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.
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  • [17] Sean Power, The Metaphysics of Temporal Experience. forthcoming.
  • [18] Erwin Tegtmeier (2005). Three Flawed Distinctions in the Philosophy of Time. IWS 2005.
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  • [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].
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  • [26] Christian Bermes, Ulrich Dierse (eds.), Schlüsselbegriffe der Philosophie des 20. Jahrhunderts. Meiner, Hamburg 2010.
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  • [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.
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  • [42] Peter Janich (1996). Die Konstitution der Zeit durch Handeln und Reden. Kodikas/Code Ars Semeiotica 19, 133-147.
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  • [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.
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  • [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

۞

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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.

۞

Prolegomena to a Morphology of Experience

May 2, 2012 § Leave a comment

Experience is a fundamental experience.

The very fact of this sentence demonstrates that experience differs from perception, much like phenomena are different from objects. It also demonstrates that there can’t be an analytic treatment or even solution of the question of experience. Experience is not only related to sensual impressions, but also to affects, activity, attention1 and associations. Above all, experience is deeply linked to the impossibility to know anything for sure or, likewise, apriori. This insight is etymologically woven into the word itself: in Greek, “peria” means “trial, attempt, experience”, influencing also the roots of “experiment” or “peril”.

In this essay we will focus on some technical aspects that are underlying the capability to experience. Before we go in medias res, I have to make clear the rationale for doing so, since, quite obviously so, experience could not be reduced to those said technical aspects, to which for instance modeling belongs. Experience is more than the techné of sorting things out [1] and even more than the techné of the genesis of discernability, but at the same time it plays a particular, if not foundational role in and for the epistemic process, its choreostemic embedding and their social practices.

Epistemic Modeling

As usual, we take the primacy of interpretation as one of transcendental conditions, that is, it is a condition we can‘t go beyond, even on the „purely“ material level. As a suitable operationalization of this principle, still a quite abstract one and hence calling for situative instantiation, we chose the abstract model. In the epistemic practice, the modeling does not, indeed, even never could refer to data that is supposed to „reflect“ an external reality. If we perform modeling as a pure technique, we are just modeling, but creating a model for whatsoever purpose, so to speak „modeling as such“, or purposed modeling, is not sufficient to establish an epistemic act, which would include the choice of the purpose and the choice of the risk attitude. Such a reduction is typical for functionalism, or positions that claim a principle computability of epistemic autonomy, as for instance the computational theory of mind does.

Quite in contrast, purposed modeling in epistemic individuals already presupposes the transition from probabilistic impressions to propositional, or say, at least symbolic representation. Without performing this transition from potential signals, that is mediated „raw“ physical fluctuations in the density of probabilities, to the symbolic it is impossible to create a structure, let it be for instance a feature vector as a set of variably assigned properties, „assignates“, as we called it previously. Such a minimal structure, however, is mandatory for purposed modeling. Any (re)presentation of observations to a modeling methods thus is already subsequent to prior interpretational steps.

Our abstract model that serves as an operationalization of the transcendental principle of the primacy of interpretation thus must also provide, or comprise, the transition from differences into proto-symbols. Proto-symbols are not just intensions or classes, they are so to speak non-empiric classes that have been derived from empiric ones by means of idealization. Proto-symbols are developed into symbols by means of the combination of naming and an associated practice, i.e a repeating or reproducible performance, or still in other words, by rule-following. Only on the level of symbols we then may establish a logic, or claiming absolute identity. Here we also meet the reason for the fact that in any real-world context a “pure” logic is not possible, as there are always semantic parts serving as a foundation of its application. Speaking about “truth-values” or “truth-functions” is meaningless, at least. Clearly, identity as a logical form is a secondary quality and thus quite irrelevant for the booting of the capability of experience. Such extended modeling is, of course, not just a single instance, it is itself a multi-leveled thing. It even starts with the those properties of the material arrangement known as body that allow also an informational perspective. The most prominent candidate principle of such a structure is the probabilistic, associative network.

Epistemic modeling thus consists of at least two abstract layers: First, the associative storage of random contexts (see also the chapter “Context” for their generalization), where no purpose is implied onto the materially pre-processed signals, and second, the purposed modeling. I am deeply convinced that such a structure is only way to evade the fallacy of representationalism2. A working actualization of this abstract bi-layer structure may comprise many layers and modules.

Yet, once one accepts the primacy of interpretation, and there is little to say against it, if anything at all, then we are lead directly to epistemic modeling as a mandatory constituent of any interpretive relationship to the world, for primitive operations as well as for the rather complex mental life we experience as humans, with regard to our relationships to the environment as well as with regard to our inner reality. Wittgenstein emphasized in his critical solipsism that the conception of reality as inner reality is the only reasonable one [3]. Epistemic modeling is the only way to keep meaningful contact with the external surrounds.

The Bridge

In its technical parts experience is based on an actualization of epistemic modeling. Later we will investigate the role and the usage of these technical parts in detail. Yet, the gap between modeling, even if conceived as an abstract, epistemic modeling, and experience is so large that we first have to shed some light on the bridge between these concepts. There are some other issues with experience than just the mere technical issues of modeling that are not less relevant for the technical issues, too.

Experience comprises both more active and more passive aspects, both with regard to performance and to structure. Both dichotomies must not be taken as ideally separated categories, of course. Else, the basic distinction into active and passive parts is not a new one either. Kant distinguished receptivity and spontaneity as two complementary faculties that combine in order to bring about what we call cognition. Yet, Leibniz, in contrast, emphasized the necessity of activity even in basic perception; nowadays, his view has been greatly confirmed by the research on sensing in organic (animals) as well as in in-organic systems (robots). Obviously, the relation between activity and passivity is not a simple one, as soon as we are going to leave the bright spheres of language.3

In the structural perspective, experience unfolds in a given space that we could call the space of experiencibility4. That space is spanned, shaped and structured by open and dynamic collections of any kind of theory, model, concept or symbol as well as by the mediality that is “embedding” those. Yet, experience also shapes this space itself. The situation reminds a bit to the relativistic space in physics, or the social space in humans, where the embedding of one space into another one will affect both participants, the embedded as well as the embedding space. These aspects we should keep in mind for our investigation of questions about the mechanisms that contribute to experience and the experience of experience. As you can see, we again refute any kind of ontological stances even to their smallest degrees.5

Now when going to ask about experience and its genesis, there are two characteristics of experience that enforce us to avoid the direct path. First, there is the deep linkage of experience to language. We must get rid of language for our investigation in order to avoid the experience of finding just language behind the language or what we call upfront “experience”; yet, we also should not forget about language either. Second, there is the self-referentiality of the concept of experience, which actually renders it into a strongly singular term. Once there are even only tiny traces of the capability for experience, the whole game changes, burying the initial roots and mechanisms that are necessary for the booting of the capability.

Thus, our first move consists in a reduction and linearization, which we have to catch up with later again, of course. We will achieve that by setting everything into motion, so-to-speak. The linearized question thus is heading towards the underlying mechanisms6:

How do we come to believe that there are facts in the world? 7

What are—now viewed from the outside of language8—the abstract conditions and the practiced moves necessary and sufficient for the actualization­­ of such statements?

Usually, the answer will refer to some kind of modeling. Modeling provides the possibility for the transition from the extensional epistemic level of particulars to the intensional epistemic level of classes, functions or categories. Yet, modeling does not provide sufficient reason for experience. Sure, modeling is necessary for it, but it is more closely related to perception, though also not being equivalent to it. Experience as a kind of cognition thus can’t be conceived as kind of a “high-level perception”, quite contrary to the suggestion of Douglas Hofstadter [4]. Instead, we may conceive experience, in a first step, as the result and the activity around the handling of the conditions of modeling.

Even in his earliest writings, Wittgenstein prominently emphasized that it is meaningless to conceive of the world as consisting from “objects”. The Tractatus starts with the proposition:

The world is everything that is the case.

Cases, in the Tractatus, are states of affairs that could be made explicit into a particular (logical) form by means of language. From this perspective one could derive the radical conclusion that without language there is no experience at all. Despite we won’t agree to such a thesis, language is a major factor contributing to some often unrecognized puzzles regarding experience. Let us very briefly return to the issue of language.

Language establishes its own space of experiencibility, basically through its unlimited expressibility that induces hermeneutic relationships. Probably mainly to this particular experiential sphere language is blurring or even blocking clear sight to the basic aspects of experience. Language can make us believe that there are phenomena as some kind of original stuff, existing “independently” out there, that is, outside the human cognition.9 Yet, there is no such thing like a phenomenon or even an object that would “be” before experience, and for us humans even not before or outside of language. It is even not reasonable to speak about phenomena or objects as if they would exist before experience. De facto, it is almost non-sensical to do so.

Both, objects as specified entities and phenomena at large are consequences of interpretation, in turn deeply shaped by cultural imprinting, and thus heavily depending on language. Refuting that consequence would mean to refute the primacy of interpretation, which would fall into one of the categories of either naive realism or mysticism. Phenomenology as an ontological philosophical discipline is nothing but a mis-understanding (as ontology is henceforth); since phenomenology without ontological parts must turn into some kind of Wittgensteinian philosophy of language, it simply vanishes. Indeed, when already being teaching in Cambridge, Wittgenstein once told a friend to report his position to the visiting Schlick, whom he refused to meet on this occasion, as “You could say of my work that it is phenomenology.” [5] Yet, what Wittgenstein called “phenomenology” is completely situated inside language and its practicing, and despite there might be a weak Kantian echo in his work, he never supported Husserl’s position of synthetic universals apriori. There is even some likelihood that Wittgenstein, strongly feeling to be constantly misunderstood by the members of the Vienna Circle, put this forward in order to annoy Schlick (a bit), at least to pay him back in kind.

Quite in contrast, in a Wittgensteinian perspective facts are sort of collectively compressed beliefs about relations. If everybody believes to a certain model of whatever reference and of almost arbitrary expectability, then there is a fact. This does not mean, however, that we get drowned by relativism. There are still the constraints implied by the (unmeasured and unmeasurable) utility of anticipation, both in its individual and its collective flavor. On the other hand, yes, this indeed means that the (social) future is not determined.

More accurately, there is at least one fact, since the primacy of interpretation generates at least the collectivity as a further fact. Since facts are taking place in language, they do not just “consist” of content (please excuse such awful wording), there is also a pragmatics, and hence there are also at least two different grammars, etc.etc.

How do we, then, individually construct concepts that we share as facts? Even if we would need the mediation by a collective, a large deal of the associative work takes place in our minds. Facts are identifiable, thus distinguishable and enumerable. Facts are almost digitized entities, they are constructed from percepts through a process of intensionalization or even idealization and they sit on the verge of the realm of symbols.

Facts are facts because they are considered as being valid, let it be among a collective of people, across some period of time, or a range of material conditions. This way they turn into kind of an apriori from the perspective of the individual, and there is only that perspective. Here we find the locus situs of several related misunderstandings, such as direct realism, Husserlean phenomenology, positivism, the thing as such, and so on. The fact is even synthetic, either by means of “individual”10 mental processes or by the working of a “collective reasoning”. But, of course, it is by no means universal, as Kant concluded on the basis of Newtonian science, or even as Schlick did in 1930 [6]. There is neither a universal real fact, nor a particular one. It does not make sense to conceive the world as existing from independent objects.

As a consequence, when speaking about facts we usually studiously avoid the fact of risk. Participants in the “fact game” implicitly agree on the abandonment of negotiating affairs of risk. Despite the fact that empiric knowledge never can be considered as being “safe” or “secured”, during the fact game we always behave as if. Doing so is the more or less hidden work of language, which removes the risk (associated with predictive modeling) and replaces it by metaphorical expressibility. Interestingly, here we also meet the source field of logic. It is obvious (see Waves & Words) that language is neither an extension of logics, nor is it reasonable to consider it as a vehicle for logic, i.e. for predicates. Quite to the contrast, the underlying hypothesis is that (practicing) language and (weaving) metaphors is the same thing.11 Such a language becomes a living language that (as Gier writes [5])

“[…] grows up as a natural extension of primitive behavior, and we can count on it most of the time, not for the univocal meanings that philosophers demand, but for ordinary certainty and communication.”

One might just modify Gier’s statement a bit by specifying „philosophers“ as idealistic, materialistic or analytic philosophers.

In “On Certainty” (OC, §359), Wittgenstein speaks of language as expressing primitive behavior and contends that ordinary certainty is “something animal”. This now we may take as a bridge that provides the possibility to extend our asking about concepts and facts towards the investigation of the role of models.

Related to this there is a pragmatist aspect that is worthwhile to be mentioned. Experience is a historicizing concept, much like knowledge. Both concepts are meaningful only in hindsight. As soon as we consider their application, we see that both of them refer only to one half of the story that is about the epistemic aspects of „life“. The other half of the epistemic story and directly implied by the inevitable need to anticipate is predictive or, equivalently, diagnostic modeling. Abstract modeling in turn implies theory, interpretation and orthoregulated rule-following.

Epistemology thus should not be limited to „knowledge“, the knowable and its conditions. Epistemology has explicitly to include the investigation of the conditions of what can be anticipated.

In a still different way we thus may repose the question about experience as the transition from epistemic abstract modeling to the conditions of that modeling. This would include the instantiation of practicable models as well as the conditions for that instantiation, and also the conditions of the application of models.In technical terms this transition is represented by a problematic field: The model selection problem, or in more pragmatic terms, the model (selection) risk.

These two issues, the prediction task and the condition of modeling now form the second toehold of our bridge between the general concept of experience and some technical aspects of the use of models. There is another bridge necessary to establish the possibility of experience, and this one connects the concept of experience with languagability.

The following list provides an overview about the following chapters:

These topics are closely related to each other, indeed so closely that other sequences would be justifiable too. Their interdependencies also demand a bit of patience from you, the reader, as the picture will be complete only when we arrive at the results of modeling.

A last remark may be allowed before we start to delve into these topics. It should be clear by now that any kind of phenomenology is deeply incompatible with the view developed here. There are several related stances, e.g. the various shades of ontology, including the objectivist conception of substance. They are all rendered as irrelevant and inappropriate for any theory about episteme, whether in its machine-based form or regarding human culture, whether as practice or as reflecting exercise.

The Modeling Statement

As the very first step we have to clearly state the goal of modeling. From the outside that goal is pretty clear. Given a set of observations and the respective outcomes, or targets, create a mapping function such that the observed data allow for a reconstruction of the outcome in an optimized manner. Finding such a function can be considered as a simple form of learning if the function is „invented“. In most cases it is not learning but just the estimation of pre-defined parameters.12 In a more general manner we also could say that any learning algorithm is a map L from data sets to a ranked list of hypothesis functions. Note that accuracy is only one of the possible aspects of that optimization. Let us call this for convenience the „outer goal“ of modeling. Would such mapping be perfect within reasonable boundaries, we would have found automatically a possible transition from probabilistic presentation to propositional representation. We could consider the induction of a structural description from observations as completed. So far the secret dream of Hans Reichenbach, Carl Schmid-Hempel, Wesley Salmon and many of their colleagues.

The said mapping function will never be perfect. The reasons for this comprise the complexity of the subject, noise in the measured data, unsuitable observables or any combinations of these. This induces a wealth of necessary steps and, of course, a lot of work. In other words, a considerable amount of apriori and heuristic choices have to be taken. Since a reliable, say analytic mapping can’t be found, every single step in the value chain towards the model at once becomes questionable and has to be checked for its suitability and reliability. It is also clear that the model does not comprise just a formula. In real-world situations a differential modeling should be performed, much like in medicine a diagnosis is considered to be complete only if a differential diagnosis is included. This comprises the investigation of the influence of the method’s parameterization onto the results. Let us call the whole bunch of respective goals the „inner goals“ of modeling.

So, being faced with the challenge of such empirical mess, how does the statement about the goals of the „inner modeling“ look like? We could for instance demand to remove the effects of the shortfalls mentioned above, which cause the imperfect mapping: complexity of the subject, noise in the measured data, or unsuitable observables.

To make this more concrete we could say, that the inner goals of modeling consist in a two-fold (and thus synchronous!) segmentation of the data, resulting in the selection of the proper variables and in the selection of the proper records, where this segmentation is performed under conditions of a preceding non-linear transformation of the embedding reference system. Ideally, the model identifies the data for which it is applicable. Only for those data then a classification is provided. It is pretty clear that this statement is an ambitious one. Yet, we regard it as crucial for any attempt to step across our epistemic bridge that brings us from particular data to the quality of experience. This transition includes something that is probably better known by the label „induction“. Thus, we finally arrive at a short statement about the inner goals of modeling:

How to conclude and what to conclude from measured data?

Obviously, if our data are noisy and if our data include irrelevant values any further conclusion will be unreliable. Yet, for any suitable segmentation of the data we need a model first. From this directly follows that a suitable procedure for modeling can’t consist just from a single algorithm, or a „one-shot procedure“. Any instance of single-step approaches are suffering from lots of hidden assumptions that influence the results and its properties in unforeseeable ways. Modeling that could be regarded as more than just an estimation of parameters by running an algorithm is necessarily a circular and—dependent on the amount of variables­—possibly open-ended process.

Predictability and Predictivity

Let us assume a set of observations S obtained from an empirical process P. Then ­­­this process P should be called “predictable” if the results of the mapping function f(m) that serves as an instance of a hypothesis h from the space of hypotheses H coincides with the outcome of the process P in such a way that f(m) forms an expectation with a deviation d<ε for all f(m). In this case we may say that f(m) predicts P. This deviation is also called “empirical risk”, and the purpose of modeling is often regarded as minimizing the empirical risk (ERM).

There are then two important questions. Firstly, can we trust f(m), since f(m) has been built on a limited number of observations? Secondly, how can we make f(m) more trustworthy, given the limitation regarding the data? Usually, these questions are handled under the label of validation. Yet, validation procedures are not the only possible means to get an answer here. It would be a misunderstanding to think that it is the building or construction of a model that is problematic.

The first question can be answered only by considering different models. For obtaining a set of different models we could apply different methods. That would be o.k. if prediction would be our sole interest. Yet, we also strive for detecting structural insights. And from that perspective we should not, of course, use different methods to get different models. The second possibility for addressing the first question is to use different sub-samples, which turns simple validation into a cross-validation. Cross-validation provides an expectation for the error (or the risk). Yet, in order to compare across methods one actually should describe the expected decrease in “predictive power”13 for different sample sizes (independent cross-validation per sample size). The third possibility for answering question (1) is related to the the former and consists by adding noised, surrogated (or simulated) data. This prevents the learning mechanism from responding to empirically consistent, but nevertheless irrelevant noisy fluctuations in the raw data set. The fourth possibility is to look for models of equivalent predictive power, which are, however, based on a different set of predicting variables. This possibility is not accessible for most statistical approaches such like Principal Component Analysis (PCA). Whatever method is used to create different models, models may be combined into a “bag” of models (called “bagging”), or, following an even more radical approach, into an ensemble of small and simple models. This is employed for instance in the so-called Random Forest method.

Commonly, if a model passes cross-validation successfully, it is considered to be able to “generalize”. In contrast to the common practice, Poggio et al. [7] demonstrated that standard cross-validation has to be extended in order to provide a characterization of the capability of a model to generalize. They propose to augment

CV1oo stability with stability of the expected error and stability of the empirical error to define a new notion of stability, CVEEE1oo stability.

This makes clear that Poggio’s et al. approach is addressing the learning machinery, not any longer just the space of hypotheses. Yet, they do not take the free parameters of the method into account. We conclude that their proposed approach still remains an uncritical approach. Thus I would consider such a model as not completely trustworthy. Of course, Poggio et al. are definitely pointing towards the right direction. We recognize a move away from naive realism and positivism, instead towards a critical methodology of the conditional. Maybe, philosophy and natural sciences find common grounds again by riding the information tiger.

Checking the stability of the learning procedure leads to a methodology that we called “data experiments” elsewhere. The data experiments do NOT explore the space of hypotheses, at least not directly. Instead they create a map for all possible models. In other words, instead of just asking about the predictability we now ask about the differential predictivity of in the space of models.

From the perspective of a learning theory Poggio’s move can’t be underestimated. Statistical learning theory (SLT)[8] explicitly assumes that a direct access to the world is possible (via identity function, perfectness of the model). Consequently, SLT focuses (only) on the reduction of the empirical risk. Any learning mechanism following the SLT is hence uncritical about its own limitation. SLT is interested in the predictability of the system-as-such, thereby not rather surprisingly committing the mistake of pre-19th century idealism.

The Independence Assumption

The independence assumption [I.A.], or linearity assumption, acts mainly on three different targets. The first of them is the relationship between observer and observed, while its second target is the relationship between observables. The third target finally regards the relation between individual observations. This last aspect of the I.A. is the least problematic one. We will not discuss this any further.

Yet, the first and the second one are the problematic ones. The I.A. is deeply buried into the framework of statistics and from there it made its way into the field of explorative data analysis. There it can be frequently met for instance in the geometrical operationalization of similarity, the conceptualization of observables as Cartesian dimensions or independent coefficients in systems of linear equations, or as statistical kernels in algorithms like the Support Vector Machine.

Of course, the I.A. is just one possible stance towards the treatment of observables. Yet, taking it as an assumption we will not include any parameter into the model that reflects the dependency between observables. Hence, we will never detect the most suitable hypothesis about the dependency between observables. Instead of assuming the independence of variables throughout an analysis it would be methodological much more sound to address the degree of dependency as a target. Linearity should not be an assumption, it should be a result of an analysis.

The linearity or independence assumption carries another assumption with it under its hood: the assumption of the homogeneity of variables. Variables, or assignates, are conceived as black-boxes, with unknown influence onto the predictive power of the model. Yet, usually they exert very different effects on the predictive power of a model.

Basically, it is very simple. The predictive power of a model depends on the positive predictive value AND the negative predictive value, of course; we may also use closely related terms sensitivity and specificity. Accordingly, some variables contribute more to the positive predictive value, other help to increase the negative predictive value. This easily becomes visible if we perform a detailed type-I/II error analysis. Thus, there is NO way to avoid testing those combinations explicitly, even if we assume the initial independence of variables.

As we already mentioned above, the I.A. is just one possible stance towards the treatment of observables. Yet, its status as a methodological sine qua non that additionally is never reflected upon renders it into a metaphysical assumption. It is in fact an irrational assumption, which induces serious costs in terms of the structural richness of the results. Taken together, the independence assumption represents one of the most harmful habits in data analysis.

The Model Selection Problem

In the section “Predictability and Predictivity” above we already emphasized the importance of the switch from the space of hypotheses to the space of models. The model space unfolds as a condition of the available assignates, the size of the data set and the free parameters of the associative (“modeling”) method. The model space supports a fundamental change of the attitude towards a model. Based on the denial of the apriori assumption of independence of observables we identified the idea of a singular best model as an ill-posed phantasm. We thus move onwards from the concept of a model as a mapping function towards ensembles of structurally heterogeneous models that together as a distinguished population form a habitat, a manifold in the sphere of the model space. With such a structure we neither need to arrive at a single model.

Methods, Models, Variables

The model selection problem addresses two sets of parameters that are actually quite different from each other. Model selection should not be reduced to the treatment of the first set, of course, as it happens at least implicitly for instance in [9]. The first set refers to the variables as known from the data, sometimes also called the „predictors“. The selection of the suitable variables is the first half of the model selection problem. The second set comprises all free parameters of the method. From the methodological point of view, this second set is much more interesting than the first one. The method’s parameters are apriori conditions to the performance of the method, which additionally usually remain invisible in the results, in contrast to the selection of variables.

For associative methods like SOM or other clustering variables the effect of de-/selecting variables can be easily described. Just take all the objects in front of you, for instance on the table, or in your room. Now select an arbitrary purpose and assign this purpose as a degree of support to those objects. For now, we have constructed the target. Now we go “into” the objects, that is, we describe them by a range of attributes that are present in most of the objects. Dependent on the selection of  a subset from these attributes we will arrive at very different groups. The groups now represent the target more or less, that’s the quality of the model. Obviously, this quality differs across the various selections of attributes. It is also clear that it does not help to just use all attributes, because some of the attributes just destroy the intended order, they add noise to the model and decrease its quality.

As George observes [10], since its first formulation in the 1960ies a considerable, if not large number of proposals for dealing with the variable selection problem have been proposed. Although George himself seem to distinguish the two sets of parameters, throughout the discussion of the different approaches he always refers just to the first set, the variables as included in the data. This is not a failure of the said author, but a problem of the statistical approach. Usually, the parameters of statistical procedures are not accessible, as any analytic procedure, they work as they work. In contrast to Self-organizing Maps, and even to Artificial Neural Networks (ANN) or Genetic Procedures, analytic procedures can’t be modified in order to achieve a critical usage. In some way, with their mono-bloc design they perfectly fit into representationalist fallacy.

Thus, using statistical (or other analytic) procedures, the model selection problem consists of the variable selection problem and the method selection problem. The consequences are catastrophic: If statistical methods are used in the context of modeling, the whole statistical framework turns into a black-box, because the selection of a particular method can’t be justified in any respect. In contrast to that quite unfavorable situation, methods like the Self-Organizing Map provide access to any of its parameters. Data experiments are only possible with methods like SOM or ANN. Not the SOM or the ANN are „black-boxes“, but the statistical framework must be regarded as such. Precisely this is also the reason for the still ongoing quarrels about the foundations of the statistical framework. There are two parties, the frequentists and the bayesians. Yet, both are struck by the reference class problem [11]. From our perspective, the current dogma of empirical work in science need to be changed.

The conclusion is that statistical methods should not be used at all to describe real-world data, i.e. for the modeling of real-world processes. They are suitable only within a fully controlled setting, that is, within a data experiment. The first step in any kind of empirical analysis thus must consist of a predictive modeling that includes the model selection task.14

The Perils of Universalism

Many people dealing with the model selection task are mislead by a further irrational phantasm, caused by a mixture of idealism and positivism. This is the phantasm of the single best model for a given purpose.

Philosophers of science long ago recognized, starting with Hume and ultimately expressed by Quine, that empirical observations are underdetermined. The actual challenge posed by modeling is given by the fact of empirical underdetermination. Goodman felt obliged to construct a paradox from it. Yet, there is no paradox, there is only the phantasm  of the single best model. This phantasm is a relic from the Newtonian period of science, where everybody thought the world is made by God as a miraculous machine, everything had to be well-defined, and persisting contradictions had to be rated as evil.

Secondarily, this moults into the affair of (semantic) indetermination. Plainly spoken, there are never enough data. Empirical underdetermination results in the actuality of strongly diverging models, which in turn gives rise to conflicting experiences. For a given set of data, in most cases it is possible to build very different models (ceteris paribus, choosing different sets of variables) that yield the same utility, or say predictive power, as far as this predictive power can be determined by the available data sample at all. Such ceteris paribus difference will not only give rise to quite different tracks of unfolding interpretation, it is also certainly in the close vicinity of Derrida’s deconstruction.

Empirical underdetermination thus results in a second-order risk, the model selection risk. Actually, the model selection risk is the only relevant risk. We can’t change the available data, and data are always limited, sometimes just by their puniness, sometimes by the restrictions to deal with them. Risk is not attached to objects or phenomena, because objects “are not there” before interpretation and modeling. Risk is attached only to models. Risk is a particular state of affair, and indeed a rather fundamental one. Once a particular model would tell us that there is an uncertainty regarding the outcome, we could take measures to deal with that uncertainty. For instance, we hedge it, or organize some other kind of insurance for it. But hedging has to rely on the estimation of the uncertainty, which is dependent on the expected predictive power of the model, not just the accuracy of the model given the available data from a limited sample.

Different, but equivalent selections of variables can be used to create a group of models as „experts“ on a given task to decide on. Yet, the selection of such „experts“ is not determinable on the basis of the given data alone. Instead, further knowledge about the relation of the variables to further contexts or targets needs to be consulted.

Universalism is usually unjustifiable, and claiming it instead usually comes at huge costs, caused by undetectable blindnesses once we accept it. In contemporary empiricism, universalism—and the respecting blindness—is abundant also with regard to the role of the variables. What I am talking about here is context, mediality and individuality, which, from a more traditional formal perspective, is often approximated by conditionality. Yet, it more and more becomes clear that the Bayesian mechanisms are not sufficient to get the complexity of the concept of variables covered. Just to mention the current developments in the field of probability theory I would like to refer to Brian  Weatherson, who favors and develops the so-called dynamic Keynesian models of uncertainty. [10] Yet, we regard this only as a transitional theory, despite the fact that it will have a strong impact on the way scientists will handle empiric data.

The mediating individuality of observables (as deliberately chosen assignates, of course) is easy to observe, once we drop the universalism qua independence of variables. Concerning variables, universalism manifests in an indistinguishability of the choices made to establish the assignates with regard to their effect onto the system of preferences. Some criteria C will induce the putative objects as distinguished ones only, if another assignate A has pre-sorted it. Yet, it would be a simplification to consider the situation in the Bayesian way as P(C|A). The problem with it is that we can’t say anything about the condition itself. Yet, we need to “play” (actually not “control”) with the conditionability, the inner structure of these conditions. As it is with the “relation,” which we already generalized into randolations, making it thereby measurable, we also have to go into the condition itself in order to defeat idealism even on the structural level. An appropriate perspective onto variables would hence treat it as a kind of media. This mediality is not externalizable, though, since observables themselves precipitate from the mediality, then as assignates.

What we can experience here is nothing else than the first advents of a real post-modernist world, an era where we emancipate from the compulsive apriori of independence (this does not deny, of course, its important role in the modernist era since Descartes).

Optimization

Optimizing a model means to select a combination of suitably valued parameters such that the preferences of the users in terms of risk and implied costs are served best. The model selection problem is thus the link between optimization problems, learning tasks and predictive modeling. There are indeed countless many procedures for optimization. Yet, the optimization task in the context of model selection is faced with a particular challenge: its mere size. George begins his article in the following way:

A distinguishing feature of variable selection problems is their enormous size. Even with moderate values of p, computing characteristics for all 2p models is prohibitively expensive and some reduction of the model space is needed.

Assume for instance a data set that comprises 50 variables. From that 1.13e15 models are possible, and assume further that we could test 10‘000 models per second, then we still would need more than 35‘000 years to check all models. Usually, however, building a classifier on a real-world problem takes more than 10 seconds, which would result in 3.5e9 years in the case of 50 variables. And there are many instances where one is faced with much more variables, typically 100+, and sometimes going even into the thousands. That’s what George means by „prohibitively“.

There are many proposals to deal with that challenge. All of them fall into three classes: they use either (1) some information theoretic measure (AIC, BIC, CIC etc. [11]), or (2) they use likelihood estimators, i.e. they conceive of parameters themselves as random variables, or (3) they are based of probabilistic measures established upon validation procedures. Particularly the instances from the first two of those classes are hit by the linearity and/or the independence assumption, and also by unjustified universalism. Of course, linearity should not be an assumption, it should be a result, as we argued above. Hence, there is no way to avoid the explicit calculation of models.

Given the vast number of combinations of symbols it appears straightforward to conceive of the model selection problem from an evolutionary perspective. Evolution always creates appropriate and suitable solutions from the available „evolutionary model space“. That space is of size 230‘000 in the case of humans, which is a „much“ larger number than the number of species ever existent on this planet. Not a single viable configuration could have been found by pure chance. Genetics-based alignment and navigation through the model space is much more effective than chance. Hence, the so-called genetic algorithms might appear on the radar as the method of choice .

Genetics, revisited

Unfortunately, for the variable selection problem genetic algorithms15 are not suitable. The main reason for this is still the expensive calculation of single models. In order to set up the genetic procedure, one needs at least 500 instances to form the initial population. Any solution for the variable selection problem should arrive at a useful solution with less than 200 explicitly calculated models. The great advantage of genetic algorithms is their capability to deal with solution spaces that contain local extrema. They can handle even solution spaces that are inhomogeneously rugged, simply for the reason that recombination in the realm of the symbolic does not care about numerical gradients and criteria. Genetic procedures are based on combinations of symbolic encodings. The continuous switch between the symbolic (encoding) and the numerical (effect) are nothing else than the pre-cursors of the separation between genotypes and phenotypes, without which there would not be even simple forms of biological life.

For that reason we developed a specialized instantiation of the evolutionary approach (implemented in SomFluid). Described very briefly we can say that we use evolutionary weights as efficient estimators of the maximum likelihood of parameters. The estimates are derived from explicitly calculated models that vary (mostly, but not necessarily ceteris paribus) with respect to the used variables. As such estimates, they influence the further course of the exploration of the model space in a probabilistic manner. From the perspective of the evolutionary process, these estimates represent the contribution of the respective parameter to the overall fitness of the model. They also form a kind of long-term memory within the process, something like a probabilistic genome. The short-term memory in this evolutionary process is represented by the intensional profiles of the nodes in the SOM.

For the first initializing step, the evolutionary estimates can be estimated themselves by linear procedure like the PCA, or by non-parametric procedures (Kruskal-Wallis, Mann-Whitney, etc.), and are available after only a few explicitly calculated models (model here means „ceteris paribus selection of variables“).

These evolutionary weights reflect the changes of the predictive power of the model when adding or removing variables to the model. If the quality of the model improves, the evolutionary weight increases a bit, and vice versa. In other words, not the apriori parameters of the model are considered, but just the effect of the parameters. The procedure is an approximating repetition: fix the parameters of the model (method specific, sampling, variables), calculate the model, record the change of the predictive power as compared to the previous model.

Upon the probabilistic genome of evolutionary weights there are many different ways one could take to implement the “evo-devo” mechanisms, let it be the issue of how to handle the population (e.g. mixing genomes, aspects of virtual ecology, etc.), or the translational mechanisms, so to speak the “physiologies” that are used to proceed from the genome to an actual phenotype.

Since many different combinations are being calculated, the evolutionary weight represents the expectable contribution of a variable to the predictive power of the model, under whatsoever selection of variables that represents a model. Usually, a variable will not improve the quality of the model irrespective to the context. Yet, if a variable indeed would do so, we not only would say that its evolutionary weight equals 1, we also may conclude that this variable is a so-called confounder. Including a confounder into a model means that we use information about the target, which will not be available when applying the model for classification of new data; hence the model will fail disastrously. Usually, and that’s just a further benefit of dropping the independence-universalism assumption, it is not possible for a procedure to identify confounders by itself. It is also clear that the capability to do so is one of the cornerstones of autonomous learning, which includes the capability to set up the learning task.

Noise, and Noise

Optimization raises its own follow-up problems, of course. The most salient of these is so-called overfitting. This means that the model gets suitably fitted to the available observations by including a large number of parameters and variables, but it will return wrong predictions if it is going to be used on data that are even only slightly different from the observations used for learning and estimating the parameters of the model. The model represents noise, random variations without predictive value.

As we have been describing above, Poggio believes that his criterion of stability overcomes the defects with regard to the model as a generalization from observations. Poggio might be too optimistic, though, since his method still remains to be confined to the available observations.

In this situation, we apply a methodological trick. The trick consists in turning the problem into a target of investigation, which ultimately translates the problem into an appropriate rule. In this sense, we consider noise not as a problem, but as a tool.

Technically, we destroy the relevance of the differences between the observations by adding noise of a particular characteristic. If we add a small amount of normally distributed noise, nothing will probably change, but if we add a lot of noise, perhaps even of secondarily changing distribution, this will result in the mere impossibility to create a stable model at all. The scientific approach is to describe the dependency between those two unknowns, so to say, to set up a differential between noise (model for the unknown) and the model (of the unknown). The rest is straightforward: creating various data sets that have been changed by imposing different amounts of noise of a known structure, and plotting the predictive power against the the amount of noise. This technique can be combined by surrogating the actual observations via a Cholesky decomposition.

From all available models then those are preferred that combine a suitable predictive power with suitable degree of stability against noise.

Résumé

In this section we have dealt with the problematics of selecting a suitable subset from all available observables (neglecting for the time being that model selection involves the method’s parameters, too). Since mostly we have more observables at our disposal than we actually presume to need, the task could be simply described as simplification, aka Occam’s Razor. Yet, it would be terribly naive to first assume linearity and then selecting the “most parsimonious” model. It is even cruel to state [9, p.1]:

It is said that Einstein once said

Make things as simple as possible, but not simpler.

I hope that I succeeded in providing some valuable hints for accomplishing that task, which above all is not a quite simple one. (etc.etc. :)

Describing Classifiers

The gold standard for describing classifiers is believed to be the Receiver-Operator-Characteristic, or short, ROC. Particularly, the area under the curve is compared across models (classifiers). The following Figure 1demonstrates the mechanics of the ROC plot.

Figure 1: Basic characteristics of the ROC curve (reproduced from Wikipedia)

Figure 2. Realistic ROC curves, though these are typical for approaches that are NOT based on sub-group structures or ensembles (for instance ANN or logistic regression). Note that models should not be selected on the basis of the Area-under-Curve. Instead the true positive rate (sensitivity) at a false positive rate FPR=0 should be used for that. As a further criterion that would indicate the stability of of the model one could use the slope of the curve at FPR=0.

Utilization of Information

There is still another harmful aspect of the universalistic stance in data analysis as compared to a pragmatic stance. This aspect considers the „reach“ of the models we are going to build.

Let us assume that we would accept a sensitivity of approx 80%, but we also expect a specificity of >99%. In other words, the cost for false positives (FP) are defined as very high, while the costs for false negatives (FN, not recognized preferred outcomes) are relatively low. The ratio of costs for error, or in short the error cost ratio err(FP)/err(FN) is high.

Table 1a: A Confusion matrix for a quite performant classifier.

Symbols: test=model; TP=true positives; FP=false positives; FN=false negatives; TN=true negatives; ppv=positive predictive value, npv=negative predictive value. FN is also called type-I-error (analogous to “rejecting the null hypothesis when it is true”), while FP is called type-II-error (analogous to “accepting the null hypothesis when it is false”), and FP/(TP+FP) is called type-II-error-rate, sometime labeled as β-error, where (1-β) is the called the “power” of the test or model. (download XLS example)

condition Pos

condition Neg

test Pos

100 (TP)

3 (FP)

0.971

ppv

test Neg

28 (FN)

1120 (TN)

0.976

npv

0.781

0.997

sensitivity

specificity

Let us further assume that there are observations of our preferred outcome that we can‘t distinguish well from other cases of the opposite outcome that we try to avoid. They are too similar, and due to that similarity they form a separate group in our self-organizing map. Let us assume that the specificity of these clusters is at 86% only and the sensitivity is at 94%.

Table 1b: Confusion matrix describing a sub-group formed inside the SOM, for instance as it could be derived from the extension of a “node”.

condition Pos

condition Neg

test Pos

0 (50)

0 (39)

0.0 (0.56)

ppv

test Neg

50 (0)

39 (0)

0.44 (1.0)

npv

0.0 (1.0)

1.0 (0.0)

sensitivity

specificity

Yet, this cluster would not satisfy our risk attitude. If we would use the SOM as a model for classification of new observations, and the new observation would fall into that group (by means of similarity considerations) the implied risk would violate our attitude. Hence, we have to exclude such clusters. In the ROC this cluster represents a value further to the right on the specificity (X-) axis.

Note that in the case of acceptance of the subgroup as a representative for a contributor of a positive prediction, the false negative is always 0 aposteriori, and in case of denial the true positives is always set to 0 (accordingly the figures for the condition negative).

There are now several important points to that, which are related to each other. Actually, we should be interested only in such sub-groups with specificity close to 1, such that our risk attitude is well served. [13] Likewise, we should not try to optimize the quality of the model across the whole range of the ROC, but only for the subgroups with acceptable error cost ratio. In other words, we use the available information in a very specific manner.

As a consequence, we have to set the ECR before calculating the model. Setting the ECR after the selection of a model results in a waste of information, time and money. For this reason it is strongly indicated to use methods that are based on building a representation by sub-groups. This again rules out statistical methods as they always take into account all available data. Zytkow calls such methods empirically empty [14].

The possibility to build models of a high specificity is a huge benefit of sub-group based methods like the SOM.16 To understand this better let us assume we have a SOM-based model with the following overall confusion matrix.

condition Pos

condition Neg

test Pos

78

1

0.9873

ppv

test Neg

145

498

0.7745

npv

0.350

0.998

sensitivity

specificity

That is, the model recognizes around 35% of all preferred outcomes. It does so on the basis of sub-groups that all satisfy the respective ECR criterion. Thus we know that the implied risk of any classification is very low too. In other words, such models recognize whether it is allowed to apply them. If we apply them and get a positive answer, we also know that it is justified to apply them. Once the model identifies a preferred outcome, it does so without risk. This lets us miss opportunities, but we won’t be trapped by false expectations. Such models we could call auto-consistent.

In a practical project that has been aiming at an improvement of the post-surgery risk classification of patients (n>12’000) in a hospital we have been able to demonstrate that the achievable validated rate of implied risk can be as low as <10e-4. [15] Such a low rate is not achievable by statistical methods, simply because there are far too few incidents of wrong classifications. The subjective cut-off points in logistic regression are not quite suitable for such tasks.

At the same time, and that’s probably even more important, we get a suitable segmentation of the observations. All observations that can be identified as positive do not suffer from any risk. Thus, we can investigate the structure of the data for these observations, e.g. as particular relationships between variables, such as correlations etc. But, hey, that job is already done by the selection of the appropriate set of variables! In other words, we not only have a good model, we also have found the best possibility for a multi-variate reduction of noise, with a full consideration of the dependencies between variables. Such models can be conceived as reversed factorial experimental design.

The property of auto-consistency offers a further benefit as it is scalable, that is, “auto-consistent” is not a categorical, or symbolic, assignment. It can be easily measured as sensitivity under the condition of specificity > 1-ε, ε→0. Thus, we may use it as a random measure (it can be described by its density) or as a scale of reference in case of any selection task among sub-populations of models. Additionally, if the exploration of the model space does not succeed in finding a model of a suitable degree of auto-consistency, we may conclude that the quality of the data is not sufficient. Data quality is a function of properly selected variables (predictors) and reproducible measurement. We know of no other approach that would be able to inform about the quality of the data without referring to extensive contextual “knowledge”. Needless to say that such knowledge is never available and encodable.

There are only weak conditions that need to be satisfied. For instance, the same selection of variables need to be used within a single model for all similarity considerations. This rules out all ensemble methods, as far as different selections of variables are used for each item in the ensemble; for instance decision tree methods (a SOM with its sub-groups is already “ensemble-like”, yet, all sub-groups are affected by the same selection of variables). It is further required to use a method that performs the transition from extensions to intensions on a sub-group level,which rules out analytic methods, and even Artificial Neural Networks (ANN). The way to establish auto-consistent models is not possible for ANN. Else, the error-cost ratio must be set before calculating the model, and the models have to be calculated explicitly, which removes linear methods from the list, such as Support Vector Machines with linear kernels (regression, ANN, Bayes). If we want to access the rich harvest of auto-consistent models we have to drop the independence hypothesis and we have to refute any kind of universalism. But these costs are rather low, indeed.

Observations and Probabilities

Here we developed a particular perspective onto the transition from observations to intensional representations. There are of course some interesting relationships of our point of view to the various possibilities of “interpreting” probability (see [16] for a comprehensive list of “interpretations” and interesting references). We also provide a new answer to Hume’s problem of induction.

Hume posed the question, how often should we observe a fact until we could consider it as lawful? This question, called the “problem of induction” points to the wrong direction and will trigger only irrelevant answer. Hume, living still in times of absolute monarchism, in a society deeply structured by religious beliefs, established a short-cut between the frequency of an observation and its propositional representation. The actual question, however, is how to achieve what we call an “observation”.

In very simple, almost artificial cases like the die there is nothing to interpret. The die and its values are already symbols. It is in some way inadequate to conceive of a die or of dicing as an empirical issue. In fact, we know before what could happen. The universe of the die consists of precisely 6 singular points.

Another extreme are so-called single-case observations of structurally rich events, or processes. An event, or a setting should be called structurally rich, if there are (1) many different outcomes, and (2) many possible assignates to describe the event or the process. Such events or processes will not produce any outcome that is could be expected by symbolic or formal considerations. Obviously, it is not possible to assign a relative frequency to a unique, a singular, or a non-repeatable event. Unfortunately, however, as Hájek points out [17], any actual sequence can be conceived of as a singular event.

The important point now is that single-case observations are also not sufficiently describable as an empirical issue. Ascribing propensities to objects-in-the-world demands for a wealth of modeling activities and classifications, which have to be completed apriori to the observation under scrutiny. So-called single-case propensities are not a problem of probabilistic theory, but one of the application of intensional classes and their usage as means for organizing one’s own expectations. As we said earlier, probability as it is used in probability theory is not a concept that could be applied meaningful to observations, where observations are conceived of as primitive “givens”. Probabilities are meaningful only in the closed world of available subjectively held concepts.

We thus have to distinguish between two areas of application for the concept of probability: the observational part, where we build up classes, and the anticipatory part, where we are interested in a match of expectations and actual outcomes. The problem obviously arises by mixing them through the notion of causality.17 Yet, there is absolutely no necessity between the two areas. The concept of risk probably allows for a resolution of the problems, since risk always implies a preceding choice of a cost function, which necessarily is subjective. Yet, the cost function and the risk implied by a classification model is also the angle point for any kind of negotiation, whether this takes place on an material, hence evolutionary scale, or within a societal context.

The interesting, if not salient point is that the subjectively available intensional descriptions and classes are dependent on ones risk attitude. We may observe the same thing only  if we have acquired the same system of related classes and the same habits of using them. Only if we apply extreme risk aversion we will achieve a common understanding about facts (in the Wittgensteinian sense, see above). This then is called science, for instance. Yet, it still remains a misunderstanding to equate this common understanding with objects as objects-out-there.

The problem of induction thus must be considered as a seriously  ill-posed problem. It is a problem only for idealists (who then solve it in a weird way), or realists that are naive against the epistemological conditions of acting in the world. Our proposal for the transition from observations to descriptions is based on probabilism on both sides, yet, on either side there is a distinct flavor of probabilism.

Finally, a methodological remark shall be allowed, closely related to what we already described in the section about “noise” above. The perspective onto “making experience” that we have been proposing here demonstrates a significant twist.

Above we already mentioned Alan Hájek’s diagnosis that the frequentist and the Bayesian interpretation of probabilities suffer from the reference class problem. In this section we extended Hájek’s concerns to the concept of propensity. Yet, if the problem shows a high prevalence we should not conceive it as a hurdle but should try to treat it dynamically as a rule.The reference class is only a problem as long as (1) either the actual class is required as an external constant, or (2) the abstract concept of the class is treated as a fixed point. According to the rule of Lagrange-Deleuze, any constant can be rewritten into a procedure (read: rules) and less problematic constants. Constants, or fixed points on a higher abstract level are less problematic, because the empirically grounded semantics vanishes.

Indeed, the problem of the reference class simply disappears if we put the concept of the class, together with all the related issues of modeling, as the embedding frame, the condition under which any notion of probability only can make sense at all. The classes itself are results of “rule-following”, which  admittedly is blind, but whose parameters are also transparently accessible. In this way, probabilistic interpretation is always performed in a universe, that is closed and in principle fully mapped. We need the probabilistic methods just because that universe is of a huge size. In other words, the space of models is a Laplacean Universe.

Since statistical methods and similar interpretations of probability are analytical techniques, our proposal for a re-positioning of statistics into such a Laplacean Universe is also well aligned with the general habit of Wittgenstein’s philosophy, which puts practiced logic (quasi-logic) second to performance.

The disappearance of the reference class problem should be expected if our relations to the world are always mediated through the activity with abstract, epistemic modeling. The usage of probability theory as a “conceptual game” aiming for sharing diverging attitudes towards risks appears as nothing else than just a particular style of modeling, though admittedly one that offers a reasonable rate of success.

The Result of Modeling

It should be clear by now, that the result of modeling is much more than just a single predictive model. Regardless whether we take the scientific perspective or a philosophical vantage point, we need to include operationalizations of the conditions of the model, that reach beyond the standard empirical risk expressed as “false classification”. Appropriate modeling provides not only a set of models with well-estimated stability and of different structures; a further goal is to establish models that are auto-consistent.

If the modeling employs a method that exposes its parameters, we even can avoid the „method hell“, that is, the results are not only reliable, they are also valid.

It is clear that only auto-consistent models are useful for drawing conclusions and in building up experience. If variables are just weighted without actually being removed, as for instance in approaches like the Support Vector Machines, the resulting methods are not auto-consistent. Hence, there is no way towards a propositional description of the observed process.

Given the population of explicitly tested models it is also possible to describe the differential contribution of any variable to the predictive power of a model. The assumption of neutrality or symmetry of that contribution, as it is for instance applied in statistical learning, is a simplistic perspective onto the variables and the system represented by them.

Conclusion

In this essay we described some technical aspects of the capability to experience. These technical aspects link the possibility for experience to the primacy of interpretation that gets actualized as the techné of anticipatory, i.e. predictive or diagnostic modeling. This techné does not address the creation or derivation of a particular model by means of employing one or several methods. The process of building a model could be fully automated anyway. Quite differently, it focuses the parametrization, validation, evaluation and application of models, particularly with respect to the task of extract a rule from observational data. This extraction of rules must not be conceived as a “drawing of conclusions” guided by logic. It is a constructive activity.

The salient topics in this practice are the selection of models and the description of the classifiers. We emphasized that the goal of modeling should not be conceived as the task of finding a single best model.

Methods like the Self-organizing Map which are based on sub-group segmentation of the data can be used to create auto-consistent models, which represent also an optimally de-noised subset of the measured data. This data sample could be conceived as if it would have been found by a factorial experimental design. Thus, auto-consistent models also provide quite valuable hints for the setup of the Taguchi method of quality assurance, which could be seen as a precipitation of organizational experience.

In the context of exploratory investigation of observational data one first has to determine the suitable observables (variables, predictors) and, by means of the same model(s), the suitable segment of observations before drawing domain-specific conclusions. Such conclusions are often expressed as contrasts in location or variation. In the context of designed experiments as e.g. in pharmaceutical research one first has to check the quality of the data, then to de-noise the data by removing outliers by means of the same data segmentation technique, before again null hypotheses about expected contrasts could be tested.

As such, auto-consistent models provide a perfect basis for learning and for extending the “experience” of an epistemic individual. According to our proposals this experience does not suffer from the various problems of traditional Humean empirism (the induction problem), or contemporary (defective) theories of probabilism (mainly the problem of reference classes). Nevertheless, our approach remains fully empirico-epistemological.

Notes

1. As many other philosophers Lyotard emphasized the indisputability of an attention for the incidential, not as a perception-as, but as an aisthesis, as a forming impression. see: Dieter Mersch, ›Geschieht es?‹ Ereignisdenken bei Derrida und Lyotard. available online, last accessed May 1st, 2012. Another recent source arguing into the same direction is John McDowell’s “Mind and World” (1996).

2. The label “representationalism” has been used by Dreyfus in his critique of symbolic AI, the thesis of the “computational mind” and any similar approach that assumes (1) that the meaning of symbols is given by their reference to objects, and (2) that this meaning is independent of actual thoughts, see also [2].

3. It would be inadequate to represent such a two-fold “almost” dichotomy as a 2-axis coordinate system, even if such a representation would be a metaphorical one only; rather, it should be conceived as a tetraedic space, given by two vectors passing nearby without intersecting each other. Additionally, the structure of that space must not expected to be flat, it looks much more like an inhomogeneous hyperbolic space.

4. “Experiencibility” here not understood as an individual capability to witness or receptivity, but as the abstract possibility to experience.

5. In the same way we reject Husserl’s phenomenology. Phenomena, much like the objects of positivism or the thing-as-such of idealism, are not “out there”, they are result of our experiencibility. Of course, we do not deny that there is a materiality that is independent from our epistemic acts, but that does not explain or describe anything. In other words we propose go subjective (see also [3]).

6. Again, mechanism here should not be misunderstood as a single deterministic process as it could be represented by a (trivial) machine.

7. This question refers to the famous passage in the Tractatus, that “The world is everything that is the case.“ Cases, in the terminology of the Tractatus, are facts as the existence of states of affairs. We may say, there are certain relations. In the Tractatus, Wittgenstein excluded relations that could not be explicated by the use of symbols., expressed by the 7th proposition: „Whereof one cannot speak, thereof one must be silent.“

8. We must step outside of language in order to see the working of language.

9. We just have to repeat it again, since many people develop misunderstandings here. We do not deny the material aspects of the world.

10. “individual” is quite misleading here, since our brain and even our mind is not in-divisable in the atomistic sense.

11. thus, it is also not reasonable to claim the existence of a somehow dualistic language, one part being without ambiguities and vagueness, the other one establishing ambiguity deliberately by means of metaphors. Lakoff & Johnson started from a similar idea, yet they developed it into a direction that is fundamentally incompatible with our views in many ways.

12. Of course, the borders are not well defined here.

13. “predictive power” could be operationalized in quite different ways, of course….

14. Correlational analysis is not a candidate to resolve this problem, since it can’t be used to segment the data or to identify groups in the data. Correlational analysis should be performed only subsequent to a segmentation of the data.

15. The so-called genetic algorithms are not algorithms in the narrow sense, since there is no well-defined stopping rule.

16. It is important to recognize that Artificial Neural Networks are NOT belonging to the family of sub-group based methods.

17. Here another circle closes: the concept of causality can’t be used in a meaningful way without considering its close amalgamation with the concept of information, as we argued here. For this reason, Judea Pearl’s approach towards causality [16] is seriously defective, because he completely neglects the epistemic issue of information.

References
  • [1] Geoffrey C. Bowker, Susan Leigh Star. Sorting Things Out: Classification and Its Consequences. MIT Press, Boston 1999.
  • [2] Willian Croft, Esther J. Wood, Construal operations in linguistics and artificial intelligence. in: Liliana Albertazzi (ed.) , Meaning and Cognition. Benjamins Publ, Amsterdam 2000.
  • [3] Wilhelm Vossenkuhl. Solipsismus und Sprachkritik. Beiträge zu Wittgenstein. Parerga, Berlin 2009.
  • [4] Douglas Hofstadter, Fluid Concepts And Creative Analogies: Computer Models Of The Fundamental Mechanisms Of Thought. Basic Books, New York 1996.
  • [5] Nicholas F. Gier, Wittgenstein and Deconstruction, Review of Contemporary Philosophy 6 (2007); first publ. in Nov 1989. Online available.
  • [6] Henk L. Mulder, B.F.B. van de Velde-Schlick (eds.), Moritz Schlick, Philosophical Papers, Volume II: (1925-1936), Series: Vienna Circle Collection, Vol. 11b, Springer, Berlin New York 1979. with Google Books
  • [7] Tomaso Poggio, Ryan Rifkin, Sayan Mukherjee & Partha Niyogi (2004). General conditions for predictivity in learning theory. Nature 428, 419-422.
  • [8]  Vladimir Vapnik, The Nature of Statistical Learning Theory (Information Science and Statistics). Springer 2000.
  • [9] Herman J. Bierens (2006). Information Criteria and Model Selection. Lecture notes, mimeo, Pennsylvania State University. available online.
  • [10 ]Brian Weatherson (2007). The Bayesian and the Dogmatist. Aristotelian Society Vol.107, Issue 1pt2, 169–185. draft available online
  • [11] Edward I. George (2000). The Variable Selection Problem. J Am Stat Assoc, Vol. 95 (452), pp. 1304-1308. available online, as research paper.
  • [12] Alan Hájek (2007). The Reference Class Problem is Your Problem Too. Synthese 156(3): 563-585. draft available online.
  • [13] Lori E. Dodd, Margaret S. Pepe (2003). Partial AUC Estimation and Regression. Biometrics 59( 3), 614–623.
  • [14] Zytkov J. (1997). Knowledge=concepts: a harmful equation. 3rd Conference on Knowledge Discovery in Databases, Proceedings of KDD-97, p.104-109.AAAI Press.
  • [15] Thomas Kaufmann, Klaus Wassermann, Guido Schüpfer (2007).  Beta error free risk identification based on SPELA, a neuro-evolution method. presented at ESA 2007.
  • [16] Alan Hájek, “Interpretations of Probability”, The Stanford Encyclopedia of Philosophy (Summer 2012 Edition), Edward N. Zalta (ed.), available online, or forthcoming.
  • [17] Judea Pearl, Causality – Models, Reasoning, and Inference. 2nd ed. Cambridge University Press, Cambridge  (Mass.) 2008 [2000].

۞

Elementarization and Expressibility

March 12, 2012 § Leave a comment

Since the beginnings of the intellectual adventure

that we know as philosophy, elements take a particular and prominent role. For us, as we live as “post-particularists,” the concept of element seems to be not only a familiar one, but also a simple, almost a primitive one. One may take this as the aftermath of the ontological dogma of the four (or five) elements and its early dismissal by Aristotle.

In fact, I think that the concept element is seriously undervalued and hence it is left disregarded much too often, especially as far as one concerns it as a structural tool in the task to organize thinking. The purpose of this chapter is thus to reconstruct the concept of “element” in an adequate manner (at least, to provide some first steps of such a reconstruction). To achieve that we have to take tree steps.

First, we will try to shed some light on its relevance as a more complete concept. In order to achieve this we will briefly visit the “origins” of the concept in (pre-)classic Greek philosophy. After browsing quickly through some prominent examples, the second part then will deal with the concept of element as a thinking technique. For that purpose we strip the ontological part of it (what else?), and turn it into an activity, a technique, and ultimately into a “game of languagability,” called straightforwardly “elementarization.”

This will forward us then to the third part, which will deal with problematics of expression and expressibility, or more precisely, to the problematics of how to talk about expression and expressibility. Undeniably, creativity is breaking (into) new grounds, and this aspect of breaking pre-existing borders also implies new ways of expressing things. To get clear about creativity thus requires to get clear about expressibility in advance.

The remainder of this essay revolves is arranged by the following sections (active links):

The Roots1

As many other concepts too, the concept of “element” first appeared in classic Greek culture. As a concept, the element, Greek “stoicheion”, in greek letters ΣΤΟΙΧΕΙΟΝ, is quite unique because it is a synthetic concept, without predecessors in common language. The context of its appearance is the popularization of the sundial by Anaximander around 590 B.C. Sundials have been known before, but it was quite laborious to create them since they required a so-called skaphe, a hollow sphere as the projection site of the gnomon’s shadow.

Figure 1a,b.  Left (a): A sundial in its ancient (primary) form based on a skaphe, which allowed for equidistant segmentation , Right (b): the planar projection involves hyperbolas and complicated segmentation.

The planar projection promised a much more easier implementation, yet, it involves the handling of hyperbolas, which even change relative to the earth’s seasonal inclination. Else, the hours can’t be indicated by an equidistant segments any more. Such, the mathematical complexity has been beyond the capabilities of that time. The idea (presumably of Anaximander) then was to determine the points for the hours empirically, using “local” time (measured by water clocks) as a reference.

Anaximander also got aware of the particular status of a single point in such a non-trivial “series”. It can’t be thought without reference to the whole series, and additionally, there was no simple rule which would have been allowing for its easy reconstruction. This particular status he called an “element”, a stoicheia (pronunciation). Anaximander’s element is best understood as a constitutive component, a building block for the purpose to build a series; note the instrumental twist in his conceptualization.

From this starting point, the concept has been generalized in its further career, soon denoting something like “basics,” or “basic principles”. While Empedokles conceived the four elements, earth, wind, water and fire almost as divine entities, it was Platon (Timaios 201, Theaitet 48B) who developed the more abstract perspective into “elements as basic principles.”

Yet, the road of abstraction does not know a well-defined destiny. Platon himself introduced the notion of “element of recognition and proofing” for stoicheia. Isokrates, then, a famous rhetorician and coeval of Platon extended the reach of stoicheia from “basic component / principle” into “basic condition.” This turn is quite significant since as a consequence it inverts the structure of argumentation from idealistic, positive definite claims to the constraints of such claims; it even opens the perspective to the “condition of possibility”, a concept that is one of the cornerstones of Kantian philosophy, more than 2000 years later. No wonder, Isokrates is said to have opposed Platon’s  arguments.

Nevertheless, all these philosophical uses of stoicheia, the elements, have been used as ontological principles in the context of the enigma of the absolute origin of all things and the search for it. This is all the more particularly remarkable as the concept itself has been constructed some 150 years before in a purely instrumental manner.

Aristotle dramatically changed the ontological perspective. He dismissed the “analysis based on elements” completely and established what is now known as “analysis of moments”, to which the concepts of “form” and “substance” are central. Since Aristotle, elemental analysis regarded as a perspective heading towards “particularization”, while the analysis of moments is believed to be directed to generalization. Elemental analysis and ontology is considered as being somewhat “primitive,” probably due to its (historic) neighborhood to the dogma of the four elements.

True, the dualism made from form and substance is more abstract and more general. Yet, as concept it looses contact not only to the empiric world as it completely devoid of processual aspects. It is also quite difficult, if not impossible, to think “substance” in a non-ontological manner. It seems as if that dualism abolishes even the possibility to think in a different manner than as ontology, hence implying a whole range of severe blind spots: the primacy of interpretation, the deeply processual, event-like character of the “world” (the primacy of “process” against “being”), the communal aspects of human lifeforms and its creational power, the issue of localized transcendence are just the most salient issues that are rendered invisible in the perspective of ontology.

Much more could be said of course about the history of those concepts. Of course, Aristotle’s introduction of the concept of substance is definitely not without its own problems, paving the way for the (overly) pronounced materialism of our days. And there is, of course, the “Elements of Geometry” by Euclid, the most abundant mathematical textbook ever. Yet, I am neither a historian nor a philologus, thus let us now proceed with some examples. I just would like to emphasize that the “element” can be conceived as a structural topos of thinking starting from the earliest witnesses of historical time.

2. Examples

Think about the chemical elements as they have been invented in the 19th century. Chemical compounds, so the parlance of chemists goes, are made from chemical elements, which have been typicized by Mendeleev according to the valence electrons and then arranged into the famous “periodic table.” Mendeleev not only constructed a quality according to which various elements could be distinguished. His “basic principle” allowed him to make qualitative and quantitative predictions of an astonishing accuracy. He predicted the existence of chemical elements, “nature’s substance”, actually unknown so far, along with their physico-chemical qualities. Since it was in the context of natural science, he also could validate that. Without the concept of those (chemical) elements the (chemical) compounds can’t be properly understood. Today a similar development can be observed within the standard theory of particle physics, where basic types of particles are conceived as elements analogous to chemical elements, just that in particle physics the descriptive level is a different one.

Here we have to draw a quite important distinction. The element in Mendeleev’s thinking is not equal to the element as the chemical elements. Mendeleev’s elements are (i) the discrete number (an integer between 1..7, and 0/8 for the noble gases like Argon etc.) that describes the free electron as a representative of electrostatic forces, and (ii) the concept of “completeness” of the set of electrons in the so-called outer shell (or “orbitals”): the number of the valence electrons of two different chemical elements tend to sum up to eight. Actually, chemical elements can be sorted into groups (gases, different kinds of metals, carbon and silicon) according to the mechanism how they achieve this magic number (or how they don’t). As a result, there is a certain kind of combinatorianism, the chemical universe is almost a Lullian-Leibnizian one. Anyway, the important point here is that the chemical elements are only a consequence of a completely different figure of thought.

Still within in chemistry, there is another famous, albeit less well-known example for abstract “basic principles”: Kekulé’s de-localized valence electrons in carbon compounds (in today’s notion: delocalized 6-π-electrons). Actually, Kekulé added the “element” of the indeterminateness to the element of the valence electron. He dropped the idea of a stable state that could be expressed by a numerical value, or even by an integer. His 6-π-orbital is a cloud that could not be measured directly as such. Today, it is easy to see that the whole area of organic chemistry is based on, or even defined by, these conceptual elements.

Another example is provided by “The Elements of Geometry” by Euclid. He called it “elements” probably for mainly two reasons. First, it was supposed that it was complete, secondly, because you could not remove any of the axioms, procedures, proofs or lines of arguments, i.e. any of its elements, without corroborating the compound concept “geometry.”

A further example from the classic is the conceptual (re-)construction of causality by Aristotle. He obviously understood that it is not appropriate to take causality as an impartible entity. Aristotle designed his idea of causality as an irreducible combination of four distinct elements, causa materialis, causa formalis, causa efficiens and causa finalis. To render this a bit more palpable, think about inflaming a wooden stick and then being asked: What is the cause for the stick being burning?

Even if I would put (causa efficiens) a wooden (causa materialis) stick (causa formalis) above an open flame (part of causa efficiens), it will not necessarily be inflamed until I decide that it should (causa finalis). This is a quite interesting structure, since it could be conceived as a precursor of the Wittgensteinian perspective of a language game.

For Aristotle it made no sense to assume that any of the elements of his causality as he conceived it would be independent from any of the others. For him it would have been nonsense to conceive of causality as any subset of his four elements. Nevertheless, exactly this was what physics did since Newton. In our culture, causality is almost always debated as if it would be identical to causa efficiens. In Newton’s words: Actioni contrariam semper et aequalem esse reactionem. [2] Later, this postulate of actio = reactio has been backed by further foundational work through larger physical theories postulating the homogeneity of physical space. Despite the success of physics, the reduction of causality to physical forces remains just that: a reduction. Applying this principle then again to any event in the world generates specific deficits, which are well visible in large parts of contemporary philosophy of science when it comes to the debate about the relation of natural science and causality (see cf. [3]).

Aristotle himself did not call the components of causality as “elements.” Yet, the technique he applied is just that: an elementarization. This technique was quite popular and well known from another discourse, involving earth, water, air, and fire. Finally, this model had to be abolished, but it is quite likely that the idea of the “element” has been inherited down to Mendeleev.

Characterizing the Concept of “Element”

As we have announced it before, we would like to strip any ontological flavor from the concept of the element. This marks the difference between conceiving them as part of the world or, alternatively, as a part of a tool-set used in the process of constructing a world. This means to take it purely instrumental, or in other words, as a language game. Such, it is also one out of the row of many examples for the necessity to remove any content from philosophy (Ontology is always claiming some kind of such content, which is highly problematical).

A major structural component of the language game “element” is that the entities denoted by it are used as anchors for a particular non-primitive compound quality, i.e. a quality that can’t be perceived by just the natural five (or six, or so) senses.

One the other hand, they are also strictly different from axioms. An axiom is a primitive proposition that serves as a starting point in a formal framework, such as mathematics. The intention behind the construction of axioms is to utilize common sense as a basis for more complicated reasoning. Axioms are considered as facts that could not seriously disputed as such. Thus, they indeed the main element in the attempt to secure mathematics as a unbroken chain of logic-based reasoning. Of course, the selection of a particular axiom for a particular purpose could always be discussed. But itself, it is a “primitive”, either a simple more or less empiric fact, or a simple mathematical definition.

The difference to elements is profound. One always can remove a single axiom from an axiomatic system without corroborating the sense of the latter. Take for instance the axiom of associativity in group theory, which leads to Lie-groups and Lie-algebras. Klein groups are just a special case of Lie Groups. Or, removing the “axiom” of parallel lines from the Euclidean axioms brings us to more general notions of geometry.

In contrast to that pattern, removing an element from an elemental system destroys the sense of the system. Elemental systems are primarily thought as a whole, as a non-decomposable thing, and any of the used elements is synthetically effective. Their actual meaning is only given by being a part of a composition with other elements. Axioms, in contrast, are parts of decomposable systems, where they act as constraints. Removing them leads usually to improved generality. The axioms that build an “axiomatic system” are not tied to each other, they are independent as such. Of course, their interaction always will create a particular conditionability, but that is a secondary effect.

The synthetic activity of elements simply mirrors the assumption that there is (i) a particular irreducible whole, and (ii) that the parts of that whole have a particular relationship to the embedding whole. In contrast to the prejudice that elemental analysis results in an unsuitable particularization of the subject matter, I think that elements are highly integrated, yet itself non-decomposable idealizations of compound structures. This is true for the quaternium of earth, wind, water and fire, but also for the valence electrons in chemistry or the elements of complexity, as we have introduced them here. Elements are made from concepts, while axioms are made from definitions.

In some way, elements can be conceived as the operationalization of beliefs. Take a belief, symbolize it and you get an element. From this perspective it again becomes obvious (on a second route) that elements could not be as something natural or even ontological; they can not be discovered as such in a pure or stable form. They can’t be used to proof propositions in a formal system, but they are indispensable to explain or establish the possibility of thinking a whole.

Mechanism and organism are just different terms that can be used to talk about the same issue, albeit in a less abstract manner. Yet, it is clear that integrated phenomena like “complexity,” or “culture,” or even “text” can’t be appropriately handled without the structural topos of the element, regardless which specific elements are actually chosen. In any of these cases it is a particular relation between the parts and the whole that is essential for the respective phenomenon as such.

If we accept the perspective that conceives of  elements as stabilized beliefs we may recognize that they may be used as building blocks for the construction of a consistent world. Indeed, we well may say that it is due to their properties as described above, their positioning between belief and axiom, that we can use them as an initial scaffold (Gestell), which in turn provides the possibility for targeted observation, and thus for consistency, understood both as substance and as logical quality.

Finally, we should shed some words on the relation between elements and ideas. Elsewhere, we distinguished ideas from concepts. Ideas can’t be equated with elements either. Just the other way round, elements may contain ideas, but also concepts, relations and systems thereof, empirical hypotheses or formal definitions. Elements are, however, always immaterial, even in the case of chemistry. For us, elements are immaterial synthetic compounds used as interdependent building blocks of other immaterial things like concepts, rules, or hypotheses.

Many, if not all concepts, are built from elements in a similar way. The important issue is that elements are synthetic compounds which are used to establish further compounds in a particular manner. In the beginning there need not to be any kind of apriori justification for a particular choice or design. The only requirement is that the compound built from them allows for some kind of beneficial usage in creating higher integrated compounds which would not be achievable without them.

4. Expressibility

Elements may well be conceived as epistemological stepping stones, capsules of belief that we use to build up beliefs. Such, the status of elements is somewhere between models and concepts, not as formal and restricted as models and not as transcendental as concepts, yet still with much stronger ties towards empiric conditions than ideas.

It is quite obvious that such a status reflects a prominent role for perception as well as for understanding. The element may well be conceived as an active zone of differentiation, a zone from which different kind of branches emerge: ideas, models, concepts, words, beliefs. We also could say that elements are close to the effects and the emergence of immanence. The ΣΤΟΙΧΕΙΟΝ itself, its origins and transformations, may count as an epitome of this zone, where thinking creates its objects. It is “here” that expressibility finds its conditions.

At that point we should recall – and keep in mind – that elements should not be conceived as an ontological category. Elements unfold as (rather than “are”) a figure of thought, an idiom of thinking, as a figure for thought. Of course, we can deliberately visit this area, we may develop certain styles to navigate in this (sometimes) misty areas. In other words, we may develop a culture of elementarization. Sadly enough, positivism, which emerged from the materialism of the 19th century on the line from Auguste Comte down to Frege, Husserl, Schlick, Carnap and van Fraassen (among others), that positivism indeed destroyed much of that style. In my opinion, much of the inventiveness of the 19th century could be attributed a certain, yet largely unconscious, attitude towards the topos of the “element.”

No question, elevating the topos of the element into consciousness, as a deliberate means of thinking, is quite promising. Hence, it is also of some importance to our question of machine-based episteme. We may just add a further twist to this overarching topic by asking about the mechanisms and conditions that are needed for the possibility of “elementarization”. Still in other words we could say that elements are the main element of creativity. And we may add that the issue of expression and expressibility is not about words and texts, albeit texts and words potentiated the dynamics and the density of expressibility.

Before we can step on to harvest the power of elementarization we have to spend some efforts on the issue of the structure of expression. The first question is: What exactly happens if we invent and impose an element in and to our thoughts? The second salient question is about the process forming the element itself. Is the “element” just a phenomenological descriptional parlance, or is it possible to give some mechanisms for it?

Spaces and Dimensions

As it is already demonstrated by Anaximander’s ΣΤΟΙΧΕΙΟΝ, elements put marks into the void. The “element game” introduces discernability, and it is central to the topos of the element that it implies a whole, an irreducible set, of which it is a constitutive part. This way, elements don’t act just sign posts that would indicate a direction in an already existing landscape. It is more appropriate to conceive of them as a generators of landscape. Even before words, whether spoken or written, elements are the basic instance of externalization, abstract writing, so to speak.

It is the abstract topos of elements that introduce the complexities around territorialization and deterritorialization into thought, a dynamics that never can come to an end. Yet, let us focus here on the generative capacities of elements.

Elements transform existing spaces or create completely new ones, they represent the condition for the possibility of expressing anything. The implications are rather strong. Looking back from that conditioning to the topos itself we may recognize that wherever there is some kind of expression, there is also a germination zone of ideas, concepts and models, and above all, belief.

The space implied by elements is particular one yet, due to the fact that it inherits the aprioris of the wholeness and non-decomposability. Non-decomposability means that the elemental space looses essential qualities if one of the constituting elements would be removed.

This may be contrasted to the Cartesian space, the generalized Euclidean space, which is the prevailing concept of space today. A Cartesian space is spanned by dimensions that are set orthogonal to each other. This orthogonality of the dimensional setup allows to change the position in just one dimension, but to keep the position in all the other dimensions unchanged, constant. The dimensions are independent from each other. Additionally, the quality of the space itself does not change if we remove one of the dimensions of a n-dimensional Cartesian space (n>1). Thus, the Cartesian space is decomposable.

Spaces are inevitably implied as soon as entities are conceived as carriers of properties, in fact, even if at least one (“1”!) property will be assigned to them. These assigned properties, or short: assignates, then could be mapped to different dimensions. A particular entity thus becomes visible as a particular arrangement in the implied space. In case of Cartesian spaces, this arrangement consists of a sheaf of vectors, which is as specific for the mapped entity as it could be desired.

Dimensions may refer to sensory modalities, to philosophical qualias, or to constructed properties of development in time, that is, concepts like frequency, density, or any kind of pattern. Dimensions may be even purely abstract, as in case of random vectors or random graphs, which we discussed here, where the assignate refers to some arbitrary probability or structural, method specific parameter.

Many phenomena remain completely mysterious if we do not succeed to setup the (approximately) right number of dimensions or aspects. This has been famously demonstrated by Abbott and his flatland [4], or by Ian Stewart and his flatter land [5]. Other examples are the so-called embedding dimension in the complex systems analysis, or the analysis of (mathematical) cusp catastrophes by Ian Stewart [6]. Dimensionality also plays an important role in the philosophy of science, where Ronald Giere uses it to develop a “scientific perspectivism.” [7]

Suppose the example of a cloud of points in the 3‑dimensional space, which forms a spiral-like shape, with the main axis of the shape parallel to the z-axis. For points in the upper half of the cloudy spiral there shall be a high probability that they are blue; those in the lower half shall be mostly red. In other words, there is a clear pattern. If we now project the points to the x-y-plane, i.e. if we reduce dimensionality we loose the possibility to recognize the pattern. Yet, the conclusion that there “is” no pattern is utterly wrong. The selection of a particular number of dimensions is a rather critical operation. Hence, taking action without reflecting on the dimensionality of the space of expressibility quite likely leads to severe misinterpretations. The cover of Douglas Hofstadter’s first book “Gödel, Escher, Bach” featured a demonstration of the effect of projection from higher to lower dimensionality (see the image below), another presentation can be found here on YouTube, featuring Carl Sagan on the topic of dimensionality.

In mathematics, the relation between two spaces of different dimensionality, the so-called manifold, may itself form an abstract space. This exercise of checking out the consequences of removing or adding a dimension/aspect from the space of expressibility is a rewarding game even in everyday life. In the case of fractals in time series developments, Mandelbrot conceptualizes even a changing dimensionality of the space which is used to embed the observations over time.

Undeniably, this decomposability contributed much to the rise and the success of what we call modern science. Any of the spaces of mathematics or statistics is a Cartesian space. Riemann space, Hilbert space, Banach space, topological spaces etc. are all Cartesian insofar as the dimensions are arranged orthogonal to each other, thus introducing independence of elements before any other definition. Though, the real revolutionary contribution of Descartes has not been the setup of independent dimensions, it is the “Copernican” move to move the “origin” around, and with that, to mobilize the reference system of a particular measurement.

But again: By performing this mapping, the wholeness of the entity will be lost. Any interpretation of the entities requires a point outside of the Cartesian dimensional system. And precisely this externalized position is not possible for an entity that itself “performs cognitive processes.”2 It would be quite interesting to investigate the epistemic role of externalization of mental affairs through cultural techniques like words, symbols, or computers, yet that task would be huge.

Despite the success of the Cartesian space as a methodological approach it obviously also remains true that there is no free lunch in the realm of methods and mappings. In case of the Cartesian space this cost is as huge as its benefit, as both are linked to its decomposability. In Cartesian space it is not possible to speak about a whole, whole entities are simply nonexistent. This is indeed as dramatic as it sounds.Yet, it is a direct consequence of the independence of the dimensions. There is nothing in the structure of the Cartesian space that could be utilized as a kind of media to establish coherence. We already emphasized that the structure of the Cartesian space implies the necessity of an external observer. This, however, is not quite surprising for a construction devised by Descartes in the age of absolutistic monarchies symbiontically tied to catholicism, where the idea of the machine had been applied pervasively to anything and everything.

There are still  further assumptions underlying the Cartesian conception of space. Probably the two most salient ones are concerning density and homogeneity. At first it might sound somewhat crazy to conceive of a space of inhomogeneous dimensionality. Such a space would have “holes” about which one could neither talk from within that space not would they be recognizable. Yet, from theoretical physics we know about the concept of wormholes, which precisely represent such inhomogeneity. Nevertheless, the “accessible” parts of such a space would remain Cartesian, so we could call the whole entity “weakly Cartesian”. A famous example is provided by Benoît Mandelbrot’s warping of dimensionality in the time domain of observations [8,9]

From an epistemological perspective, the Cartesian space is just a particular instance for the standardization or even institutionalization of the inevitable implication of spaces. Yet, the epistemic spaces are not just 3-dimensional as Kant assumed in his investigation, epistemic spaces may comprise a large and even variable number of dimensions. Nevertheless, Kant was right about the transcendental character of space, though the space we refer to here is not just the 3d- or (n)d-physical space.

Despite the success of Cartesian space, which builds on the elements of separability, decomposability and externalizable position of the interpreter, it is perfectly clear that it is nothing else than just a particular way of dealing with spaces. There are many empirical, cognitive or mental contexts for which the assumptions underlying the Cartesian space are severely violated. Such contexts usually involve the wholeness of the investigated entity as a necessary apriori. Think of complexity, language, the concept of life forms with its representatives like urban cultures, for any of these domains the status of any part of it can’t be qualified in any reasonable manner without referring always to the embedding wholeness.

The Aspectional Space

What we need is a more general concept of space, which does not start with any assumption about decomposability (or its refutation). Since it is always possible to proof and to drop the assumption of dependence (non-decomposability), but never for the assumption of independence (decomposability) we should start with a concept of space which keeps the wholeness intact.

Actually, it is not too difficult to start with a construction of such a space. The starting point is provided by a method to visualize data, the so-called ternary diagram. Particularly in metallurgy and geology ternary diagrams are abundantly in use for the purpose of expressing mixing proportions. The following figure 2a shows a general diagram for three components A,B,C, and Figure 2b shows a concrete diagram for a three component steel alloy at 900°C.

Figure 2a,b: Ternary diagrams in metallurgy and geology are pre-cursors of aspectional spaces.

Such ternary diagrams are used to express the relation between different phases where the influential components all influence each other. Note that the area of the triangle in such a ternary diagram comprises the whole universe as it is implied by the components. However, in principle it is still possible (though not overly elegant) to map the ternary diagram as it is used in geology into Cartesian space, because there is a strongly standardized way about how to map values. Any triple of values (a,b,c) is mapped to the axes A,B,C such that these axes are served counter-clockwise beginning with A. Without that rule a unique mapping of single points from the ternary space to the Cartesian space would not be possible any more. Thus we can see that the ternary diagram does not introduce a fundamental difference as compared to the Cartesian space defined by orthogonal axes.

Now let us drop this standard of the arrangement of axes. None of the axes should be primary against any other. Obviously, the resulting space is completely different from the spaces shown in Fig.2. We can keep only one of n dimensions constant while changing position in this space (by moving along an arc around one of the corners). Compare this to the Cartesian space, where it is possible to change just one and keep the other constant. For this reason we should call the boundaries of such a space not “axes” or “dimensions” and more. By convention, we may call the scaling entities “aspection“, derived from “aspect,” a concept that, similarly to the concept of element, indicates the non-decomposability of the embedding context.

As said, our space that we are going to construct for a mapping of elements can’t be transformed into a Cartesian space any more. It is an “aspectional space”, not a dimensional space. Of course, the aspectional space, together with the introduction of “aspections” as a companion concept for “dimension” is not just a Glass Bead Game. We urgently need it if we want to talk transparently and probably even quantitatively about the relation between parts and wholes in a way that keeps the dependency relations alive.

The requirement of keeping the dependency relations exerts an interesting consequence. It renders the corner points into singular points, or more precisely, into poles, as the underlying apriori assumption is just the irreducibility of the space. In contrast to the ternary diagram (which is thus still Cartesian) the aspectional space is neither defined at the corner points nor along the borders (“edges”). In  other words, the aspectional space has no border, despite the fact that its volume appears to be limited. Since it would be somehow artificial to exclude the edges and corners by dedicated rules we prefer to achieve the same effect (of exclusion) by choosing a particular structure of the space itself. For that purpose, it is quite straightforward to provide the aspectional space with a hyperbolic structure.

The artist M.C. Escher produced a small variety of confined hyperbolic disks that perfectly represent the structure of our aspectional space. Note that there are no “aspects,” it is a zero-aspectional space. Remember that the 0-dimensional mathematical point represents a number in Cartesian space. This way we even invented a new class of numbers!3 A value in this class of number would (probably) represent the structure of the space, in other words the curvature of the hyperbola underlying the scaling of the space. Yet, the whole mathematics around this space and these numbers is undiscovered!

Figure 3: M.C. Eschers hyperbolic disk, capturing infinity on the table.

Above we said that this space appears to be limited. This impression of a limitation would hold only for external observers. Yet, our interest in aspectional spaces is precisely given by the apriori assumption of non-decomposability and the impossibility of such an external position for cognitive activities. Aspectional spaces are suitable just for those cases where such an external position is not available. From within such a hyperbolic space, the limitation would not be experiencable, a at least not by simple means: the propagation of waves would be different as compared to the Cartesian space.

Aspections, Dimensions

So, what is the status of the aspectional space, especially as compared to the dimensional Cartesian space? A first step of such a characterization would investigate the possibility of transforming those spaces into each other. A second part would not address the space itself, but its capability to do some things uniquely.

So, let us start with the first issue, the possibility for a transition between the two types of species. Think of a three-aspectional space. The space is given by the triangularized relation, where the corners represent the intensity or relevance of a certain aspect. Moving around on this plane changes the distance to at least two (n-1) of the corners, but most moves change the distance to all three of the corners. Now, if we reduce the conceptual difference and/or the possible difference of intensity between all of the three corners we experience a sudden change of the quality of the aspectional space when we perform the limes transition into a state where all differential relevance has been expelled; the aspects would behave perfectly collinear.

Of course, we then would drop the possibility for dependence, claiming independence as a universal property, resulting in a jump into Cartesian space. Notably, there is no way back from the dimensional Cartesian space into aspectional spaces. Interestingly, there is a transformation of the aspectional space which produces a Cartesian space, while the opposite is not possible.

This formal exercise sheds an interesting light to the life form of the 17th century Descartes. Indeed, even in assuming the possibility of dependence one would grant parts of the world autonomy, something that has been categorically ruled out at those times. The idea of God as it was abundant then implied the mechanical character of the world.

Anyway, we can conclude that aspectional spaces are more general than Cartesian spaces as there is a transition only in one direction. Aspectional spaces are indeed formal spaces as Cartesian spaces are. It is possible to define negative numbers, and it is possible to provide them with different metrices or topologies.

Figure 4: From aspectional space to dimensional space in 5 steps. Descartes’ “origin” turns out to be nothing else than the abolishment or conflation of elements, which again could be interpreted as a strongly metaphysically influenced choice.

Now to the second aspect about the kinship between aspections and dimensions. One may wonder, whether the kind of dependency that could be mapped to aspectional spaces could not be modeled in dimensional spaces as well, for instance, by some functional rule acting on the relation between two dimensions. A simple example would be the regression, but also any analytic function y=f(x).

At first sight it seems that this could result in similar effects. We could, for instance, replace two independent dimensions by a new dimension, which has been synthesized in a rule-based manner, e.g. by applying a classic analytical closed-form function. The dependency would disappear and all dimensions again being orthogonal, i.e. independent to each other. Such an operation, however, would require that the dimensions are already abstract enough such that they can be combined by closed analytical functions. This then reveals that we put the claim of independence already into the considerations before anything else. Claiming the perfect equality of functional mapping of dependency into independence thus is a petitio principii. No wonder we find it possible to do so in a later phase of the analysis. It is thus obvious, that the epistemological state of a dependence secondary to the independence of dimensions is a completely different from the primary dependence.

A brief Example

A telling example4 for such an aspectional space is provided by the city theory of David Grahame Shane [10]. The space created by Shane in order to fit in his interests in a non-reductionist coverage of the complexity of cities represents a powerful city theory, from which various models can be derived. The space is established through the three elements of armature, enclave and (Foucaultian) heterotopia. Armature is, of course a rather general concept–designed to cover more or less straight zones of transmission or the guidance for such–, which however expresses nicely the double role of “things” in a city. It points to things as part of the equipment of a city as well as their role as anchor (points). Armatures, in Shane’s terminology, are things like gates, arcades, malls, boulevards, railways, highway, skyscraper or particular forms of public media, that is, particular forms of passages. Heterotopias, on the other hand, are rather compli­cated “things,” at least it invokes the whole philo­sophi­cal stance of the late Foucault, to whom Shane explicitly refers. For any of these elements, Shane then provides extensions and phenomenological instances, as values if you like, from which he builds a metric for each of the three basic aspects. Through­out his book he demonstrates the usefulness of his approach, which is based on these three elements. This usefulness becomes tangible because Shane’s city theory is an aspectional space of expressibility which allows to compare and to relate an extreme variety of phenomena regarding the city and the urban organization. Of course, we must expect other such spaces in principle; this would not only be interesting, but also a large amount of work to complete. Quite likely, however, it will be a just an extension of Shane’s concept.

5. Conclusion

Freeing the concept of “element” from its ontological burden turns it into a structural topos of thinking. The “element game” is a mandatory condition for the creation of spaces that we need in order to express anything. Hence, the “element game,” or briefly, the operation of “elementarization,” may be regarded as the prime instance of externalization and as such also as the hot spot of the germination of ideas, concepts and words, both abstract and factual. For our concerns here about machine-based episteme it is important that the notion of the element provides an additional (new?) possibility to ask about the mechanism in the formation of thinking.

Elementarization also represents the conditions for “developing” ideas and to “settle” them. Yet, our strictly non-ontological approach helps to avoid premature and final territorialization in thought. Quite to the contrary, if understood as a technique, elementarization helps to open new perspectives.

Elementarization appears as a technique to create spaces of expressibility, even before words and texts. It is thus worthwhile to consider words as representatives of a certain dynamics around processes of elementarization, both as an active as well as a passive structure.

We have been arguing that the notion of space does not automatically determine the space to be a Cartesian space. Elements to not create Cartesian spaces. Their particular reference to the apriori acceptance of an embedding wholeness renders both the elements as well as the space implied by them incompatible with Cartesian space. We introduced the notion of “aspects” in order to reflect to the particular quality of elements. Aspects are the result of a more or less volitional selection and construction.

Aspectional spaces are spaces of mutual dependency between aspects, while Cartesian spaces claim that dimensions are independent from each other. Concerning the handling and usage of spaces, parameters have to be sharply distinguished both from aspects as well as from dimensions. In Mathematics or in natural sciences, parameters are distinguished from variables. Variables are to be understood as containers for all allowed instances of values of a certain dimension. Parameters are modifying just the operation of placing such a value into the coordinate system. In other words, they do not change the general structure of the space used for or established by performing a mapping, and they even do not change the dimensionality of the space itself. For designers as well as scientists, and more general for any person acting with or upon things in the world, it is thus more than naive to play around with parameters without explicating or challenging the underlying space of expressibility, whether this is a Cartesian or an aspectional space. From that it also follows that the estimation of parameters can’t be regarded as an instance of learning.

Here we didn’t mention the mechanisms that could lead to the formation of elements.Yet, it is quite important to understand that we didn’t just shift the problematics of creativity to another descriptional layer, without getting a better grip to it. The topos of the element allows us to develop and to apply a completely different perspective to the “creative act.”

The mechanisms that could be put into charge for generating elements will be the issue of the next chapter. There we will deal with relations and its precursors. We also will briefly return to the topos of comparison.

Part 3: A Pragmatic Start for a Beautiful Pair

Part 5: Relations and Symmetries (forthcoming)

Notes

1. Most of the classic items presented here I have taken from Wilhelm Schwabe’s superb work about the ΣΤΟΙΧΕΙΟΝ [1], in latin letters “stoicheion.”

2. The external viewpoint has been recognized as an unavailable desire already by Archimedes long ago.

3. Just consider the imaginary numbers that are basically 2-dimensional entities, where the unit 1 expresses a turn of -90 degrees in the plane.

4. Elsewhere [11] I dealt in more detail with Shane’s approach, a must read for anyone dealing with or interested in cities or urban culture.

  • [1] Wilhelm Schwabe. ‘Mischung’ und ‘Element’ im Griechischen bis Platon. Wort- u. begriffsgeschichtliche Untersuchungen, insbes. zur Bedeutungsentwicklung von ΣΤΟΙΧΕΙΟΝ. Bouvier, Bonn 1980.
  • [2] Isaac Newton: Philosophiae naturalis principia mathematica. Bd. 1 Tomus Primus. London 1726, S. 14 (http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=294021)
  • [3] Wesley C. Salmon. Explanation and Causality. 2003.
  • [4] Abbott. Flatland.
  • [5] Ian Stewart Flatter Land.
  • [6] Ian Stewart & nn, Catastrophe Theory
  • [7] Ronald N. Giere, Scientific Perspectivism.
  • [8] Benoit B. Mandelbrot, Fractals: Form, Chance and Dimension.Freeman, New York 1977.
  • [9] Benoit B. Mandelbrot, Fractals and Scaling in Finance. Springer, New York 1997.
  • [10] David Grahame Shane, Recombinant Urbanism, Wiley, New York 2005.
  • [11] Klaus Wassermann (2011). Sema Città-Deriving Elements for an applicable City Theory. in: T. Zupančič-Strojan, M. Juvančič, S. Verovšek, A. Jutraž (eds.), Respecting fragile places, 29th Conference on Education in Computer Aided Architectural Design in Europe
    eCAADe. available online.

۞

A Pragmatic Start for a Beautiful Pair

February 17, 2012 § Leave a comment

The status of self-referential things is a very particular one.

They can be described only by referring to the concept of the “self.”

Of course, self-referential things are not without conditions, just as any other thing, too. It is, however, not possible to describe self-referential things completely just by means of those conditions, or dependencies. Logically, there is an explanatory gap regarding their inward-directed dependencies. The second peculiarity with self-referential things is that there are some families of configurations for which they become generative.

For strongly singular terms no possible justification exists. Nevertheless, they are there, we even use them, which means that the strong singularity does not imply isolation at all. The question then is about how we can/do achieve such an embedding, and which are the consequences of that.

Choosability

Despite the fact that there is no entry point which could by apriori be taken as a justified or even salient one we still have to make a choice which one actually to take. We suppose that there is indeed such a choice. It is a particular one though. We do not assume that the first choice is actually directed to an already identified entity as this would mean that there already would have been a lot of other choices in advance. We would have to select methods and atoms to fix, i.e. select and choose the subject of a concrete choice, and so on.

The choice we propose to take is neither directed to an actual entity, nor is it itself a actual entity. We are talking about a virtual choice. Practically, we start with the assumption of choosability.

Actually, Zermelo performed the same move when trying to provide a sound basis for set theory [1] after the idealistic foundation developed by Frege and others had failed so dramatically, leading into the foundational crisis of formal sciences [2]. Zermelo’s move was to introduce choosability as an axiom, called the axiom of choice.

For Zermelo’s set theory the starting point, or if you prefer, the anchor point, lies completely outside the realm of the concept that is headed for. The same holds for our conceptualization of formalization. This outside is the structure of pragmatic act of choice itself. This choice is a choice qua factum, it is not important that we choose from a set from identified entities.

The choice itself proposes by its mere performance that it is possible to think of relations and transformations; it is the unitary element of any further formalization. In Wittgenstein’s terms, it is part of the abstract life form. In accordance to Wittgenstein’s critique of Moore’s problems1, we can also say that it is not reasonable, or more precise: it is without any sense, to doubt on the act of choosing something, even if we did not think about anything particular. The mere executive aspect of any type of activity is sufficient for any a posteriori reasoning that a choice has been performed.

Notably, the axiom of choice implies the underlying assumption of intensive relatedness between yet undetermined entities. In doing so, this position represents a fundamental opposite to the attitude of Frege, Russell and any modernist in general, who always start with the assumption of the isolated particle. For these reasons we regard the axiom of choice as one of the most interesting items in mathematics!

The choice thus is a Deleuzean double-articulation [3], closely related to his concept of the transcendental status of difference; we also could say that the choice has a transcendental dualistic characteristics. On the one hand there is nothing to justify. It is mere movement, or more abstract, a pure mapping or transformation, just as a matter of fact. On the other hand, it provides us with the possibility of just being enabled to conceive mere movement as such a mapping transformation; it enables us to think the unit before any identification. Transformation comes first; Deleuze’s philosophy similarly puts the difference into the salient transcendental position. To put it still different, it is the choice, or the selection, that is inevitably linked to actualization. Actualization and choice/selection are co-extensive.

Just another Game

So, let us summarize briefly the achievements. First, we may hold that similarly to language, there is no justification for formalization. Second, as soon as we use language, we also use symbols. Symbols on the other hand take, as we have seen, a double-articulated position between language and form. We characterized formalization as a way to give a complicated thing a symbolic form that lives within a system of other forms. We can’t conceive of forms without symbols. Language hence always implies, to some degree, formalization. It is only a matter of  intensity, or likewise, a matter of formalizing the formalization, to proceed from language to mathematics. Third, both language and formalization belong to particular class of terms, that we characterized as strongly singular terms. These terms may be well put together with an abstract version of Kant’s organon.

From those three points follows that concepts that are denoted by strongly singular terms, such as formalization, creativity, or “I”, have to be conceived, as we do with language, as particular types of games.

In short, all these games are being embedded in the life form of or as a particular (sub-)culture. As such, they are not themselves language games in the original sense as proposed by Wittgenstein.

These games are different from the language game, of course, mainly because the underlying mechanisms as well as embedding landscape of purposes is different. These differences become clearly visible if we try to map those games into the choreostemic space. There, they will appear as different choreostemic styles. Despite the differences, we guess that the main properties of the language game apply also to the formalization game. This concerns the setup, the performance of such games, their role, their evaluation etc.etc., despite the effective mechanisms might be slightly different; for instance, Brandom’s principle of the “making it explicit” that serves well in the case of language is almost for sure differently parameterized for the formalizatin or the creativity game. Of course, this guess has to be subject of more detailed investigations.

As there are different natural languages that all share the same basement of enabling or hosting the possibility of language games, we could infer—based on the shared membership to the family of strongly singular terms— that there are different forms of formalization. Any of course, everybody knows at least two of such different forms of formalization: music and mathematics. Yet, once found the glasses that allow us to see the multitude of games, we easily find others. Take for instance the notations in contemporary choreography, that have been developed throughout the 20ieth century. Or the various formalizations that human cultures impose onto themselves as traditions.

Taken together it is quite obvious that language games are not a singularity. There are other contexts like formalization, modeling or the “I-reflexivity” that exist for the same reason and are similarly structured, although their dynamics may be strikingly different. In order to characterize any possible such game we could abstract from the individual species by proceeding to the -ability. Cultures then could be described precisely as the languagability of their members.

Conclusion

Based on the concept of strongly singular terms we first proof that we have to conceive of formalization (and symbol based creativity) in a similar way as we do for language. Both are embedded into a life form (in the Wittgensteinian sense). Thus it makes sense to propose to transfer the structure of the “game” from the domain of natural language to other areas that are arranged around strongly singular terms, such as formalization or creativity in the symbolic domain. As a nice side effect this brought us to the proper generalization of the Wittgensteinian language games.

Yet, there is still more about creativity that we have to clarify before we can relate it to other “games” like formalization and to proof the “beauty” of this particular combination. For instance, we have to become clear about the differences of systemic creativity, which can be observed in quasi-material arrangements (m-creativity), e.g. as self-organization, and the creativity that is at home in the realm of the symbolic (s-creativity).

The next step is thus to investigate the issue of expressibility.

Part 2: Formalization and Creativity as Strongly Singular Terms

Part 4: forthcoming: Elementarization and Expressibility

.
Notes

1. In an objection to Wittgenstein, Moore raised the skeptic question about the status of certain doubts: Can I doubt that this hand belongs to me? Wittgenstein denied the reasonability of such kind of questions.

  • [1] Zermelo, Set theory
  • [2] Hahn, Grundlagenkrise
  • [3] Deleuze & Guattari, Milles Plateaus

۞

Formalization and Creativity as Strongly Singular Terms

February 16, 2012 § Leave a comment

Formalization is based on the the use of symbols.

In the last chapter we characterized formalization as a way to give a complicated thing a symbolic form that lives within a system of other forms.

Here, we will first discuss a special property of the concepts of formalization and creativity, one that they share for instance with language. We call this property strong singularity. Then, we will sketch some consequences of this state.

What does “Strongly Singular” mean?

Before I am going to discuss (briefly) the adjacent concept of “singular terms” I would like to shed a note on the newly introduced term of “strong singularity”.

The ordinary Case

Let us take ordinary language, even as this may be a difficult thing to theorize about. At least, everybody is able to use it. We can do a lot of things with language, the common thing about these things is, however, that we use it in social situations, mostly in order to elicit two “effects”: First, we trigger some interpretation or even inference in our social companion, secondly, we indicate that we did just that. As a result, a common understanding emerges, formally taken, a homeomorphism, which in turn then may serve as the basis for the assignment of so-called “propositional content”. Only then we can “talk about” something, that is, only then we are able to assign a reference to something that is external to the exchanged speech.

As said, this is the usual working of language. For instance, by saying “Right now I am hearing my neighbor exercising piano.” I can refer to common experience, or at least to a construction you would call an imagination (it is anyway always a construction). This way I refer to an external subject and its relations, a fact. We can build sentences about it, about which we even could say whether they correspond to reality or not. But, of course, this already would be a further interpretation. There is no direct access to the “external world”.

In this way we can gain (fallaciously) the impression that we can refer to external objects by means of language. Yet, this is a fallacy, based on an illegitimate shortcut, as we have seen. Nevertheless, for most parts of our language(s) it is possible to refer to external or externalized objects by exchanging the mutual inferential / interpretational assignments as described above. I can say “music” and it is pretty clear what I mean by that, even if the status of the mere utterance of a single word is somewhat deficient: it is not determined whether I intended to refer to music in general, e.g. as the totality of all pieces or the cultural phenomenon, or to a particular piece, to a possibility of its instantiation or the factual instance right now. Notwithstanding this divergent variety, it is possible to trigger interpretations and to start a talk between people about music, while we neither have to play or to listen to music at that moment.

The same holds for structural terms that regulate interpretation predominantly by their “structural” value. It is not that important for us here, whether the externalization is directed to objects or to the speech itself. There is an external, even a physical justification for the starting to engage in the language game about such entities.

Something different…

Now, this externalization is not possible for some terms. The most obvious is “language”. We neither can talk about language without language, nor can we even think “language” or have the “feeling” of language without practicing it. We also can’t investigate language without using or practicing it. Any “measurement” about language inevitably uses language itself as the means to measure, and this includes any interpretation of speech in language as well. This self-referentiality further leads to interesting phenomena, such as “n-isms” like the dualism in quantum physics, where we also find a conflation of scales. If we would fail to take this self-referentiality into consideration we inevitably will create faults or pseudo-paradoxa.

The important issue about that is that there is no justification of language which could be expressed outside of language, hence there is no (foundational) justification for it at all. We find a quite unique setting, which corrodes any attempt for a “closed” , i.e. formal analysis of language.

The extension of the concept “language” is at the same time an instance of it.

It is absolutely not surprising that the attempt for a fully mechanic, i.e. apriori determined or algorithmic analysis of language must fail. Wittgenstein thus arrived at the conclusion that language is ultimately embedded as a practice in the life form [1] (we would prefer the term “performance” instead). He demanded, that justifications (of language games as rule-following) have to come to an end1; for him it was fallacious to think that a complete justification—or ultimate foundation—would be possible.

Just to emphasize it again: The particular uniqueness of terms like language is that they can not be justified outside of themselves. Analytically, they start with a structural singularity. Thus the term “strong singularity” that differs significantly from the concept of the so-called “singular term” as it is widely known. We will discuss it below.

The term “strong singularity” indicates the absence of any possibility for an external justification.

In §329 of the Philosophical Investigations, Wittgenstein notes:

When I think in language, there aren’t ”meanings” going through my mind in addition to the verbal expressions: the language is itself the vehicle of thought.

It is quite interesting to see that symbols do not own this particular property of strong singularity. Despite that they are a structural part of language they do not share this property. Hence we may conceive it as a remarkable instance of a Deleuzean double articulation [2] in midst thinking itself. There would be lot to say about it, but it also would not fit here.

Further Instances

Language now shares the property of strong singularity with formalization .  We can neither have the idea nor the feeling of formalization without formalization, and we even can not perform formalization without prior higher-order formalization. There is no justification of formalization which could be expressed outside of formalization, hence there is no (foundational) justification for it at all. The parallel is obvious: Would it then be necessary, for instance, to conclude that formalization is embedded in the life form much in the same way as it is the case for language? That mere performance precedes logics? Precisely this could be concluded from the whole of Wittgenstein’s philosophical theory, as Colin Johnston suggested [3].

Per­forma­tive activity precedes any possibility of applying logics in the social world; formulated the other way round, we can say that transcendental logics is getting instantiated into an applicable quasi-logics. Before this background, the idea of truth functions determining a “pure” or ideal truth value is rendered into an importunate misunder­standing. Yet, formali­zation and language are not only similar with regard to this self-referentiality, they are also strictly different. Nevertheless, so the hypothesis we try to strengthen here, formalization resembles language in that we can not have the slightest thought or even any mental operation without formalization. It is even the other way round, in that any mental operation invokes a formalizing step.

Formalization and language are not the only entities, which exhibit self-referentiality and which can not defined by any kind of outside stance. Theory, model and metaphor belong to the family, too, not to forget finally about thinking, hence creativity, at large. A peculiar representative of these terms is the “I”. Close relatives, though not as critical as the former ones, are concepts like causality or information. All these terms are not only self-referential, they are also cross-referential. Discussing any of them automatically involves the others. Many instances of deep confusion derive from the attempt to treat them separately, across many domains from neurosciences, socio­logy, computer sciences and mathematics up to philosophy. Since digital techno­logies are based seriously on formalization and have been developing yet further into a significant deep structure of our contemporary life form, any area where software technology is pervasively used is endangered by the same misunderstandings. One of these areas is architecture and city-planning, or more general, any discipline where language or the social in involved as a target of the investigation.

There is last point to note about self-referentiality. Self-referentiality may likely lead to a situation that we have described as “complexity”. From this perspective, self-referentiality is a basic condition for the potential of novelty. It is thus interesting to see that this potential is directly and natively implanted into some concepts.

Singular Terms

Now we will briefly discuss the concept of “singular term” as it is usually referred to. Yet, there is not a full agreement about this issue of singular terms, in my opinion mainly due to methodological issues. Many proponents of analytical philosophy simply “forget that there are speaking”, in the sense mentioned above.

The analytical perspective

Anyway, according to the received view, names are singular terms. It is said that the reference of singular terms are singular things or objects, even if they are immaterial, like the unicorn. Yet, the complete distinctive list of singular terms would look like this:

  • – proper names (“Barack Obama”);
  • – labeling designation (“U.S. President”);
  • – indexical expressions (“here”, “this dog”).

Such singular terms are distinguished from so-called general terms. Following Tugendhat [4], who refers in turn to Strawson [5], the significance of a general term F consists from the conditions to be fulfilled, such that F matches one or several objects. In other words, the significance of a singular term is given by a rule for identification, while the significance of a general term is given by a rule for classification. As a consequence, singular terms require knowledge about general terms.

Such statements are typical for analytical philosophy.

There are serious problems with it. However, even the labeling is misleading. It is definitely NOT the term that is singular. Singular is at most a particular contextual event, which we decided to address by a name. Labelings and indexical expressions are not necessarily “singular,” and quite frequently the same holds for names. Think about “John Smith” first as a name, then as a person…  This mistake is quite frequent in analytic philosophy. We can trace it even to the philosophy of mathematics [6], when it comes to certain claims of set theory about infinity.

The relevance for the possibility of machine-based episteme

There can be little doubt, as we already have been expressing it elsewhere, that human cognition can’t be separated from language. Even the use of most primitive tools, let alone be the production and distribution of them, requires the capability for at least a precursor of language, some first steps into languagability.

We know by experience that, in our mother tongue, we can understand sentences that we never heard before. Hence, understanding of language (quite likely as any understanding) is bottom-up, not top-down, at least in the beginning of the respective processes. Thus we have to ask about the sub-sentential components of a sentence.

Such components are singular terms. Imagine some perfectly working structure that comprises the capability for arbitrary classification as well as the capability for non-empirical analogical thinking, that is based on a dynamic symmetries. The machine wold not only be able to perform the transition from extensions to intensions, it would even be able to abstract the intension into a system of meta-algebraic symmetry relations. Such a system, or better, the programmer of it then would be faced with the problem of naming and labeling. Somehow the intensions have to be made addressable. A private index does not help, since such an index would be without any value for communication purposes.

The question is how to make the machine referring to the proper names? We will see elsewhere (forthcoming: “Waves, Words, and Images“), that this question will lead us to the necessity of multi-modality in processing linguistic input, e.g. language and images together into the same structure (which is just another reason why to rely on self-organizing maps and our methodology of modeling).

Refutation of the analytical view

The analytical position about singular term does not provide any help or insight into the the particular differential quality of terms as words that denote a concept.2   Analytical statements as cited above are inconsistent, if not self-contradictory. The reason is simple. Words as placeholders for concepts can not have a particular meaning attached to them by principle. The meaning, even that of subsentential components, is an issue of interpretation, and the meaning of a sentence is given not only by its own totality, it is also dependent on the embedding of the sentence itself into the story or the social context, where it is performed.

Since “analytic” singular terms require knowledge about general terms, and the general terms are only determined if the sentence is understood, it is impossible to identify or classify single terms, whether singular or general, before the propositional content of the sentence is clear to the participants. That propositional content of the sentence, however, is, as Robert Brandom in chapter 6 of his [7] convincingly argues, only accessible through their role in the inferential relations between the participants of the talk as well as the relations between sentences. Such we can easily see that the analytical concept of singular terms is empty, if not self-nullifying.

The required understanding of the sentence is missing in the analytical perspective, the object is dominant against the sentence, which is against any real-life experience. Hence, we’d also say that the primacy of interpretation is not fully respected. What we’d need instead is a kind of bootstrapping procedure that works within a social situation of exchanged speech.

Robert Brandom moves this bootstrapping into the social situation itself, which starts with a medial symmetry between language and socialness. There is, coarsely spoken, a rather fixed choreography to accomplish that. First, the participants have to be able to maintain what Brandom calls a de-ontic account. The sequence start with a claim, which includes the assignment of a particular role. This role must be accepted and returned, which is established by signalling that the inference / interpretation will be done. Both the role and the acceptance are dependent on the claim, on the de-ontic status of the participants and on the intended meaning. (now I have summarized about 500 pages of Brandom’s book…, but, as said, it is a very coarse summary!)

Brandom (chp.6) investigates the issue of singular terms. For him, the analytical perspective is not acceptable, since for him, as it the case for us, there is the primacy of interpretation.

Brandom refutes the claim of analytical philosophy that singular names designate single objects. Instead he strives to determine the necessity and the characteristics of singular terms by a scheme that distinguishes particular structural (“syntactical”) and semantic conditions. These conditions are further divergent between the two classes of possible subsentential structures, the singular terms (ST) and predicates (P). While syntactically, ST take the role of substitution-of/substitution-by and P take the structural role of providing a frame for such substitutions, in the semantic perspective ST are characterised exclusively by so called symmetric substitution-inferential commitments (SIC), where P also take asymmetric SIC. Those inferential commitments link the de-ontic, i.e. ultimately socialness of linguistic exchange, to the linguistic domain of the social exchange. We hence may also characterize the whole situation as it is described by Brandom as a cross-medial setting, where the socialness and linguistic domain provide each other mutually a medial embedding.

Interestingly, this simultaneous cross-mediality represents also a “region”, or a context, where materiality (of the participants) and immateriality (of information qua interpretation) overlaps. We find, so to speak, an event-like situation just before the symmetry-break that we ay identify as meaning. To some respect, Brandom’s scheme provides us the pragmatic details of of a Peircean sign situation.

The Peirce-Brandom Test

This has been a very coarse sketch of one aspect of Brandom’s approach. Yet, we have seen that language understanding can not be understood if we neglect the described cross-mediality. We therefore propose to replace the so-called Turing-test by a procedure that we propose to call the Peirce-Brandom Test. That test would proof the capability to take part in semiosis, and the choreography of the interaction scheme would guarantee that references and inferences are indeed performed. In contrast to the Turing-test, the Peirce-Brandom test can’t be “faked”, e.g. by a “Chinese Room.” (Searle [8]) Else, to find out whether the interaction partner is a “machine” or a human we should not ask them anything, since the question as a grammatical form of social interaction corroborates the complexity of the situation. We just should talk to it/her/him.The Searlean homunculus inside the Chinese room would not be able to look up anything anymore. He would have to be able to think in Chinese and as Chinese, q.e.d.

Strongly Singular Terms and the Issue of Virtuality

The result of Brandom’s analysis is that the label of singular terms is somewhat dispensable. These terms may be taken as if they point to a singular object, but there is no necessity for that, since their meaning is not attached to the reference to the object, but to their role in in performing the discourse.

Strongly singular terms are strikingly different from those (“weakly) singular terms. Since they are founding themselves while being practiced through their self-referential structure, it is not possible to find any “incoming” dependencies. They are seemingly isolated on their passive side, there are only outgoing dependencies towards other terms, i.e. other terms are dependent on them. Hence we could call them also “(purely) active terms”.

What we can experience here in a quite immediate manner is pure potentiality, or virtuality (in the Deleuzean sense). Language imports potentiality into material arrangements, which is something that programming languages or any other finite state automaton can’t accomplish. That’s the reason why we all the time heftily deny the reasonability to talk about states when it comes to the brain or the mind.

Now, at this point it is perfectly clear why language can be conceived as ongoing creativity. Without ongoing creativity, the continuous actualization of the virtual, there wouldn’t be anything that would take place, there would not “be” language. For this reason, the term creativity belongs to the small group of strongly singular terms.

Conclusion

In this series of essays about the relation between formalization and creativity we have achieved an important methodological milestone. We have found a consistent structural basis for the terms language, formalization and creativity. The common denominator for all of those is self-referentiality. On the one hand this becomes manifest in the phenomenon of strong singularity, on the other hand this implies an immanent virtuality for certain terms. These terms (language, formalization, model, theory) may well be taken as the “hot spots” not only of the creative power of language, but also of thinking at large.

The aspect of immanent virtuality implicates a highly significant methodological move concerning the starting point for any reasoning about strongly singular terms. Yet, this we will check out in the next chapter.

Part 1: The Formal and the Creative, Introduction

Part 3: A Pragmatic Start for a Beautiful Pair


Notes

1.  Wittgenstein repeatedly has been expressing this from different perspectives. In the Philosophical Investigations [1], PI §219, he states: “When I obey the rule, I do not choose. I obey the rule blindly.” In other words, there is usually no reason to give, although one always can think of some reasons. Yet, it is also true that (PI §10) “Rules cannot be made for every possible contingency, but then that isn’t their point anyway.” This leads us to §217: “If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say: ‘This is simply what I do’.” Rules are are never intended to remove all possible doubt, thus  PI  §485: “Justification by experience comes to an end. If it did not it would not be justification.” Later Quine proofed accordingly from a different perspective what today is known as the indeterminacy of empirical reason (“Word and Object”).

2. There are, of course, other interesting positions, e.g. that elaborated by Wilfrid Sellars [9], who distinguished different kinds of singular terms: abstract singular terms (“triangularity”), and distributive singular terms (“the red”), in addition to standard singular terms. Yet, the problem of which the analytical position is suffering also hits the position of Sellars.

  • References
  • [1] Ludwig Wittgenstein, Philosophical Investigations.
  • [2] Gilles Deleuze, Felix Guattari, Milles Plateaus.
  • [3] Colin Johnston (2009). Tractarian objects and logical categories. Synthese 167: 145-161.
  • [4] Ernst Tugendhat, Traditional and Analytical Philosophy. 1976
  • [5] Strawson 1974
  • [6] Rodych, Victor, “Wittgenstein’s Philosophy of Mathematics”, The Stanford Encyclopedia of Philosophy (Summer 2011 Edition), Edward N. Zalta (ed.), http://plato.stanford.edu.
  • [7] Robert Brandom, Making it Explicit. 1994
  • [8] John Searle (1980). Minds, Brains and Programs. Behav Brain Sci 3 (3), 417–424.
  • [9] Wilfrid Sellars, Science and Metaphysics. Variations on Kantian Themes, Ridgview Publishing Company, Atascadero, California [1967] 1992.

۞

The Formal and the Creative

February 15, 2012 § Leave a comment

If there is such a category as the antipodic at all,

it certainly applies to the pair of the formal and the creative, at least as long as we consult the field of propositions1 that is labeled as the “Western Culture.” As a consequence, in many cultures, and even among mathematicians, these qualities tend to be conceived as completely separated.

We think that this rating is based on a serious myopia, one that is quite common throughout rationalism, especially if that comes as a flavor of idealism. In a small series of essays—it is too much material for a single one—we will investigate the relation between these qualities, or concepts, of the formal and the creative. Today, we just will briefly introduce some markers.

The Basic Context

The relevance of this endeavor is pretty obvious. On the one hand we have the part of creativity. If machine-based episteme implies the necessity to create new models, new hypothesis and new theories we should not only get clear about the necessary mechanisms and the sufficient conditions for its “appearance.” In other chapters we already mentioned complexity and evolutionary processes as the primary, if not the only candidates for such mechanisms. These domains are related to the transition from the material to the immaterial, and surely, as such they are indispensable for any complete theory about creativity. Yet, we also have to take into consideration the space of the symbolic, i.e. of the immaterial, of information and knowledge, which we can’t find in the domains of complexity and evolution, at least not without distorting them too much. There is a significant aspect of creativity that is situated completely in the realm of the symbolic (to which we propose to include diagrams as well). In other words, there is an aspect of creativity that is related to language, to story-telling, understood as weaving (combining) a web of symbols and concepts, that often is associative in its own respect, whether in literature, mathematics, reading and writing, or regarding the DNA.

On the other hand, we have the quality of the formal, or when labelled as a domain of activity, formalization. The domain of the formal is fully within the realm of the symbolic. And of course, the formal is frequently conceived as the cornerstone, if not essence, of mathematics. Before the beginning of the 20ieth century, or around its onset, the formal was almost a synonym to mathematics. At that time, the general movement to more and more abstract structures in mathematics, i.e. things like group theory, or number theory, lead to the enterprise to search for the foundations of mathematics, often epitomized as the Hilbert Program. As a consequence, kind of a “war” broke out, bearing two parties, the intuitionists and the formalists, and the famous foundational crisis started, which is lasting till today. Gödel then proofed that even in mathematics we can not know perfectly. Nevertheless, for most people mathematics is seen as the domain where reason and rationalism is most developed. Yet, despite mathematicians are indeed ingenious (as many other people), mathematics itself is conceived as safe, that is static and non-creative. Mathematics is about symbols under analytic closure. Ideally, there are no “white territories” in mathematics, at least for the members of the formalist party.

The mostly digital machines finally pose a particular problem. The question is whether a deterministic machine, i.e. a machine for which a complete analytic description can exist, is able to develop creativity.

This question has been devised many times in the history of philosophy and thinking, albeit in different forms. Leibniz imagined a mathesis universalis and characteristica universalis as well. In the 20ieth century, Carnap tried to proof the possibility of a formal language that could serve as the ideal language for science [1]. Both failed, Carnap much more disastrously than Leibniz. Leibniz also thought about the transition from the realm of the mechanic to the realm of human thought, by means of his ars combinatoria, which he had imagined to create any possible thought. We definitely will return to Leibniz and his ideas later.

A (summarizing) Glimpse

How will we proceed, and what will we find?

First we will introduce and discuss some the methodological pillars for our reasoning about the (almost “dialectic”) relation between creativity and formalization; among those the most important ones are the following:

  • – the status of “elements” for theorizing;
  • – the concept of dimensions and space;
  • – relations
  • – the domain of comparison;
  • – symmetries as a tool;
  • – virtuality.

Secondly, we will ask about the structure of the terms “formal” and “creative” while they are in use, especially however, we are interested in their foundational status. We will find, that both, formalization and creativity belong to a very particular class of language games. Notably, these terms turn out to be singular terms, that are at the same time not names. They are singular because their foundation as well as the possibility to experience them are self-referential. (ceterum censeo: a result that is not possible if we’d stick to the ontological style by asking “What is creativity…”)

The experience of the concepts associated to them can’t be externalized. We can not talk about language without language, nor can we think “language” without practicing it. Thus, they also can’t be justified by external references, which is a quite remarkable property.

In the end we hopefully will have made clear that creativity in the symbolic space is not achievable without formalization. They are even co-generative.

Introductory Remarks

Let us start with creativity. Creativity has always been considered as something fateful. Until the beginnings of psychology as a science by William James, smart people have been smart by the working of fate, or some gods. Famous, and for centuries unchallenged, the passage in Plato’s Theaitetos [2], where Sokrates explains his role in maieutics by mentioning that the creation of novel things is task of the gods. The genius as well as concept of intuition could be regarded just a rather close relatives of that. Only since the 1950ies, probably not by pure chance, people started to recognize creativity as a subject in its own right [3]. Yet, somehow it is not really satisfying to explain creativity by calling it “divergent” or “lateral” thinking [4]. Nothing is going to be explained by replacing one term by another. Nowadays, and mostly in the domain of design research, conditions for creativity are often understood in terms of collaborations. People even resort to infamous swarm intelligence, which is near a declaration of bankruptcy.

Any of these approaches are just replacing some terms with some other terms, trying to conjure some improvement in understanding. Most of the “explanations” indeed look rather like rain dancing than a valuable analysis. Recently a large philosophical congress in Berlin, with more than 1200 inscribed participants, and two books comprising around 2000 pages focused on the subject largely in the same vein and without much results [5]. We are definitely neither interested in any kind of metaphysical base-jumping by referring directly or indirectly to intuition, and the accompanying angels in the background, nor in phenomenological, sociological or superficial psychological approaches, tying to get support by some funny anecdotes.

The question really is, what are we talking about, and how, when referring to the concept of creativity. Only because this question is neither posed nor answered, we are finding so much esoterics around this topic. Creativity surely exceeds problem solving, although sometimes it occurs righteous when solving a problem. It may be observed in calm story telling, in cataclysmic performances of artists, or in language.

Actually, our impression is that creativity is nothing that sometimes “is there”, and sometimes not. In language it is present all the time, much like it is the case for analogical thinking. The question is which of those phenomena we call “creative,” coarsely spoken, which degree of intensity regarding novelty and usefulness of that novelty we allow to get assigned a particular saliency. Somehow, constraints seem to play an important role, as well as the capability to release it, or apply it, at will. Then, however, creativity must be a technique, or at least based on tools which we could learn to use. It is, however, pretty clear that we have to distinguish between the assignment of the saliency (“this or that person has been creative”) and the phenomenon and its underlying mechanisms. The assignment of the term is introducing a discreteness that is not present on the level of the mechanism, hence we never will understand about what we are talking about if we take just the parlance as the source and the measure.

The phenomenon of language provides a nice bridge to the realm of the formal. Today, probably mainly due to the influence of computer sciences, natural languages are distinguished from artificial languages, which often are also called formal languages. It is widely accepted, that formalization either is based on formal languages or that the former creates an instance of the latter. The concept of formal language is important in mathematics, computer science and science at large. Instantiated as programming languages, formal languages are of an enormous relevance for human society; one could even say that these languages themselves establish some kind of a media.

Yet, the labeling of the discerned phenomena as “natural” and “formal” always strikes me. It is remarkable that human languages are so often also called “natural” languages. Somehow, human language appears so outstanding to humans that they call their language in a funny paradoxical move a “natural” thing, as if this language-thing would have been originated outside human culture. Today, as we know about many instances of cultural phenomena in animals, the strong dichotomy between culture and nature blurred considerably. A particular driver of this is provided by the spreading insight that we as humans are also animals: our bodies contain a brain. Thus, we and our culture also build upon this amazing morphological structure, continuously so. We as humans are just the embodiment of the dichotomy between nature and culture, and nothing could express the confusion about this issue more than the notion of “natural language.” A bit shamefaced we call the expressions of whales and dolphins “singing”, despite we know that they communicate rather complicated matters. We are just unable to understand anything of it. The main reason for that presumable being that we do not share anything regarding their Lebensform, and other references than the Lebensform are not relevant for languages.

Language, whether natural or formal, is supposed to be used to express things. Already here we now have been arriving in deep troubles as the previous sentence is anything than innocent. First, speaking about things is not a trivial affair. A thing is a difficult thing. Taking etymology into consideration, we see that things are the results of negotiations. As a “result,” in turn, “things” are reductions, albeit in the realm of the abstract. The next difficulty is invoked by the idea that we can “express” things in a formal language. There has been a large debate on the expressive capabilities of formal languages, mainly induced by Carnap [1], and carried further by Quine [6], Sneed [7], Stegmüller [8], Spohn [9], and Moulines [10], among others, up to today.

In our opinion, the claim of the expressibility of formal language, and hence the proposed usage of formal languages as a way to express scientific models and theories, is based on probably more than just one deep and drastic misunderstanding. We will elucidate this throughout this series; other arguments has been devised for instance by Putnam in his small treatise about the “meaning of meaning” [11], where he famously argued that “analyticity is an inexplicable noise” without any possibility for a meaningful usage. That’s also a first hint that analyticity is not about the the same thing(s) as formalization.

Robert Brandom puts the act of expressing within social contexts into the center of his philosophy [12], constructing a well-differentiated perspective upon the relation between principles in the usage of language and its structure. Following Brandom, we could say that formal language can not be expressive almost by its own definition: the mutual social act of requesting an interpretation is missing there, as well as any propositional content. If there is no propositional content, nothing could be expressed. Yet, propositional content comes into existence only by a series of events where the interactees in a social situation ascribe it mutually to each other and are also willing to accept that assignment.

Formal languages consist of exactly defined labeled sets, where each set and its label represents a rewriting rule. In other words, formal languages are finite state machines; they are always expressible as a compiler for a programming language. Programming languages organize the arrangement of rewriting rules, they are however not an entity capable for semantics. We could easily conclude that formal languages are not languages at all.

A last remark about formalization as a technique. Formalization is undeniably based on the use, or better, the assignment of symbols to particular, deliberately chosen contexts, actions, recipes or processes. Think of proofs of certain results in mathematics where the symbolized idea later refers to the idea and its proof. Such, they may act as kind of abbreviations, or they will denote abstractions. They also may support the visibility of the core of otherwise lengthy reasonings. Sometimes, as for instance in mathematics, formalization requires several components, e.g. the item or subject, the accompanying operators or transformations (take that as “usage”), and the reference to some axiomatics or a explicit description of the conditions and the affected items. The same style is applied in physics. Yet, this complete structure is not necessary for an action to count as a formalization. We propose to conceive of formalization as the selection of elements (will be introduced soon) that consecutively are symbolized. Actually, it is not necessary to write down a “formula” about something in order to formalize that something. It is also not necessary, so we are convinced, to apply a particular logic when establishing the formalization through abstraction. It is just the symbolic compression that allows to achieve further results which would remain inaccessible otherwise. Or briefly put, to give a complicated thing a symbolic form that lives within a system of other forms.

Finally, there is just one thing we always should keep in mind. Using, introducing or referring to a formalization irrevocably implies an instantiation when we are going to apply it, to bring it back to more “concrete” contexts. Thus, formalization is deeply linked to the Deleuzean figure of thought of the “Differential.” [13]

part 2: Strong Singularity of certain Terms

Part 3: A Pragmatic Start for a Beautiful Pair

Part 4: Elementarization and Expressibility

.
Notes

1. Here we refer to Michel Foucault’s concept of the “field of propositions” / “field of proposals”, which he developed in the book “The Archaeology of Knowledge.”

  • [1] Rudolf Carnap, Logische Syntax der Sprache, Wien 1934 [2. Aufl. 1968].
  • [2] Platon, Theaitetos.
  • [3] Guilford,  Creativity , 1950
  • [4] DeBono about lateral thinking
  • [5] Günther Abel (ed.), Kreativität. Kolloquiumsband XX. Kongress der Deutschen Philosophie. Meiner Verlag, Hamburg 2007.
  • [6] Quine, Two Dogmas of Empiricism.
  • [7] Sneed
  • [8] Stegmüller
  • [9] Spohn
  • [10] Moulines
  • [11] Hilary Putnam, The Meaning of Meaning
  • [12] Robert Brandom, Making it Explicit.
  • [13] Gilles Deleuze, Difference and Repetition.

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