate description from the perspective of the putatively rational urbanist. The editors of the Global Urbanist site distinguish 7 major regions for this globe, they identify 6 top-level domains and for each of them 10 sub-domains. Any of these 60 areas could be assigned a couple of scientific domains. Taking into account the definition of science as a domain with a particular vocabulary, urbanism is probably well comparable to the attempt of building the tower of Babel.

All of this is indeed, I already mentioned it, impressive. Yet, what is completely missing on that site is a section for theory. Some kind of bottom-line, a frame is missing. The whole site provides reports on conferences about case studies and other so-called hands-on approaches, close to the factual conditions. At least for the Global Urbanist, which certainly provides a representative sample, HdM’s forecasting proposal from 2008 turned true as a matter of fact, it seems.

If we take the modernist conceptualization of theory into consideration, HdM have been completely right in expressing their doubts about the reasonability of theory in urbanism. From within modernism, the concept of theory has achieved a very clear definition, displayed extensively in Stegmüller’s series [3], which continues the legacy of Popper, Carnap, and Sneed, accompanied and extended by the work by Salmon Wesley and van Fraassen. Well, at least the late van Fraassen stumbled into some doubts about the analyticity of theories. For our concerns here it is important to see that the concept of theory is a matter of the philosophy of science, not of the sciences themselves.

Well, domain-specific theories not only introduce dedicated terms and rules that allow the derivation of models. The first important claim of the modernist notion of theory is that this derivation of models from a theory can be formalized. The second important claim about theories is that they have to be falsifiable, which implies and presupposes that any two theories could be separated in a clear-cut manner. The result of the these claims is devastating. Theories couldn’t be distinguished from models anymore, since any model also introduces theoretical terms. Since falsifiability and uniqueness are also required, both the difference to models as well as the value of the concept “theory” vanishes. Thus, analytic theories indeed don’t exist. They are not even possible. In some sense, modernism is an attitude free from any theory, just as HdM claimed. And HdM would be also right in rejecting another idea about theory that can be met often in architecture, namely, that theory ought to deal with that which is permanent and always valid, notably the rules of art and law of statics. In their exclamation that we cited in the beginning HdM did not deplore, of course, the missing of theories with regard to urbanism… they praised it.

Yet, the failure of modernism and positivism to provide an appropriate concept of theory does not mean at all that we have to drop theoreticity completely and once and for all. We just have to revoke the modernist conceptualization of “theory”. This gap we are now going to fill.

As we have argued in a previous essay about theory in general, theories are orthoregulative milieus for the invention of models. It is the models that we use for anticipation. This notion of theory relates modeling with the Form of Life in which said modeling takes place. As a consequence, it is clear that the subject of theories are models and the process of creating models. The subject of theory is not empirical issues, quite contrary to the modernist (positivist) attempt. Inversely, we can see that any anticipation, even any model that has some utility, whether it is a formalizable one or a de-facto model, implies a theory, since nothing could be done outside of any condition. There is no rule-based activity without at least one theory. The true conceptual antipode of theory is therefore not practice, but rather performance. This conception solves a number of riddles about theories. For instance, different theories may well overlap, even producing a common sub-set of models that are hardly separable when directly compared as such. It also opens a much more appropriate perspective onto the fuzzy evolutionary network of theories than Kuhn [4] has been able to conceive it. Revolutions, whether scientific or not, are a matter of underdevelopment, symptoms of the possibility of disconnected singularities, hence not any more appropriate for our current techno-scientific, globalized societies today. (Though there is no guarantee for the ability to prevent underdevelopment.)

What does this concept of theory mean for the practice of urbanism, for the practice of building within a city, whether it expands the city or differentiate it? Why is it justified to commiserate the missing of theory on the Global Urbanist website?

As a first hint we may take Frank Lloyd Wright’s frequently cited credo about the relation of principles and form:

“Do not try to teach design. Teach principles.”

Certainly, Wright did not provide an architectural theory that could have been understood easily. Despite he himself provided 9 principles, these principles can’t count as a reflected theory, albeit Wright’s approach is clearly heading towards the concept of theory as we understand it. Think for instance about his insisting on the aspect of instantiation as actualization, even as he didn’t use such wording. The required philosophy (Deleuze) was to be written down only years later. Doubtless Wright’s approach was an early one, and one that has to be developed much further. But his message is quite clear: Theory precedes form, or in philosophical terms, potentiality precedes actuality, and concepts precede representation. Well, what applies to architecture fits also to the affairs around urbanism.

Yet, principles are a weak foundation. They remain axiomatic, messing representations and values, hence remaining completely within naïve realism or phenomenology. This holds for other “principled” theoretical approaches as well, e.g. that of Christopher Alexander, LeCorbusier, or those of Bernhard Tschumi, notwithstanding their respective appeal. On the other hand, praising some philosophical stance, let us say, the deconstructivism as unfolded by Derrida, and trying to coin it more or less directly into architecture is just as deficient. Jumping on some ism-bandwagon doesn’t qualify as theory, neither in architecture, nor in urbanism or any other domain.

Let me highlight the issue with a small anecdote. Recently, Sam Mendes, the celebrated director of the latest James Bond 007 movie, reflected about the use of action elements in an interview regarding the making-of of the movie. After a few weeks of taking more and more action shots, perfecting them eventually, he said, you will arrive at a point where you have ask yourself: What is it that you actually want to do and show?

Obviously, Mendes relates a particular action to the dynamics of the whole story, and that “wholeness” is quite extensive in the case of the 007 series, after 22 other James Bond movies. Previously, and as an extension to the Austin/Searle speech-act-theory [5], we called this aspect the delocutionary aspect of an utterance. It concerns the story-telling—through which is also actualizes—and the play whose subject is the playing itself. Taking this delocutionary aspect into consideration, formally and content-wise, implies precisely the conceptualization of theory as an orthoregulative milieu. In contrast to that, the Austin/Searle theory remains completely compatible with a modernist, i.e. positivistic and reductionist approach, since its top-most level relates just to a strategy, that is to a predefined or at least a predefinable purpose, but fails to relate to the openness of social intercourse. Delocutionary aspects, in contrast, resist any kind of apriori assignment, since they precisely declare to play with the potential of assignment, thereby abolishing any actual apriori assignment.

Well, the same scheme applies—and I think quite well so—to the presentation of topics on the Global Urbanist site. A lot of activities, undisputably interesting, but no framing. More clearly: mostly like a herd of chickens running wildly across the limited ground within a well-defined cage. That does not mean that the reports could not be inspiring. Yet, they could be inspiring only before the background of a suitable theory. Otherwise, case reports can count just as kind of soulful portrays which hardly can provide any kind of “lesson learnt” whatsoever.

Let us take a brief view onto an example of activism devoid of theory (in our sense). Kerwin Datu, editor-in-chief of The Global Urbanist, reported about the World Urban Forum in Naples in the beginning of September 2012. He distils four key elements of spatial planning of expanding cities (emphasis by Datu).

The first is the inevitable expansion proposition: that urbanization is a process that cannot be stopped, only shaped, by effective spatial planning.

The second is the sustainable densities proposition: that in place of the commonplace mantra that cities need to densify, Angel argues that it needs only to be optimised. Cities should be dense enough to sustain a public transport system, but not so dense that they generate health risks for their inhabitants.

Third is the decent housing proposition. ‘Adequate housing is possible only when land is in ample supply,’ a situation that many local authorities must do a lot more to create. In many cities there is an effective coalition that restricts land supply to generate superprofits for landowners, with severe impacts on the affordability of housing for all.

And fourth is the public works proposition: ‘as a city expands, space for public works must be secured in advance of development,’ […].

For once, it appears that the basic principles of planning for urbanization have been identified, and packaged in a form simple enough for laypeople (which most politicians are when it comes to spatial planning) can understand. Of course, in a conference as large and fragmented as the World Urban Forum, it remains to be seen whether any urban leaders are willing to listen.

As Datu emphasizes, a lot of ministers and mayors have been attending, thus politically important people who indeed could make the difference. Yet, the results are just depressing, aren’t they? If these four points indeed would be taken as the “basic principles of planning for urbanization”, well, then no wonder the conditions in many cities are simply bad. These results of the World Urban Forum are obviously almost nil, precisely because there are no design commitments regarding the social quality. It represents the effect of misplaced, physicalist reductionism. Doing spatial planning just from the perspective of almost physical elements is nothing but deficient. A further reason for the irrelevance of these “results” is that there is not the slightest reference to even a simple theory of differentiation, well, to any theory. Obviously, politically important people are confused and disoriented. What a dark age…

Given that we again would like to drop a remark about the parentage of theory in a field concerning the topic of the Urban. Approaching the problems from a meta-perspective, from some distance so-to-speak, by applying some particular domain science, for instance sociology, statistics, geography, fluid physics, engineering of control, etc. is not sufficient for calling the approach a “theory”. Imposing the implied theoretical stances of any particular science onto the field of the Urban and so importing those stances reverses the roles. This way, one does not achieve anything that is related to the Urban. One just creates a kind of sub-species of the respective science, that is sociology about urban populations, geography about spatial pattern dynamics, etc. Clearly, that does not solve the problem of how to address the Urban itself. Sticking to this hope may well be called scientism. And that is clearly misplaced with regard to the Urban.

Quite interestingly, a few recent articles published on the Global Urbanist site argue in favor of bottom-up approaches4, emphasizing that large-scale projects inevitably fail in most cases, and stretching the point of planning-with instead of a planning-for attitude. This bottom-up attitude is running contrary to—the fallacious—modernist scientism. We will return to this issue later. Yet, the respective articles are case-studies that hardly could be generalized, hence their value is quite limited. This is even true for AMO’s and Koolhaas’ investigation of Lagos, Nigeria [6]. What we would need is—again—a proper theory of differentiation. Koolhaas and his AMO/OMA obviously recognized that. As we argued recently, they approached that problematic field practically through their buildings, and more theoretical through their delocutionary essays (Generic City, Junkspace, the first an alleged movie script, the second kind of text for staged play). This engagement continued with their recently published work about the Japanese Metabolists and their concepts [7], provided as a collection of interviews and reviews [8].

2. Clearance for Take-Off

From all of that it should be clear that we would like to suggest to reject the attitude that denies the relevance of theory for dealing with the Urban, whether it is suggested explicitly—as in the case of Herzog&deMeuron—or implicitly—as the Global Urbanists prefer.

The whole endeavor of theorizing about the Urban must respect the role of theory: theory is NOT concerned about those empirical facts or material arrangements that we can observe in any particular city. As soon as we are engaged in observing we have been moving into the realm of modeling.5

Our conceptualization of “theory” renders the task of creating—or at least that of approaching—a theory more easy. We can set the empirical manifold of the Urban apart, at least for the time being. Later we will see that the treatment of the vast and almost infinite body of empirical facts concerning the Urban can be structured neatly before the background of the theoretical move. Anyway, leaving the particularity of the Urban behind allows us to focus on methodological as well as delocutionary issues.

One of these issues concerns the pervasiveness of the Urban. As we have been deriving this in a previous article, nowadays the Urban is synonymic with human culture at large. There is no single aspect on this globe anymore that would not be significantly affected by human culture and that is, human urban culture. “ More than ever, the city is all we have.” [1] Anything that we could say about the Urban is already enclosed by the Urban, it always takes place with respect to and even within the Urban.

The situation is thus much like it is the case for language. Any investigation not only presupposes language, it takes place within it, especially however any investigation of language itself. This insight, first recognized by Wittgenstein, paved the way for a (small?) revolution in philosophy, eventually called the Linguistic Turn in the 1970ies.

Language, Reason, Concept, the Urban, or culture are examples for performable conceptual entities for which an objectifying externalization is impossible.6 Whenever we refer to them we already need them to express them. It is meaningless and methodologically silly to try to objectify them, say as we usually pretend to do for concepts like chair, table ball etc. Yet, even in those cases the explication could never be finitized, i.e. finally closed. This setting corrodes any attempt for a “closed”, i.e. formal analysis of the Urban, much like it does in the case of language. In other words, we find a strong self-referentiality. Wittgenstein phrased it as the “paradox of rule-following” in §201 in his Philosophical Investigations [9].

For Wittgenstein the consequence has been clear: Language, as form, as a performance as well as with regard to the conveyed meaning has to be anchored in the form of life. It is not possible to establish an investigation, whether about language or anything other, that would be complete by itself. In philosophical terms: No investigation about some observable can provide sufficient reason, which quickly amounts to the fact that there is no such thing as self-sufficient sufficient reason at all.

Hence, the attempt of a “scientific language” (Carnap) is nonsense. Language is performed much like a game or a play, where the rules are quite volatile and in themselves subject of the play. There are some rules that we follow, yet the rules are neither complete, nor fully determinable, neither stable nor “justifiable” at all.

In written German for instance, we find clearly separated sentences and each word has a clear positional value and a distinct grammatical type. Yet, the borders of a sentence, or a few of them, is almost never a representative of a proposal. And what is going to be said is almost never representable as a proposal. While this aspect is present in written language, writing can be conceived as a means to limit this effect—or to play explicitly with it. In spoken language, however, the situation aggravates dramatically, as even sentences appear almost never as a complete(d) unit. Instead, what is created by talking together, on any side of the discourse, is much more a probabilistic field of densities and potentials that is only usable = understandable as a multi-channel diachronically organized braid of possible stories, from which we as participants agree on focusing to a particular one. Yet, this focus certainly does not remove any of the other threads. I am absolutely sure that this “structure” applies to any other language, at least Indo-European language as well. I mean, that’s the whole issue of rhetoric.

Hence Wittgenstein came up with the idea that language always comes as a language game [9]. Meaning is nothing else than usage, which in case of language refers to the couple of “interpretation” and the “prompt to interpret”. Thus, meaning is neither a private affair, nor a mental one, nor could it be determined by somebody or apriori.

Why do I anatomize the language process with such an emphasis, despite our main topic is the Urban, and the particular form of reason(s) that spring out from it?

Well, there are two reasons for that. Firstly, I want to demonstrate that the grammatical rules and all the rules that we actually could talk about with respect to language games do not, by no means, tell us anything about the nature of the play. Even in chess, which is a strictly determinable game, we find different styles in the way the players contribute to the individuation of the game. Secondly, it should have become clear that language can’t be conceived in any way as a process that contains precisely determinable entities, or that even would be itself determinable. The impression of clarity is an illusion triggered by the habits around its usage. Language and its usage is essentially is a probabilistic process, despite the school grammars, and despite the positivist propaganda of contemporary linguistics.

Language games can be instantiated in extremely different ways, of course. Ultimately, we even could not claim that there is a determinable content in practiced speech. Content appears only upon a bag of retrograde interpretations, each spanning across a different time span, each of them with different resolution, each of them with different intensity. Language games and the putative content change with context, such that there won’t be a ever such a thing like an repeated utterance. Everything we say, we say it for the first time, despite and because we practice a certain style, caring thereby for our grown and growing habits.

We now can ask for the consequences of all of that for a theory of the Urban. I think, we just could perform the analogous move, that is, we may introduce the concept of the “Urban Game”. Everything we said above about language games applies to Urban Games as well.

We will discuss this concept of the Urban Game in more detail in a later piece. For the time being, we just would like to touch two issues. Firstly, we may say that the “Urban Game” takes the role of the Wittgensteinian “showing”. They are not only shaped by the urban environment, many of them would not even take place at all. While they could be described, of course, with respect to their visible parts, such descriptions would not catch up with their consequences, their sense and meaning. There is no single, crisp effect associated to them, they just release kind of “excitation” into the probabilistic network of the urban fabric. Essentially, we can’t describe the effect without pointing to the entirety of the city, its whole becoming. In this way, Urban Games work as kind of media, conveying the amorphous, unspecific showing (up) of the culture (reflexively: “es zeigt sich”), and also as a means to show the expectation of this mediated excitation (transitively). This refers to quite different activities and moves, as the category of Urban Games comprises the whole spectrum between legislation and installation. Secondly, the concept of “Urban Game” certainly allows to respect the aforementioned self-referentiality. And as we have seen, it demands for probabilistic concepts when describing them, like it is the case for language games. Probably even more important, it also provides a stable conceptual bridge between the individual and the communal level of urban affairs.

Regarding architecture, a typical Urban Game is the semiosical (!) play with styles. Semiosis is the spreading and branched and “culturally embedded” probabilistic process of creating new (Peircean) signs, i.e. to establish a new sign-practice. Venturi and his collaborators have been the first (and since then seriously neglected ones) that emphasized the importance of the dimension of the sign. While Koolhaas in his Junkspace [10] pejoratively lamented about the fact that

Through our ancient evolutionary equipment, our irrepressible attention span, we helplessly register, provide insight, squeeze meaning, read intention; we cannot stop making sense out of the utterly senseless… (p.188)

it is also certainly true that the city is a quite special breeding site for new signs, demanding ever for more interpretation, despite all the habituation [11]. And equally certainly, a term like “architectural incongruence” isn’t helpful to any extent, particularly when used in combination with the idea of a “mature streetscape”. For Michael Conzen, proponent of the British school of urban morphologists and who coined these terms, the semiotic dimension is simply irrelevant, calling them “linguistic problems” [12]. One has to know that Conzen beliefs in the reasonability to investigate the layout of the town map as a separate subject, albeit influenced by culture at large, while (as a geographer) at the same time he rejects the outbound attempt to benefit from other disciplines like biology. In his attempt to stay aware of the need of theory, he readily adopts phenomenological patterns, pimped by leaning towards Cassirer. Yet, Conzen not only completely fails to understand the role of theory, by means of that orientation he also remains entirely within the modernist tradition, even in its raw version, that is, not understanding the importance of the linguistic turn. In the next essay we will discuss this issue further.

It is important to see that in the context of the Urban neither language games nor of course Urban Games are necessarily bound to a particular speaker in a particular situation. Urban arrangements transform everything into probabilistic affairs.

The “Urban Game” always comprises language games, of course. Else, it provides a bridge between issues of matter, power and language. The language-driven perspective, which is also a semiotically7 driven perspective, includes the speech-act, which in our case includes the extension of the delocutionary act, that is, the open play that goes beyond mere rule-following.8

There are important consequences for any theory about Urban, for a critique of Urban Reason, but also for any kind of practice. We can refer only to the most important ones here:

  • 1. The Urban can’t be addressed analytically, hence it is also impossible to implement any kind of representational top-down control or planning without annihilating the Urban.
  • 2. The Urban Game is a potentially rule-changing social performance.
  • 3. There is no “complete” empirical description of the Urban, that is, any anticipatory model will fail at least partially. This failure has to be covered by an appropriate treatment of and attitude towards risk.
  • 4. The Urban can’t be constructed.
  • 5. The Urban may appear in an unlimited diversity.

Note that these items are not based on “values” or “attitudes”. They are the result of a rigorous philosophical argument.

There is still another issue that we can derive from language philosophy. With regard to language it is misguided to ask about some kind of absolute, global or stable meaning. Instead we have to ask: Which (kind of) language game she or he is playing? Since we are interested in theory here, this transforms immediately into a methodological issue. Regarding the Urban, we have to be clear about the relation between actions and concepts.

3. Schemata of a Critique of Urban Reason

For our purposes it is sufficient to distinguish two aspects of actions. Firstly, there is the aspect of rule-following. The rules implied by an action are chosen either due to some anticipatory “calculation” or due to the influence of the form of life. It is reasonable to expect that in most cases both sources are active. Whether the actions are based on free will or not is not relevant for us here.

The second aspect of actions that we’d like to distinguish concerns about what often is considered as “unintended effects”. Of course, the issues around acting upon the external world are much larger than just that. Actions unfold into material re-arrangements, they are a major component of irreversibility, hence they provoke what we previously called the “existential resistance”. The changes “then” are subject of further interpretation.

These two aspects, rule-following and the couple of acting and interpreting that are tied together through irreversibility, make clear that there is no direct link between concepts and actions. From a quite different perspective we achieved the same result earlier when introducing the choreostemic space. There we argued that in any move besides modeling and concepts also mediality and virtuality have to be taken into consideration, notably all of them conceived as transcendent entities (not: transcendental!). Also related to this issue is what the philosopher John McDowell called the unboundedness of concepts, according to him an inevitable consequence of the Myth of the Given. [13]

From this we can now proceed to the basic structure of theory building. Yet, insofar as we don’t want to just provide some rules, seemingly out of the blue, we‘d like to stress the point that we propose a “conscious,” that is a critical approach. A critical approach concerns about the conditions that are implied by setting it up. One of these concerns, and probably the major one, is language, regarded as a transcendent condition. Another one is the transcendentality itself, which causes the concept of Concept to be not only transcendent, but also virtual. A critical approach to theory building can’t stop, however, here, just stating that there are transcendent aspects. We also need to explicate the (abstract) mechanisms that are in charge in the field made from theory, structural models, predictive models and the organization of operations.

In a first and rather coarse step we can distinguish three layers that are important for theory building regarding the Urban:

  • – The operational level, including politics, legislation, immaterial and material logistics, the construction of infrastructure and all individual activities as well;
  • – The categorical work, providing the concepts that determine what could be expressed at all concerning the Urban;
  • – The model layer between the first two areas, providing concepts that enable us to describe the dynamics of the Urban on the structural level.

Here, a small remark about the operational level is probably indicated. Operations have to be distinguished from actions. We conceive of operations here indeed as the application of operators to the material world, whether physical or social. Actions comprise, in contrast to that, much more, e.g. models and concepts. Yet, precisely those we tried to make visible, including their relations among each other. The concept of action is hiding that inner structure. Operations can’t be regarded just as rule-following. To operate means to flexibly adapt to unforeseen contextual influences in order to actualize the respective model(s). It is clear that matter will exert some “resistance” to that, existential resistance. The world can’t be mapped to analytical descriptions by principle, hence operations always have to deal with some gap and ignorance.

This may be depicted as shown in the following figure 1. The brackets here should not be understood as objective borders, of course, it just reflects a particular focus. On both sides, regarding the conceptual area, i.e. philosophy, and the operational area, i.e. largely politics, are manifolds by themselves. Actually, there is no clear border between the fields, just “gravitational” spots. Additionally, one should resist analytical habits that would imply a certain directionality in this field. The field may be entered from either side, and any kind of sequence is possible, given the actual context and the individuality of persons engaging in the process. Yet, the scheme allows to organize that sequence, or to simply talk about it. That is, the process of theory building as well as its application are critical also insofar as the externalization may trigger a secondary symbolization.

Figure 1: Generalized methodological layering for the binding of abstract thought to operations.

The scheme is a projection of the choreostemic space, both simplifying and extending it. The “concept” area is subject of philosophy. Note that the three layers are mutually dependent; the dependency of these layers works in either direction. More exactly we may say that these fields are dependent on each other in a particular way. They build a high-dimensional fluid moebius fractal.

Let us briefly visit the two conceptual components, the moebioid and the fractal. A fractal can be created in several ways, which however are all traceable to a procedure called self-affine mapping. An example for a simple self-affine mapping in 2-dimensional space with 2 surfaces is the leaf of the fern (see figure 2a), by the Peano-curve, the Sierpinski triangle, or the Koch snowflake curve. Inversely, fractals are created also recursive sub-division procedures.

A moebioid is a n-dimensional body with a topological “defect”. Despite a 3-dimensional moebioid exists in 3 dimensions, it has only 1 topological surface, instead of the usual 2 surfaces. There is no “inside” or “outside” with it, as you can observe if draw a closed circle. (Astonishingly, you can even fill water “into” a Moebius bottle despite their is no “inside”.) A moebioid is also conceivable as a knot, though not built from threads but from surfaces. As it is the case for trivial, that is smooth knots, moebioids become flat = unknotted in higher dimensions. A fractal moebioid, however, can’t be unknotted in higher dimensions. (I have no proof for this, it is just a conjecture)

Just as a small remark: This concept about theory work (and the potential working of theory) has been deeply inspired by Deleuze&Guattari’s “What is Philosophy”[14], particularly the sections about concepts and the “Plane of Immanence”. You will find a strong resemblance, for instance concerning the fractal structure, the distinction between the concept and the field they generate, etc.. Nevertheless, what we propose here is an extension of Deleuze’s work, so to speak, down-stream towards politics and logistics. Deleuze himself always refused to approach these areas, focusing on philosophical aspects. [15] Actually, I regard the binding between theory and politics, mediated through models, as one of the most interesting ones, not just with regard to architecture and urbanism, and for sure I will prepare a dedicated essay about it (working title so far: “Braidings between Immanence and Politics: The Case of Urban Tales.”).

Back to our scheme from figure 1. Our requirement is that any of the three fields contains any sequence from the three fields. Fortunately, the sequences do not grow very much due to pragmatic reasons. In other words, it needs to be treated by a self-affine mapping in order to approximate the actual arrangements in socio-mental settings, while at the same time the actual form of the “embedding” or framing is only a matter of relative phase, i.e. pseudo-location on the surface of the moebioid. Additionally, the resulting figure should not be expected to be a fixed geometrical entity. Rather, it is fluid, pruning some sequences, bringing any of the field-like components to the surface through foldings, etc. A distantly approximating impression is provided by figure 2b, just click to to see the projections moving.

Operations can not do without deeply integrated models, as it is the case for concepts. There are no “pure” models, or concepts, either, of course. Which compartment is surrounded by the others is dependent on the respective purpose, i.e. context and style, I suppose. in the following we will try to develop this scheme into an abstract space that could be used to trace the dynamics of the Urban.

Figure 2a: The fern leaf as a simple example for a self-affine mapping.

The next two images provide visualizations of projections of objects (not of fractals!) in high-dimensional spaces, the first in figure 2b more “conventional” (it is different aspects of a Calabi-Yau-manifold, which takes an important role in String theory, found here), the second in figure 2c more artistic and moebioid (found here).

Figure 2b: A grid of projections of the 6-dimensional Calabi-Yau-manifolds into 3-dimensional space. Note that a projection from higher to lower dimensionality not only creates knots and moebius figures, there is also no single definite projection, hence the grid.

Figure 2c: This image actually has been produced by weaving a lightstick, capturing it with long exposure times, not by any kind of digital rendering of numericals.

Despite the scheme from figure 1 is still quite coarse, we nevertheless can say that the most important part of this scheme is the one referring to theory, the categorical work. This includes all the modes that are being used to apply abstract concepts for the derivation of the concepts assignable to the intermediate layer. Hence, the categorical work fully constrains what could be expressed about the Urban, but also what could be recognized, modeled, anticipated and integrated into the symbolic constitution of a particular urban instance, whether it is by means of population dynamics or of more or less centrally organized activities. It constrains entirely what can be thought and said, whether on the level of the generic model, on the level of actual models, or with respect or logistic or political actions.

From that we can conclude three things. (1) The conceptual part has to be abstract enough. Reasoning about geometric forms, generative grammars and other forms of “automated” (or state-bound) methods to generate forms, the “origin of the pictorial” following Paul Klee or Wassily Kandinsky, all of such approaches are certainly not abstract enough, neither for doing theory work in architecture nor in the context of the Urban. (2) We need appropriate concepts and techniques to derive such concepts for creating structural models. (3) Both together have to allow for the derivation of political actions that are compatible with basic philosophical insights, with appropriate ethical and political positions. This would include, for instance, the discourse about sustainability, which is definitely neither a trivial nor a eco-technical issue.

Anyway, we may propose that the methodological layering shown above is indeed a generalizable scheme for the binding of abstract thought to operations. We just have to add that it should be conceived more as a high-dimensional methodological field with blurred borders between the components. As we already mentioned, there are many proposals that suffer from a considerable methodological “binding problem”, from either side. This causes critical developments particularly in those domains where we can find self-referentiality, for instance in linguistics or urbanism through their subjects “language” and/or “culture”. Examples for such critical developments are the whole movement of idealism, or, somehow as its pretended counterpart, the denial of theory. As a further abundant methodological fault we may count representationalism and the closely related believe in the dominance of common sense, as Deleuze has been pointing out (for details see this previous essay).

Of course, we have to explicate the model layer. Yet, before that we first have to take the thread up again that is put down by the importance and the guiding role of the concepts.

It is quite important to understand that concepts are transcendent, but neither universal nor eternal. They are not transcendental either, which would mean that they represent the demand for some kind of ultimate origin. There is also nothing with them that could be called “truth”. Concepts act more like hubs for semiotic processes that allow for and organize certain kinds of “vectorial traffic”, yet without maintaining any kind of materiality—even not a symbolic one—on their own. This position of the concepts inherits towards language.

Precisely here we can exclude any philosophical framework as a proper candidate that does not respect the primacy of concepts and language in the genealogy of a theory.9 Among the rejected attitudes we comprise phenomenology, external realism, existentialism, positivism, structuralism, and deconstructivism.

So, we can ask now: What else?

4. The Core

Actually, it is quite simple. The core of any Urban Theory, as well as its critique, must necessarily comprise the following two questions:

  • 1.How to speak about the Urban?
  • 2.How to actualize the Urban Games?

These questions are far from being “only of theoretical” significance, “theoretical” used here in the inappropriate, common sense way. It is for instance simply meaningless to address questions of sustainability without first answering those, as it is superfluous to engage in research about planning without a proper answer to those. What we also meet here is the eternal (and internal) tension of conservatism: what to conserve, the status quo, the dynamics or the potential? In order not to demolish itself, it must stick to the conservation status quo, which on the other hand abolishes any reasonability. We certainly have to care not to trap the concept of sustainability in the same dilemma.

Another area where the dominance of language and the conceptual may appear surprising is public services, particularly concerning the essential flows, i.e. energy and water. We will discuss this in more detail in the application section below.

What we find here is nothing else than a very practical consequence of Wittgenstein’s famous, almost proverbial, proposal: The borders of one’s language constitute the borders of one’s world. Inversely, we always can conclude that in case these questions will not be addressed explicitly they necessarily are answered implicitly. Yet, this also means that the answers will be most likely inconsistent, arbitrary, and contingent, without any possibility to set up a reasonable discourse about the urgent local issues.

It is of utmost importance to understand that these important questions can’t be answered without reference to two rather divergent areas, albeit they are also deeply and strongly linked to each other: (1) the predominant Form of Life that is practiced in a community, and (2) the metaphysical setup on the level of the individuals.

It is precisely here that we find the entrance point for “modernism”, whether the “original”, i.e. European version, or in its segregated form in the case of Singapore. Across the decades and centuries there is of course a co-evolution of the Form of Life and its accompanying metaphysics.

5. Metaphysics

As we have described earlier, modernism can be described by a characteristic set of beliefs. The dominant component of this set, however, is the strong belief in the necessity of metaphysical independence. Note that the idea of identity builds just the other side of the coin, essentially, independence and identity are almost synonymic from the philosophical perspective. In our essays about the role of logic and our add-on to the Deleuzean dual concept of Difference & Repetition, the choreostemic space, we discussed the alternative to identity and independence: transcendental difference.

Though historically comprehensible, independence is as little justifiable as any other metaphysical belief. The fact is simply that you can tell different and different kind of stories, some being more extensible and more fruitful than others. Anyway, this belief into independence informed everything in Western societies at least for several hundred years up to present times, with origins deep in classic Greek thought and with a particular blossoming at the end of the 19th century and the 1950ies/1960ies. Even Descartes and a whole series of scientists from Newton to Helmholtz would not have been thinking the way they did without it.

This independence has a range of strong correlates. One of the most influential is the belief in the indispensability of centralized control. A more abstract companion is the belief in centers and middle points itself [16], together with the cosmology of the sphere [17]. Traces of that can be found in architecture—from Boullée to Buckminster—as well as in urbanism, particularly as the phantasm of the “ideal city” that has been prevailing throughout the centuries.

Figure 3a: Etienne L. Boullée, Kenotaph for Newton (1784)

Figure 3b: Claude-Nicolas Ledoux, Dwelling for the Gardener in an utopian ideal city, ~1800.

The sphere and the implied importance of the concept of the center-point did not only show up as utopian buildings. It was also used, and is still being used, for the layout of cities. The phantasm of the “ideal city” has been poisoning the discourse about the Urban up to our days.

Figure 4a: Nowa Huta, a Polish city built to praise the heroism of the mine workers in former communist Poland.

Figure 4b: Palma Nova, near Venice, Italy. Note, that in former times the costs for the fortification caused a drive for circular layouts for geometrical reasons. Palma Nova still exists. Yet, in former times people didn’t want to live there.

.

Even today density is often misunderstood as a center of a radial symmetrical arrangement, with Manhattan being the great and pleasant exception.

With regard to methodology, statistics as it is practiced since the mid of the 19th century up today, is deeply structured by the independence assumption, which, as a matter of fact, renders it incapable to deal with patterns. In urban environments, the deep modernistic belief in independence led to forms reflecting crystalline growth, that is, the most primitive form of growth, which also is the least adaptive one.

Fortunately, things are changing. Well, they change slowly, but steady. The first incentive stems from biology, of course. In biology, nothing makes sense under the assumption of independence. Everything is meaningful only if conceived as a historically constrained processual manifold, called evolution, yet which also includes complexity. The second incentive comes—astonishingly—from physics, yet from the “non-classical” area of physics, in particular the physics on sub-atomic scales.

Changing the metaphysical setup in order to pave the way for a more appropriate understanding of the Urban means to drop the addiction to the sphere, of independence, of the object, of the territory, to leave behind the strive for identity as a constant as well as the representational attitude in (“explicit”) controlling and planning. Maybe you already detected the remote reference to the philosophy of Gilles Deleuze here.10 It is rather important to understand that all these items are not “universal” in any respect. They just follow from certain methodological considerations, influenced for instance by the insight into the primacy of language. Yet, even if language and concepts can be considered to play a transcendent role, universality does not follow from that.

6. Dropping the Spheres

The revolution that started to erode the deterministic scientific cosmogony towards a de-centered metaphysical cosmology is still running at high rates. In many areas its main messages are still not assimilated. Modernism and its detrimental offspring prevail.

The first “step” into that revolution was the discovery of in-computability. In-computability is a principle barrier that could not be overcome by more accurate measures. Actually, on the level of the sub-atomic world accuracy does not make much sense. Basically, there are three contributions:

  • 1. Poincaré’s investigation of the three-body-problem (~1900), leading to the first description of chaotic systems.
  • 2. The invention of Quantum physics from Planck (~1890) to Schrödinger (~1950), including the Heisenberg Uncertainty Principle.
  • 3. The investigation of dissipative processes by Prigogine (~1975).

The second “step”, which also stretches across several decades, derives from the paradoxical situation of quantum physics. On the one hand, the so-called “Standard Model” is quite successful. For instance, a simple principle has been deduced that allowed the prediction of the existence of formerly unknown sub-nuclear particles. There is some kind of order for the set of particles.

Figure 5. The “periodic System” of elementary particles according to the Standard Model. Despite the usual graphical depiction conveys seemingly a certain degree of simplicity, it is neither not that simple, nor does it display the open issues. In other words, it is some kind of propaganda.

On the other hand, it fails completely, as it does not allow to create a super-symmetric theory, that is, a theory that combines all of the four fundamental forces in nature.

As a result, some—if not many—basic observations are still unexplained, on the mesocosmic, rather small scales as well as on the cosmic scales (cf. [23]). Let us just pick three of the most salient gaps. First, there is no explanation of electro-magnetism that goes beyond its phenomenal description. In other words, physicists still don’t understand exactly what a “charge” is, say of an electron. Secondly, the “condensation” of elementary particles from “clouds” of extremely high “temperature”, e.g. sub-nuclear gluon plasma, is not understood. All physicists can say is simply: it happens. One of the gaps, according to the physicist Quigg, of the Standard Model concerns what makes a top quark a top quark and an electron an electron. Both seemingly don’t have further internal structure, both have electrical charge, though the quark only 1/3 of an elementary charge owned by the electron. Thirdly, now on the cosmic scale, there is complete ignorance in physics about the so-called “dark matter”. Would the “Standard Model” be indeed applicable and accurate, neither of the three phenomena should remain inexplicable.11

This situation gave rise to a still heavily disputed theoretical framework that is completely different from the “Standard Model” (SM). It is the so-called String Theory, more recently extended into M-Theory (MST).

The difference between those two frameworks is tremendous. In fact, they follow different and incommensurable metaphysical belief sets, which provides the reason that their case is particularly interesting for us.

Aspect

Standard Model

String Theory

conventional Space-Time

presupposes it

induces it

Basic Form

spherical particles or sections of space with 3-d rotational symmetry

1-dimensional strings of energy of approximately defined, positive length, the Planck length (10-33m)

Sub-atomic Particles

extremely concentrated energy, but the mechanism of creating inertial as well as rest mass is unknown

amplitude of vibration

Type of Particles

existential, produce of condensation frThere are many fundamental differences between the two frameworks, yet, the basic ones that are interesting for us here are the following:om gluon plasma, but mechanisms/rules are unknown

modes of vibration

Particle-Wave Dualism

phenomenal existent

irrelevant

4 Basic Forces

gravitation remains incommensurable (even if the Higgs Boson would be confirmed)

gravitation is a consequence, a unified theory is possible

Structure of Space

3 spatial dimensions+1 temporal dimension, presupposed

~10 abstract dimensions, from which the mesocosmic space derives through “overlapping” of low-dimensional (2d) projections

Basic Characteristics of the Framework

existential, claims desperately a “God”-particle, the Higgs-boson

generative, existence is not a central concept

Philosophical Status of the implied Image of Thought

based on identity and representation, with energy as an onto-realistic fact

based on difference and form (information), with energy as a mediator

Conceptual Status

it is a model (indeed)

it is a theory, i.e. an orthoregulative set of rules about how to generate a model

Note that it does not make sense to think of the strings as kind of objects. It is not possible to draw them, despite there are many artistic interpretations around. The basic architectonic difference between the frameworks is their relation to the concept of mechanism. The Standard Model is based on 19th century attitudes, expressing the initial claim that logic is imprinted to nature. There is no place for incorporating information as a separate entity. Causality and information are not distinguished, which ultimately leads to pseudo- paradoxes12. There is even the claim of perfect analyticity, that is, calculability, despite quantum physics itself proposes the uncertainty principle. It is precisely this architectonic flaw of trying contradictory things that lead to the “paradoxes” of current mainstream interpretations of the Quantum world.

The String Theory, in contrast, comprises a proposal of a mechanism that creates kinds of matter based on different information. String Theory describes the form of energy, where different forms—in this case different modes of “vibration”—lead to different kinds of matter. It concerns all particles, even photons, i.e. electromagnetic waves.

Both models, however, share an extremely important property: in some way or another, the describe a probabilistic, yet quantized world.

The sub-atomic world is not a continuous one. That means that it is impossible to have a smooth transition from a “natural law”, expressed in an analytic formula, and the observation of the behavior of those tiny “objects”. At some point we thus need an abstract transition that creates a quantum. Despite physics can only state that there is the quantum, incapable to “explain” the why, we may well say that this transition is induced by a transfer of information, e.g. by a measurement. In other words, the objects and their phenomenal appearance is dependent on the measurement, whether this is imposed by another particle without an experimenter or by the apparatus and the actions of the experimenter. Before measurement, however, particles are not particles at all. There are only waves of probability. That transition is called decoherence. The whole arrangement is thus one of information. The quantum introduces one of the conditions of identifiability: discontinuity. The other condition is memory, which we find only in the String Theory. As we already said above, the greatest defect in Standard Theory is the architectonic flaw that it conflates causality and information, which in turn is a consequence of its representational characteristic.

Nevertheless, from all of that it should be clear that quantum physics developed a strikingly different tool-set as compared to that of statistical mechanics. There, particles—atoms or molecules in this case—are conceived as tiny billiard balls, almost without spatial extension. Initially, statistical mechanics did not know anything about information. Yet, statistical mechanics introduced another important perspective into the realm of potential expressions: the population. In some way, we may conceive the whole 19th century as the century of the discovery or invention of the population, from the French Revolution to Darwin to Helmholtz.

In quantum physics, particularly in String Theory, the modernist assumptions collapse.

  • 1. There are no objects independent of measurement, quite to the contrary, measurement is a form of information transfer that induces the way how the microscopic world transits=transforms=decoheres into a macro world.
  • 2. There is no independence at all.
  • 3. The basic mode of description is based on probability, that is information and risk.
  • 4. Induced generation and probabilistic relation supersede existential claims.
  • 5. Computability is a matter of context and performing interaction.
  • 6. There is no complete analytic, i.e. symbolic description for the transition from micro to macro.

So, if the modernist belief set has been already seriously corroded even in physics, why should we continue to stick to it in a field like urbanism? We’d suggest to drop existentialist attitudes completely, concerning both theoretical as well as performative and material aspects, and with it all the anti-cultural procedures like representational top-down planning.

Some important questions could be derived here. What else can we learn from the example of quantum physics, particularly for urbanism? Is there a “standard model” in urbanism, drawing mainly on existential claims like objecthood? How would a stringy theory of the Urban look like? How could we assimilate a probabilistic perspective into our methodological setup?

At least one aspect of those open issues could be addressed right now. We have seen that in quantum physics the separation between observer and the observed breaks down. The reason is that measurement takes place on the same scale, within the same actualization or form of matter. Measurement itself introduces indistinguishability. The result is known as wave-particle dualism, linked by decoherence. And it is probably not the last strangeness physicists are enforced to handle, just think about the yet unknown quality of what they call dark matter and dark energy.

Well, the similarity of scale and kind is not limited to physics. We find it everywhere in cultural studies. Unfortunately enough, it is rarely recognized at all. It is still to be unleashed what decoherence could mean for cultural and urban studies, but for sure there are similar kinds of processes, strictly limiting what can be measured. Probably, we could even say that the self-referentiality introduced by the sameness of measurement scales shows up as quantum effect as well. One of the possible candidates for a cultural “quantum” is nothing else than the sign as it is formulated by Peircean semiotics. For “quantum” just means that there is no countability, nor identifiability beyond it. Probably, we have to be aware of “quantum effects”, mediated by different “particles”, in any cultural study.

Indeed, the Peircean sign is fully compatible with probabilistic foundations, for it marks a continuous field of actional densities, from which eventually an actual vector or reference is taken. This way we could say that Peircean signs and the signs in the Urban are isomorph (at least). The urban quantum-sign raises the issue of the symbol, which is often treated in a rather unsuitable manner, mainly in the context of the question of identity or identification and the related issue of historical continuity. Yet, the topics of the symbol, there symbolicalness and symbolability we have to postpone to a later piece (without forgetting about the probabilistic foundations).

7. Revisiting the Core

After this small excursion into the world of physics, which allowed us to harvest some promising conceptual tools, we return to our starting point, the topic of approaching a theory about the Urban. This we sketched by the following two questions:

  • 1. How to speak about the Urban?
  • 2. How to actualize the Urban Games?

The first of those questions could be said to relate to the field between the conceptual and the performative13, while the second would link the performative with the story-telling and the political. Again, the two questions or perspectives do certainly not delineate ideally (geometrically) separated fields. We already mentioned that Urban Games comprise language games. Additionally, they work from different directions, creating a complex dynamics. As a suitable metaphor for this we may cite fluid dynamics, especially of free streams such like the Gulf stream.

Figure 6a: The Gulf stream in the North Atlantic, departing from the east coast of America westward towards Europe (source). Red color means high differential velocity. A lot of vortices can be seen in a highly complex dynamics, creating patterns of mutual embedding.

Figure 6b. Vortices in a turbulent stream. As in case of the Gulf steam, there is no clear border, i.e. no separability between two mixing streams.

Let us focus the first issue for now, the mode and the possibility of explications as it is constrained by conceptual tools on various levels.

From previous work and the results achieved here so far we can fix some basic requirements for the explication of the model layer from figure 1.

Table 2: Basic requirements for a theory about the Urban.

Aspect

Characteristics

type of processes

differentiation, behavior

methodological frame

probabilistic, generative

architectonic constraint

satisfying self-referentiality

internal structural dynamics

construction by elementarization

The four basic types of structural model perspectives that match these requirements are

Growth

establishing persistent form (“Gestalt”, morphos) by attachment (either positive or negative), or more general, by a change in magnitude in some property (or properties); we may call it morphodiny (grk. dino, abstractly: to give, provide)

Networks

describing the form of matter capable for re-arranging information;

Associativity

for the transition from probabilistic processes to propositional statements, i.e. the basis for symbolification and encoding/decoding;

Complexity

for pattern creation and morphogenesis, i.e. the transition from order to organization as a self-stabilizing process.14

All of them we introduced in previous essays, yet in a slightly different context, which means that in the future we will provide updates to them such to match better the wording of urbanism.

These structural models share four eminently important properties: (1) They are all relational. (2) They are all built from “elements”. (3) These elements in turn provide docking sites for the even more abstract conceptual layer and the metaphysical attitudes behind them. (4) They allow to derive anticipatory models that directly engage with operational issues.

It is crucial to understand that these four categories are simply different perspectives, or language games, useful for talking about differentiation. Whenever we find a process that produces something different, whether as novelty or as some kind of alteration, we may take one of these perspectives. Yet, we won’t be able to talk about form and the “becoming different” without those categories as a group. In general terms, these four categories are to be conceived again as elements that we can use to construct a space (an aspectional one!), or likewise a scale that allows to compare things

A second group of categories is needed to take the perspective of the process itself. We may distinguish the basic qualities in the arrangement of matter and information, which is nothing else than the orchestration of dynamical change.

The scale is actually being built along the differential weight of matter or information. If the weight of matter or plans (symbolic quasi-matter) is more pronounced than that of information, then we call it usually development, if the matter becomes less relevant, we find either evolution, or still further down in the same direction, learning;

Thus we can see that form (morphos), adaptation and behavior build an almost continuous space, and thus, quite important, also a subjectivating scale to describe the dynamics of things. In turn, talking about changing things by just referring to one of these perspectives, whether on the objectivating or on the subjectivating scale, always must be rated as a inadmissible reduction.

Note that the “Relational Turn” is completely incompatible with modernism and its belief set. From a modernist perspective, the particular role of the above mentioned four structural perspectives remains simply invisible, for it is even impossible to talk about the dynamic effects and emergences of relationality within the limits of modernist concepts. Interestingly, throughout the 20ieth century, more and more scientific disciplines discovered the necessity for  relational turn, from biology (Rashevsky, 1935, Rosen 1991 [28]) thru economics to architecture (Lorenzo-Hemmer [29]).

In order to support the transition into the are of anticipatory models, the structural models have to support some quite essential processes. Any of them has to…

  • — be formalizable,
  • — be capable to provide scales for different kinds of measurement ,
  • — be operationalizable for actual construction of measurements,
  • — allow for active comparatistics.

Without support for these constructive properties a structural model would be hardly of any value.

Figure 7: Three methodological layers. The model layer showing only the main types of structural models. The other component of the model layer, the anticipatory models are not shown.

All four types of structural models can be used also for describing the transition between the material and the informational. Interestingly, they apply both with respect to the empirically observable processes as well as the methodological concerns, where they serve the transfer from concepts to action.

Finally, we can fill the model layer with more concrete aspects, creating something like an associative field. Of course, and in striking contrast to the short list of structural models, this field is by far not complete. Actually, on the level of anticipatory modeling we find already the influence of the unlimited number of forms of life. This does not mean that a particular form of life would provide an infinite number of possible moves. Quite the contrary is true. However, it definitely does mean that the forms of life can’t be constrained, or limited in their number, apriori, or top-down. Anything else results directly in chauvinist or imperialist patterns.

Figure 8: A possible explication of the model layer, now showing a mixture of structural and anticipatory models as an associative field.

Concepts like the aspection, the choreosteme, or the theory of theory can be used as conceptual tools, but they are also conceptual categories.15 Some of its components are still quite abstract and strictly non-representative. Thus, the intermediate “model” layer in its entirety may be also conceived as a multinomial or multi-perspectival generic model.

Similar to the model layer the explication could be done for both the conceptual layer as well as the operational domain. Together they probably establish what Foucault once called the field of proposals and propositions. Since we here are interested in and arguing towards the Urban, this field also represents a possible instantiation of “Urban Reason”. We just should not forget that story-telling, the playful delocutionary speech-act, provides the nodes and strings and knots that will bind everything together.

Once we manage to be able to keep all three areas alive simultaneously, whether we are engaged in political operations or in philosophical concepts, we can expect to understand the schemata that can be used to perform a Critique of Urban Reason. From this vantage point, finally, again being conscious about delocution, the playful story-telling, we can start to think the construction of the city. Probably only from this perspective.

8. Tokens, Types

If we consider the four basic constituents of the model layer also as major mechanisms of actual differentiation processes, then an interesting issue appears. Given the enormous variety of urban forms, concerning morphology, material and immaterial organization, and cultural processes, we could address the question whether we could derive a classificatory scheme, or distinguish certain types.

One could think of at least two purposes of such a classification, albeit both are concerned with the topos of the “Urban in Time”. We may for instance ask about the evolution of Urban life forms, in a similar way as it is done in biology with respect to natural evolution. This purpose would be directed to the past, putatively allowing for a better understanding of the history of the city and of urban arrangements.

David Shane proposed an approach to the description of forms that could well be called a hermeneutical one, thus being closely related to this evolutionary attitude [29]. When describing the forms he derives abstract elements of construction, attaches empirical instances and distils an evolutionary sequence of the form of the city. He distinguishes Archi Città, Cine Città and Tele Città. Each of them is characterized by a particular cultural setup that precipitates in typical morphological structures. Thus, Shane is able to build a kind of metric for “measuring” by the distinguished elements of “citiness”. These elements comprise two morphological forms on the level of built matter: armatures and enclaves. Highly interesting, however, he also includes Foucaultian heterotopias as a third element of citiness. He even proceeds differentiates heterotopia induced by material crisis from heterotopia of immaterial illusion. The heterotopia comprises incommensurable components, hence it is nothing else than an instance of the opposing forces that is a major element of complexity. Shane’s approach clearly exceeds for instance Tom Mayne’s approach who distinguishes different kinds of armatures and maneuvers in order to build a morphological taxonomy. Mayne also invokes the concept of complexity, yet, he doesn’t arrive at a comparable level of generality. Not quite surprising, Mayne’s work tends to the figural and representational. One of his main clients is the federal government of the U.S.A.

Both, Shane and Mayne are heading for a taxonomy. Shane’s achievement in his “Recombinant Urbanism” [30] is more abstract and thus more general than Mayne’s “Combinatory urbanism” [31]. Mayne got caught by the primacy of aspects of form, to which he assigns behavior, rather than the opposite as it is the case in Shane’s approach. For Shane, behavior comes first. Thus, Shane is able to reflect about city theory while Mayne provides case studies. These are beautiful to look at, but there is no theory, even as Mayne tries to distil a “method” from it as common denominator.

Yet, even Shane does not arrive at a theory of differentiation. He just describes it, almost in a phenomenological manner. Underpinning the description with plausible arguments does not yield a theory of differentiation. Hence, Shane’s approach is still not suitable to derive a taxonomy of city-contexts. But his results are perfectly compatible with the abstract structure we propose here.

Another “problem” with the approach as proposed by Shane is its tendency towards global interpretations. An extension of his work would be needed focusing more on the dynamic mechanisms. Together then it would be possible to create a classification scheme for urban neighborhoods that would tell the urbanist which “species” he is dealing with.

The second purpose of a classification or a taxonomy is not directed to the past, but rather more to the future. The model of differentiation could provide a means to anticipate struggles and to organize precisely the differentiation in the desired manner, without getting caught by inherent limitations due to metaphysical blindness. The paradigmatic example for such a potential deadlock is provided by the case of Singapore, as we have discussed in the previous essay. Another example is Mumbai, where the city administration imposes embryological principles onto a self-organizing urban body. This creates a deep mismatch since the city itself is at least on the verge of developing the capability for learning, that is, a very dynamic form of differentiation (at least in some parts of it).

This brings us to the application perspective.

9. The Application Perspective

In this last section we will show some examples for the “binding problem” regarding the relation between theory and operation.

So far we have introduced the abstract structure that is necessary for binding theory, models and operations together. We are convinced that without this structure, that any neglect of this structure leads to pathological consequences, particularly with respect to all those domains that deal with observations from the social or cultural realm. These consequences could be labelled the “binding problem”. Note that there is no particular addressee, since it concerns any concept and any operation, whether on the level of urban politics or on the level of implementing urban infrastructure.

Philosophical stances develop their specific binding deficit, think for instance of analytical philosophy where one can find the dismissal of metaphysics, while political operations may induce likewise instances of another kind of typical binding deficit. Common to all these deficits is some structural inconsistency, or even internal contradiction concerning central issues of the respective stance, often appearing as kind of (pseudo-)paradox.

Metaphysics is involved in this binding whether one is aware of it or not. We have argued that metaphysical belief sets constrain what can be perceived, recognized, expressed and conceived. Now let us see how such belief unfolds in actual reality.

The examples we choose for this essay are the supply of water and energy, and the movement that called itself “Metabolism”.

Water

One of the most striking examples is provided by the challenge of providing clean water in urban areas of developing countries. The problem is usually rendered into terms of necessary investment and uncontrolled growth of slums, accompanied by corruption or other forms of weakness in government. Together, these factors seem to prevent the installation of a sufficiently stable system of water pipes. Well, the actual problem, however, is precisely this rendering. Why? 

If we resort to the results discussed above we immediately can ask about the theoretical conditions that lead to that rendering. These conditions have nothing to do with the living conditions or political conditions. It is the metaphysical belief in central control and the belief in the possibility of rationalist, if not even deterministic planning that is creating the visible part of the problem.16 Central control as well as the belief in rigorous planning are both top-down approaches, hence they are applicable only to development, yet not to open evolution. Development, on the other hand, requires a fixation of side-conditions, which results in a particular model of differentiation: the abstract embryo. (Again: note that the biological type serves as a structural sibling, not even as a model!) Actually, we all should stop talking exclusively about “urban development”. Concerning the differentiation processes it is quite urgently to be completed with “urban evolution” and “urban learning”.

Usually, in urban differentiation processes the fixation of side-conditions is not possible, whether due to ethical or practical reasons. The result is that the problem persists, and with it the suffering of the people, the examples are countless, particularly all around in Africa. It is both a scandal as well as it is ridiculous that provision of water has been declared to be the major problem of the urban areas in the South.

Dropping the belief in planning, control and development immediately directs the attention to local solutions. Any local solution for material resources need an identifiable source, available storage and the organization of flows. Everybody can see the material arrangements of that basic setup. It is not an anonymous flow anymore. Regarding water, all of that can be established—astonishingly enough—in a strictly local manner, even in less developed areas.

Recently, Najiyah Alwazir described a project called RAINS that was conducted in Sanaa, the capital of Jemen. The project designed a solution for the problem of water shortage, which is a quite pressing issue in the mostly arid climate of Jemen. As a developing or even “underdeveloped” country, Jemen does not provide a stable, pervasive and abundant infrastructure. According to RAINS, the core element of the solution is thus the installation of appropriate private=local storage capacities, since in Sanaa there is a short raining period two times a year. Storage devices can be made almost from everything, especially however from various sorts of plastic. Yet, storing water for months is not without problems. For instance, it needs to be heated which requires additional energy.

But where to take water from locally, when there is none, if the raining season doesn’t provide enough water, or huge storage devices can’t be realized? Well, it is not true that there is no water. There is almost always water around, even in arid areas of the tropical or subtropical latitudes. It is in the air. The respective technology is blastingly simple. Basically, it is a windmill that creates pressure in the closed circuit of a heat pump, in other contexts also known as refrigerator. (read the respective story here). Nicely enough, the technology can be scaled, from hi-tech to low-tech, from small to big. A mid-sized turbine produces up to 1000 liters per day. Yet, low-tech turbines would work as well, requiring only very little investment, besides the fact that it creates lots of workplaces.

Without any exaggeration we can say that if there will be (is?) any scarcity of water (or energy, as we will see in the next section), then exclusively due to modernist stupidity or cynical politics. Scenarios like that imagined in the projective documentation about the consequences of global warming, “Les temps changent,” [32] are complete nonsense, since they mechanically recite the catastrophe against which there is allegedly no measure that society, i.e. the centrally administered state could take.

Water is not only an essential resource for living beings. The principle “water from air” can be integrated into any kind of architecture in order to use it as the basis of passive cooling. It should be clear that such infrastructural solutions become thinkable only if the modernist belief set is left behind.

Energy

Not only in developing countries, or the urban areas in the South, problems prevail due to the addiction to modernist belief sets. In industrialized countries there is a quite similar issue.

Currently, countries like Germany or Switzerland are propagating the so-called “Energy Turn” (official grm.: “Energiewende”), meaning that the required energy supply should be organized through so-called “regenerative sources” (which actually is a mis-nomer), that is from wind energy and solar energy. The problem imposed by this change is that the individual source is both rather small and rather volatile regarding its output, as compared with large power plants.

The modernist “solution” has been propagated as the so-called “smart grid”. A lot of computers are thought to be needed to distribute the electricity from many small sources and to minimize the peak-capacities, using the existing grid. Yet, smart grids do not change the principle for distributing the electrical energy at all: it remains centralized.

Thinking locally leads to a completely different solution, quite analogous to the water story. We need local producers, which in this case is simply the solar panel on the roof. And we need some storage, in other words batteries. In fact, what can be forecasted is a whole new culture of energy storage, across many scales. Fortunately, the market already started to offer such storage devices. IBC Solar offers devices for individual buildings, and ABB is working on large scale storage devices. There is also a solution involving methane and fuel cells in a closed loop system. The most funny thing, however, is the possibility to create methane, the main component of mineral gas, directly from the CO2 from air and hydrolyzed water (descriptions in german, in engl.). The tendency is the same as in the case of water: decentralization, and democratization, emergence of local infrastructures for storage and distribution. Astonishingly, the involved chemical reaction is known for more than 100 years, and wind power is an equally traditional source of energy. It was modernist thinking preventing its appearance on the engineers’ (and investors) radar. And nowadays, they again think of it only in large, expensive, technically difficult to handle installations, which therefore would have to be administered and run following the paradigm of centralization.

It is clear that the result could be a completely different kind of organization for the grid and a completely different kind of differentiation processes. Bottom-up processes lead automatically to the emergence of cluster- or cell-like organization.17 Such an organization not only automatically provides redundancy. It also will create suitably designed and unforeseeable business opportunities on the fly, which in ecology is called niche creation. To large parts it will be privately owned (on the level of cells), just the overarching informational organization may be provided by institutions. Such, institutions become clients rather than remaining providers. It is clear, that only in such a bottom-up organized energy culture we will see a true market for usable energy differences, quite in contrast to the oligopolistic (at best) fake we have to deal with today.

Most important, however, replacing top-down with bottom-up ultimately results in a change of metaphysical attitudes. Away from the orientation towards the lithosphere, turning around towards the solar stream of usable energy. In one of the next essays we will discuss this in more details by means of reviewing an upcoming book about the issue.

Metabolism

As a third example for illustrating the binding problem regarding the relation between theory and operation we will briefly visit the idea of metabolism, or organicism in a wider perspective, with regard to architecture and urbanism.

Metabolism is a biological concept. It describes the capability of living cells or even whole organisms to grow, to differentiate and to maintain their structure. Etymologically, metabolism means “a change”, that is the observation of a particular change. Metabolic processes are observable as large variety of well-orchestrated changes, that form a dynamic “equilibrium”, i.e. a phenomenologically more or less stable macroscopic appearance, which however rests on myriads of changes on the microscopic level. Yet, it must be understood, that metabolic processes are dissipative processes, meaning that they create a surplus of entropy in order to build up structures, that is, negentropy. Creating a surplus of entropy requires quite excessive consumption of energy differences, turning them into heat radiation.

Above all, metabolism is not simply a particular change. Its orchestration requires a preceding structure, including the respective functional compartments. And this change is devised to a particular function, the synthesis of new morphological structures as well as their break-down and recycling. Such, biological metabolism denotes “change within structures that leads to change of morphology”. This does not mean, however, that the shortcut “metabolism is morpho-change” is allowed. Rather we have to consider that we have different levels of integration with respect to the changes, linked together by emergence and deposits—just as in any complex system.

The idea of metabolism was by no means revolutionary at that time in the beginnings of the 1960ies. It just extended a line of thinking that prevailed in architecture and urbanism at least for 30 years in advance. In architecture and urbanism, the idea of organicism appeared the first time in the work of Frank Lloyd Wright, already in the first or second decade of the 20th century. Yet, his notion of organicism had only little to do with organisms, or the Kantian organon. Wright called himself a modernist, and such his assimilation aimed for things like “super-nature,” designs better than nature. He tried to extract principles that almost naturally would lead to good design. All of this is utterly naïve, of course.

A next important step was the adoption of the concept of the organism into the Charta of Athens in 1933. Planners obviously felt overwhelmed by the complexity and vitality of cities, and perhaps by their own ignorance about that, that the notion of “city as organism” has been quite popular. Additionally, corporeality has been subject of heroism all around the developed countries throughout the 1930ies. A bit later Sigfried Giedion (1941) referenced organisms explicitly as a template for built architecture in his famous “Space, Time and Architecture: The Growth of a New Tradition”. Yet, growth is not developed as a concept there, and time is conceived just as “history”, but rather not as an intrinsic result of the Urban, something which had to wait until Aldo Rossi’s (1984) critique of modernist conceptions of cities and architecture.

Yet, a city is not an organism, of course. Despite both entities, cities as well as organisms, can be said to be complex entities, the actual mechanisms are quite different. Simply spoken, in a city, we do not find a Golgi-apparatus, and in the cell we don’t find  mayors or administration.

This topic appeared also in the discourse about urban morphology. In the recent two decades or so, the quarrel between the various schools on urban morphology happened to become really serious. The Italian school around Caniggia traditionally embraced the idea of the organism as kind of a template for thinking about urban form. Yet, they didn’t used it as a template for deriving a theoretical position, they approached it more in a sympathetic mood. This caused a fierce critique by Michael Conzen [12], one of the popes of the area:

In a recent issue of Urban Morphology, Nicola Marzot offered an interpretation of my approach to urban morphology as compared to that of Caniggia who ‘equated human history and natural history. Each entailed th processes of birth, development, maturity and death. And there was a clear implication of the products of human endeavours.’ If Caniggia really said that he would have committed an obvious absurdity, for the existence of an urban settlement is a fundamentally different thing from the life of a human individual. (p.78)

Yet, Conzen too has obviously been completely unable to derive a theoretical position himself from his almost infinite catalog of particulars. Of course, he is a pope, and as such he could not do without installing the need for exegesis.

What is needed is a suitable binding between predictive models that are used in operations and structural models that allow a transition or integration towards the conceptual level. In fact, and quite unfortunately, up today and with the exception of the approach we proposed earlier, even the concept of complexity wasn’t presented in a useful form so far. One of the dramatic effects of misunderstood organicism as envisioned by the Athens Charta was the program of de-densifying the core of the cities. Of course, the opposite, densification, can’t be limited to just the material aspects as for instance in case of the Banlieues of Paris (F), which additionally follows the crystalline growth model. In the context of the Urban, densification has to be understood always as an issue of mediality. Media in turn require densified semiosis, which will emerge only on the basis of sufficient diversity of life forms within the same physical space.

In both cases, with Wright and with the Athens Carta, we can observe a binding problem in the theory work, leading to a literal, representational adoption of concepts from another domain. As Girard puts it,

one should avoid allegory, which consists in replacing the object with its metaphor. ([33] p.136, his emphasis)

What is missing in both cases, in Wright’s writing as well as in the Athens Charta, is a proper concept of differentiation18 that could have been used as a binding element.

Before the background of the discourse about sustainability19 and regenerative cities20 the ideas of the Japanese Metabolists from the early 1960ies gain increasing attention. Koolhaas & Obrist are just the most recent ones publishing an anthology about them, though probably the most serious one, as it consists of lots of interviews with still living former proponents of the group and with sketches of drawings.

What is this Japanese “Metabolism” about? In a recent interview with a German newspaper about his book Koolhaas praises their intention [34]:

Kiyonori Kikutake explains why at that time they haven’t been satisfied by the time-honored laws about form and function any more, and they tried to transfer the life cycle of birth and growth to town planning and construction and architecture.21

If nothing else, then this citation definitely demonstrates Koolhaas’ interest in a theory of differentiation for urbanism and architecture. Yet, it also uncovers Koolhaas’ own deficits, which he shares with many other “experts” of the field. On his conscious radar only expansion appears, albeit in his practice he applied embryological principles several times, e.g. in case of Casa da Musica.

Kiyonori Kikutake [35] writes

Metabolism” is the name of the group […]. We regard human society as a vital process […]. The reason why we use such a biological word, the metabolism, is that, we believe, design and technology should be a denotation of human vitality.

And Kisho Kurokawa specifies (cited after [36] p.81):

…if spaces were composed on the basis of the theory of the metabolic cycle, it would be possible to replace only those parts that had lost their usefulness and in this way to contribute to the conservation of resources by using buildings longer.

Later, Kurokawa extended the Metabolists’ approach into a theory of “symbiosis” to be applied to urbanism, architecture and their relation to nature. Yet, despite their approach—as far it is conveyed in their writings—is certainly sympathetic, it is not so much more than that. It provides an early support of the idea of sustainability, but there are neither structural nor predictive models, there is no theory of differentiation and no reflection about metaphysical conditions. There is just a fluffy use of a biological metaphor and the operations, that is, building as operation and politics of building. Not quite surprisingly, they conceive of themselves also as modernists, publishing the “last manifesto” in urbanism. Looking to their built matter, it becomes clear that the Metabolists’ approach is deeply infected by cybernetics. The implied model of differentiation and morphogenesis that they applied is close to crystalline growth, as it is demonstrated by the Nagakin Capsule Tower from 1972. It looks like an unorderly grown crystal. Thus it fits to the overall impression that in case of the Capsule Tower (and its many replicates throughout Japan) the core idea of the Metabolists never got realized. Not a single capsule has been replaced. Crystals do not replace parts of themselves, dependent on the physical circumstances they either grow forever, fall into everlasting stasis or get destroyed. At least Kikutake’s private “Sky House” has been slightly modified throughout its life cycle ([37], p.17). But there is nothing particular “metabolizing” with it.

In both type of buildings, the communal as well as the solitary one, “metabolism” has been implemented on the physical level. We have to rate this just as an indication of missing abstraction. Above we said that the shortcut “metabolism is morpho-change” isn’t allowed at all, since this would neglect the emergence relation between morpho-structures and producer changes in the complex system “cell”, for which biologists developed a particular perspective of metabolism. The Metabolists neglect precisely this layering of the complex system. Such, however, the Metabolists’ theory is nothing else than a metaphor, victimized to flatness by modernist reduction.

In some way, this renders the Metabolists that always claimed to propose a “utopia” as late descendants of the idea of the “Ideal City”. As the label already conveys, it’s just idealism, which always suffers from the double illusion implied by all top-down approaches.

Japanese Metabolism headed for adaptivity. Such they have been years ahead of the mainstream. Yet, the honourable intention haven’t been backed by structural models, there are no predictive models present in their approach, no abstraction towards a theory of differentiation, no reflection about the conditionability. Well, okay, even philosophy wasn’t developed far enough, Deleuze still breeding on the foundations of his philosophy. And cell biology itself has been completely absorbed by cybernetics, as one can see in the works of Monod. It is not our intention to blame anybody here. But it must be clear, that the Japanese Metabolism could not be transferred into our times due to its structural deficiencies.

10. Urban Strings

In an interview about his S,M,L,XL, conducted in 2001, Koolhaas mentioned that

“Compared with the metropolises of the industrial nations, Lagos is 50 to 100 years ahead.“[38]22

Given the seemingly chaotic condition of Lagos, the failure of its official urban services and organizations, in other words, its immaterial infrastructures, that seems like a bold and weird statement. Yet, Koolhaas addresses nothing less than a change in the metaphysical setup.

“We have been interested in the fact that at the one hand all organizational systems fail, on the other hand, however, the city nevertheless is functioning. […] The reason for that being that the inhabitants organize themselves in micro-systems.”23

Bottom-up organizational processes are not compatible with the major claims of the modernist belief set, particularly the idea of independence. Self-organization starting on the micro-level requires the metaphysical primacy of relation.

As we mentioned already several times, here and in previous essay, our impression is that Koolhaas is clearly interested in the processual aspects of differentiation, where others not even got a grip to the fact that we are in need of a metaphysics of differentiation. As a guest editor of an issue of the “wired”, he mentioned [39]:

“Where space was considered permanent, it now feels transitory—on its way to becoming.”

In an earlier interview from 1994, he explicitly referred to a characteristic of complex systems, opposing forces, denying the economically and politically motivated”Taylorization” into defined fields of function. Regarding the central station in Lille, a mega-structure Koolhaas was engaged to generate, he relied on the “alchemia of mixed use”, something that he had been cherishing in his famous “Delirious New York”.

The understanding of complex, self-organizing entities differs dramatically from linear entities. Analytic and thus a comprehensive symbolic representation, e.g. as some kind of a “law” is possible only for the latter. Trying to do the same for the former usually ends in some kind of disaster. For in that case anticipation based on the assumption of linearity inevitably fail at any point in time for whatever reason, that is for no particular reason, despite the fact that for some time the model could have been working quite well. Complex entities can’t be controlled, as there is no law, there are just mechanisms, actualized in a manifold of mutually penetrating populations. The best one can try is to tune the side-conditions of the respective processes. Yet, there is no guarantee for a particular outcome.

In other words, if urbanism claims to respect the moral and ethical conditions of the inhabitants (see for instance this, then traditional attitudes to planning and development have to be dropped. Respect for people is incompatible to the mere concept of development. Implementing plans is always and necessarily accompanied by violence, even if that violence is not visible from within the plan.

Yet, if we talk about mechanisms, the question raises, which are the subjects of those mechanisms? Where to find them and how to talk about these mechanisms?

If we consider the case of models of complex systems, such as the Gray-Scott-model, we’d probably distinguish certain elementary species. In case of the Urban, these species can’t be representational or even material, I guess, as it is the case in those models, which assume them to be particular kinds of molecules.

So, we may adjust our question slightly. We now can ask, what are the elementary, abstract species that we need to build appropriate models of the Urban?

Approaching this question requires a framework, and a reasonable choice is that of differentiation, from the metaphysical level down to the operational and back. Previously we identified three levels of actualization for differentiation, which can be rendered into different forms. The basic form is certainly the trinity of development, evolution and learning. Yet, there are transpositions of this basic theme; any of those would be worthwhile to be subject for further investigation, yet, we just list them here:

  • – embryos, populations (or brains) and evolution (minds as hosts of ideas),
  • – plans, probabilization and mediatization,
  • – automation, participation and (abstract) creativity,
  • – form, process and virtualization,
  • – the particular, the species and the general (concepts).

These basic aspects all have to be thought of as principles that actualize exclusively in local contexts. The geographic space of a city could be consequently thought of as a highly dynamic and volatile patchwork of such actualizations, and each of those could be assigned to one of the three levels or types of differentiation. This patchwork is by no means randomly arranged, of course. We have to think of it more in terms of said complex system, built from several components. Yet, again, in contrast to the simulated models, we should defy the temptation of assuming any kind of global rules for the interaction of the respective “species”.

Any possible pairing within the trinity of differentiation is inherently contradictory, albeit this contradiction is not a mutual one, it is a directed one. Embryos neither evolve nor do they learn. Learning, however, definitely comprises “embryonic” as well as “evolutionary” phases, without exhausting them. Inversely, while there is quite some play in learning processes, there is only little of it in evolutionary and almost none in embryonic processes.

Building upon notions from biology, even if we use it in a quite abstract way as structural schemata, immediately relate us to a number of objections. The most thorough ones have been posed by Anthony Giddens in his “Constitution of Society” (1986) regarding evolution. Yet, albeit Giddens is certainly right in criticizing the direct application or transfer of the biological theory about evolution into the realm of the social, his critique commits the same mistake (p.228). His image of evolution remains by far too naive, and partially even severely misunderstood, as to justify his objections against evolutionary theory and his final rejection. Nevertheless, he correctly emphasizes that talking about the realm of the social involves processes of largely “immaterial” signification. While such processes imply learning, it also remains true that this does not imply an incompatibility with a generalized theory of evolution. The same holds for adapting the notion of the embryo, or of growth. We just have to be always aware that these are modes of talking.

It is clear, that we can speak about differentiation only by also invoking probabilistic concepts. On the other hand, differentiation not only concerns individuals in their life history, but also as subjects of those differentiation processes.

This highlights an interesting issue, as play is eminently social and development is not less distinct a matter of automation. We can read the whole period of unfolding modernism, starting with the end of the Middle Ages, as a continued battle between participation and automation. In some way, cities and the Urban form of life provide just a further, upfolded field for the eternal contest between control and play, between constraints and overturn, between automation and participation. Yet, it is also true that it is the Urban as a life form that transformed battlegrounds into playing fields, thereby rendering the aterritorial into a local as well as a global social practice. Hopefully, it is the Urban and the respective life form that renders the nation and the underlying detrimental ideas insignificant.

The patches in the urban patchwork of various kinds of differentiation processes certainly influence each other, but it is an issue of future research to determine whether and to which grade the interaction of those differentiation processes can be arranged in separate classes.

So, let’s return to the question of the species. Probably it is quite reasonable to assume the species being subject to the mechanisms of the Urban to be just the instances of those three types of differentiation processes. In figure 7 above we introduced 4 types of structural models as candidates for solving the binding problem in theory works, namely growth, networks, associativity and complexity.

Result 1

This assemblage we now can simplify by subsuming it to the concept of differentiation as we have discussed it so far, of course, without dropping those four components, as they are growth, networks, associativity and complexity. Yet, this differentiation still resides in the realm of models, hence we have to call it “generic differentiation”. The abstract (meta-)structure suitable to overcome the binding problem regarding theories about cultural processes as well as their political instantiation would look like so:

Figure 9: Generic Differentiation as key element for solving the binding problem of theory works. Three things are important here: (i) the charts depicts the elementary module of a fluid moebioid fractal, since there is no separability between the three parts. They are mutually embedded into each other. (ii) “Concept” is a transcendent entity (see this for the argument). (iii) The brackets need to be conceived as the “realm of method”, which is something that we still have to accomplish (in one of the next essays). A similar structure may be suitable for the foundation of a planning theory (also to be discussed in some future essay).

Note, that the basic metaphysical stance of this methodological structure builds upon the “probabilistic relational”, which directly derives from the (Deleuzean) transcendental difference as soon as we care about any kind of application, or rule following. Deleuze bound the repetition as sort of a still transcendental application closely to his concept of the transcendental difference.

The field of models can be summarized by the differential (in the Deleuzean sense) of the four basic types of designs, namely growth, networks, associativity and complexity. Any of them leads to some kind of “change,” whether as a horizontal difference or a vertical differential. Else, any of them is capable to “associate” or to “grow”, they all are kind of networks (just of various degree of fluidity), and they all refer to complexity, and last but not least they all are (basic) forms for the description of the transition from mainly material to mainly immaterial contexts (material/immaterial here used in the common sense as a first conceptual approach, yet, actually there is no categorical difference between them: just think about the quasi-materiality of symbols and the form of energy in String theory). We can’t delve further into this matter here, but I think it will be highly rewarding to develop a vocabulary and expressions in order to establish the respective space that then could be called the “Space of Generic Differentiation”.

Result 2

Above, in the context of figure 1, we already mentioned that this scheme as we have developed it starting with figure 1 up to here is only the atomic module of a fluid moebioid fractal. (not the city or any other empiric entity is meant to be a fractal here, but rather the dynamics of theory itself!) This very same module is part of any theory work, yet, both the weights of the three parts as well as the parameters for the mapping into the more mature forms must be expected to be very different.

Such, we finally arrived at a conceptualization for theory work that is applicable to any science, even to philosophy. One of the nice things is that it makes the categorical difference between hard and social sciences to vanish, without neglecting the actual differences. But we definitely removed the existentialist contamination or even intoxication from the socio-mental landscape.

Result 3

A small remark about the philosophical consequences shall be allowed here. We already mentioned, thru result 1 and result 2, that the structure shown in figure 9 above would represent the basic module for the category of change. Of course, we do not conceive change as something that could be objectively determined, because there is something in the outer world that cold be called “pure change”. We propose neither to follow Kant in his favor for physicalist aprioris, nor the external (=naive) realists.

Instead, our category of change “socializes” the Kantian approach. As such it complements the structure that we called the choreostemic space. That space describes the fundamental conditionability of becoming, without telling anything about the actual mechanisms to move around in this space. The category of change (as the moebioid fractal) focuses the individual and his actual moves, that is its use of concepts and its corporeal activities. After the linguistic turn there is no space for physics any more, regarding the realm of human affairs. The apriori is not space and time, it is generic differentiation, concepts and the political corporeality.

Note that time is a language game about the scale of measurement for changes. If there is no change, or if change is not determinable, then there is no time. Examples for that are the “life form” of the photon or black holes, where no signal can be transferred any more, because photons get fixed.

Result 4

Above, in the chapter about String Theory, we said that it describes the form of energy, where different forms lead to different kinds of matter. Could we assimilate or even transfer the structure of that theory into a critical theory about the Urban?

Well, the first thing for which we have to identify a parallel is the notion of energy. Probably the hottest candidate for a similar role with regard to the Urban, that is for culture, is mediality. Like in the case of energy, density plays a crucial role for it (cf. [40]). All of the four components of our generic differentiation are strongly dependent on mediality, induced by densification processes. Changing levels, this holds true even for generic differentiation itself, as part of the theoretical structure as shown in figure 9.

We certainly can say that the form of mediality, that is, the way it gets instantiated, is able to create very different urban styles. Think about the difference between a Maya city, with some 70’000 inhabitants, where most of the mediality is related to religious affairs, and then about a typical radio city (Berlin 1939?), a TV city (Los Angeles), and an internet city (Seoul?). Or about Manhattan, where mediality found a quite unique instantiation, comprising interpersonal contacts and high density of heterotopias. Or about Shanghai with its extreme neon density.

As mediality gets actualized in different ways, so the proportion of our four components of the Generic Differentiation. Without any doubt one can find the traces of the establishment of a particular proportion, that is, the location  of the Urban Game in a particular “region” in the (yet to be formulated) space of Generic Differentiation, in the built assemblage of urban neighborhoods, as well as in its individual and characteristic “urban look & feel”. Or in other word, the “quality” of a particular “city”. Generic differentiation is somehow the inverse or a n abstract consequence of mediality.

Result 5

Here in this figure 9, much like for the figures above, we don’t provide any detail about the conceptual and the operational side. Of course, both areas comprise their own rich structure. Yet, in order to avoid the binding problem, both the concepts and the operations need to be compatible to the model layer, at least insofar as the three components develop suitable docking sites.

Result 6

The structure in figure 9 above can be read in two very different ways. This is not  just due to the possibility of different vantage points, its more a kind of a principle duality.

The first one derives from a choreostemic perspective. In this case the structure describes the forces that lead to particular trajectories in the choreostemic space, representing a particular style to think about the city and to act within it, whether as an individual or as a population.

The second way to conceive of the structure is as the Urban itself, as the life form of the Urban, that is as the actualization of a Foucaultian field of proposals. In both cases the three areas of concept, differentiation and operation are not at all separated or separable. They form a field of simultaneous activity throughout, with varying degrees of overlapping and mutual infection.

In such a setting, story-telling takes an important role: it creates a dynamic fabric from all the relational elements, the tiny Urban Strings, of which myriads over myriads are produced all the time, released to float around in unpredictable yet beautifully arranged patterns, spanning from logistics to anticipation and metaphysics, providing the mere possibility for Urban meaning and Urban Reason.24

Notes

1. As in the preceding essays, we use the capital “U” if we refer to the urban as a particular quality and as a concept, in order to distinguish it from the ordinary adjective that refers to common sense understanding.

2.The terminus “speaking about” is by no means a trivial one. First, it implies that language is used and in turn we have to respect the transcendental role of language (for more details see here, and here). This has been not only the center point of Wittgenstein’s philosophy, it also resulted in a “revolution” throughout philosophy—unfortunately largely only in philosophy so far, the so-called “Linguistic Turn.” Particularly scientists are often quite forgetful about that. Secondly, “speaking about” also means that concepts have to be used. As we discussed in the context of the choreostemic space, concepts are also transcendent.

3. Here, philosophy is not understood as a domain that creates rules of a good life. Instead, we conceive it as a technique of thinking; as such it is helpful to explore the rules and principles of human affairs as a social process. Philosophy has no representational content!

4. Case of Bombay, informal workers.

5. For more details please the essays about modeling.

6. Previously we called such concepts “Strongly Singular Terms”. For details please refer to “Formalization and Creativity as Strongly Singular Terms”.

7. Concerning semiotics as always: CS Peirce.

8. Umberto Eco (2002): Semiotik der Theateraufführung. In: Wirth, Uwe (Hrsg.): Performanz. Zwischen Sprachphilosophie und Kulturwissenschaft. Frankfurt/M. S.262-276.

9. This is even true for the “hardest science” of all, physics. Even as physics benefits from the luxury of a stable external referent, though that referent has to be recognized as an unknown. This stability allows for a closed and quite fast loop between building and testing anticipatory models on the one hand, and inventing concepts on the other. This stability is possible only if the subject of the respective investigations is strictly a-historic, a-contextual and an-individual. Nevertheless it remains true that even the concepts of physics are at least partially dependent on the respective form of life. In sciences that deal with historic contingency like biology and all of the human sciences including architecture and urbanism, this stability is not present in principle.

10. Gilles Deleuze developed a dedicated counterdraft to these concepts, mainly in Difference & Repetition [18], A Thousand Plateaus [19], and Logic of Sense [20].

11. Note that even the discovery of the putative Higgs-Boson wouldn’t change much with regard to these open issues.

12. Usually, paradoxes are just a consequence of contradictions either in the metaphysical setup or in the course of their instantiation. Pseudo-paradoxes can be provoked also by choosing to few dimensions for the description of a problem. (for details see Deleuzean Move, footnote 3, and Vagueness: The Structure of Non-Existence.)

13. In German language the book “Performanz” edited by the semiotician Uwe Wirth [21]; unfortunately, I don’t know of any comparable work in English language.

14. Talking about complexity and story-telling may remind inevitably to Charles Jencks’ “jumping universe”, where he, among other things invokes the science of complexity and post-modernism as kind of twin-siblings. We clearly disassociate from Jencks’ writings, for multiple reasons so. It is nothing else than esoterism. He not only fails to accurately use the concept of fractals and chaos, he also misses to describe the mechanisms through which that “chaos” gets actualized. He does not provide any model for growth and differentiation, just using fractals as the universal weaponry. It is not really surprising that he finally ends up with cosmogonic phantasies.

We not only reject this kind of poor “theorizing,” but also post-modernism as a valuable way of talking about architecture or urbanism. Both suffer seriously from the binding problem, ending in wild speculations. It is telling that Jencks tries to proof the existence of a battle between modernist and post-modernist thinking. Nothing could be more unmasking. Above all, his crusade seems to be politically motivated. What we try instead in this series of essays is to provide a sound abstract structure for a value-free theory, from which a rich scape of models can be derived.

The post-modernist attitude of “not only function, but also fiction” (H.Klotz, The history of postmodern architecture, 1986) remains flat and representationalist, such as Hollein’s Juweliergeschäft (Wien 1972-1974). As Venturi once demonstrated, any arbitrary facade is semiotically active. Yet, the interpretation is not on the side of the designer! Thus, the “fiction” of the post-modernists are misplaced, and miles away from the story-telling Koolhaas is organizing for us and into which we may embed and integrate ourselves. In a later piece we will discuss the metaphysics, the hidden resentment and the limitations of post-modernism in greater detail.

15. Most of the items of that layer that is mediating between theory and operations we already discussed in earlier essays. Note that the set of possible terms of that map is far from being complete, albeit it certainly provides a useful cross-section. Links : choreosteme, complexity, model, orthoregulation, learning, memory, evolution, theory, aspection, network, probabilism, adaptivity, associativity, behavioral coating, operationalization.

16. Note that these beliefs are not to be mixed up with values. Values themselves are anyway highly problematic. Values are quite effective to abolish any discourse, since—by definition—they are not justifiable. Hence it is dangerous to invoke them “too early”. Actually, values that purport some representational attitude about a moral “good(ness)”, should be dropped altogether, except some last solitary and transcendental principle. According to Wilhelm Vossenkuhl [26], a German philosopher (mainly Kant, Wittgenstein and Ethics) and political scientist, all the other claimed values should be replaced by the techné of organizing discourses about the difficult challenges.

17. For details about morphogenesis through self-organization and complexity see this essay.

18. Differentiation not only includes morphogenesis sensu strictu, that is with regard to “purely” material aspects. It is anyway not possible to separate the material from the immaterial as the modernists and positivists always claimed. Differentiation and growth apply to the immaterial as well. In our essay about Koolhaas and Singapore we explicated three perspectives onto differentiation, for which we find varying grades of materiality: development, evolution and learning. also note that Deleuze’s work may be conceived as a philosophy of differentiation, whether concerning development, evolution or learning.

19. Sustainability that is backed by the the idea of protection [24,25,26]

20. Recently, Anna Leidreiter proposed to change perspective from mere sustainability (see previous footnote) to regeneration and “circular metabolism”. Despite we certainly agree with the intention, her approach is still suffering from the binding problem. There is no theory of differentiation, just a more or less metaphorical use of the concept of metabolism. Metabolism anyway is always organized by many overlapping “cycles”. It is naïve or even wrong that natural ecosystems run without producing waste, as she claims. In natural ecosystems there is a lot of decay, debris and sedimentation. How would debris look like with respect to the Urban?

Fitting to these suggestions is another point. Earlier we already pointed out that sustainability requires persistent adaptivity, and this in turn can be achieved only by complexity, that is self-organization, transition from order to organization, and emergence. As such it can’t be directly implemented, of course. In other words, planning and sustainability exclude each other.

21. German original: „Kiyonori Kikutake erklärt, warum ihnen die altehrwürdigen Gesetze der Form und Funktion damals nicht mehr ausreichten und sie versuchten, den Lebenszyklus von Geburt und Wachstum auf Städtebau und Architektur zu übertragen.“

22. German original: „Lagos ist den Metropolen der Industrienationen um 50 bis 100 Jahre voraus.“

23. German original : „Wir haben uns dafür interessiert, wie einerseits alle Organisationssysteme versagen, die Stadt aber andererseits trotzdem funktioniert. Das liegt daran, dass die Einwohner sich in Mikrosystemen organisieren.“

24. We are well aware of the fact that a concept like “generic differentiation”, particularly if it comprises growth and networks as sub-concepts, relates to the discourse about urban form, or urban morphology. For 15 years now, this discourse gets more and more organized through the journal “Urban Morphology”, issued by the International Seminar on Urban Form ISUF. This discourse suffers considerably from the binding problem, hence, any kind of naivity can be found there. Typically for the underdeveloped stage of the field is the fact that there are (still) at least two “schools”, inherited from times long ago (the French, the Italian, the Anglo-Saxon schools). Of course, there are also the great pioneers (pope-eneers?), celebrated individuals like Caniggia or Conzen. Yet, identifying the more valuable contributions requires (and deserves) a dedicated treatment. This will be the topic our next piece: How to speak about (urban) forms?

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  • [33] Jean-Yves Girard, LOCUS SOLUM: From the rules of logic to the logic of rules (2001). Journal Mathematical Structures in Computer Science archive, Vol 11(3), p.301-506. available online.
  • [34] Barbara Nolte, „Unser westlicher Blick liefert Zerrbilder“, Interview mit Rem Koolhaas, 12.02.2012 in: Der Tagesspiegel (Berlin). available online.
  • [35] Kiyonori Kikutake et al. Preface, Metabolism: Proposals for New Urbanism. Tokyo 1960.
  • [36] Jennifer Johung, Replacing Home: From Primordial Hut to Digital Network in Contemporary Art. Minnesota University Press, Minneapolis 2012.
  • [37] Zhongjie Lin, Kenzo Tange and the Metabolist Movement: Urban Utopias of Modern Japan. Routledge, New York 2010.
  • [38] Ulrike Knöfel und Marianne Wellershoff (2001). „Eine der besten Erfindungen“, Interview mit Rem Koolhaas, 15.10.2001, in: DER SPIEGEL 42/2001, available online.
  • [39] Rem Koolhaas (2003). Editorial, The New World. 30 Spaces for the 21st Century. wired, Issue 11.06 | June 2003. available online.
  • [40] Vera Bühlmann, inhabiting media. Thesis, Basel 2009.

۞

Behavior

September 7, 2012 § Leave a comment

Animals behave. Of course, one could say.

Yet, why do we feel a certain naturalness here, in this relation between the cat as an observed and classified animal on the one side and the language game “behavior” on the other? Why don’t we say, for instance, that the animal happens? Or, likewise, that it is moved by its atoms? To which conditions does the language game “behavior” respond?

As strange as this might look like, it is actually astonishing that physicists easily attribute the quality of “behavior” to their dog or their cat, albeit they rarely will attribute them ideas (for journeys or the like). For physicists usually claim that the whole world can be explained in terms of the physical laws that govern the movement of atoms (e.g. [1]). Even physicists, it seems, exhibit some dualism in their concepts when it comes to animals. Yet, physicists claimed for a long period of time, actually into the mid of the 1980ies, that behavioral sciences actually could not count as a “science” at all, despite the fact that Lorenz and Tinbergen won the Nobel prize for medical sciences in 1973.

The difficulties physicists obviously suffer from are induced by a single entity: complexity. Here we refer to the notion of complexity that we developed earlier, which essentially is built from the following 5 elements.

  • – Flux of entropy, responsible for dissipation;
  • – Antagonistic forces, leading to emergent patterns;
  • – Standardization, mandatory for temporal persistence on the level of basic mechanisms as well as for selection processes;
  • – Compartmentalization, together with left-overs leading to spatio-temporal persistence as selection;
  • – Self-referential hypercycles, leading to sustained 2nd order complexity with regard to the relation of the whole to its parts.

Any setup for which we can identify this set of elements leads to probabilistic patterns that are organized on several levels. In other words, these conditioning elements are necessary and sufficient to “explain” complexity. In behavior, the sequence of patterns and the sequence of more simple elements within patterns are by far not randomly arranged, yet, it is more and more difficult to predict a particular pattern the higher its position in the stack of nested patterns, that is, its level of integration. Almost the same could be said about the observable changes in complex systems.

Dealing with behavior is thus a non-trivial task. There are no “laws” that would be mapped somehow into the animal such that an apriori defined mathematical form would suffice for a description of the pattern, or the animal as a whole. In behavioral sciences, one first has to fix a catalog of behavioral elements, and only by reference to this catalog we can start to observe in a way that will allow for comparisons with other observations. I deliberately avoid the concept of “reproducibility” here. How to know about that catalog, often called behavioral taxonomy? The answer is we can’t know in the beginning. To reduce observation completely to the physical level is not a viable alternative either. Observing a particular species, and often even a particular social group or individual improves over time, yet we can’t speak about that improvement. There is a certain notion of “individual” culture here that develops between the “human” observer and the behaving system, the animal. The written part of this culture precipitates in the said catalog, but there remains a large part of habit of observing that can’t be described without performing it. Observations on animals are never reproducible in the same sense as it is possible with physical entities. The ultimate reason being that the latter are devoid of individuality.

A behavioral scientist may work on quite different levels. She could investigate some characteristics of behavior in relation to the level of energy consumption, or to differential reproductive success. On this level, one would hardly go into the details of the form of behavior. Quite differently to this case are those investigations that are addressing the level of the form of the behavior. The form becomes an important target of the investigation if the scientist is interested in the differential social dynamics of animals belonging to different groups, populations or species. In physics, there is no form other than the mathematical. Electrons are (treated in) the same (way) by physicists all over the world, even across the whole universe. Try this with cats… You will loose the cat-ness.

It is quite clear that the social dynamics can’t be addressed by means of mere frequencies of certain simple behavioral elements, such like scratching, running or even sniffing at other animals. There might be differences, but we won’t understand too much of the animal, of course, particularly not with regard to the flow of information in which the animal engages.

The big question that arose during the 1970ies and the 1980ies was, how to address behavior, its structure, its patterning, and thereby to avoid a physicalist reduction?

Some intriguing answers has been given in the respective discourse since the beginning of the 1950ies, though only a few people recognized the importance of the form. For instance, to understand wolves Moran and Fentress [2] used the concept of choreography to get a descriptional grip on the quite complicated patterns. Colmenares, in his work about baboons, most interestingly introduced the notion of the play to describe the behavior in a group of baboons. He distinguished more than 80 types of social games as an arrangement of “moves” that span across space and time in a complicated way; this behavioral wealth rendered it somewhat impossible to analyze the data at that time. The notion of the social game is so interesting because it is quite close to the concept of language game.

Doing science means to translate observations into numbers. Unfortunately, in behavioral sciences this translation is rather difficult and in itself only little standardized (so far) despite many attempts, precisely for the reason that behavior is the observable output of a deeply integrated complex system, for instance the animal. Whenever we are going to investigate behavior we carefully have to instantiate the selection of the appropriate level we are going to investigate. Yet, in order to understand the animal, we even could not reduce the animal onto a certain level of integration. We should map the fact of integration itself.

There is a dominant methodological aspect in the description of behavior that differs from those in sciences more close to physics. In behavioral sciences one can invent new methods by inventing new purposes, something that is not possible in classic physics or engineering, at least if matter is not taken as something that behaves. Anyway, any method for creating formal descriptions invokes mathematics.

Here it becomes difficult, because mathematics does not provide us any means to deal with emergence. We can’t, of course, blame mathematics for that. It is not possible in principle to map emergence onto an apriori defined set of symbols and operations.

The only way to approximate an appropriate approach is by a probabilistic methodology that also provides the means to distinguish various levels of integration. The first half of this program is easy to accomplish, the second less so. For the fact of emergence is a creative process, it induces the necessity for interpretation as a constructive principle. Precisely this has been digested by behavioral science into the practice of the behavioral catalog.

1. This Essay

Well, here in this essay I am not interested mainly in the behavior of animals or the sciences dealing with the behavior of animals. Our intention was just to give an illustration of the problematic field that is provoked by the “fact” of the animals and their “behavior”.  The most salient issue in this problematic field is the irreducibility, in turn caused by the complexity and the patterning resulting from it. The second important part on this field is given by the methodological answers to these concerns, namely the structured probabilistic approach, which responds appropriately to the serial characteristics of the patterns, that is, to the transitional consistency of the observed entity as well as the observational recordings.

The first of these issues—irreducibility—we need not to discuss in detail here. We did this before, in a previous essay and in several locations. We just have to remember that empiricist reduction means to attempt for a sufficient description through dissecting the entity into its parts, thereby neglecting the circumstances, the dependency on the context and the embedding into the fabric of relations that is established by other instances. In physics, there is no such fabric, there are just anonymous fields, in physics, there is no dependency on the context, hence form is not a topic in physics. As soon as form becomes an issue, we leave physics, entering either chemistry or biology. As said, we won’t go into further details about that. Here, we will deal mainly with the second part, yet, with regard to two quite different use cases.

We will approach these cases, the empirical treatment of “observations” in computational linguistics and in urbanism, first from the methodological perspective, as both share certain conditions with the “analysis” of animal behavior. In chapter 8 we will give more pronounced reasons about this alignment, which at first sight may seem to be, well, a bit adventurous. The comparative approach, through its methodological arguments, will lead us to the emphasis of what we call “behavioral turn”. The text and the city are regarded as behaving entities, rather than the humans dealing with them.

The chapters in this essay are the following:

Table of Content (active links)

2. The Inversion

Given the two main conceptual landmarks mentioned above—irreducibility and the structured probabilistic approach—that establish the problematic field of behavior, we now can do something exciting. We take the concept and its conditions, detach it from its biological origins and apply it to other entities where we meet the same or rather similar conditions. In other words, we practice a differential as Deleuze understood it [3]. So, we have to spend a few moments for dealing with these conditions.

Slightly re-arranged and a bit more abstract than it is the case in behavioral sciences, these conditions are:

  • – There are patterns that appear in various forms, despite they are made from the same elements.
  • – The elements that contribute to the patterns are structurally different.
  • – The elements are not all plainly visible; some, most or even the most important are only implied.
  • – Patterns are arranged in patterns, implying that patterns are also elements, despite the fact that there is no fixed form for them.
  • – The arrangement of elements and patterns into other patterns is dependent on the context, which in turn can be described only in probabilistic terms.
  • – Patterns can be classified into types or families; the classification however, is itself non-trivial, that is, it is not supported.
  • – The context is given by variable internal and external influences, which imply a certain persistence of the embedding of the observed entity into its spatial, temporal and relational neighborhood.
  • – There is a significant symbolic “dimension” in the observation, meaning that the patterns we observe occur in sequence space upon an alphabet of primitives, not just in the numerical space. This symbolistic account is invoked by the complexity of the entity itself. Actually, the difference between symbolic and numerical sequences and patterns are much less than categorical, as we will see. Yet, it makes a large difference either to include or to exclude the methodological possibility for symbolic elements in the observation.

Whenever we meet these conditions, we can infer the presence of the above mentioned problematic field, that is mainly given by irreducibility and­­­—as its match in the methodological domain—the practice of a structured probabilistic approach. This list provides us an extensional circumscription of abstract behavior.

A slightly different route into this problematic field draws on the concept of complexity. Complexity, as we understand it by means of the 5 elements provided above (for details see the full essay on this subject), can itself be inferred by checking for the presence of the constitutive elements. Once we see antagonisms, compartments, standardization we can expect emergence and sustained complexity, which in turn means that the entity is not reducible and in turn, that a particular methodological approach must be chosen.

We also can clearly state what should not be regarded as a member of this field. The most salient one is the neglect of individuality. The second one, now in the methodological domain, is the destruction of the relationality as it is most easy accomplished by referring to raw frequency statistics. It should be obvious that destroying the serial context in an early step of the methodological mapping from observation to number also destroys any possibility to understand the particularity of the observed entity. The resulting picture will not only be coarse, most probably it also will be utterly wrong, and even worse, there is no chance to recognize this departure into the area that is free from any sense.

3. The Targets

At the time of writing this essay, there are currently three domains that suffer most from the reductionist approach. Well, two and a half, maybe, as the third, genetics, is on the way to overcome the naïve physicalism of former days.

This does not hold for the other two areas, urbanism and computational linguistics, at least as far as it is relevant for text mining  and information retrieval1. The dynamics in the respective communities are of course quite complicated, actually too complicated to achieve a well-balanced point of view here in this short essay. Hence, I am asking to excuse the inevitable coarseness regarding the treatment of those domains as if they would be homogenous. Yet, I think, that in both areas the mainstream is seriously suffering from a mis-understood scientism. In some way, people there strangely enough behave more positivist than researchers in natural sciences.

In other words, we follow the question how to improve the methodology in those two fields of urbanism and computerized treatment of textual data. It is clear that the question about methodology implies a particular theoretical shift. This shift we would like to call the “behavioral turn”. Among other changes, the “behavioral turn” as we construct it allows for overcoming the positivist separation between observer and the observed without sacrificing the possibility for reasonable empiric modeling.2

Before we argue in a more elaborate manner about this proposed turn in relation to textual data and urbanism, we first would like two accomplish two things. First, we briefly introduce two methodological concepts that deliberately try to cover the context of events, where those events are conceived as part of a series that always also develops into kind of a network of relations. Thus, we avoid to conceive of events as a series of separated points.

Secondly, we will discuss current mainstream methodology in the two fields that we are going to focus here. I think that the investigation of the assumptions of these approaches, often remaining hidden, sheds some light onto the arguments that support the reasonability of the “behavioral turn”.

4. Methodology

The big question remaining to deal with is thus: how to deal with the observations that we can make in and about our targets, the text or the city?

There is a clear starting point for the selection of any method as a method that could be considered as appropriate. The method should inherently respond to the seriality of the basic signal. A well-known method of choice for symbolic sequences are Markov chains, another important one are random contexts and random graphs. In the domain of numerical sequences wavelets are the most powerful way to represent various aspects of a signal at once.

Markov Processes

A Markov chain is the outcome of applying the theory of Markov processes onto a symbolic sequence. A Markov process is a neat description of the transitional order in a sequence. We also may say that it describes the conditional probabilities for the transitions between any subset of elements. Well, in this generality it is difficult to apply. Let us thus start with the most simple form, the Markov process of 1st order.

A 1st order Markov process describes just and only all pairwise transitions that are possible for given “alphabet” of discrete entries (symbols). These transitions can be arranged in a so-called transition matrix if we obey to the standard to use the preceding part of the transitional pair as row header and the succeeding part of the transitional pair as a column header. If a certain transition occurs, we enter a tick into the respective cell, given by the address row x column, which derives from the pair prec -> succ. That’s all. At least for the moment.

Such a table captures in some sense the transitional structure of the observed sequence. Of course, it captures only a simple aspect, since the next pair does not know anything about the previous pair. A 1st order Markov process is thus said to have no memory. Yet, it would be a drastic misunderstanding to generalize the absence of memory to any kind of Markov process. Actually, Markov processes can precisely be used to investigate the “memories” in a sequence, as we will see in a moment.

Anyway, on any kind of such a transition table we can do smart statistics, for instance to identify transitions that are salient for the “exceptional” high or low frequency. Such a reasoning takes into account the marginal frequencies of such a table and is akin to correspondence analysis. Van Hooff developed this “adjusted residual method” and  has been applying it with great success in the analysis of observational data on Chimpanzees [4][5].

These residuals are residuals against a null-model, which in this case is the plain distribution. In other words, the reasoning is simply the same as always in statistics, aiming at establishing a suitable ratio of observed/expected, and then to determine the reliability of a certain selection that is based on that ratio. In the case of transition matrices the null-model states that all transitions occur with the same frequency. This is of course, simplifying, but it is also simple to calculate. There are of course some assumptions in that whole procedure that are worthwhile to be mentioned.

The most important assumption of the null-model is that all elements that are being used to set up the transitional matrix are independent from each other, except their 1st order dependency, of course. This also means that the null-model assumes equal weights for the elements of the sequence. It is quite obvious that we should assume so only in the beginning of the analysis. The third important assumption is that the process is stationary, meaning the kind and the strength of the 1st order dependencies do not change for the entire observed sequence.

Yet, nothing enforces us to stick to just the 1st order Markov processes, or to apply it globally. A 2nd order Markov process could be formulated which would map all transitions x(i)->x(i+2). We may also formulate a dense process for all orders >1, just by overlaying all orders from 1 to n into a single transitional matrix.

Proceeding this way, we end up with an ensemble of transitional models. Such an ensemble is suitable for the comparatist probabilistic investigation of the memory structure of a symbolic sequence that is being produced by a complex system. Matrices can be compared (“differenced”) regarding their density structure, revealing even spurious ties between elements across several steps in the sequence. Provided the observed sequence is long enough, single transition matrices as well as ensembles thereof can be resampled on parts of sequences in order to partition the global sequence, that is, to identify locally stable parts of the overall process.

Here you may well think that this sounds like a complicated “work-around” for a Hidden Markov Model (HMM). Yet, despite a HMM is more general than the transition matrix perspective in some respect, it is also less wealthy. In HMM, the multiplicity is—well—hidden. It reduces the potential complexity of sequential data into a single model, again with the claim of global validity. Thus, HMM are somehow more suitable the closer we are to physics, e.g. in speech recognition. But even there their limitation is quite obvious.

From the domain of ecology we can import another trick for dealing with the transitional structure. In ecosystems we can observe the so-called succession. Certain arrangements of species and their abundance follow rather regularly, yet probabilistic to each other, often heading towards some stable final “state”. Given a limited observation about such transitions, how can we know about the final state? Using the transitional matrix the answer can be found simply by a two-fold operation of multiplying the matrix with itself and intermittent filtering by renormalization. This procedure acts as a frequency-independent filter. It helps to avoid type-II errors when applying the adjusted residuals method, that is, transitions with a weak probability will be less likely dismissed as irrelevant ones.

Contexts

The method of Markov processes is powerful, but is suffers from a serious problem. This problem is introduced by the necessity to symbolize certain qualities of the signal in advance to its usage in modeling.

We can’t use Markov processes directly on the raw textual data. Doing so instead would trap us in the symbolistic fallacy. We would either ascribe the symbol itself a meaning—which would result in a violation of the primacy of interpretation—or it would conflate the appearance of a symbol with its relevance, which would constitute a methodological mistake.

The way out of this situation is provided by a consequent probabilization. Generally we may well say that probabilisation takes the same role for quantitative sciences as the linguistic turn did for philosophy. Yet, it is still an attitude that is largely being neglected as a dedicated technique almost everywhere in any science. (for an example application of probabilisation with regard to evolutionary theory see this)

Instead of taking symbols as they are pretended to be found “out there”, we treat them as outcome of an abstract experiment, that is, as a random variable. Random variables establish them not as dual concepts, as 1 or 0, to be or not to be, they establish themselves as a probability distribution. Such a distribution contains potentially an infinite number of discretizations. Hence, probabilistic methods are always more general than those which rely on “given” symbols.

Kohonen et al. proposed a simple way to establish a random context [6]. The step from symbolic crispness to a numerical representation is not trivial, though. We need a double-articulated entity that is “at home” in both domains. This entity is a high-dimensional random fingerprint. Such a fingerprint consists simply of a large number, well above 100, of random values from the interval [0..1]. According to the Lemma of Hecht-Nielsen [7]  any two of such vectors are approximately orthogonal to each other. In other words, it is a name expressed by numbers.

After a recoding of all symbols in a text into their random fingerprints it is easy to establish  probabilistic distributions of the neighborhood of any word. The result is a random context, also called a random graph. The basic trick to accomplish such a distribution is to select a certain, fixed size for the neighborhood—say five or seven positions in total—and then arrange the word of interest always to a certain position, for instance into the middle position.

This procedure we do for all words in a text, or any symbolic series. Doing so, we get a collection of random contexts, that overlap. The final step then is a clustering of the vectors according to their similarity.

It is quite obvious that this procedure as it has been proposed by Kohonen sticks to strong assumptions, despite its turn to probabilization. The problem is the fixed order, that is, the order is independent from context in his implementation. Thus his approach is still limited in the same way as the n-gram approach (see chp.5.3 below). Yet, sometimes we meet strong inversions and extensions of relevant dependencies between words. Linguistics speak of injected islands with regard to wh*-phrases. Anaphors are another example. Chomsky critized the approach of fixed–size contexts very early.

Yet, there is no necessity to limit the methodology to fixed-size contexts, or to symmetrical instances of probabilistic contexts. Yes, of course this will result in a situation, where we corrupt the tabularity of the data representation. Many rows are different in their length and there is (absolutely) no justification to enforce a proper table by filling “missing values” into the “missing” cells of the table

Fortunately, there is another (probabilistic) technique that could be used to arrive at a proper table, without distorting the content by adding missing values. This technique is random projection, first identified by Johnson & Lindenstrauss (1984), which in the case of free-sized contexts has to be applied in an adaptive manner (see [8] or [9] for a more recent overview). Usually, a source (n*p) matrix (n=rows, p=columns=dimensions) is multiplied with a (p*k) random matrix, where the random numbers follow a Gaussian distribution), resulting in a target matrix of only k dimensions and n rows. This way a matrix of 10000+ columns can be projected into one made only from 100 columns without loosing much information. Yet, using the lemma of Hecht-Nielsen we can compress any of the rows of a matrix individually. Since the random vectors are approximately orthogonal to each other we won’t introduce any information across all the data vectors that are going to be fed into the SOM. This stepwise operation becomes quite important for large amounts of documents, since in this case we have to adopt incremental learning.

Such, we approach slowly but steadily the generalized probabilistic context that we described earlier. The proposal is simply that in dealing with texts by means of computers we have to apply precisely the most general notion of context, which is devoid from structural pre-occupations as we can meet them e.g. in the case of n-grams or Markov processes.

5. Computers Dealing with Text

Currently, so-called “text mining” is a hot topic. More and more of human communication is supported by digitally based media and technologies, hence more and more texts are accessible to computers without much efforts. People try to use textual data from digital environments for instance to do sentiment analysis about companies, stocks, or persons, mainly in the context of marketing. The craziness there is that they pretend to classify a text’s sentiment without understanding it, more or less on the frequency of scattered symbols.

The label “text mining” reminds to “data mining”; yet, the structure of the endeavors are drastically different. In data mining one is always interested in the relevant variables n order to build a sparse model that even could be understood by human clients. The model then in turn is used to optimize some kind of process from which the data for modeling has been extracted.

In the following we will describe some techniques, methods and attitudes that are highly unsuitable for the treatment of textual “data”, despite the fact that they are widely used.

Fault 1 : Objectivation

The most important difference between the two flavor of “digital mining” concerns however, the status of the “data”. In data mining, one deals with measurements that are arranged in a table. This tabular form is only possible on the basis of a preceding symbolization, which additionally is strictly standardized also in advance to the measurement.

In text mining this is not possible. There are no “explanatory” variables that could be weighted. Text mining thus just means to find a reasonable selection of text in response to a “query”. For textual data it is not possible to give any criterion how to look at a text, how to select a suitable reference corpus for determining any property of the text, or simply to compare it to other texts before its interpretation. There are no symbols, no criteria that could be filled into a table. And most significant, there is no target that could be found “in the data”.

It is devoid of any sense to try to optimize a selection procedure by means of a precision/recall ratio. This would mean that the meaning of text could be determined objectively before any interpretation, or, likewise, that the interpretation of a text is standardisable up to a formula. Both attempts are not possible, claiming otherwise is ridiculous.

People responded to these facts with a fierce endeavor, which ironically is called “ontology”, or even “semantic web”. Yet, neither will the web ever become “semantic” nor is database-based “ontology” a reasonable strategy (except for extremely standardized tasks). The idea in both cases is to determine the meaning of an entity before its actual interpretation. This of course is utter nonsense, and the fact that it is nonsense is also the reason why the so-called “semantic web” never started to work. They guys should really do more philosophy.

Fault 2 : Thinking in Frequencies

A popular measure for describing the difference of texts are variants of the so-called tf-idf measure. “tf” means “term frequency” and describes the normalized frequency of a term within a document. “idf” means “inverse document frequency”, which, actually, refers to the frequency of a word across all documents in a corpus.

The frequency of a term, even its howsoever differentialized frequency, can hardly be taken as the relevance of that term given a particular query. To cite the example from the respective entry in Wikipedia, what is “relevant” to select a document by means of the query “the brown cow”? Sticking to terms makes sense only if and only if we accept an apriori contract about the strict limitation to the level of the terms. Yet, this has nothing to do with meaning. Absolutely nothing. It is comparing pure graphemes, not even symbols.

Even if it would be related to meaning it would be the wrong method. Simply think about a text that contains three chapters: chapter one about brown dogs, chapter two about the relation of (lilac) cows and chocolate, chapter three about black & white cows. There is no phrase about a brown cow in the whole document, yet, it would certainly be selected as highly significant by the search engine.

This example nicely highlights another issue. The above mentioned hypothetical text could nevertheless be highly relevant, yet only in the moment the user would see it, triggering some idea that before not even was on the radar. Quite obviously, despite the search would have been different, probably, the fact remains that the meaning is neither in the ontology nor in the frequency and also not in text as such—before the actual interpretation by the user. The issue becomes more serious if we’d consider slightly different colors that still could count as “brown”, yet with a completely different spelling. And even more, if we take into account anaphoric arrangement.

The above mentioned method of Markov processes helps a bit, but not completely of course.

Astonishingly, even the inventors of the WebSom [6], probably the best model for dealing with textual data so far, commit the frequency fallacy. As input for the second level SOM they propose a frequency histogram. Completely unnecessary, I have to add, since the text “within” the primary SOM can be mapped easily to a Markov process, or to probabilistic contexts, of course. Interestingly, any such processing that brings us from the first to the second layer reminds somewhat more to image analysis than to text analysis. We mentioned that already earlier in the essay “Waves, Words and Images”.

Fault 3 : The Symbolistic Fallacy (n-grams & co.)

Another really popular methodology to deal with texts is n-grams. N-grams are related to Markov processes, as they also take the sequential order into account. Take for instance (again the example from Wiki) the sequence “to be or not to be”. The transformation into a 2-gram (or bi-gram) looks such “to be, be or, or not, not to, to be,” (items are between commas), while the 3-gram transformation produces “to be or, be or not, or not to, not to be”. In this way, the n-gram can be conceived as a small extract from a transition table of order (n-1). N-grams share a particular weakness with simple Markov models, which is the failure to capture long-range dependencies in language. These can be addressed only by means of deep grammatical structures. We will return to this point later in the discussion of the next fault No.4 (Structure as Meaning).

The strange thing is that people drop the tabular representation, thus destroying the possibility of calculating things like adjusted residuals. Actually, n-grams are mostly just counted, which is committing the first fault of thinking in frequencies, as described above.

N-gram help to build queries against databases that are robust against extensions of words, that is prefixes, suffixes, or forms of verbs due to flexing. All this has, however, nothing to do with meaning. It is a basic and primitive means to make symbolic queries upon symbolic storages more robust. Nothing more.

The real problem is the starting point: taking the term as such. N-grams start with individual words that are taken blindly as symbols. Within the software doing n-grams, they are even replaced by some arbitrary hash code, i.e. the software does not see a “word”, it deals just with a chunk of bits.

This way, using n-grams for text search commits the symbolistic fallacy, similar to ontologies, but even on a more basic level. In turn this means that the symbols are taken as “meaningful” for themselves. This results in a hefty collision with the private-language-argument put forward by Wittgenstein a long time ago.

N-grams are certainly more advanced than the nonsense based on tf-idf. Their underlying intention is to reflect contexts. Nevertheless, they fail as well. The ultimate reason for the failure is the symbolistic starting point. N-grams are only a first, though far too trivial and simplistic step into probabilization.

There is already a generalisation of n-grams available as described in published papers by Kohonen & Kaski: random graphs, based on random contexts, as we described it above. Random graphs overcome the symbolistic fallacy, especially if used together with SOM. Well, honestly I have to say that random graphs imply the necessity of a classification device like the SOM. This should not be considered as being a drawback, since n-grams are anyway often used together with Bayesian inference. Bayesian methods are, however, not able to distil types from observations as SOM are able to do. That now is indeed a drawback since in language learning the probabilistic approach necessarily must be accompanied with the concept of (linguistic) types.

Fault 4 : Structure as Meaning

The deep grammatical structure is an indispensable part of human languages. It is present from the sub-word level up to the level of rhetoric. And it’s gonna get really complicated. There is a wealth of rules, most of them to be followed rather strict, but some of them are applied only in a loose manner. Yet, all of them are rules, not laws.

Two issues are coming up here that are related to each other. The first one concerns the learning of a language. How do we learn a language? Wittgenstein proposed, simply by getting shown how to use it.

The second issue concerns the status of the models about language. Wittgenstein repeatedly mentioned that there is no possibility for a meta-language, and after all we know that Carnap’s program of a scientific language failed (completely). Thus we should be careful when applying a formalism to language, whether it is some kind of grammar, or any of the advanced linguistic “rules” that we know of today (see the lexicon of linguistics for that). We have to be aware that these symbolistic models are only projective lists of observations, arranged according to some standard of a community of experts.

Linguistic models are drastically different from models in physics or any other natural science, because in linguistics there is no outer reference. (Computational) Linguistics is mostly on the stage of a Babylonian list science [10], doing more tokenizing than providing useful models, comparable to biology in the 18th century.

Language is a practice. Language is a practice of human beings, equipped with a brain and embedded in a culture. In turn language itself is contributing to cultural structures and is embedded into it. There are many spatial, temporal and relational layers and compartments to distinguish. Within such arrangements, meaning happens in the course of an ongoing interpretation, which in turn is always a social situation. See Robert Brandom’s Making it Explicit as an example for an investigation of this aspect.

What we definitely have to be aware of is that projecting language onto a formalism, or subordinating language to an apriori defined or standardized symbolism (like in formal semantics) looses essentially everything language is made from and referring to. Any kind of model of a language is implicitly also claiming that language can be detached from its practice and from its embedding without loosing its main “characteristics”, its potential and its power. In short, it is the claim that structure conveys meaning.

This brings us to the question about the role of structure in language. It is a fact that humans not only understand sentences full of grammatical “mistakes”, and quite well so, in spoken language we almost always produce sentences that are full of grammatical mistakes. In fact, “mistakes” are so abundant that it becomes questionable to take them as mistakes at all. Methodologically, linguistics is thus falling back into a control science, forgetting about the role and the nature of symbolic rules such as it is established by grammar. The nature is an externalization, the role is to provide a standardization, a common basis, for performing interpretation of sentences and utterances in a reasonable time (almost immediately) and in a more or less stable manner. The empirical “given” of a sentence alone, even a whole text alone, can not provide enough evidence for starting with interpretation, nor even to finish it. (Note that a sentence is never a “given”.)

Texts as well as spoken language are nothing that could be controlled. There is no outside of language that would justify that perspective. And finally, a model should allow for suitable prediction, that is, it should enable us to perform a decision. Here we meet Chomsky’s call for competence. In case of language, a linguistic models should be able to produce language as a proof of concept. Yet, any attempt so far failed drastically, which actually is not really a surprise. Latest here it should become clear that the formal models of linguistics, and of course all the statistical approaches to “language processing” (another crap term from computational linguistics) are flawed in a fundamental way.

From the perspective of our interests here on the “Putnam Program” we conceive of formal properties as Putnam did in his “Meaning of “Meaning””. Formal properties are just that: properties among other properties. In our modeling essay we proposed to replace the concept of properties by the concept of the assignate, in order to emphasize the active role of the modeling instance in constructing and selecting the factors. Sometimes we use formal properties of terms and phrases, sometimes not, dependent on context, purpose or capability. There is neither a strict tie of formal assignates to the entity “word” or “sentence” nor could we detach them as part of formal approach.

Fault 5 : Grouping, Modeling and Selection

Analytic formal models are a strange thing, because such a model essentially claims that there is no necessity for a decision any more. Once the formula is there, it claims a global validity. The formula denies the necessity for taking the context as a structural element into account. It claims a perfect separation between observer and the observed. The global validity also means that the weights of the input factors are constant, or even that there are no such weights. Note that the weights translates directly into the implied costs of a choice, hence formulas also claim that the costs are globally constant, or at least, arranged in a smooth differentiable space. This is of course far from any reality for almost any interesting context, and of course for the contexts of language and urbanism, both deeply related to the category of the “social”.

This basic characteristic hence limits the formal symbolic approach to physical, if not just to celestial and atomic contexts. Trivial contexts, so to speak. Everywhere else something rather different is necessary. This different thing is classification as we introduced it first in our essay about modeling.

Searching for a text and considering a particular one as a “match” to the interests expressed by the search is a selection, much like any other “decision”. It introduces a notion of irreversibility. Searching itself is a difficult operation, even so difficult that is questionable whether we should follow this pattern at all. As soon as we start to search we enter the grammatological domain of “searching”. This means that we claim the expressibility of our interests in the search statement.

This difficulty is nicely illustrated by an episode with Gary Kasparov in the context of his first battle against “Deep Blue”. Given the billions of operations the super computer performed, a journalist came up with the question “How do find the correct move so fast?” Obviously, the journalist was not aware about the mechanics of that comparison. Kasparov answered: “ I do not search, I just find it.” His answer is not perfectly correct, though, as he should have said “I just do it”. In a conversation we mostly “just do language”. We practice it, but we very rarely search for a word, an expression, or the like. Usually, our concerns are on the strategic level, or in terms of speech act theory, on the illocutionary level.

Such we arrive now at the intermediary result that we have some kind of non-analytical models on the one hand, and the performance of their application on the other. Our suggestion is that most of these models are situated on an abstract, orthoregulative level, and almost never on the representational level of the “arrangement” of words.

A model has a purpose, even if it is an abstract one. There are no models without purpose. The purpose is synonymic to the selection. Often, we do not explicitly formulate a purpose, we just perform selections in a consistent manner. It is this consistency in the selections that imply a purpose. The really important thing to understand is also that the abstract notion of purpose is also synonymic to what we call “perspective”, or point of view.

One could mention here the analytical “models”, but those “models” are not models because they are devoid of a purpose. Given any interesting empirical situation, everybody knows that things may look quite different, just dependent on the “perspective” we take. Or in our words, which abstract purpose we impose to the situation. The analytic approach denies such a “perspectivism”.

The strange thing now is that many people mistake the mere clustering of observation on the basis of all contributing or distinguished factors as a kind of model. Of course, that grouping will radically change if we withdraw some of the factors, keeping only a subset of all available ones. Not only the grouping changes, but also the achievable typology and any further generalization will be also very different. In fact, any purpose, and even the tuning of the attitude towards the risk (costs) of unsuitable decisions changes the set of suitable factors. Nothing could highlight more the nonsense to call naïve take-it-all-clustering a “unsupervised modeling”. First, it is not a model. Second, any clustering algorithm or grouping procedure follows some optimality criterion, that is it supervises it despite claiming the opposite. “Unsupervised modeling” claims implicitly that it is possible to build a suitable model by pure analytic means, without any reference to the outside at all. This is, f course, not possible. It is this claim that is introducing a contradiction to the practice itself, because clustering usually means classification, which is not an analytic move at all. Due to this self-contradiction the term “unsupervised modeling” is utter nonsense. It is not only nonsense, it is even deceiving, as people get vexed by the term itself: they indeed believe that they are modeling in a suitable manner.

Now back to the treatment of texts. One of the most advanced procedures—it is a non-analytical one—is the WebSom. We described it in more detail in previous essays (here and here). Yet, as the second step Kohonen proposes clustering as a suitable means to decide about the similarity of texts. He is committing exactly the same mistake as described before. The trick, of course, is to introduce (targeted) modeling to the comparison of texts, despite the fact that there are no possible criteria apriori. What seems to be irresolvable disappears, however, as a problem if we take into account the self-referential relations of discourses, which necessarily engrave into the interpreter as self-modifying structural learning and historical individuality.

6. The Statistics of Urban Environments

The Importance of Conceptual Backgrounds

There is no investigation without implied purpose, simply because any investigation has to perform more often many selections rather than just some. One of the more influential selections that has to be performed considers the scope of the investigation. We already met this issue above when we discussed the affairs as we can meet it in behavioral sciences.

Considering investigations about social entities like urban environments, architecture or language. “scope” largely refers to the status of the individual, and in turn, to the status of time that we instantiate in our investigation. Both together establish the dimension of form as an element of the space of expressibility that we choose for the investigation.

Is the individual visible at all? I mean, in the question, in the method and after applying a methodology? For instance, as soon as we ask about matters of energy, individuals disappear. They also disappear if we apply statistics to raw observations, even if at first hand we would indeed observe individuals as individuals. To retain the visibility of individuals as individuals in a set of relations we have to apply proper means first. It is clear, that any cumulative measure like those from socio-economics also cause the disappearance of the context and the individual.

If we keep the individuals alive in our method, the next question we have to ask concerns the relations between the individuals. Do we keep them or do we drop them? Finally, regarding the unfolding of the processes that result from the temporal dynamics of those relations, we have to select whether we want to keep aspects of form or not. If you think that the way a text unfolds or the way things are happening in the urban environment is at least as important as their presence,  well in this case you would have to care about patterns.

It is rather crucial to understand that these basic selections determine the outcome of an investigation as well as of any modeling or even theory building as grammatological constraints. Once we took a decision on the scope, the problematics of that choice becomes invisible, completely transparent. This is the actual reason for the fact that choosing a reductionist approach as the first step is so questionable.

In our earlier essay about the belief system in modernism we emphasized the inevitability of the selection of a particular metaphysical stance, ways before we even think about the scope of an investigation in a particular domain. In case of modernistic thinking, from positivism to existentialism, including any shape of materialism, the core of the belief system is metaphysical independence, shaping all the way down towards politics methods, tools, attitudes and strategies. If you wonder whether there is an alternative to modernistic thinking, take a look to our article where we introduce the concept of the choreostemic space.

Space Syntax

In the case of “Space Syntax” the name is program. The approach is situated in urbanism; it has been developed and is still being advocated by Bill Hillier. Originally, Hillier was a geo-scientist, which is somewhat important to follow his methodology.

Put into a nutshell, the concept of space syntax claims that the description of the arrangement of free space in a built environment is necessary and sufficient for describing the quality of a city. The method of choice to describe that arrangement is statistics, either through the concept of probabilistic density of people or through the concept of regression, relating physical characteristics of free space with the density of people. Density in turn is used to capture the effect of collective velocity vectors. If people start to slow down, walking around in different directions, density increases. Density of course also increases as a consequence of narrow passages. Yet, in this case the vectors are strongly aligned.

The spatial behavior of individuals is a result and a means of social behavior in many animal species. Yet it makes a difference whether we consider the spatial behavior of individuals or the arrangement of free space in a city as a constraint of the individual spatial behavior. Hillier’s claim of “The Space is the Machine” is mistaking the one for the other.

In his writings, Hillier over and over again commits the figure of the petitio principii. He starts with the strong belief in analytics and upon that he tries to justify the use of analytical techniques. His claim of “The need for an analytic theory of architecture” ([11], p.40) is just one example. He writes

The answer proposed in this chapter is that once we accept that the object of architectural theory is the non-discursive — that is, the configurational — content of space and form in buildings and built environments, then theories can only be developed by learning to study buildings and built environments as non-discursive objects.

Excluding the discourse as a constitutional element only the analytic remains. He drops any relational account, focusing just the physical matter and postulating meaning of physical things, i.e. meaning as an apriori in the physical things. His problem is just his inability to distinguish different horizons of time, of temporal development. Dismissing time means to dismiss memory, and of course also culture. For a physicalist or ultra-modernist like him this blindness is constitutive. He never will understand the structure of his failure.

His dismissal of social issues as part of a theory serves eo ipso as his justification of the whole methodology. This is only possible due to another, albeit consistent, mistake, the conflation of theory and models. Hillier is showing us over and over again only models, yet not any small contribution to an architectural theory. Applying statistics shows us a particular theoretical stance, but is not to be taken as such! Statistics instantiates those models, that is his architectural theory is following largely the statistical theory. We repeatedly pointed to the problems that appear if we apply statistics to raw observations.

The high self-esteem Hillier expresses in his nevertheless quite limited writings is topped by treating space as syntax, in other words as a trivial machine. Undeniably, human beings have a material body, and buildings take space as material arrangements. Undeniably matter arranges space and constitutes space. There is a considerably discussion in philosophy about how we could approach the problematic field of space. We won’t go into details here, but Hillier simply drops the whole stuff.

Matter arranges in space. This becomes quickly a non-trivial insight, if we change perspective from abstract matter and the correlated claim of the possibility of reductionism to spatio-temporal processes, where the relations are kept taken as a starting point. We directly enter the domain of self-organization.

By means of “Space Syntax” Hillier claimed to provide a tool for planning districts of a city, or certain urban environments. If he would restrict his proposals to certain aspects of the anonymized flow of people and vehicles, it would be acceptable as a method. But it is certainly not a proper tool to describe the quality of urban environments, or even to plan them.

Recently, he delivered a keynote speech [12] where he apparently departed from his former Space Syntax approach, that reaches back to 1984. There he starts with the following remark.

On the face of it, cities as complex systems are made of (at least) two sub-systems: a physical sub-system, made up of buildings linked by streets, roads and infrastructure; and a human sub-system made up of movement, interaction and activity. As such, cities can be thought of as socio-technical systems. Any reasonable theory of urban complexity would need to link the social and technical sub-systems to each other.

This clearly is much less reductionist, at first sight at least, than “Space Syntax”. Yet, Hillier remains aligned to hard-core positivism. Firstly, in the whole speech he fails to provide a useful operationalization of complexity. Secondly, his Space Syntax simply appears wrapped in new paper. Agency for him is still just spatial agency. The relevant urban networks for him is just the network of streets. Thirdly, it is bare nonsense to separate a physical and a human subsystem, and then to claim the lumping together of those as a socio-technical system. He obviously is unaware of more advance and much more appropriate ways of thinking about culture, such as ANT, the Actor-Network-Theory (Bruno Latour), which precisely drops the categorical separation of physical and human. This separation has been first critized by Merlau-Ponty in the 1940ies!

Hillier served us just as an example, but you may have got the point. Occasionally, one can meet attempts that at least try to integrate a more appropriate concept of culture and human being in urban environments. Think about Koolhaas and his AMO/OMA, for instance, despite the fact that Koolhaas himself also struggles with the modernist mindset (see our introductions into “JunkSpace” or “The Generic City”). Yet, he at least recognized that something is fundamentally problematic with that.

7. The Toolbox Perspective

Most of the interesting and relevant systems are complex. It is simply a methodological fault to use frequencies of observational elements to describe these systems, whether we are dealing with animals, texts, urban environments or people (dogs, cats) moving around in urban environments.

Tools provide filters, they respond to certain issues, both of the signal and of the embedding. Tools are artifacts for transformation. As such they establish the relationality between actors, things and processes. Tools produce and establish Heidegger’s “Gestell” as well as they constitute the world as a fabric of relations as facts and acts, as Wittgenstein emphasized so often and already in the beginning of the Tractatus.

What we like to propose here is a more playful attitude towards the usage of tools, including formal methods. By “playful” we refer to Wittgenstein’s rule following, but also to a certain kind of experimentation, not induced by theory, but rather triggered by the know-how of some techniques that are going to be arranged. Tools as techniques, or techniques as tools are used to distil symbols from the available signals. Their relevancy is determined only by the subsequent step of classification, which in turn is (ortho-)regulated by strategic goal or cultural habits. Never, however, should we take a particular method as a representative for the means to access meaning from a process, let it a text or an urban environment.

8. Behavior

In this concluding chapter we are going to try to provide more details about our move to apply the concept of behavior to urbanism and computational linguistics.

Text

Since Friedrich Schleiermacher in 1830ies, hermeneutics is emphasizing a certain kind of autonomy of the text. Of course, the text itself is not a living thing as we consider it for animals. Before it “awakes” it has to be entered into mind matter, or more generally, it has to be interpreted. Nevertheless, an autonomy of the text remains, largely due to the fact that there is no Private Language. The language is not owned by the interpreting mind. Vilem Flusser proposed to radically turn the perspective and to conceive the interpreter as medium for texts and other “information”, rather than the other way round.

Additionally, the working of the brain is complex, least to say. Our relation to our own brain and our own mind is more that of an observer than that of a user or even controller. We experience them. Both together, the externality of language and the (partial) autonomy of the brain-mind lead to an arrangement where the text becomes autonomous. It inherits complimentary parts of independence from both parts of the world, from the internal and the external.

Furthermore, human languages are unlimited in their productivity. It is not only unlimited, it also is extensible. This pairs with its already mentioned deep structure, not only concerning the grammatical structure. Using language, or better, mastering language means to play with the inevitable inner contradictions that appear across the various layers, levels, aspects and processes of applied language. Within practiced language, there are many time horizons, instantiated by structural and semantic pointers. These aspects render the original series of symbols into an associative network of active components, which contributes further to the autonomy of texts. Roland Barthes notes (in [17]) that

The Plural of the Text depends … not on the ambiguity of its contents but on what might be called the sterographic plurality of its weave of signifiers (etymologically, the text is a tissue, a woven fabric). The reader of the Text may be compared to someone at a loose end.

Barthes implicitly emphasizes that the text does not convey a meaning, the meaning is not in the text, it can’t be conceived as something externalizable. In this essay he also holds that a text can’t be taken as just a single object. It is a text only in the context of other texts, and so the meaning that it develops upon interpretation is also dependent on the corpus into which it is embedded.

Methodologically, this (again) highlights the problematics that Alan Hajek called the reference class problem [13]. It is impossible for an interpreter to develop the meaning of a text outside of a previously chosen corpus. This dependency is inherited by any phrase, any sentence and any word within the text. Even a label like “IBM” that seems to be bijectively unique regarding the mapping of the graphem to its implied meaning is dependent on that. Of course, it will always refer somehow to the company. Yet, without the larger context it is not clear in any sense to which aspect of that company and its history the label refers to in a particular case. In literary theory this is called intertextuality. Further more, it is almost palpable here in this example that signs refer only to signs (the cornerstone of Peircean semiotics), and that concepts are nothing that could be defined (as we argued earlier in more detail).

We may settle here that a text as well as any part of it is established even through the selection of the embedding corpus, or likewise, a social practice, a life-form. Without such an embedding the text simply does not exist as a text. We just would find a series of graphemes. It is a hopeless exaggeration , if not self-deception, if people call the statistical treatment of texts “text mining”. reading it in another way, it may be considered even as a cynical term.

It is this dependence on local and global contexts, synchronically and diachronically, that renders the interpretation of a text similar to the interpretation of animal behavior.

Taken together, conceiving of texts as behaving systems is probably less a metaphor than it appears at first sight. Considering the way we make sense of a text, approaching a text is in many ways comparable with approaching an animal of a familiar species. We won’t know exactly what is going to happen, the course of events and action depends significantly on ourselves. The categories and ascribed properties necessary to establish an interaction are quite undefined in the beginning, also available only as types of rules, not as readily parameterized rules itself. And like in animals, the next approach will never be a simple repetition of the former one, even one knows the text quite good.

From the methodological perspective the significance of such a “behavioral turn”3 can’t be underestimated. For instance, nobody would interpret an animal by a rather short series of photographs, and keep the conclusion thereof once and for all. Interacting with a text as if it would behave demands for a completely different set of procedures. After all, one would deal with an open interaction. Such openness must be responded to with an appropriate attitude of the willingness for open structural learning.  This holds not only for human interpreters, but rather also for any interpreter, even if it would be software. In other words, the software dealing with text must itself be active in a non-analytical manner in order to constitute what we call a “text”. Any kind of algorithm (in the definition of Knuth) does not deal with text, but just and blindly with a series of dead graphemes.

The Urban

For completely different material reasons cities can be considered also as autonomous entities. Their patterns of growth and differentiation looks much more like that of ensembles of biological entities than that of minerals. Of course, this doesn’t justify the more or less naïve assignment of the “city as organism”. Urban arrangements are complex in the sense we’ve defined it, they are semiogenic and associative. There is a continuous contest between structure as regulation and automation on the one side and liquification as participation and symbolization on the other, albeit symbols may play for both parties.

Despite this autonomy, it remains a fact that without human activity cities are as little alive as texts are. This raises the particular question of the relationships between a city and its inhabitants, between the people as citizens of the city that they constitute. This topic has been subject of innumerable essay, novels, and investigations. Recently, a fresh perspective onto that has been opened by Vera Bühlmann’s notion of the “Quantum City”.[14]

We can neither detach the citizens from their city, not vice versa. Nevertheless, the standardized and externalized collective contribution across space and time creates an arrangement that produces dissipative flows and shows a strong meta-stability that transcends the activities of the individuals. This stability should not be mistaken as a “state”, though. Like for any other complex system, including texts, we should avoid to try to assign a “state” to a particular city, or even a part of it. Everything is a process within a complex system, even if it appears to be rather stable. yet, this stability depends on the perspective of the observer. In turn, the seeming stability does not mean that a city-process could not be destroyed by human activity, let it be by individuals (Nero), by a collective, or by socio-economic processes. Yet, again as in case of complex systems, the question of causality would be the wrong starting point for addressing the issue of change as it would be a statistical description.

Cities and urban environments are fabrics of relations between a wide range of heterogenic and heterotopic (See Foucault or David Shane [15]) entities and processes across a likewise large range of temporal scales, meeting any shade between the material and the immaterial. There is the activity of single individuals, of collectives of individuals, of legislative and other norms, the materiality of the buildings and their changing usage and roles, different kinds of flows and streams as well as stores and memories.

Elsewhere we argued that this fabric may be conceived as a dynamic ensemble of associative networks [16]. Those should be clearly distinguished from logistic networks, whose purpose is given by organizing any kind of physical transfer. Associative networks re-arrange, sort, classify and learn. Such, they are also the abstract location of the transposition of the material into the immaterial. Quite naturally, issues of form and their temporal structure arise, in other words, behavior.

Our suggestion thus is to conceive of a city as en entity that behaves. This proposal has (almost) nothing to do with the metaphor of the “city as organism”, a transfer that is by far too naïve. Changes in urban environments are best conceived as “outcomes” of probabilistic processes that are organized as overlapping series, both contingent and consistent. The method of choice to describe those changes is based on the notion of the generalized context.

Urban Text, Text and Urbanity, Textuality and Performance

Urban environments establish or even produce a particular kind of mediality. We need not invoke the recent surge of large screens in many cities for that. Any arrangement of facades encodes a rich semantics that is best described employing a semiotic perspective, just as Venturi proposed it. Recently, we investigated the relationship between facades, whether made from stone or from screens, and the space that they constitute [17].

There is yet another important dimension between the text and the city. For many hundred years now, if not even millenia, cities are not imaginable without text in one or the other form. Latest since the early 19th century, text and city became deeply linked to one another with the surge of newspapers and publishing houses, but also through the intricate linkage between the city and the theater. Urban culture is text culture, far more than it could be conceived as an image culture. This tendency is only intensified through the web, albeit urbanity now gets significantly transformed by and into the web-based aspects of culture. At least we may propose that there is a strong co-evolution between the urban (as entity and as concept) and mediality, whether it expresses itself as text, as movie or as webbing.

The relationship between the urban and the text has been explored many times. It started probably with Walter Benjamin’s “flâneur” (for an overview see [18]). Nowadays, urbanists often refer to the concept of the “readability” of a city layout, a methodological habit originated by Kevin Lynch. Yet, if we consider the relation between the urban and the textual, we certainly have to take an abstract concept of text, we definitely have to avoid the idea that there are items like characters or words out there in the city. I think, we should at least follow something like the abstract notion of textuality, as it has been devised by Roland Barthes in his “From Work to Text” [19] as a “methodological field”. Yet, this probably is still not abstract enough, as urban geographers like Henri Lefebvre mistook the concept of textuality as one of intelligibility [20]. Lefebvre obviously didn’t understand the working of a text. How should he, one might say, as a modernist (and marxist) geographer. All the criticism that was directed against the junction between the urban and textuality conceived­—as far as we know—text as something object-like, something that is out there as such, awaiting passively to be read and still being passive as it is being read, finally maybe even as an objective representation beyond the need (and the freedom for) interpretation. This, of course, represents a rather limited view on textuality.

Above we introduced the concept of “behaving texts”, that is, texts as active entities. These entities become active as soon as they are mediatized with interpreters. Again: not the text is conceived as the media or in a media-format, but rather the interpreter, whether it is a human brain-mind or a a suitable software tat indeed is capable for interpreting, not just for pre-programmed and blind re-coding. This “behavioral turn” renders “reading” a text, but also “writing” it, into a performance. Performances, on the other hand, comprise always and inevitable a considerable openness, precisely because they let collide the immaterial and the material from the side of the immaterial. Such, performances are the counterpart of abstract associativity, yet also settling at the surface that sheds matter from ideas.

In the introduction to their nicely edited book ”Performance and the City” Kim Solga, D.Hopkins and Shelley Orr [18] write, citing the urban geographer Nigel Thrift:

Although de Certeau conceives of ‘walking in the city’ not just as a textual experience but as a ‘series’ of embodied, creative’ practices’ (Lavery: 152), a ‘spatial acting-out of place’ (de Certeau: 98, our emphasis), Thrift argues that de Certeau: “never really leaves behind the operations of reading and speech and the sometimes explicit, sometimes implicit claim that these operations can be extended to other practices. In turn, this claim [ … ] sets up another obvious tension, between a practice-based model of often illicit ‘behaviour’ founded on enunciative speech-acts and a text-based model of ‘representation’ which fuels functional social systems.” (Thrift 2004: 43)

Quite obviously, Thrift didn’t manage to get the right grip to Certeau’s proposal that textual experience may be conceived—I just repeat it— as a series of embodied, creative practices. It is his own particular blindness that lets Thrift denunciate texts as being mostly representational.

Solsa and colleagues indeed emphasize the importance of performance, not just in their introduction, but also through their editing of the book. Yet, they explicitly link textuality and performance as codependent cultural practices. They write:

While we challenge the notion that the city is a ‘text’ to be read and (re)written, we also argue that textuality and performativity must be understood as linked cultural practices that work together to shape the body of phenomenal, intellectual, psychic, and social encounters that frame a subject’s experience of the city. We suggest that the conflict, collision, and contestation between texts and acts provoke embodied struggles that lead to change and renewal over time. (p.6)

Such, we find a justification for our “behavioral turn” and its application to texts as well as to the urban from a rather different corner. Even more significant, Solsa et al. seem to agree that performativity and textuality could not be detached from the urban at all. Apparently, the urban as a particular quality of human culture more and more develops into the main representative of human culture.

Yet, neither text nor performance, nor their combination count for a full account of the mediality of the urban. As we already indicated above, the movie as kind of a cross-media from text, image, and performance is equally important.

The relations between film and the urban, between architecture and the film, are also quite wide-spread. The cinema, somehow the successor of the theatre, could be situated only within the city. From the opposite direction, many would consider a city without cinemas as being somehow incomplete. The co-evolutionary story between both is still being under vivid development, I think.

There is particularly one architect/urbanist who is able to blend the film and the building into each other. You may know him quite well, I refer to Rem Koolhaas. Everybody knows that he has been an experimental moviemaker in his youth. It is much less known that he deliberately organized at least one of his buildings as kind of a movie: The Embassy of the Netherlands in Berlin (cf. [21]).

Here, Koolhaas arranged the rooms along a dedicated script. Some of the views out of the window he even trademarked to protect them!

Figure 1: Rem Koolhaas, Dutch Embassy, Berlin. The figure shows the script of pathways as a collage (taken from [21]).

9. The Behavioral Turn

So far we have shown how the behavioral turn could be supported and which are some of the first methodological consequences, if we embrace it. Yet, the picture developed so far is not complete, of course.

If we accept the almost trivial concept that autonomous entities are best conceived as behaving entities—remember that autonomy implies complexity—, then we further can ask about the structure of the relationship between the behaving subject and its counterpart, whether this is also a behaving subject or whether it is conceived more like passive object. For Bruno Latour, for instance, both together form a network, thereby blurring the categorical distinction between both.

Most descriptions of the process of getting into touch with something nowadays is dominated by the algorithmic perspective of computer software. Even Designer started to speak about interfaces. The German term for the same thing—“Schnittstelle”—is even more pronounced and clearly depicts the modernist prejudice in dealing with interaction. “Schnittstelle” implies that something, here the relation, is cut into two parts. A complete separation between interacting entities is assumed apriori. Such a separation is deeply inappropriate, since it would work only in strictly standardized environments, up to being programmed algorithmically. Precisely this was told us over and over again by designers of software “user interfaces”. Perhaps here we can find the reason for so many bad designs, not only concerning software. Fortunately, though just through a slow evolutionary process, things improve more and more. So-called “user-centric” design, or “experience-oriented” design became more abundant in recent years, but their conceptual foundation is still rather weak, or a wild mixture of fashionable habits and strange adaptations of cognitive science.

Yet, if we take the primacy of interpretation serious, and combine it with the “behavioral turn” we can see a much more detailed structure than just two parts cut apart.

The consequence of such a combination is that we would drop the idea of a clear-cut surface even for passive objects. Rather, we could conceive objects as being stuffed with a surrounding field that becomes stronger the closer we approach the object. By means of that field we distinguish the “pure” physicality from the semiotically and behaviorally active aspects.

This field is a simple one for stone-like matter, but even there it is still present. The field becomes much more rich, deep and vibrant if the entity is not a more or less passive object, but rather an active and autonomous subject. Such as an animal, a text, or a city. The reason being that there are no apriori and globally definable representative criteria that we could use to approach such autonomous entities. We only can know about more or less suitable procedures about how to derive such criteria in the particular case, approaching a particular individual {text, city}. The missing of such criteria is a direct correlate for their semantic productivity, or, likewise, for their unboundedness.

Approaching a semantically productive entity—such entities are also always able to induce new signs, they are semiosic entities—is reminds to approaching a gravitational field. Yet it is also very different from a gravitational field, since our semio-behavioral field shows increasing structural richness the closer the entities approach to each other. It is quite obvious that only by means of such a semio-behavioral field we can close the gap between the subject and the world that has been opened, or at least deepened by the modernist contributions from the times of Descartes until late computer science. Only upon a concept like the semio-behavioral field, which in turn is a consequence of the behavioral turn, we can overcome the existential fallacy as it has been purported and renewed over and over again by the dual pair of material and immaterial. The language game that separates the material and immaterial inevitably leads into the nonsensical abyss of existentialism. Dual concepts always come with tremendous costs, as they prevent any differentiated way of speaking about the matter. For instance, it prevents to recognize the materiality of symbols, or more precisely, the double-articulation of symbols between the more material and the more immaterial aspects of the world.

The following series of images may be taken as a metaphorical illustration of that semio-behavioral field. We call it the zona extima of the behavioral coating of entities.

Figure 2a: The semio-behavioral field around an entity.

Figure 2b: The situation as another entity approaches perceptively.

Figure 2c: Mutual penetration of semio-behavioral fields.

Taken together we may say, that whenever {sb,sth} gets into contact with {sb, sth}, we do so through the behavioral coating. This zone is of contact is not intimate (as Peter Sloterdijk describes it), it is rather extimate, though there is a smooth and graded change of quality from extimacy to intimacy as the distance decreases. The zona extima is a borderless (topological) field, driven by purposes (due to modelling), it is medial, behaviorally  choreographed as negotiation, exposure, call & request.

The concept of extimation, or also the process of extimating, is much more suitable than “interaction” to describe what‘s going on when we act, behave, engage, actively perceive, encounter with or towards the other. The interesting thing with the web-based media is that some aspects of zona extima can be transferred.

10. Conclusion

In this essay we try to argument in favor of a behavioral turn as a general attitude when it comes to conceive the interaction of any kind of two entities. The behavioral turn is a consequence of three major and interrelated assumptions:

  • – primacy of interpretation in the relation to the world;s;
  • – primacy of process and relation against matter and point;
  • – complexity and associativity in strongly mediatized environments.

All three assumptions are strictly outside of anything that phenomenological, positivist or modernist approaches can talk about or even practice.

It particularly allows to overcome the traditional and strict separation between the material and the immaterial, as well as the separation between the active and the passive. These shifts can’t be underestimated; they have far-reaching consequences upon the way we practice and conceive our world.

The behavioral turn is the consequence of a particular attitude that respects the bi-valency of world as a dynamic system of populations of relations. It is less the divide between the material and the immaterial, which anyway is somewhat an illusion deriving from the metaphysical claim of the possibility of essences. For instance, the jump that occurs between the realms of the informational and the causal establishes as a pair of two complimentary but strictly and mutually exclusive modes of speaking about the orderliness in the world. In some way, it is also the orderliness in the behavior of the observer—as repetition—that creates the informational that the observer than may perceive. The separation is thus a highly artificial one, in either direction. It is simply silly to discuss the issue of causality without referring to the informational aspects (for a full discussion of the issue see this essay). In any real-world case we always find both aspects together, and we find it as behavior.

Actually, the bi-valent aspect that I mentioned before refers to something quite different, in fact so different that we even can’t speak properly about it. It refers to these aspects that are apriori to modeling or any other comprehension, that are even outside to the performance of the individual itself. What I mean is the resistance of existential arrangements, inclusive the body that the comprehending entity is partially built from. This existential resistance introduces something like outer space for the cultural sphere. Needless to say that we can exist only within this cultural sphere. Yet, any action upon the world enforces us to take a short trip into the vacuum, and if we are lucky the re-entrance is even productive. We may well expect an intensification of the aspect of the virtual, as we argued here. Far from being suitable to serve as a primacy (as existentialism misunderstood the issue), the existential resistance, the absolute outside, enforces us to bark on the concept of behavior. Only “behavior” as a perceptional and performative attitude allows to extract coherence from the world without neglecting the fact of that resistance or contumacy.

The behavioral turn triggers a change in the methodology for empiric investigations as well. The standard set of methods for empiric descriptions changes, using the relation and the coherent series always as the starting point, best in its probabilized form, that is, as generalized probabilistic context. This also prevents the application of statistical methods directly to raw data. There should always be some kind of grouping or selection preceding the statistical reasoning. Otherwise we would try to follow the route that Wittgenstein blocked as a “wrong usage of symbols” (in his rejection of the reasonability of Russel/Whitehead’s Principia Mathematica). The concept of abstract behavior inclusive the advanced methodology that avoids to start with representational symbolification is clearly a sound way out of this deep problem from which any positivist empiric investigation suffers.

Interaction, including any action upon some other entity, when understood within the paradigm of behavior, becomes a recurrent, though not repetitive, self-adjusting process. During this process means and symbols may change and be replaced all the way down until a successful handshake. There is no objectivity in this process other than the mutual possibility for anticipation. Despite the existential resistance and contumacy that is attached to any re-shaping of the world, and even more so if we accomplish it by means of tools, this anticipation is, of course, greatly improved upon the alignment to cultural standards, contributing to the life-world as a shared space of immanence.

This provides us finally a sufficiently abstract, but also a sufficiently rich or manifold perspective on the issue of the roles of symbols regarding the text, the urban and the anime, the animal-like. None of those could be comprehended without first creating a catalog or a system of symbols. These symbols, both material and immaterial and thus kind of a hinge, a double-articulation, are rooted both in the embedding culture (as a de-empirifying selective force) and the individual, which constitutes another double-articulation. The concept of abstract behavior, given as a set of particular conditions and attitudes, allows to respond appropriately to the symbolic.

The really big question concerning our choreostemic capabilities—and those of the alleged machinic—therefore is: How to achieve the fluency in dealing with the symbolic without presuming it as a primary entity? Probably by exercising observing. I hope that the suggestions expressed so far in these essay provide some robust starting points. …we will see.

Notes

1. Here we simply cite the term of “information retrieval”, we certainly do not agree that the term is a reasonable one, since it is deeply infected by positivist prejudices. “Information” can’t be retrieved, because it is not “out there”. Downloading a digitally encoded text is neither a hunting nor a gathering for information, because information can’t be considered to be an object. Information is only present during the act of interpretation (more details about the status of information you can find here). Actually, what we are doing is simply “informationing”.

2. The notion of a “behavioral turn” is known from geography since the late 1960ies [22][23], and also from economics. In both fields, however, the behavioral aspect is related to the individual human being. In both areas, any level of abstraction with regard to the concept of behavior is missing. Quite in contrast to those movements, we do not focus on the neglect of the behavioral domain when it comes to human society, but rather the transfer of the abstract notion of behavior to non-living entities.

Another reference to “behavioral sciences” can be found in social sciences. Yet, in social sciences “behavioral” is often reduced to “behaviorist”, which of course is nonsense. A similar misunderstanding is abundant in political sciences.

3. Note that the proposed „behavioral turn“ should not be mistaken as a “behavioristic” move, as sort of a behaviorism. We strictly reject the stimulus-response scheme of the behaviorism. Actually, behaviorism as it has been developed by Watson and Pavlov has only little to do with behavior at all. It is nothing else than an overt reductionist program, rendering any living being into a trivial machine. Unfortunately, the primitive scheme of behaviorism is experiencing kind of a come-back in so-called “Behavioral Design”, where people talk about “triggers” much in the same way as Pavlov did (c.f. BJ Fogg’s Behavior Model).

References

  • [1] Michael Epperson (2009). Quantum Mechanics and Relational Realism: Logical Causality and Wave Function Collapse. Process Studies, 38(2): 339-366.
  • [2] G. Moran, J.C. Fentress (1979). A Search for Order in Wolf Social Behavior. pp.245-283. in: E. Klinghammer (ed.), The Behavior and Ecology of Wolves. Symp. held on 23-24.5.1975 in Wilmington N.C.), Garland STPM Press, New York..
  • [3] Gilles Deleuze, Difference and repetitionGilles Deleuze, Difference and Repetition.
  • [4] J.A.R.A.M. Van Hooff (1982). Categories and sequences of behaviour: methods of description and analysis. in: Handbook of methods in nonverbal behavior research (K.R. Scherer& P. Ekman, eds). Cambridge University Press, Cambridge.
  • [5] P.G.M. van der Heijden, H. de Vries, J.A.R.A.M. van Hooff (1990). Correspondence analysis of transition matrices, with special attention to missing entries and asymmetry. Anim.Behav. 40: 49-64.
  • [6] Teuvo Kohonen, Samuel Kaski, K. Lagus und J. Honkela (1996). Very Large Two-Level SOM for the Browsing of Newsgroups. In: C. von der Malsburg, W. von Seelen, J. C. Vorbrüggen and B. Sendhoff, Proceedings of ICANN96, International Conference on Artificial Neural Networks, Bochum, Germany, July 16-19, 1996, Lecture Notes in Computer Science, Vol. 1112, pp.269-274. Springer, Berlin.
  • [7] Hecht-Nielsen (1994).
  • [8] Javier Rojo Tuan, S. Nguyen (2010). Improving the Johnson-Lindenstrauss Lemma. available online.
  • [9] Sanjoy Dasgupta, Presentation given about: Samuel Kaski (1998), Dimensionality Reduction by Random Mapping: Fast Similarity Computation for Clustering, Helsinki University of Technology 1998. available online.
  • [10] Michel Serres, Nayla Farouki. Le trésor. Dictionnaire des sciences. Falmamrion, Paris 1998. p.394.
  • [11] Bill Hillier, Space Syntax. E-edition, 2005.
  • [12] Bill Hillier (2009). The City as a Socio-technical System: a spatial reformulation in the light of the levels problem and the parallel problem. Keynote paper to the Conference on Spatial Information Theory, September 2009.
  • [13] Alan Hájek (2007). The Reference Class Problem is Your Problem Too. Synthese 156 (3):563-585.
  • [14] Vera Bühlmann (2012). In the Quantum City – design, and the polynomial grammaticality of artifacts. forthcoming.
  • [15] David G. Shane. Recombinant Urbanism. 2005.
  • [16] Klaus Wassermann (2010). SOMcity: Networks, Probability, the City, and its Context. eCAADe 2010, Zürich. September 15-18, 2010. available online.
  • [17] Klaus Wassermann, Vera Bühlmann, Streaming Spaces – A short expedition into the space of media-active façades. in: Christoph Kronhagel (ed.), Mediatecture, Springer, Wien 2010. pp.334-345. available here. available here.
  • [18] D.J. Hopkins, Shelley Orr and Kim Solga (eds.), Performance and the City. Palgrave Macmillan, Basingstoke 2009.
  • [19] Roland Barthes, From Work to Text. in: Image, Music, text: Essay Selected and translated. Transl. Stephen Heath, Hill&Wang, New York 1977. also available online @ google books p.56.
  • [20] Henri Lefebvre, The Production of Space. 1979.
  • [21] Vera Bühlmann. Inhabiting media. Thesis, University of Basel (CH) 2009.
  • [22] Kevin R Cox, Jennifer Wolch and Julian Wolpert (2008). Classics in human geography revisited. “Wolpert, J. 1970: Departures from the usual environment in locational analysis. Annals of the Association of American Geographers 50, 220–29.” Progress in Human Geography (2008) pp.1–5.
  • [23] Dennis Grammenos. Urban Geography. Encyclopedia of Geography. 2010. SAGE Publications. 1 Oct. 2010. available online.

۞

Beyond Containing: Associative Storage and Memory

February 14, 2012 § Leave a comment

Memory, our memory, is a wonderful thing. Most of the time.

Yet, it also can trap you, sometimes terribly, if you use it in inappropriate ways.

Think about the problematics of being a witness. As long as you don’t try to remember exactly you know precisely. As soon as you start to try to achieve perfect recall, everything starts to become fluid, first, then fuzzy and increasingly blurry. As if there would be some kind of uncertainty principle, similar to Heisenberg’s [1]. There are other tricks, such as asking a person the same question over and over again. Any degree of security, hence knowledge, will vanish. In the other direction, everybody knows about the experience that a tiny little smell or sound triggers a whole story in memory, and often one that have not been cared about for a long time.

The main strengths of memory—extensibility, adaptivity, contextuality and flexibility—could be considered also as its main weakness, if we expect perfect reproducibility for results of “queries”. Yet, memory is not a data base. There are neither symbols, nor indexes, and at the deeper levels of its mechanisms, also no signs. There is no particular neuron that would “contain” information as a file on a computer can be regarded able to provide.

Databases are, of course, extremely useful, precisely because they can’t do in other ways as to reproduce answers perfectly. That’s how they are designed and constructed. And precisely for the same reason we may state that databases are dead entities, like crystals.

The reproducibility provided by databases expels time. We can write something into a database, stop everything, and continue precisely at the same point. Databases do not own their own time. Hence, they are purely physical entities. As a consequence, databases do not/can not think. They can’t bring or put things together, they do not associate, superpose, or mix. Everything is under the control of an external entity. A database does not learn when the amount of bits stored inside it increases. We also have to be very clear about the fact that a database does not interpret anything. All this should not be understood as a criticism, of course, these properties are intended by design.

The first important consequence about this is that any system relying just on the principles of a database also will inherit these properties. This raises the question about the necessary and sufficient conditions for the foundations of  “storage” devices that allow for learning and informational adaptivity.

As a first step one could argue that artificial systems capable for learning, for instance self-organizing maps, or any other “learning algorithm”, may consist of a database and a processor. This would represent the bare bones of the classic von Neumann architecture.

The essence of this architecture is, again, reproducibility as a design intention. The processor is basically empty. As long as the database is not part of a self-referential arrangement, there won’t be something like a morphological change.

Learning without change of structure is not learning but only changing the value of structural parameters that have been defined apriori (at implementation time). The crucial step however would be to introduce those parameters at all. We will return to this point at a later stage of our discussion, when it comes to describe the processing capabilities of self-organizing maps.1

Of course, the boundaries are not well defined here. We may implement a system in a very abstract manner such that a change in the value of such highly abstract parameters indeed involves deep structural changes. In the end, almost everything can be expressed by some parameters and their values. That’s nothing else than the principle of the Deleuzean differential.

What we want to emphasize here is just the issue that (1) morphological changes are necessary in order to establish learning, and (2) these changes should be established in response to the environment (and the information flowing from there into the system). These two condition together establish a third one, namely that (3) a historical contingency is established that acts as a constraint on the further potential changes and responses of the system. The system acquires individuality. Individuality and learning are co-extensive. Quite obviously, such a system is not a von Neumann device any longer, even if it still runs on a such a linear machine.

Our claim here is that the “learning” requires a particular perspective on the concept of “data” and its “storage.” And, correspondingly, without the changed concept about the relation between data and storage, the emergence of machine-based episteme will not be achievable.

Let us just contrast the two ends of our space.

  • (1) At the logical end we have the von Neumann architecture, characterized by empty processors, perfect reproducibility on an atomic level, the “bit”; there is no morphological change; only estimation of predefined parameters can be achieved.
  • (2) The opposite end is made from historically contingent structures for perception, transformation and association, where the morphology changes due to the interaction with the perceived information2; we will observe emergence of individuality; morphological structures are always just relative to the experienced influences; learning occurs and is structural learning.

With regard to a system that is able to learn, one possible conclusion from that would be to drop the distinction between storage of encoded information and the treatment of that  encodings. Perhaps, it is the only viable conclusion to this end.

In the rest of this chapter we will demonstrate how the separation between data and their transformation can be overcome on the basis of self-organizing maps. Such a device we call “associative storage”. We also will find a particular relation between such an associative storage and modeling3. Notably, both tasks can be accomplished by self-organizing maps.

Prerequisites

When taking the perspective from the side of usage there is still another large contrasting difference between databases and associative storage (“memories”). In case of a database, the purpose of a storage event is known at the time of performing the storing operation. In case of memories and associative storage this purpose is not known, and often can’t be reasonably expected to be knowable by principle.

From that we can derive a quite important consequence. In order to build a memory, we have to avoid storing the items “as such,” as it is the case for databases. We may call this the (naive) representational approach. Philosophically, the stored items do not have any structure inside the storage device, neither an inner structure, nor an outer one. Any item appears as a primitive qualia.

The contrast to the process in an associative storage is indeed a strong one. Here, it is simply forbidden to store items in an isolated manner, without relation to other items, as an engram, an encoded and reversibly decodable series of bits. Since a database works perfectly reversible and reproducible, we can encode the graphem of a word into a series of bits and later decode that series back into a graphem again, which in turn we as humans (with memory inside the skull) can interpret as words. Strictly taken, we do NOT use the database to store words.

More concretely, what we have to do with the items comprises two independent steps:

  • (1) Items have to be stored as context.
  • (2) Items have to be stored as probabilized items.

The second part of our re-organized approach to storage is a consequence of the impossibility to know about future uses of a stored item. Taken inversely, using a database for storage always and strictly implies that the storage agent claims to know perfectly about future uses. It is precisely this implication that renders long-lasting storage projects so problematic, if not impossible.

In other words, and even more concise, we may say that in order to build a dynamic and extensible memory we have to store items in a particular form.

Memory is built on the basis of a population of probabilistic contexts in and by an associative structure.

The Two-Layer SOM

In a highly interesting prototypical model project (codename “WEBSOM”) Kaski (a collaborator of Kohonen) introduced a particular SOM architecture that serves the requirements as described above [2]. Yet, Kohonen (and all of his colleagues alike) did not recognize so far the actual status of that architecture. We already mentioned this point in the chapter about some improvements of the SOM design; Kohonen fails to discern modeling from sorting, when he uses the associative storage as a modeling device. Yet, modeling requires a purpose, operationalized into one or more target criteria. Hence, an associative storage device like the two-layer SOM can be conceived as a pre-specific model only.

Nevertheless, this SOM architecture is not only highly remarkable, but we also can easily extend it appropriately; thus it is indeed so important, at least as a starting point, that we describe it briefly here.

Context and Basic Idea

The context for which the two-layer SOM (TL-SOM) has been created is document retrieval by classification of texts. From the perspective of classification,texts are highly complex entities. This complexity of texts derives from the following properties:

  • – there are different levels of context;
  • – there are rich organizational constraints, e.g. grammars
  • – there is a large corpus of words;
  • – there is a large number of relations that not only form a network, but which also change dynamically in the course of interpretation.

Taken together, these properties turn texts into ill-defined or even undefinable entities, for which it is not possible to provide a structural description, e.g. as a set of features, and particularly not in advance to the analysis. Briefly, texts are unstructured data. It is clear, that especially non-contextual methods like the infamous n-grams are deeply inappropriate for the description, and hence also for the modeling of texts. The peculiarity of texts has been recognized long before the age of computers. Around 1830 Friedrich Schleiermacher founded the discipline of hermeneutics as a response to the complexity of texts. In the last decades of the 20ieth century, it was Jacques Derrida who brought in a new perspective on it. in Deleuzean terms, texts are always and inevitably deterritorialized to a significant portion. Kaski & coworkers addressed only a modest part of these vast problematics, the classification of texts.

The starting point they took by was to preserve context. The large variety of contexts makes it impossible to take any kind of raw data directly as input for the SOM. That means that the contexts had to be encoded in a proper manner. The trick is to use a SOM for this encoding (details in next section below). This SOM represents the first layer. The subject of this SOM are the contexts of words (definition below). The “state” of this first SOM is then used to create the input for the SOM on the second layer, which then addresses the texts. In this way, the size of the input vectors are standardized and reduced in size.

Elements of a Two-Layer SOM

The elements, or building blocks, of a TL-SOM devised for the classification of texts are

  • (1) random contexts,
  • (2) the map of categories (word classes)
  • (3) the map of texts

The Random Context

A random context encodes the context of any of the words in a text. let us assume for the sake of simplicity that the context is bilateral symmetric according to 2n+1, i.e. for example with n=3 the length of the context is 7, where the focused word (“structure”) is at pos 3 (when counting starts with 0).

Let us resort to the following example, that take just two snippets from this text. The numbers represent some arbitrary enumeration of the relative positions of the words.

sequence A of words rel. positions in text “… without change of structureis not learning …”53        54    55    56       57 58     59
sequence B of words rel. positions in text “… not have any structureinside the storage …”19    20  21       22         23    24     25

The position numbers we just need for calculating the positional distance between words. The interesting word here is “structure”.

For the next step you have to think about the words listed in a catalog of indexes, that is as a set whose order is arbitrary but fixed. In this way, any of the words gets its unique numerical fingerprint.

Index Word Random Vector
 …  …
1264  structure 0.270    0.938    0.417    0.299    0.991 …
1265  learning 0.330    0.990    0.827    0.828    0.445 …
 1266  Alabama 0.375    0.725    0.435    0.025    0.915 …
 1267  without 0.422    0.072    0.282    0.157    0.155 …
 1268  storage 0.237    0.345    0.023    0.777    0.569 …
 1269  not 0.706    0.881    0.603    0.673    0.473 …
 1270  change 0.170    0.247    0.734    0.383    0.905 …
 1271  have 0.735    0.472    0.661    0.539    0.275 …
 1272  inside 0.230    0.772    0.973    0.242    0.224 …
 1273  any 0.509    0.445    0.531    0.216    0.105 …
 1274  of 0.834    0.502    0.481    0.971    0.711 …
1274  is 0.935    0.967    0.549    0.572    0.001 …
 …

Any of the words of a text can now be replaced by an apriori determined vector of random values from [0..1]; the dimensionality of those random vectors should be around  80 in order to approximate orthogonality among all those vectors. Just to be clear: these random vectors are taken from a fixed codebook, a catalog as sketched above, where each word is assigned to exactly one such vector.

Once we have performed this replacement, we can calculate the averaged vectors per relative position of the context. In case of the example above, we would calculate the reference vector for position n=0 as the average from the vectors encoding the words “without” and “not”.

Let us be more explicit. For example sentence A we translate first into the positional number, interpret this positional number as a column header, and fill the column with the values of its respective fingerprint. For the 7 positions (-3, +3) we get 7 columns:

sequence A of words “… without change of structure is not learning …”
rel. positions in text        53        54    55    56       57 58     59
 grouped around “structure”         -3       -2    -1       0       1    2     3
random fingerprints
per position
0.422  0.170  0.834  0.270  0.935  0.706  0.330
0.072  0.247  0.502  0.938  0.967  0.881  0.990
0.282  0.734  0.481  0.417  0.549  0.603  0.827

…further entries of the fingerprints…

The same we have to do for the second sequence B. Now we have to tables of fingerprints, both comprising 7 columns and N rows, where N is the length of the fingerprint. From these two tables we calculate the average value and put it into a new table (which is of course also of dimensions 7xN). Such, the example above yields 7 such averaged reference vectors. If we have a dimensionality of 80 for the random vectors we end up with a matrix of [r,c] = [80,7].

In a final step we concatenate the columns into a single vector, yielding a vector of 7×80=560 variables. This might appear as a large vector. Yet, it is much smaller than the whole corpus of words in a text. Additionally, such vectors can be compressed by the technique of random projection (math. foundations by [3], first proposed for data analysis by [4], utilized for SOMs later by [5] and [6]), which today is quite popular in data analysis. Random projection works by matrix multiplication. Our vector (1R x  560C) gets multiplied with a matrix M(r) of 560R x 100C, yielding a vector of 1R x 100C. The matrix M(r) also consists of flat random values. This technique is very interesting, because no relevant information is lost, but the vector gets shortened considerable. Of course, in an absolute sense there is a loss of information. Yet, the SOM only needs the information which is important to distinguish the observations.

This technique of transferring a sequence made from items encoded on an symbolic level into a vector that is based on random context can be applied to any symbolic sequence of course.

For instance, it would be a drastic case of reductionism to conceive of the path taken by humans in an urban environment just as a sequence locations. Humans are symbolic beings and the urban environment is full of symbols to which we respond. Yet, for the population-oriented perspective any individual path is just a possible path. Naturally, we interpret it as a random path. The path taken through a city needs to be described both by location and symbol.

The advantage of the SOM is that the random vectors that encode the symbolic aspect can be combined seamlessly with any other kind of information, e.g. the locational coordinates. That’s the property of the multi-modality. Which particular combination of “properties” then is suitable to classify the paths for a given question then is subject for “standard” extended modeling as described inthe chapter Technical Aspects of Modeling.

The Map of Categories (Word Classes)

From these random context vectors we can now build a SOM. Similar contexts will arrange in adjacent regions.

A particular text now can be described by its differential abundance across that SOM. Remember that we have sent the random contexts of many texts (or text snippets) to the SOM. To achieve such a description a (relative) frequency histogram is calculated, which has as much classes as the SOM node count is. The values of the histogram is the relative frequency (“probability”) for the presence of a particular text in comparison to all other texts.

Any particular text is now described by a fingerprint, that contains highly relevant information about

  • – the context of all words as a probability measure;
  • – the relative topological density of similar contextual embeddings;
  • – the particularity of texts across all contextual descriptions, again as a probability measure;

Those fingerprints represent texts and they are ready-mades for the final step, “learning” the classes by the SOM on the second layer in order to identify groups of “similar” texts.

It is clear, that this basic variant of a Two-Layer SOM procedure can be improved in multiple ways. Yet, the idea should be clear. Some of those improvements are

  • – to use a fully developed concept of context, e.g. this one, instead of a constant length context and a context without inner structure;
  • – evaluating not just the histogram as a foundation of the fingerprint of a text, but also the sequence of nodes according to the sequence of contexts; that sequence can be processed using a Markov-process method, such as HMM, Conditional Random Fields, or, in a self-similar approach, by applying the method of random contexts to the sequence of nodes;
  • – reflecting at least parts of the “syntactical” structure of the text, such as sentences, paragraphs, and sections, as well as the grammatical role of words;
  • – enriching the information about “words” by representing them not only in their observed form, but also as their close synonyms, or stuffed with the information about pointers to semantically related words as this can be taken from labeled corpuses.

We want to briefly return to the first layer. Just imagine not to measure the histogram, but instead to follow the indices of the contexts across the developed map by your fingertips. A particular path, or virtual movement appears. I think that it is crucial to reflect this virtual movement in the input data for the second layer.

The reward could be significant, indeed. It offers nothing less than a model for conceptual slippage, a term which has been emphasized by Douglas Hofstadter throughout his research on analogical and creative thinking. Note that in our modified TL-SOM this capacity is not an “extra function” that had to be programmed. It is deeply built “into” the system, or in other words, it makes up its character. Besides Hofstadter’s proposal which is based on a completely different approach, and for a different task, we do not know of any other system that would be able for that. We even may expect that the efficient production of metaphors can be achieved by it, which is not an insignificant goal, since all the practiced language is always metaphoric.

Associative Storage

We already mentioned that the method of TL-SOM extracts important pieces of information about a text and represents it as a probabilistic measure. The SOM does not contain the whole piece of text as single entity, or a series of otherwise unconnected entities, the words. The SOM breaks the text up into overlapping pieces, or better, into overlapping probabilistic descriptions of such pieces.

It would be a serious misunderstanding to perceive this splitting into pieces as a drawback or failure. It is the mandatory prerequisite for building an associative storage.

Any further target oriented modeling would refer to the two layers of a TL-SOM, but never to the raw input text.Such it can work reasonable fast for a whole range of different tasks. One of those tasks that can be solved by a combination of associative storage and true (targeted) modeling is to find an optimized model for a given text, or any text snippet, including the identification of the discriminating features.  We also can turn the perspective around, addressing the query to the SOM about an alternative formulation in a given context…

From Associative Storage towards Memory

Despite its power and its potential as associative storage, the Two-Layer SOM still can’t be conceived as a memory device. The associative storage just takes the probabilistically described contexts and sorts it topologically into the map. In order to establish “memory” further components are required that provides the goal orientation.

Within the world of self-organizing maps, simple (!) memories are easy to establish. We just have to combine a SOM that acts as associative storage with a SOM for targeted modeling. The peculiar distinctive feature of that second SOM for modeling is that it does not work on external data, but on “data” as it is available in and as the SOM that acts as associative storage.

We may establish a vivid memory in its full meaning if we establish two further components: (1) targeted modeling via the SOM principle, (2) a repository about the targeted models that have been built from (or using) the associative storage, and (3) at least a partial operationalization of a self-reflective mechanism, i.e. a modeling process that is going to model the working of the TL-SOM. Since in our framework the basic SOM module is able to grow and to differentiate, there is no principle limitation of/for such a system any more, concerning its capability to build concepts, models, and (logical) habits for navigating between them. Later, we will call the “space” where this navigation takes place “choreosteme“: Drawing figures into the open space of epistemic conditionability.

From such a memory we may expect dramatic progress concerning the “intelligence” of machines. The only questionable thing is whether we should call such an entity still a machine. I guess, there is neither a word nor a concept for it.

u .

Notes

1. Self-organizing maps have some amazing properties on the level of their interpretation, which they share especially with the Markov models. As such, the SOM and Markov models are outstanding. Both, the SOM as well as the Markov model can be conceived as devices that can be used to turn programming statements, i.e. all the IF-THEN-ELSE statements occurring in a program as DATA. Even logic itself, or more precisely, any quasi-logic, is getting transformed into data.SOM and Markov models are double-articulated (a Deleuzean notion) into logic on the one side and the empiric on the other.

In order to achieve such, a full write access is necessary to the extensional as well as the intensional layer of a model. Hence, artificial neuronal networks (nor, of course, statistical methods like PCA) can’t be used to achieve the same effect.

2. It is quite important not to forget that (in our framework) information is nothing that “is out there.” If we follow the primacy of interpretation, for which there are good reasons, we also have to acknowledge that information is not a substantial entity that could be stored or processed. Information is nothing else than the actual characteristics of the process of interpretation. These characteristics can’t be detached from the underlying process, because this process is represented by the whole system.

3. Keep in mind that we only can talk about modeling in a reasonable manner if there is an operationalization of the purpose, i.e. if we perform target oriented modeling.

  • [1] Werner Heisenberg. Uncertainty Principle.
  • [2] Samuel Kaski, Timo Honkela, Krista Lagus, Teuvo Kohonen (1998). WEBSOM – Self-organizing maps of document collections. Neurocomputing 21 (1998) 101-117.
  • [3] W.B. Johnson and J. Lindenstrauss. Extensions of Lipshitz mapping into Hilbert space. In Conference in modern analysis and probability, volume 26 of Contemporary Mathematics, pages 189–206. Amer. Math. Soc., 1984.
  • [4] R. Hecht-Nielsen. Context vectors: general purpose approximate meaning representations self-organized from raw data. In J.M. Zurada, R.J. Marks II, and C.J. Robinson, editors, Computational Intelligence: Imitating Life, pages 43–56. IEEE Press, 1994.
  • [5] Papadimitriou, C. H., Raghavan, P., Tamaki, H., & Vempala, S. (1998). Latent semantic indexing: A probabilistic analysis. Proceedings of the Seventeenth ACM Symposium on the Principles of Database Systems (pp. 159-168). ACM press.
  • [6] Bingham, E., & Mannila, H. (2001). Random projection in dimensionality reduction: Applications to image and text data. Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 245-250). ACM Press.

۞

The Self-Organizing Map: SOMe Design Issues

February 4, 2012 § 1 Comment

It is the duality of persistent, quasi-material yet simulated structures

and the highly dynamic, volatile and-most salient-informational aspects that are so characteristic for learning entities like Self-Organizing Maps (SOM) or Artificial Neural Networks (ANN). It should not be regarded as a surprise that the design of manifold aspects of the persistent, quasi-material part of SOM or ANN is quite influential and hence also important.

Here we explore some of the aspects of that design. Sure, there is something like a “classic” version of the SOM, named after its inventor, the so-called “Kohonen-SOM.” Kohonen developed several slightly different SOM mechanisms over many years, starting with statistical covariance matrices. All of them comprise great ideas, for sure. Yet, in a wider perspective it is clear that there are many properties of the SOM that are presumably quite sub-optimal for realizing a generally applicable learning mechanism.

The Elements of SOMs

We shall recapitulate very briefly the principle of SOM below, more detailed descriptions can be found in many places in the Web (one of the best for the newbie, with some formulas and a demo software: ai-junkie), see also our document here that relates some issues to references, as well as our intro in plain language.

Yet, the question beyond all the mathematical formula stuff is: “What are the elements of a SOM?”

We propose to distinguish the following four basic elements:

  • (1) a Collection of Items
    that have memory for observations, or reflecting them, where all the items start with the same structure for these observations (items are often called “nodes”, or in a more romantic attitude “neurons”);
  • (2) the Spatial Layout Principles
    and the relational arrangement of this items;
  • (3) an Influence Mechanism
    that link the items together, and which together with the spatial layout defines the topology of the piece;
  • (4) a Perceptional Mechanism
    that introduces observations into the SOM in a particular manner.

In the case of the SOM these elements are configured in a way that creates a particular class of “learning” that we can describe as competitive-collaborative abstraction.

Those basic elements of a SOM can be parameterized—and thus also implemented—in very different ways. If we would take only the headlines of that list we could also subsume artificial neural networks (ANN) with these elements. Yet, even the items of a SOM and those of a ANN are drastically different. Else, the meaning of concepts like “layout” or “influence mechanism” are very different. This results in a completely different architecture regarding the relation of the “data”, or if you like potential observations, and the structure (SOM or ANN). Basically, ANNs are analytic,which means that the abstraction is (has to be done) done before the interaction of the structure with the data. In strong contrast to this approach, SOM build up an abstraction while interacting with the data. This abstraction is mostly consisting of the transition from extensional data to intensional representation. Thus SOM are able to find a structure, while ANN only can move within the apriori defined structure. In contrast to ANN, SOM are associative mechanisms (which is the reason why we are so fond of them)

Yet, it is also true for SOMs that the parametrization of the instances of the four elements as listed above have a significant influence on the capabilities and the potential of the resulting actual associative structure. Note that the design of the internals of the SOM does not refer to the issues of the usage or the embedding of the SOM into a wider context of modeling, or the structure of modeling itself.

In the following we will discuss the usual actualizations of those four elements, the respective drawbacks and better alternatives.

The SOM itself

Often one can find schematic representations like the one shown in the following figure 1:

Then this is usually described in this way: “The network is created from a 2D lattice of ‘nodes’, each of which is fully connected to the input layer.

Albeit this is a possible description, it is a highly misleading one, with some quite unfavorable consequences: as we will see, it hides some important opportunities offered by the SOM mechanism.

Instead of speaking in an opaque manner about the “input layer” we simply can use the concept of “structured observations”. The structure is just given by the features used to establish or describe the observations. The important step that simplifies everything is to give all the nodes the same structure as the observations, at least in the beginning and as the trivial case; we will see that both assumptions may “develop away” as an effect of self-organization.

Anyway, the complicated connectivity in figure 1 changes into the following structure for the simple case:

Figure 2: An interpretation of the SOM grid, where the nodes are stuffed with the same structure (ordered set of variables) as the observations. This interpretation allows for a localizing of structures that is not achievable by the standard interpretation as shown in Fig.1.

To see what we gain by this change we have to visit briefly and partially the SOM mechanism.

The SOM mechanism compares a particular “incoming” observation to “all” nodes and determines a best matching node. The intensional part of this node then gets changed as a function of the given weight vector and the new observation. Some kind of intermediate between the observational vector and the intensional vector of the node is established. As a consequence, the nodes develop different intensional descriptions. This change upon matching with an observation then will be spread in the vicinity of the selected node, decaying with the distance, while this distance additionally is shrinking with increasing duration of the learning process. This is called the lateral control mechanism (LCM) by Kohonen (see Kohonen’s book 2001 p.179). This LCM is one of the most striking differences to so-called artificial neural networks (ANN).

It is now rather straightforward to think that the node keeps the index of the matching observation in its local memory. Over the course of learning, a node collects many records, which are all similar. This gathering of observations into an explicit collection is one of the MOST salient differences of our interpretation of the SOM to most of the standard interpretations! 

Figure 3: As Fig.2, showing the extensional container of one of the nodes.

The consequences are highly significant: The SOM is not a tool for visualization any more, it is a mechanism with inherent and nevertheless transparent abstraction! To be explicit: While we retain the full power of the SOM mechanism we also not only get an explicit clustering, but even the opportunity for a fully validated modeling, inclusive a full description of the structure of the risk of mis-classification, hence there is no “black box” any more (as in contrast say to ANN, or even statistical methods).

Now we can see what we gained from changing the description, dropping the unholy concept of “input layer.” It now becomes clearly visible that nodes can be conceived of as containers, comprised of an extensional and an intensional part (as Carnap used the terms). The intensional part is what usually is called the weight vector of a node.The extensional part is the list of observations matching this intension.

The intensional part of a node thus represents a type. The extensional part of our revised SOM node represents the matching tokens.

But wait! As it is usual done, we called the intensional part of the node the “weight vector”. Yet, this is a drastic misnomer. It is not “weights” of the variables. It is simply a value that can be calculated in different ways, and which is influenced from different sides. It is a function of

  • – the underlying extensional part = the list of records;
  • – the similarity functional that is used for this node
  • – the general network dynamics;
  • – any kind of dynamic rule relating the new observation.

It is thus much more adequate to talk about an “intensionality profile” than about weights. Of course, we can additionally introduce real “weights” for each of the positions in a structure profile vector.

A second important advance of dropping this bad concept of “input layer” is that we can localize this function that results in the actualization of the intensional part of the node. For instance, we can localize the similarity function. As part of the similarity function we could even consider to implement a dynamic rule (dependent on the extensional content of the node) that excludes certain positions = variables as arguments from the determination of the similarity!

The third important consequence is that we created a completely new compartment, the “extensional container” of a node. Using the concept of “input layer” this compartment is simply not visible. Thus, the concept of the input layer violates central insights from the theory of epistemic action.

This “extensional container” is not just a list of records. We can conceive it as a “functional” compartment, that allows for a great deal of new flexibility and dynamics. This inner dynamics could be used to create new elements of the intensional part of the node, e.g. about the variance of the tokens contained in the “extensionality container”. Or about their relation as measured by the correlation. In fact, we could use any mechanism to create new positions in the intensional profile of node, even the properties of an embedded SOM, a small population of artificial neurons, the result parameters of statistical functions taking the list of observations as input and so on.

It is quite important to understand that the particular dynamics in the extensionality container is purely local. Notably the possibility for this dynamics also makes it possible to implement local differentiation of the SOM network, just as it is induced by the observations itself.

There is even a fourth implication of dropping the concept of input layer, which lead us to the separation between intensional and extensional aspects. This implication concerns the numerical production of the intensionality profile. Obviously we can regard the transition from the extensional description to the intensional representation. This abstraction, as any, is accompanied by a loss of information. Referring to the collection of intensional representations means to use them as a model. It is now very important to recognize that there is no explicit down-stream connection to the observations any more. All we have at our disposal are intensional representations that emerged as a consequence of the interaction of three components: (1) the observations, (2) the quasi-material aspects of the modeling procedure(particularly the associative part of it, of course), and (3) the imposed target/risk settings.

As a consequence we have to care explicitly about the variance structure within the extensional containers. More precisely, the internal variance of the extensional containers have to be “comparable.” If we would not care about that, we could not consider the intensional representations as comparable. We simply would compare apples with oranges, since some of the intensional representations simply would represent “a large mess”. On the level of intensionality profile one can’t see the variance anymore, hence we have to avoid the establishment of extensional groups (“micro-clusters”) that do not collect observations that are “similar” with regard to their descriptional values vector (inside the apriori given space of assignates). Astonishingly, this requirement of a homogenized extensional variance measure is overlooked even by Kohonen and his group, not to mention the implementations by countless epigonal fellows. It is clear that only the explicit distinction between intensional and extensional part of a model allows for the visibility of this important structural element.

Finally, and as a fifth consequence, we would like to emphasize that the explicit distinction between intensional and extensional parts opens the road towards a highly interesting region. We already mentioned that the transition from extensional description to intensional representation is a kind of abstraction. Yet, it is a simple kind of abstraction, closely tied to quasi-material aspects of the associative mechanism.

We may, however, easily derive the production of idealistic representations from that, if not even to say “ideas” in the philosophical sense. To achieve that we just have to extend the SOM with a production facility, the capability to simulate. This is of course not a difficult task. We will describe the details elsewhere (essay is scheduled), thus just a brief outline here. The “trick” is to use the intensional representations as seeds for generating surrogate observations by means of a Monte-Carlo simulation, such that the variance of the observations is a bit smaller than that of the empiric observations. Both, the empiric and surrogated “data” (nothing is “given” in the latter case) share the same space of assignates. The variance threshold can be derived dynamically from the SOM itself, it need not be predetermined at implementation time. As the next step one drops the extensional containers of the SOM and feeds the simulated data into it. After several loops of such self-referential modeling the intensional descriptions have “lost” their close ties to empirical data, yet, they are not completely unrelated. We still may use it as a kind of “template” in modeling, or for instance as a kind of null-model. In other words, the SOM contains the first traces of Platonic ideas.

Modeling. What else?

Above we emphasized that the SOM provides the opportunity for a fully validated modeling if we distinguish explicitly intensional and extensional parts in the make-up of the nodes. The SOM is, however, a strange thing, that can act in completely different ways.

In the chapter about modeling we concluded that a model without a purpose is not a model, or it is at most a strongly deficient model. Nevertheless, many people claim to create models without implying a purpose to the learning SOM. They call it “unsupervised clustering”. This is, of course, nonsense. It should be called more appropriately, “clustering with a deliberately hidden purpose,” since all the parameters of the SOM mechanisms and even the implementation act as constraints for the clustering, too. Any clustering mechanism applies a lot of  criteria that influence the results. These constraints are supervised by the software, and the software has been produced by a human being (often called programmer), so this human being is supervising the clustering with a long arm. For the same reason one can not say the SOM is learning something and also not that we would train the SOM, without giving it a purpose.

Though the digesting of information by a SOM without a purpose being present is neither modeling nor learning, what can we conceive such a process as then?

The answer is pretty simple, and remember it becomes visible only after having dropped illegitimate ascriptions of mistaken concepts. This clustering has a particular epistemological role:

Self-organizing Maps that are running without purpose (i.e. target variables) are best described as associative storage devices. Nothing more, but above all, also nothing less.

Actually, this has to be rated as one of the greatest currently unrecognized opportunities in the field of machine learning. The reason is again inadequate wording. Of course, the input for such a map should be probabilized (randomized), and it has been already demonstrated how to accomplish this… guess by whom… by Teuvo Kohonen himself, while he was inventing the so-called WebSom. Kohonen proposed random neighborhoods for presenting snippets of texts to the SOM, which are a simple version of random contexts.

Importantly, once one recognizes the categorical differences between the target oriented modeling and the associative storage, it becomes immediately clear that there are strictly different methodological, hence quasi-morphological requirements. Astonishingly, even Kohonen himself, and any of his fellows as well, did not recognize the conceptual difference between the two flavors. He used SOMs created without target variable, i.e. without implying a purpose, as models for performing selections. Note that the principal mechanism of the SOM is the same for both approaches. There are just differences in the cost function(s) regarding the selection of variables.

There should be no doubt that any system intended to advance towards an autonomous machine-based episteme has to combine the two mechanism. There are sill other mechanisms, such like virtual movements, or virtual sequences in the abstract SOM space (we will describe that elsewhere), or the self-referential SOM for developing “crisp ideas”, but such a combination of associative storage and target oriented modeling is definitely inevitable (in our perspective… but we have strong arguments!).

SOM and Self-Organization

A small remark should be made here: Self-organizing maps are not in the same strong sense self-organizing as for instance Turing systems, or other Reaction-Diffusion Systems (RDS). A SOM gets organized by the interaction of its mechanisms and structures and the data. A SOM does not create patterns by it-SELF. Without feeding data into it, nothing happens, in stark contrast to self-organizing systems in the strong sense (see the example we already cited here), or take a look here from where we reproduced this parameter map for Gray-Scott Models.

Figure 4: The parameter map for Gray-Scott models, a particular Reaction-Diffusion System. Only for certain combinations of the two parameters of the system interesting patterns appear, and only for part of them the system remains dynamical, i.e. changing the layout of the patterns continuously.

As we discuss it in the chapter on complexity, it is pretty clear which kind of conditions must be at work to create the phenomenon of self-organization. None of them is present in Self-Organizing Maps; above all, SOMs are neither dissipative, nor are there antagonist influences.

Yet, it is not too difficult to create a self-organizing map that is really self-organizing. What is needed is either a second underlying process or inhibitory elements organized as population. In natural brains, we find both kinds of processes. The key for choosing the right starting point for implementing a system that is showing the transition from SOM to RDS is the complete probabilization of the idea of the network.

Our feeling is that at least one of them is mandatory in order to allow the system to develop logic as a category in an autonomous manner, i.e. not pre-programmed. As any other understanding, the ability to think in logical terms, or using logic as a category should not be programmed into a computer. That ability should emerge from the implemented conditions. Our claim that some concept is quite the opposite to something other is quite likely based on such processes. It is highly indicate in this context that the brain is indeed showing Turing patterns on the level of activity patterns, i.e. the patterns are not made of material entities, but are completely immaterial. Else, like in chemical clocks like the Belousov-Zhabotinsky system, another RDS, the natural brain shows a strong rhythmicity, both in its “local” activity patterns, as well as in the overall activity, affecting billions of cells at a time.

So far, the strong self-organization is not implemented in our FluidSOM.

Spatial Layout Principles

The spatial layout principle is a very important design aspect. It concerns not only the actual geometrical arrangement of nodes, but also their mobility as representations of physical entities. In the case of SOM this has to be taken quite abstract. The “physical entities” represented by the nodes are not neurons. The nodes represent functional roles of populations of neurons.

Usually, the SOM is defined as a collection of nodes that are arranged in a particular topology. This topology may be

  • – grid like, 2-(3) dimensional;
  • – as kind of a swarm in 2 dimensions;
  • – as a gas, freely moving nodes.

The obvious difference between them is the degree of physical freedom for the nodes to move around. In grids, nodes are fixed and cannot  move, while in the SOM gas the “nodes” are much more mobile.

There is also a quite important, yet not so obvious commonality between them. Firstly, in all of these layout principles the logical SOM nodes are identical with the “physical” items, i.e. representations of crossings in a grid, swarming entities, or gaseous containers. Thus, the data aspect of the nodes is not cleanly separated from its spatial behavior. If we separate it, the behavior of the nodes and the spatial aspects can be handled more transparently, i.e. the relevant parameters are better accessible.

Secondly, the space where those nodes are embedded is conceived as being completely neutral, as if those nodes would be arranged in deep space. Yet, everything we know of learning entities points to their mediality. In other words, the space that embeds the nodes should not be “empty”.

Using a Grid

In most of the cases the SOM is defined as a collection of nodes that are arrangement as a regular grid (4(8)n, 6n). Think of it as a fixed network like a regular wire fence, or the atomic bonds in a model of a crystal.

This layout is by far the most abundant one, yet it is the most restricted one. It is almost impossible, at least very difficult to make such a SOM dynamic, e.g. to provide it the potential to grow or to differentiate.

The advantage of grids is that it is quite easy to calculate the geometrical distance between the nodes, which is a necessary step to determine the influence between any two nodes. If the nodes are mobile, this measurement requires much much more efforts in terms of implementation.

Using Metaphors for Mobility: Swarms, or Gases

Here, the nodes may range freely. Their movement is strongly influenced (or even) restricted by the moves of its neighbors. Here, experience tells us the flocks of birds, or fishes, or bacteria, do not learn efficiently on the level of the swarm. Structures are destroyed to easy. The same is true for the gas metaphor.

Flexible Phase in a Mediating Space

Our proposal is to render the “phase” flexible according to the requirements that are important in a particular stage of learning. The nodes may be strictly arranged like in a crystal, or quite mobile, they may move around according to physical forces or according to their informational properties like the gathered data.

Ideally, the crystalline phases and the fluid phases are dependent on just a two or three parameters. One example for this is the “repulsive field”, a collection of items in a 2D space which repel each other. If the kinetic energy of those items is not too large, and the range of repellent force is not too low, this automatically leads to a hexagonal pattern. Yet, the pattern is not programmed as an apriori pattern. It is a result of properties of the items (and the embedding space). Such, the emergent arrangement is never affected by something like a “layout defect.”

Inserting a new item or removing one is very easy in such a structure. More important, the overall characteristics of the system does not change despite the fact that the actual pattern changes.

The Collection of Items : “Nodes”

In the classic SOM, nodes serve a double purpose:

  • P1 – They serve as container for references that point to records of data (=observations);
  • P2 – They present this extensional list in an integrated, “intensional” form ;

The intensional form of the list is simply the weight vector of that node. In the course of learning, the list of the records contained in a particular node will be selected such that they are increasingly similar.

Note that keeping the references to the data records is extremely important. It is NOT part of most SOM implementations. If we would not do it, we could not use the SOM as a modeling tool at all. This might be the reason why most people use the SOM just as visualization tool for data (which is a dramatic misunderstanding)

The nodes are not “directly” linked. Whether they influence each other or not is dependent on the distance between them and the neighborhood function. The neighborhood function determines the neighborhood, and it is a salient property of the SOM mechanism that this function changes over time. Important for our understanding of machine-based epistemology is that the relations between nodes in a SOM are potentially of a probabilistic character.

However, if we use a fixed grid, a fixed distance function, and a deterministically behaving neighborhood function, the resulting relations are not probabilistic any more.

Else, in case of default SOM, the nodes are passive. They even do not perform the calculation of the weight vector, which is performed by a central “update” loop in most implementations. In other words, in a standard SOM a node is a data structure.Here we arrive at a main point in our critique of the SOM

The common concept of a SOM is equivalent to a structural constant.

What we need, however, is something completely different. Even on the level of the nodes we need entities, that can change their structure and their relationality.

The concept of FluidSOM must be based on active nodes.

These active nodes are semi-autonomous. They calculate the weight vector themselves, based either on new input data, or some other “chemical” influences. They may develop a few long-range outgoing fibers or masses of more or less stable (but not “fixed”!) input relations to other nodes. The active meta-nodes in a fluid self-organizing map  may develop a nested mini-SOM, or may incorporate any other mechanism for evaluating the data to which it is pointing to, e.g. a small neural network of a fixed structure (see mn-SOM). Meta-nodes also may branch out a further SOM instances locally into relative “3D”, e.g. dependent on its work load, or again, on some “chemical influences”

We see, that meta-nodes are dynamic structures, sth like a category of categories. This flexibility is indispensable for growing and differentiation.

This introduces the seed of autonomy on the lowest possible level. Here, within the almost material processes, it is barely autonomy, it is really a mechanic activity. Yet, this activity is NOT triggered by some reason any more. It is just there, as a property of the matter itself.

We are convinced that the top-level behavioral autonomy is (at least for large parts) an emergent property that grows out of the a-reasonable activity on the micro-material level.

Data, Reflection

The profile vector of a SOM node usually contains for all mutable variables (non-ID/TV) the average of the values in the extensional list. That is, the profile vector itself does not know anything about TV or index variable…  which is solely the business of the Node.
In our case, however, and based on the principle of “strict locality,” the weight vector also may contain a further section, which is referring to dynamic properties of the node, or the data. We introduced this in a different way above when discussing the extensionality container of SOM nodes. For instance, the deviation of the data in the node against a model function (such as a correlation) such internal measurements can not be predefined, and they are also not stable input data since they are constantly changing (due to the list of data in the node, the state of other  nodes etc.).

This introduces the possibility of self-referentiality on the lowest possible level. Similar to the case of autonomy, we find the seed for self-referentiality on the topmost-level (call it consciousness…) in midst the material layer.

Programming Style

If there is one lesson we can draw from the studies of naturally occurring brains, then it is the fact that there is no master code between neurons, no “Mentalese.” The brain does not work on the base of its own language. Equivalently, there are no logical circuits implementing logic calculus. As a correlate we can say that the brain is not a thing that consists of a definite wiring. A brain is not a finite state automaton, it does not make any sense to ascribe states to brains. Instead, everything going on in a brain is probabilistic, even on the sub-cellular level. It is not determined in a definite manner, how many vesicles have to burst in a synaptic gap to cause a transmission of the signal, it is not determined how many neurons exactly make up a working group for a particular “function” etc.etc. The only thing we can say is that certain fibers collect from certain “regions”, typically millions of neurons, to other such regions.

Note that any software program IS representable by just such a definite wiring. Hence, what we need is a mechanism that can transcend its own being as mechanism. We already discussed this issue in another chapter, where we identified abstract growth as a possible route to that achievement.

The processing of information in the brain is probabilistic, despite the fact that on the top level it “feels” different for us. Now, when starting to program artificial associative structures that are able to do similar things as a brain can accomplish, we have to respect this principle of probabilization.

We not only have to avoid hard-coded wiring between procedures. We have to avoid any explicit wiring at all. In terms of software architecture this translates into the proposal that we should not rely just on object-oriented programming (OOP). For instance, we would represent nodes in a SOM as objects, and the properties of these objects again would be other objects. OOP is an important, but certainly not a sufficient design element for a machine that shall develop its own episteme.

What we have to actualize in our implementation is not just OOP, but a messaging based architecture, where all elements are only loosely coupled. The Lateral Control Mechanism (LCM) of the Kohonen SOM is a nice example for this, the explicit wiring in ANN is perfect counter-example, a DON’T DO IT. Yet, as we will see in the next section, the LCM should not be considered as a symmetric and structurally constant functional entity!

Concerning programming style, on an even lower level this translates into the heavy use of so-called interfaces, as they are so prevalent in Java. Not objects are wired or passed around, but only interfaces. Interfaces are forward contracts about the standards for the interaction of different parts, that actually can change while the “program” is running.

Of course, these considerations regard only to the lowest, indeed material levels of an associative system, yet, they are necessary. If we start with wires of any kind, we won’t achieve our goals. From the philosophical perspective it does not come as a surprise that the immanence of autonomous abstraction is to be found only in open processes, which include the dimension of mediality. Even in the interaction of its tiniest parts the system should not rely on definite encodings.

Functional Differentiation

During their development, natural systems differentiate in their parts. Bodies are comprised of organs, organs are made of different cell types, within all members of a cell a further differentiation of their actual and context-specific role may occur. The same can be observed in social insects, or any other group of social beings. They are morphologically almost identical, yet, their experience let them do their tasks differentially, or even let them do different tasks. Why then should we assume that all neurons in a large compound should act absolutely equally?

To illustrate the point we should visit a particular African termite species (Schedorhinotermes lamanianus) on which I worked as a young biologist. They are feeding on rodden/rodding wood. Well, since these pieces of wood are much larger than the termites, a problem occurs. The animals have to organize their collective foraging, i.e. where to stay and gnaw onto the wood, and where to travel to return the harvested pieces back to home nest, where they then put it to a processing chamber stuffed with a special kind of fungus. The termites then actually feed that fungus, and mostly not the wood. (though they have also bacteria in their gut to do the job of digesting the cellulose and the lignine.

Important for us is the foraging process. To organize gnawing sites and traveling routes they use pheromones, and no wonder, they use just 2 for that, which build a Turing system, as I proofed with a small bio-test together with a colleague.

In the nervous system of animals we find a similar problematics. The brain is not just a large network, over and over symmetric like a crystal. Of course not. There are compartments (see our chapter about complexity), there are fibers. The various parts of the brain even differ strongly with respect to their topological structure, their “wiring”. Why the heck should an artificial system look like a perfect crystal? In a crystal their will be no stable emergence, hence no structural learning. By the way, we should not expect structural learning in swarms either, for a very similar reason, albeit that reason instantiates in the opposite manner: complete perturbation prevents the emergence of compartments, too, hence no structural learning will be observed (That’s the reason why we do not have swarms in the skull…)

Back to our neurons. We reject the approach of a direct representational simulation of neurons, or parts of the brain. Instead we propose to focus the principles as elements of construction. Any system that is intended to show structural learning, is in urgent need of the basic differentiation into “local” and “tele” (among others). Here we meet even a structural parallelism to large urban compounds.

We can implement the emergence of such fibers in a straightforward manner, if we make it dependent on the occurrence of reproducing / repeating co-excitation of regions. This implies that we have to soften the SOM principle of the “winner-takes-it-all” approach. At least in large networks, any given observation should possibly leave its trace in different regions. Yet, our experience with very large maps indicate that this may happen almost inevitably. We just used very simple observations consisting of only 3 features (r,g, and b, such forming the RGB color triplet) and a large SOM, consisting of around 1’000’000 nodes. The topology was 4n, and the map was placed on a torus (no borders). After approx 200’000 observations, the uniqueness for color concepts started to become eroded. For some colors, two conceptual regions appeared.

In the further development of such SOMs, it is then quite naturally to let fibers grow between such regions, changing the topology of the SOM from that of a crystal to that of a brain. While the first is almost perfectly isotropic in exactly 3 dimensions, the topology of the brain is (due to the functional differentiation into tele-fibres) highly anisotropic in a high and variable dimensionality.

Conclusion

Here we discussed some basic design issues about self-organizing maps and introduced some improvements. We have seen that wording matters when it comes to represent even a mechanism. The issues we touched have been

  • – explicit distinction of intensionality and extensionality in the conceptualization of the SOM mechanism, leading to a whole “new” domain of SOM architectures;
  • – producing idealistic representations from a collection of extensional descriptions;
  • – dynamics in the extensionality domain, including embedding of other structures, thus proceeding to the principle of compartmentalization, functional differentiation and morphological growth;
  • – the distinction between modeling and associative storage, which require different morphological structures once they are distinguished;
  • – stuffing the SOM with self-organization in the strong sense;
  • – spatial layout, fixed rid versus the emergent patterns in a repulsion field of freely moving particles; distinguishing material particles from functional abstract nodes;
  • – nodes as active components of the grid;
  • – self-referentiality on the microscopic level that gives rise to emergent self-referentiality on the macroscopic level;
  • – programming style, which should not only be as abstract (and thus as general) as possible, but also has to proceed from strictly defined, strongly coupled object-oriented style to loosely coupled system based on messaging, even on the lowest levels of implementation, e.g. the interaction of nodes;
  • – functional differentiation of nodes, leading to dynamic, fractional dimensionality and topological anisotropy;

Yet, there are still much more aspects that have to be considered if one would try to approach processes on machinic substrate that could be give rise to what we call “thinking.” In discussing the design issues listed above, we remain quite on the material level. But of course, morphology is important. Nevertheless we should not conceive of morphology as a perfect instance of a blueprint, it is more about the potential, if not to say the “virtuality”, that is implied as immanence by the morphology. Beyond that morphology, we have to design the processes of dynamic change of that morphology, which we usually call growth, or tissue differentiation. Even on top of that, we have to think about the informational, i.e. immaterial processes, that only eventually lead to morphological correlates.

Anyway, when thinking about machine-based episteme, we obviously have to forget about crystals and swarms, about perfectness and symmetry in morphological structures. Instead, the design of all of the issues, whether material or immaterial, should be designed with the perspective towards an immanence of virtuality in mind, based on probabilized mechanisms.

In a further chapter (scheduled) we will try to approach two other design issues about the implementation of an advanced Self-organizing Map in more detail that we already mentioned briefly here, again oriented at basic abstract elements and the principles found in natural brains: inhibitory processes and probabilistic negation on the one hand and the chemical milieu on the other. Above we already indicated that we expect a continuum between Self-organizing Maps and Reaction-Diffusion Systems, which in our perspective is highly significant for the working of brains, whether natural or artificial ones.

۞

FluidSOM (Software)

January 25, 2012 § 7 Comments

The FluidSOM is a modular component of a SOM population

that is suitable to follow the “Growth & Differentiate” paradigm.

Self-Organizing Maps (SOM) are usually established on fixed grids, using a 4n or 6n topology. Implementations as swarms or gas are quite rare and also are burdened with particular problems. After all, we don’t have “swarms” or “gases” in our heads (at least most of us for most of the time…). This remains true even if we would consider only the informational part of the brain.

The fixed grid prohibits a “natural” growth or differentiation of the SOM-layer. Actually, this impossibility to differentiate also renders structural learning impossible. If we consider “learning” as something that is different from mere adjustment of already available internal parameters, then we could say that the inability to differentiate morphologically also means that that there is no true learning at all.

These limitations, among others, are overcome by our FluidSOM. Instead of fixed grid, we use a quasi-crystalline fluid of particles. This makes it very easy to add or to remove, to merge or to split “nodes”. The quasi-grid will always take a state of minimized tensions (at least after shaking it a bit … )

Instead of fixed grid, we use a quasi-crystalline fluid of particles. This makes it very easy to add or to remove, to merge or to split “nodes”. The quasi-grid will always take a state of minimized tensions (at least after shaking it a bit … )

As said, the particles of the collection may move around “freely”, there is no grid to which they are bound apriori. Yet, the population will arrange in an almost hexagonal arrangement… if certain conditions hold:

  • – The number of particles fits the dimensions of the available surface area.
  • – The particles are fully symmetric across the population regarding their properties.
  • – The parameters for mobility and repellent forces are suitably chosen

Deviations from a perfect hexagonal arrangement are thus quite frequent. Sometimes hexagons enclose an empty position, or pentagons establish instead of hexagons, frequently so near the border or immediately after a change of collection (adding/removing a particle). This, however, is not a drawback at all, especially not in in case of SOM layers that are relatively large (starting with N>~500). In really large layers comprising >100’000 nodes, the effect is neglectable. The advantage of such symmetry breaks on the geometrical level, i.e. on the quasi-material level, is that it provides a starting point for natural pathway of differentiation.

There is yet another advantage: The fluid layer contains particles that not necessarily are identical to the nodes of the SOM, and also the relations between nodes are not bound to the hosting grid.

The RepulsionField class allows for a confined space or for a borderless topology (a torus), the second of which is often more suitable to run a SOM.

Given all the advantages, there is the question why are fixed grids so dramatically preferred against fluid layouts? The answer is simple: it is not simple at all to implement them in a way that allows for a fast and constant query time for neighborhoods. If it takes 100ms to determine the neighborhood for a particular location in a large SOM layer, it would not be possible to run such a construct as a SOM at all: the waiting time would be prohibitive. Our Repulsion Field addresses this problem with buffering, such it is almost as fast as the neighborhood query in fixed grids.

So far, only the RepulsionField class is available, but the completed FluidSOM should follow soon.

The Repulsion Field of the FluidSOM is available through the Google project hosting in noolabfluidsom.

The following four screenshot images show four different selection regimes for the dynamic hexagonal grid:

  • – single node selection, here as an arbitrary group
  • – minimal spanning tree on this disjoint set of nodes
  • – convex hull on the same set
  • – conventional patch selection as it occurs in the learning phase of a SOM

As I already said, those particles may move around such that the total energy of the field gets minimized. Splitting a node as a metaphor for natural growth leads to a different layout, yet in a very smooth manner.

Fig 1a-d: The Repulsion Field used in FluidSOM.
Four different modes of selection are demonstrated.

To summarize, the change to the fluidic architecture comprises

  • – possibility for a separation of physical particles and logical node components
  • – possibility for dynamic seamless growth or differentiation of the SOM lattice, including the mobility of the “particles” that act as node containers;

Besides that FluidSOM offers a second major advance as compared to the common SOM concept. It concerns the concept of the nodes. In FluidSOM, nodes are active entities, stuffed with a partial autonomy. Nodes are not just passive data structures, they won’t “get updated2 by a central mechanism. In a salient contrast they maintain certain states comprised by activity and connectivity as well as their particular selection of a similarity function. Only in the beginning all nodes are equal with respect to those structural parameters. As a consequence of these properties, nodes in FluidSOM are able to outgrow (pullulate) new additional instances of FluidSOM as kind of offspring.

These two advances removes many limitations of the common concept of SOM (for more details see here).

There is last small improvement to introduce. In the snapshots shown above you may detect some “defects,” often as either holes within a perfect hexagon, or sometimes also as a pentagon. But generally it looks quite regular. Yet, this regularity is again more similar to crystals than to living tissue. We should not take the irregularity of living tissue as a deficiency. In nature there are indeed highly regular morphological structures, e.g. in the retina of the eyes in vertebrates, or the faceted eyes of insects. In some parts (motor brains) of some brains (especially birds) we can find quite regular structures. There is no reason to assume that evolutionary processes could not lead to regular cellular structures. Yet, we never will find “crystals” in any kind of brain, not even in insects.

Taking this as an advice, we should introduce a random factor into the basic settings of the particles, such that the emerging pattern will not be regular anymore. The repulsion principle still will lead to a locally stable configuration, though. Yet, strong re-arrangement flows are not excluded either. The following figure show the resulting layout for a random variation (within certain limits) of the repellent force.

Figure 2: The Repulsion Field of FluidSOM, in which the particle are individually parameterized with regard to the repellent force. This leads to significant deviations  from the hexagonal symmetry.

This broken symmetry is based on a local individuality with regard to repellent force attached to it. Albeit this individuality is only local and of a rather weak character, together with the fact of the symmetry break it helps to induce it is nevertheless important as a seed for differentiation. It is easy to imagine that the repellent forces are some (random) function of the content-related role of the nodes that are transported by the particles. For instance, large particles, could decrease or increase this repellent force, leading to a particular morphological correlates to the semantic activity of the nodes in a FluidSOM.

A further important property for the determining the neighborhood of a particle is directionality. The RepulsionField supports this selection mode, too. It is, however, completely controlled on the level of the nodes. Hence we will discuss it there.

Here you may directly download a zip archive containing a runnable file demonstrating the repulsion field (sorry for the size (6 Mb), it is not optimized for the web). Please note that you have to install java first (on Windows). Else, I recommend to read the file “readme.txt” which explains the available commands.

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