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.


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!


  • [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,, 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 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.



September 7, 2012 § Leave a comment

Animals behave. Of course, one could say.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1. This Essay

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

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

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

The chapters in this essay are the following:

Table of Content (active links)

2. The Inversion

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

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

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

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

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

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

3. The Targets

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

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

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

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

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

4. Methodology

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

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

Markov Processes

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

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

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

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

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

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

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

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

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

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


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

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

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

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

Kohonen et al. proposed a simple way to establish a random context [6]. The step from symbolic crispness to a numerical representation is not trivial, though. We need a double-articulated entity that is “at home” in both domains. This entity is a high-dimensional random fingerprint. Such a fingerprint consists simply of a large number, well above 100, of random values from the interval [0..1]. According to the Lemma of Hecht-Nielsen [7]  any two of such vectors are approximately orthogonal to each other. In other words, it is a name expressed by numbers.

After a recoding of all symbols in a text into their random fingerprints it is easy to establish  probabilistic distributions of the neighborhood of any word. The result is a random context, also called a random graph. The basic trick to accomplish such a distribution is to select a certain, fixed size for the neighborhood—say five or seven positions in total—and then arrange the word of interest always to a certain position, for instance into the middle position.

This procedure we do for all words in a text, or any symbolic series. Doing so, we get a collection of random contexts, that overlap. The final step then is a clustering of the vectors according to their similarity.

It is quite obvious that this procedure as it has been proposed by Kohonen sticks to strong assumptions, despite its turn to probabilization. The problem is the fixed order, that is, the order is independent from context in his implementation. Thus his approach is still limited in the same way as the n-gram approach (see chp.5.3 below). Yet, sometimes we meet strong inversions and extensions of relevant dependencies between words. Linguistics speak of injected islands with regard to wh*-phrases. Anaphors are another example. Chomsky critized the approach of fixed–size contexts very early.

Yet, there is no necessity to limit the methodology to fixed-size contexts, or to symmetrical instances of probabilistic contexts. Yes, of course this will result in a situation, where we corrupt the tabularity of the data representation. Many rows are different in their length and there is (absolutely) no justification to enforce a proper table by filling “missing values” into the “missing” cells of the table

Fortunately, there is another (probabilistic) technique that could be used to arrive at a proper table, without distorting the content by adding missing values. This technique is random projection, first identified by Johnson & Lindenstrauss (1984), which in the case of free-sized contexts has to be applied in an adaptive manner (see [8] or [9] for a more recent overview). Usually, a source (n*p) matrix (n=rows, p=columns=dimensions) is multiplied with a (p*k) random matrix, where the random numbers follow a Gaussian distribution), resulting in a target matrix of only k dimensions and n rows. This way a matrix of 10000+ columns can be projected into one made only from 100 columns without loosing much information. Yet, using the lemma of Hecht-Nielsen we can compress any of the rows of a matrix individually. Since the random vectors are approximately orthogonal to each other we won’t introduce any information across all the data vectors that are going to be fed into the SOM. This stepwise operation becomes quite important for large amounts of documents, since in this case we have to adopt incremental learning.

Such, we approach slowly but steadily the generalized probabilistic context that we described earlier. The proposal is simply that in dealing with texts by means of computers we have to apply precisely the most general notion of context, which is devoid from structural pre-occupations as we can meet them e.g. in the case of n-grams or Markov processes.

5. Computers Dealing with Text

Currently, so-called “text mining” is a hot topic. More and more of human communication is supported by digitally based media and technologies, hence more and more texts are accessible to computers without much efforts. People try to use textual data from digital environments for instance to do sentiment analysis about companies, stocks, or persons, mainly in the context of marketing. The craziness there is that they pretend to classify a text’s sentiment without understanding it, more or less on the frequency of scattered symbols.

The label “text mining” reminds to “data mining”; yet, the structure of the endeavors are drastically different. In data mining one is always interested in the relevant variables n order to build a sparse model that even could be understood by human clients. The model then in turn is used to optimize some kind of process from which the data for modeling has been extracted.

In the following we will describe some techniques, methods and attitudes that are highly unsuitable for the treatment of textual “data”, despite the fact that they are widely used.

Fault 1 : Objectivation

The most important difference between the two flavor of “digital mining” concerns however, the status of the “data”. In data mining, one deals with measurements that are arranged in a table. This tabular form is only possible on the basis of a preceding symbolization, which additionally is strictly standardized also in advance to the measurement.

In text mining this is not possible. There are no “explanatory” variables that could be weighted. Text mining thus just means to find a reasonable selection of text in response to a “query”. For textual data it is not possible to give any criterion how to look at a text, how to select a suitable reference corpus for determining any property of the text, or simply to compare it to other texts before its interpretation. There are no symbols, no criteria that could be filled into a table. And most significant, there is no target that could be found “in the data”.

It is devoid of any sense to try to optimize a selection procedure by means of a precision/recall ratio. This would mean that the meaning of text could be determined objectively before any interpretation, or, likewise, that the interpretation of a text is standardisable up to a formula. Both attempts are not possible, claiming otherwise is ridiculous.

People responded to these facts with a fierce endeavor, which ironically is called “ontology”, or even “semantic web”. Yet, neither will the web ever become “semantic” nor is database-based “ontology” a reasonable strategy (except for extremely standardized tasks). The idea in both cases is to determine the meaning of an entity before its actual interpretation. This of course is utter nonsense, and the fact that it is nonsense is also the reason why the so-called “semantic web” never started to work. They guys should really do more philosophy.

Fault 2 : Thinking in Frequencies

A popular measure for describing the difference of texts are variants of the so-called tf-idf measure. “tf” means “term frequency” and describes the normalized frequency of a term within a document. “idf” means “inverse document frequency”, which, actually, refers to the frequency of a word across all documents in a corpus.

The frequency of a term, even its howsoever differentialized frequency, can hardly be taken as the relevance of that term given a particular query. To cite the example from the respective entry in Wikipedia, what is “relevant” to select a document by means of the query “the brown cow”? Sticking to terms makes sense only if and only if we accept an apriori contract about the strict limitation to the level of the terms. Yet, this has nothing to do with meaning. Absolutely nothing. It is comparing pure graphemes, not even symbols.

Even if it would be related to meaning it would be the wrong method. Simply think about a text that contains three chapters: chapter one about brown dogs, chapter two about the relation of (lilac) cows and chocolate, chapter three about black & white cows. There is no phrase about a brown cow in the whole document, yet, it would certainly be selected as highly significant by the search engine.

This example nicely highlights another issue. The above mentioned hypothetical text could nevertheless be highly relevant, yet only in the moment the user would see it, triggering some idea that before not even was on the radar. Quite obviously, despite the search would have been different, probably, the fact remains that the meaning is neither in the ontology nor in the frequency and also not in text as such—before the actual interpretation by the user. The issue becomes more serious if we’d consider slightly different colors that still could count as “brown”, yet with a completely different spelling. And even more, if we take into account anaphoric arrangement.

The above mentioned method of Markov processes helps a bit, but not completely of course.

Astonishingly, even the inventors of the WebSom [6], probably the best model for dealing with textual data so far, commit the frequency fallacy. As input for the second level SOM they propose a frequency histogram. Completely unnecessary, I have to add, since the text “within” the primary SOM can be mapped easily to a Markov process, or to probabilistic contexts, of course. Interestingly, any such processing that brings us from the first to the second layer reminds somewhat more to image analysis than to text analysis. We mentioned that already earlier in the essay “Waves, Words and Images”.

Fault 3 : The Symbolistic Fallacy (n-grams & co.)

Another really popular methodology to deal with texts is n-grams. N-grams are related to Markov processes, as they also take the sequential order into account. Take for instance (again the example from Wiki) the sequence “to be or not to be”. The transformation into a 2-gram (or bi-gram) looks such “to be, be or, or not, not to, to be,” (items are between commas), while the 3-gram transformation produces “to be or, be or not, or not to, not to be”. In this way, the n-gram can be conceived as a small extract from a transition table of order (n-1). N-grams share a particular weakness with simple Markov models, which is the failure to capture long-range dependencies in language. These can be addressed only by means of deep grammatical structures. We will return to this point later in the discussion of the next fault No.4 (Structure as Meaning).

The strange thing is that people drop the tabular representation, thus destroying the possibility of calculating things like adjusted residuals. Actually, n-grams are mostly just counted, which is committing the first fault of thinking in frequencies, as described above.

N-gram help to build queries against databases that are robust against extensions of words, that is prefixes, suffixes, or forms of verbs due to flexing. All this has, however, nothing to do with meaning. It is a basic and primitive means to make symbolic queries upon symbolic storages more robust. Nothing more.

The real problem is the starting point: taking the term as such. N-grams start with individual words that are taken blindly as symbols. Within the software doing n-grams, they are even replaced by some arbitrary hash code, i.e. the software does not see a “word”, it deals just with a chunk of bits.

This way, using n-grams for text search commits the symbolistic fallacy, similar to ontologies, but even on a more basic level. In turn this means that the symbols are taken as “meaningful” for themselves. This results in a hefty collision with the private-language-argument put forward by Wittgenstein a long time ago.

N-grams are certainly more advanced than the nonsense based on tf-idf. Their underlying intention is to reflect contexts. Nevertheless, they fail as well. The ultimate reason for the failure is the symbolistic starting point. N-grams are only a first, though far too trivial and simplistic step into probabilization.

There is already a generalisation of n-grams available as described in published papers by Kohonen & Kaski: random graphs, based on random contexts, as we described it above. Random graphs overcome the symbolistic fallacy, especially if used together with SOM. Well, honestly I have to say that random graphs imply the necessity of a classification device like the SOM. This should not be considered as being a drawback, since n-grams are anyway often used together with Bayesian inference. Bayesian methods are, however, not able to distil types from observations as SOM are able to do. That now is indeed a drawback since in language learning the probabilistic approach necessarily must be accompanied with the concept of (linguistic) types.

Fault 4 : Structure as Meaning

The deep grammatical structure is an indispensable part of human languages. It is present from the sub-word level up to the level of rhetoric. And it’s gonna get really complicated. There is a wealth of rules, most of them to be followed rather strict, but some of them are applied only in a loose manner. Yet, all of them are rules, not laws.

Two issues are coming up here that are related to each other. The first one concerns the learning of a language. How do we learn a language? Wittgenstein proposed, simply by getting shown how to use it.

The second issue concerns the status of the models about language. Wittgenstein repeatedly mentioned that there is no possibility for a meta-language, and after all we know that Carnap’s program of a scientific language failed (completely). Thus we should be careful when applying a formalism to language, whether it is some kind of grammar, or any of the advanced linguistic “rules” that we know of today (see the lexicon of linguistics for that). We have to be aware that these symbolistic models are only projective lists of observations, arranged according to some standard of a community of experts.

Linguistic models are drastically different from models in physics or any other natural science, because in linguistics there is no outer reference. (Computational) Linguistics is mostly on the stage of a Babylonian list science [10], doing more tokenizing than providing useful models, comparable to biology in the 18th century.

Language is a practice. Language is a practice of human beings, equipped with a brain and embedded in a culture. In turn language itself is contributing to cultural structures and is embedded into it. There are many spatial, temporal and relational layers and compartments to distinguish. Within such arrangements, meaning happens in the course of an ongoing interpretation, which in turn is always a social situation. See Robert Brandom’s Making it Explicit as an example for an investigation of this aspect.

What we definitely have to be aware of is that projecting language onto a formalism, or subordinating language to an apriori defined or standardized symbolism (like in formal semantics) looses essentially everything language is made from and referring to. Any kind of model of a language is implicitly also claiming that language can be detached from its practice and from its embedding without loosing its main “characteristics”, its potential and its power. In short, it is the claim that structure conveys meaning.

This brings us to the question about the role of structure in language. It is a fact that humans not only understand sentences full of grammatical “mistakes”, and quite well so, in spoken language we almost always produce sentences that are full of grammatical mistakes. In fact, “mistakes” are so abundant that it becomes questionable to take them as mistakes at all. Methodologically, linguistics is thus falling back into a control science, forgetting about the role and the nature of symbolic rules such as it is established by grammar. The nature is an externalization, the role is to provide a standardization, a common basis, for performing interpretation of sentences and utterances in a reasonable time (almost immediately) and in a more or less stable manner. The empirical “given” of a sentence alone, even a whole text alone, can not provide enough evidence for starting with interpretation, nor even to finish it. (Note that a sentence is never a “given”.)

Texts as well as spoken language are nothing that could be controlled. There is no outside of language that would justify that perspective. And finally, a model should allow for suitable prediction, that is, it should enable us to perform a decision. Here we meet Chomsky’s call for competence. In case of language, a linguistic models should be able to produce language as a proof of concept. Yet, any attempt so far failed drastically, which actually is not really a surprise. Latest here it should become clear that the formal models of linguistics, and of course all the statistical approaches to “language processing” (another crap term from computational linguistics) are flawed in a fundamental way.

From the perspective of our interests here on the “Putnam Program” we conceive of formal properties as Putnam did in his “Meaning of “Meaning””. Formal properties are just that: properties among other properties. In our modeling essay we proposed to replace the concept of properties by the concept of the assignate, in order to emphasize the active role of the modeling instance in constructing and selecting the factors. Sometimes we use formal properties of terms and phrases, sometimes not, dependent on context, purpose or capability. There is neither a strict tie of formal assignates to the entity “word” or “sentence” nor could we detach them as part of formal approach.

Fault 5 : Grouping, Modeling and Selection

Analytic formal models are a strange thing, because such a model essentially claims that there is no necessity for a decision any more. Once the formula is there, it claims a global validity. The formula denies the necessity for taking the context as a structural element into account. It claims a perfect separation between observer and the observed. The global validity also means that the weights of the input factors are constant, or even that there are no such weights. Note that the weights translates directly into the implied costs of a choice, hence formulas also claim that the costs are globally constant, or at least, arranged in a smooth differentiable space. This is of course far from any reality for almost any interesting context, and of course for the contexts of language and urbanism, both deeply related to the category of the “social”.

This basic characteristic hence limits the formal symbolic approach to physical, if not just to celestial and atomic contexts. Trivial contexts, so to speak. Everywhere else something rather different is necessary. This different thing is classification as we introduced it first in our essay about modeling.

Searching for a text and considering a particular one as a “match” to the interests expressed by the search is a selection, much like any other “decision”. It introduces a notion of irreversibility. Searching itself is a difficult operation, even so difficult that is questionable whether we should follow this pattern at all. As soon as we start to search we enter the grammatological domain of “searching”. This means that we claim the expressibility of our interests in the search statement.

This difficulty is nicely illustrated by an episode with Gary Kasparov in the context of his first battle against “Deep Blue”. Given the billions of operations the super computer performed, a journalist came up with the question “How do find the correct move so fast?” Obviously, the journalist was not aware about the mechanics of that comparison. Kasparov answered: “ I do not search, I just find it.” His answer is not perfectly correct, though, as he should have said “I just do it”. In a conversation we mostly “just do language”. We practice it, but we very rarely search for a word, an expression, or the like. Usually, our concerns are on the strategic level, or in terms of speech act theory, on the illocutionary level.

Such we arrive now at the intermediary result that we have some kind of non-analytical models on the one hand, and the performance of their application on the other. Our suggestion is that most of these models are situated on an abstract, orthoregulative level, and almost never on the representational level of the “arrangement” of words.

A model has a purpose, even if it is an abstract one. There are no models without purpose. The purpose is synonymic to the selection. Often, we do not explicitly formulate a purpose, we just perform selections in a consistent manner. It is this consistency in the selections that imply a purpose. The really important thing to understand is also that the abstract notion of purpose is also synonymic to what we call “perspective”, or point of view.

One could mention here the analytical “models”, but those “models” are not models because they are devoid of a purpose. Given any interesting empirical situation, everybody knows that things may look quite different, just dependent on the “perspective” we take. Or in our words, which abstract purpose we impose to the situation. The analytic approach denies such a “perspectivism”.

The strange thing now is that many people mistake the mere clustering of observation on the basis of all contributing or distinguished factors as a kind of model. Of course, that grouping will radically change if we withdraw some of the factors, keeping only a subset of all available ones. Not only the grouping changes, but also the achievable typology and any further generalization will be also very different. In fact, any purpose, and even the tuning of the attitude towards the risk (costs) of unsuitable decisions changes the set of suitable factors. Nothing could highlight more the nonsense to call naïve take-it-all-clustering a “unsupervised modeling”. First, it is not a model. Second, any clustering algorithm or grouping procedure follows some optimality criterion, that is it supervises it despite claiming the opposite. “Unsupervised modeling” claims implicitly that it is possible to build a suitable model by pure analytic means, without any reference to the outside at all. This is, f course, not possible. It is this claim that is introducing a contradiction to the practice itself, because clustering usually means classification, which is not an analytic move at all. Due to this self-contradiction the term “unsupervised modeling” is utter nonsense. It is not only nonsense, it is even deceiving, as people get vexed by the term itself: they indeed believe that they are modeling in a suitable manner.

Now back to the treatment of texts. One of the most advanced procedures—it is a non-analytical one—is the WebSom. We described it in more detail in previous essays (here and here). Yet, as the second step Kohonen proposes clustering as a suitable means to decide about the similarity of texts. He is committing exactly the same mistake as described before. The trick, of course, is to introduce (targeted) modeling to the comparison of texts, despite the fact that there are no possible criteria apriori. What seems to be irresolvable disappears, however, as a problem if we take into account the self-referential relations of discourses, which necessarily engrave into the interpreter as self-modifying structural learning and historical individuality.

6. The Statistics of Urban Environments

The Importance of Conceptual Backgrounds

There is no investigation without implied purpose, simply because any investigation has to perform more often many selections rather than just some. One of the more influential selections that has to be performed considers the scope of the investigation. We already met this issue above when we discussed the affairs as we can meet it in behavioral sciences.

Considering investigations about social entities like urban environments, architecture or language. “scope” largely refers to the status of the individual, and in turn, to the status of time that we instantiate in our investigation. Both together establish the dimension of form as an element of the space of expressibility that we choose for the investigation.

Is the individual visible at all? I mean, in the question, in the method and after applying a methodology? For instance, as soon as we ask about matters of energy, individuals disappear. They also disappear if we apply statistics to raw observations, even if at first hand we would indeed observe individuals as individuals. To retain the visibility of individuals as individuals in a set of relations we have to apply proper means first. It is clear, that any cumulative measure like those from socio-economics also cause the disappearance of the context and the individual.

If we keep the individuals alive in our method, the next question we have to ask concerns the relations between the individuals. Do we keep them or do we drop them? Finally, regarding the unfolding of the processes that result from the temporal dynamics of those relations, we have to select whether we want to keep aspects of form or not. If you think that the way a text unfolds or the way things are happening in the urban environment is at least as important as their presence,  well in this case you would have to care about patterns.

It is rather crucial to understand that these basic selections determine the outcome of an investigation as well as of any modeling or even theory building as grammatological constraints. Once we took a decision on the scope, the problematics of that choice becomes invisible, completely transparent. This is the actual reason for the fact that choosing a reductionist approach as the first step is so questionable.

In our earlier essay about the belief system in modernism we emphasized the inevitability of the selection of a particular metaphysical stance, ways before we even think about the scope of an investigation in a particular domain. In case of modernistic thinking, from positivism to existentialism, including any shape of materialism, the core of the belief system is metaphysical independence, shaping all the way down towards politics methods, tools, attitudes and strategies. If you wonder whether there is an alternative to modernistic thinking, take a look to our article where we introduce the concept of the choreostemic space.

Space Syntax

In the case of “Space Syntax” the name is program. The approach is situated in urbanism; it has been developed and is still being advocated by Bill Hillier. Originally, Hillier was a geo-scientist, which is somewhat important to follow his methodology.

Put into a nutshell, the concept of space syntax claims that the description of the arrangement of free space in a built environment is necessary and sufficient for describing the quality of a city. The method of choice to describe that arrangement is statistics, either through the concept of probabilistic density of people or through the concept of regression, relating physical characteristics of free space with the density of people. Density in turn is used to capture the effect of collective velocity vectors. If people start to slow down, walking around in different directions, density increases. Density of course also increases as a consequence of narrow passages. Yet, in this case the vectors are strongly aligned.

The spatial behavior of individuals is a result and a means of social behavior in many animal species. Yet it makes a difference whether we consider the spatial behavior of individuals or the arrangement of free space in a city as a constraint of the individual spatial behavior. Hillier’s claim of “The Space is the Machine” is mistaking the one for the other.

In his writings, Hillier over and over again commits the figure of the petitio principii. He starts with the strong belief in analytics and upon that he tries to justify the use of analytical techniques. His claim of “The need for an analytic theory of architecture” ([11], p.40) is just one example. He writes

The answer proposed in this chapter is that once we accept that the object of architectural theory is the non-discursive — that is, the configurational — content of space and form in buildings and built environments, then theories can only be developed by learning to study buildings and built environments as non-discursive objects.

Excluding the discourse as a constitutional element only the analytic remains. He drops any relational account, focusing just the physical matter and postulating meaning of physical things, i.e. meaning as an apriori in the physical things. His problem is just his inability to distinguish different horizons of time, of temporal development. Dismissing time means to dismiss memory, and of course also culture. For a physicalist or ultra-modernist like him this blindness is constitutive. He never will understand the structure of his failure.

His dismissal of social issues as part of a theory serves eo ipso as his justification of the whole methodology. This is only possible due to another, albeit consistent, mistake, the conflation of theory and models. Hillier is showing us over and over again only models, yet not any small contribution to an architectural theory. Applying statistics shows us a particular theoretical stance, but is not to be taken as such! Statistics instantiates those models, that is his architectural theory is following largely the statistical theory. We repeatedly pointed to the problems that appear if we apply statistics to raw observations.

The high self-esteem Hillier expresses in his nevertheless quite limited writings is topped by treating space as syntax, in other words as a trivial machine. Undeniably, human beings have a material body, and buildings take space as material arrangements. Undeniably matter arranges space and constitutes space. There is a considerably discussion in philosophy about how we could approach the problematic field of space. We won’t go into details here, but Hillier simply drops the whole stuff.

Matter arranges in space. This becomes quickly a non-trivial insight, if we change perspective from abstract matter and the correlated claim of the possibility of reductionism to spatio-temporal processes, where the relations are kept taken as a starting point. We directly enter the domain of self-organization.

By means of “Space Syntax” Hillier claimed to provide a tool for planning districts of a city, or certain urban environments. If he would restrict his proposals to certain aspects of the anonymized flow of people and vehicles, it would be acceptable as a method. But it is certainly not a proper tool to describe the quality of urban environments, or even to plan them.

Recently, he delivered a keynote speech [12] where he apparently departed from his former Space Syntax approach, that reaches back to 1984. There he starts with the following remark.

On the face of it, cities as complex systems are made of (at least) two sub-systems: a physical sub-system, made up of buildings linked by streets, roads and infrastructure; and a human sub-system made up of movement, interaction and activity. As such, cities can be thought of as socio-technical systems. Any reasonable theory of urban complexity would need to link the social and technical sub-systems to each other.

This clearly is much less reductionist, at first sight at least, than “Space Syntax”. Yet, Hillier remains aligned to hard-core positivism. Firstly, in the whole speech he fails to provide a useful operationalization of complexity. Secondly, his Space Syntax simply appears wrapped in new paper. Agency for him is still just spatial agency. The relevant urban networks for him is just the network of streets. Thirdly, it is bare nonsense to separate a physical and a human subsystem, and then to claim the lumping together of those as a socio-technical system. He obviously is unaware of more advance and much more appropriate ways of thinking about culture, such as ANT, the Actor-Network-Theory (Bruno Latour), which precisely drops the categorical separation of physical and human. This separation has been first critized by Merlau-Ponty in the 1940ies!

Hillier served us just as an example, but you may have got the point. Occasionally, one can meet attempts that at least try to integrate a more appropriate concept of culture and human being in urban environments. Think about Koolhaas and his AMO/OMA, for instance, despite the fact that Koolhaas himself also struggles with the modernist mindset (see our introductions into “JunkSpace” or “The Generic City”). Yet, he at least recognized that something is fundamentally problematic with that.

7. The Toolbox Perspective

Most of the interesting and relevant systems are complex. It is simply a methodological fault to use frequencies of observational elements to describe these systems, whether we are dealing with animals, texts, urban environments or people (dogs, cats) moving around in urban environments.

Tools provide filters, they respond to certain issues, both of the signal and of the embedding. Tools are artifacts for transformation. As such they establish the relationality between actors, things and processes. Tools produce and establish Heidegger’s “Gestell” as well as they constitute the world as a fabric of relations as facts and acts, as Wittgenstein emphasized so often and already in the beginning of the Tractatus.

What we like to propose here is a more playful attitude towards the usage of tools, including formal methods. By “playful” we refer to Wittgenstein’s rule following, but also to a certain kind of experimentation, not induced by theory, but rather triggered by the know-how of some techniques that are going to be arranged. Tools as techniques, or techniques as tools are used to distil symbols from the available signals. Their relevancy is determined only by the subsequent step of classification, which in turn is (ortho-)regulated by strategic goal or cultural habits. Never, however, should we take a particular method as a representative for the means to access meaning from a process, let it a text or an urban environment.

8. Behavior

In this concluding chapter we are going to try to provide more details about our move to apply the concept of behavior to urbanism and computational linguistics.


Since Friedrich Schleiermacher in 1830ies, hermeneutics is emphasizing a certain kind of autonomy of the text. Of course, the text itself is not a living thing as we consider it for animals. Before it “awakes” it has to be entered into mind matter, or more generally, it has to be interpreted. Nevertheless, an autonomy of the text remains, largely due to the fact that there is no Private Language. The language is not owned by the interpreting mind. Vilem Flusser proposed to radically turn the perspective and to conceive the interpreter as medium for texts and other “information”, rather than the other way round.

Additionally, the working of the brain is complex, least to say. Our relation to our own brain and our own mind is more that of an observer than that of a user or even controller. We experience them. Both together, the externality of language and the (partial) autonomy of the brain-mind lead to an arrangement where the text becomes autonomous. It inherits complimentary parts of independence from both parts of the world, from the internal and the external.

Furthermore, human languages are unlimited in their productivity. It is not only unlimited, it also is extensible. This pairs with its already mentioned deep structure, not only concerning the grammatical structure. Using language, or better, mastering language means to play with the inevitable inner contradictions that appear across the various layers, levels, aspects and processes of applied language. Within practiced language, there are many time horizons, instantiated by structural and semantic pointers. These aspects render the original series of symbols into an associative network of active components, which contributes further to the autonomy of texts. Roland Barthes notes (in [17]) that

The Plural of the Text depends … not on the ambiguity of its contents but on what might be called the sterographic plurality of its weave of signifiers (etymologically, the text is a tissue, a woven fabric). The reader of the Text may be compared to someone at a loose end.

Barthes implicitly emphasizes that the text does not convey a meaning, the meaning is not in the text, it can’t be conceived as something externalizable. In this essay he also holds that a text can’t be taken as just a single object. It is a text only in the context of other texts, and so the meaning that it develops upon interpretation is also dependent on the corpus into which it is embedded.

Methodologically, this (again) highlights the problematics that Alan Hajek called the reference class problem [13]. It is impossible for an interpreter to develop the meaning of a text outside of a previously chosen corpus. This dependency is inherited by any phrase, any sentence and any word within the text. Even a label like “IBM” that seems to be bijectively unique regarding the mapping of the graphem to its implied meaning is dependent on that. Of course, it will always refer somehow to the company. Yet, without the larger context it is not clear in any sense to which aspect of that company and its history the label refers to in a particular case. In literary theory this is called intertextuality. Further more, it is almost palpable here in this example that signs refer only to signs (the cornerstone of Peircean semiotics), and that concepts are nothing that could be defined (as we argued earlier in more detail).

We may settle here that a text as well as any part of it is established even through the selection of the embedding corpus, or likewise, a social practice, a life-form. Without such an embedding the text simply does not exist as a text. We just would find a series of graphemes. It is a hopeless exaggeration , if not self-deception, if people call the statistical treatment of texts “text mining”. reading it in another way, it may be considered even as a cynical term.

It is this dependence on local and global contexts, synchronically and diachronically, that renders the interpretation of a text similar to the interpretation of animal behavior.

Taken together, conceiving of texts as behaving systems is probably less a metaphor than it appears at first sight. Considering the way we make sense of a text, approaching a text is in many ways comparable with approaching an animal of a familiar species. We won’t know exactly what is going to happen, the course of events and action depends significantly on ourselves. The categories and ascribed properties necessary to establish an interaction are quite undefined in the beginning, also available only as types of rules, not as readily parameterized rules itself. And like in animals, the next approach will never be a simple repetition of the former one, even one knows the text quite good.

From the methodological perspective the significance of such a “behavioral turn”3 can’t be underestimated. For instance, nobody would interpret an animal by a rather short series of photographs, and keep the conclusion thereof once and for all. Interacting with a text as if it would behave demands for a completely different set of procedures. After all, one would deal with an open interaction. Such openness must be responded to with an appropriate attitude of the willingness for open structural learning.  This holds not only for human interpreters, but rather also for any interpreter, even if it would be software. In other words, the software dealing with text must itself be active in a non-analytical manner in order to constitute what we call a “text”. Any kind of algorithm (in the definition of Knuth) does not deal with text, but just and blindly with a series of dead graphemes.

The Urban

For completely different material reasons cities can be considered also as autonomous entities. Their patterns of growth and differentiation looks much more like that of ensembles of biological entities than that of minerals. Of course, this doesn’t justify the more or less naïve assignment of the “city as organism”. Urban arrangements are complex in the sense we’ve defined it, they are semiogenic and associative. There is a continuous contest between structure as regulation and automation on the one side and liquification as participation and symbolization on the other, albeit symbols may play for both parties.

Despite this autonomy, it remains a fact that without human activity cities are as little alive as texts are. This raises the particular question of the relationships between a city and its inhabitants, between the people as citizens of the city that they constitute. This topic has been subject of innumerable essay, novels, and investigations. Recently, a fresh perspective onto that has been opened by Vera Bühlmann’s notion of the “Quantum City”.[14]

We can neither detach the citizens from their city, not vice versa. Nevertheless, the standardized and externalized collective contribution across space and time creates an arrangement that produces dissipative flows and shows a strong meta-stability that transcends the activities of the individuals. This stability should not be mistaken as a “state”, though. Like for any other complex system, including texts, we should avoid to try to assign a “state” to a particular city, or even a part of it. Everything is a process within a complex system, even if it appears to be rather stable. yet, this stability depends on the perspective of the observer. In turn, the seeming stability does not mean that a city-process could not be destroyed by human activity, let it be by individuals (Nero), by a collective, or by socio-economic processes. Yet, again as in case of complex systems, the question of causality would be the wrong starting point for addressing the issue of change as it would be a statistical description.

Cities and urban environments are fabrics of relations between a wide range of heterogenic and heterotopic (See Foucault or David Shane [15]) entities and processes across a likewise large range of temporal scales, meeting any shade between the material and the immaterial. There is the activity of single individuals, of collectives of individuals, of legislative and other norms, the materiality of the buildings and their changing usage and roles, different kinds of flows and streams as well as stores and memories.

Elsewhere we argued that this fabric may be conceived as a dynamic ensemble of associative networks [16]. Those should be clearly distinguished from logistic networks, whose purpose is given by organizing any kind of physical transfer. Associative networks re-arrange, sort, classify and learn. Such, they are also the abstract location of the transposition of the material into the immaterial. Quite naturally, issues of form and their temporal structure arise, in other words, behavior.

Our suggestion thus is to conceive of a city as en entity that behaves. This proposal has (almost) nothing to do with the metaphor of the “city as organism”, a transfer that is by far too naïve. Changes in urban environments are best conceived as “outcomes” of probabilistic processes that are organized as overlapping series, both contingent and consistent. The method of choice to describe those changes is based on the notion of the generalized context.

Urban Text, Text and Urbanity, Textuality and Performance

Urban environments establish or even produce a particular kind of mediality. We need not invoke the recent surge of large screens in many cities for that. Any arrangement of facades encodes a rich semantics that is best described employing a semiotic perspective, just as Venturi proposed it. Recently, we investigated the relationship between facades, whether made from stone or from screens, and the space that they constitute [17].

There is yet another important dimension between the text and the city. For many hundred years now, if not even millenia, cities are not imaginable without text in one or the other form. Latest since the early 19th century, text and city became deeply linked to one another with the surge of newspapers and publishing houses, but also through the intricate linkage between the city and the theater. Urban culture is text culture, far more than it could be conceived as an image culture. This tendency is only intensified through the web, albeit urbanity now gets significantly transformed by and into the web-based aspects of culture. At least we may propose that there is a strong co-evolution between the urban (as entity and as concept) and mediality, whether it expresses itself as text, as movie or as webbing.

The relationship between the urban and the text has been explored many times. It started probably with Walter Benjamin’s “flâneur” (for an overview see [18]). Nowadays, urbanists often refer to the concept of the “readability” of a city layout, a methodological habit originated by Kevin Lynch. Yet, if we consider the relation between the urban and the textual, we certainly have to take an abstract concept of text, we definitely have to avoid the idea that there are items like characters or words out there in the city. I think, we should at least follow something like the abstract notion of textuality, as it has been devised by Roland Barthes in his “From Work to Text” [19] as a “methodological field”. Yet, this probably is still not abstract enough, as urban geographers like Henri Lefebvre mistook the concept of textuality as one of intelligibility [20]. Lefebvre obviously didn’t understand the working of a text. How should he, one might say, as a modernist (and marxist) geographer. All the criticism that was directed against the junction between the urban and textuality conceived­—as far as we know—text as something object-like, something that is out there as such, awaiting passively to be read and still being passive as it is being read, finally maybe even as an objective representation beyond the need (and the freedom for) interpretation. This, of course, represents a rather limited view on textuality.

Above we introduced the concept of “behaving texts”, that is, texts as active entities. These entities become active as soon as they are mediatized with interpreters. Again: not the text is conceived as the media or in a media-format, but rather the interpreter, whether it is a human brain-mind or a a suitable software tat indeed is capable for interpreting, not just for pre-programmed and blind re-coding. This “behavioral turn” renders “reading” a text, but also “writing” it, into a performance. Performances, on the other hand, comprise always and inevitable a considerable openness, precisely because they let collide the immaterial and the material from the side of the immaterial. Such, performances are the counterpart of abstract associativity, yet also settling at the surface that sheds matter from ideas.

In the introduction to their nicely edited book ”Performance and the City” Kim Solga, D.Hopkins and Shelley Orr [18] write, citing the urban geographer Nigel Thrift:

Although de Certeau conceives of ‘walking in the city’ not just as a textual experience but as a ‘series’ of embodied, creative’ practices’ (Lavery: 152), a ‘spatial acting-out of place’ (de Certeau: 98, our emphasis), Thrift argues that de Certeau: “never really leaves behind the operations of reading and speech and the sometimes explicit, sometimes implicit claim that these operations can be extended to other practices. In turn, this claim [ … ] sets up another obvious tension, between a practice-based model of often illicit ‘behaviour’ founded on enunciative speech-acts and a text-based model of ‘representation’ which fuels functional social systems.” (Thrift 2004: 43)

Quite obviously, Thrift didn’t manage to get the right grip to Certeau’s proposal that textual experience may be conceived—I just repeat it— as a series of embodied, creative practices. It is his own particular blindness that lets Thrift denunciate texts as being mostly representational.

Solsa and colleagues indeed emphasize the importance of performance, not just in their introduction, but also through their editing of the book. Yet, they explicitly link textuality and performance as codependent cultural practices. They write:

While we challenge the notion that the city is a ‘text’ to be read and (re)written, we also argue that textuality and performativity must be understood as linked cultural practices that work together to shape the body of phenomenal, intellectual, psychic, and social encounters that frame a subject’s experience of the city. We suggest that the conflict, collision, and contestation between texts and acts provoke embodied struggles that lead to change and renewal over time. (p.6)

Such, we find a justification for our “behavioral turn” and its application to texts as well as to the urban from a rather different corner. Even more significant, Solsa et al. seem to agree that performativity and textuality could not be detached from the urban at all. Apparently, the urban as a particular quality of human culture more and more develops into the main representative of human culture.

Yet, neither text nor performance, nor their combination count for a full account of the mediality of the urban. As we already indicated above, the movie as kind of a cross-media from text, image, and performance is equally important.

The relations between film and the urban, between architecture and the film, are also quite wide-spread. The cinema, somehow the successor of the theatre, could be situated only within the city. From the opposite direction, many would consider a city without cinemas as being somehow incomplete. The co-evolutionary story between both is still being under vivid development, I think.

There is particularly one architect/urbanist who is able to blend the film and the building into each other. You may know him quite well, I refer to Rem Koolhaas. Everybody knows that he has been an experimental moviemaker in his youth. It is much less known that he deliberately organized at least one of his buildings as kind of a movie: The Embassy of the Netherlands in Berlin (cf. [21]).

Here, Koolhaas arranged the rooms along a dedicated script. Some of the views out of the window he even trademarked to protect them!

Figure 1: Rem Koolhaas, Dutch Embassy, Berlin. The figure shows the script of pathways as a collage (taken from [21]).

9. The Behavioral Turn

So far we have shown how the behavioral turn could be supported and which are some of the first methodological consequences, if we embrace it. Yet, the picture developed so far is not complete, of course.

If we accept the almost trivial concept that autonomous entities are best conceived as behaving entities—remember that autonomy implies complexity—, then we further can ask about the structure of the relationship between the behaving subject and its counterpart, whether this is also a behaving subject or whether it is conceived more like passive object. For Bruno Latour, for instance, both together form a network, thereby blurring the categorical distinction between both.

Most descriptions of the process of getting into touch with something nowadays is dominated by the algorithmic perspective of computer software. Even Designer started to speak about interfaces. The German term for the same thing—“Schnittstelle”—is even more pronounced and clearly depicts the modernist prejudice in dealing with interaction. “Schnittstelle” implies that something, here the relation, is cut into two parts. A complete separation between interacting entities is assumed apriori. Such a separation is deeply inappropriate, since it would work only in strictly standardized environments, up to being programmed algorithmically. Precisely this was told us over and over again by designers of software “user interfaces”. Perhaps here we can find the reason for so many bad designs, not only concerning software. Fortunately, though just through a slow evolutionary process, things improve more and more. So-called “user-centric” design, or “experience-oriented” design became more abundant in recent years, but their conceptual foundation is still rather weak, or a wild mixture of fashionable habits and strange adaptations of cognitive science.

Yet, if we take the primacy of interpretation serious, and combine it with the “behavioral turn” we can see a much more detailed structure than just two parts cut apart.

The consequence of such a combination is that we would drop the idea of a clear-cut surface even for passive objects. Rather, we could conceive objects as being stuffed with a surrounding field that becomes stronger the closer we approach the object. By means of that field we distinguish the “pure” physicality from the semiotically and behaviorally active aspects.

This field is a simple one for stone-like matter, but even there it is still present. The field becomes much more rich, deep and vibrant if the entity is not a more or less passive object, but rather an active and autonomous subject. Such as an animal, a text, or a city. The reason being that there are no apriori and globally definable representative criteria that we could use to approach such autonomous entities. We only can know about more or less suitable procedures about how to derive such criteria in the particular case, approaching a particular individual {text, city}. The missing of such criteria is a direct correlate for their semantic productivity, or, likewise, for their unboundedness.

Approaching a semantically productive entity—such entities are also always able to induce new signs, they are semiosic entities—is reminds to approaching a gravitational field. Yet it is also very different from a gravitational field, since our semio-behavioral field shows increasing structural richness the closer the entities approach to each other. It is quite obvious that only by means of such a semio-behavioral field we can close the gap between the subject and the world that has been opened, or at least deepened by the modernist contributions from the times of Descartes until late computer science. Only upon a concept like the semio-behavioral field, which in turn is a consequence of the behavioral turn, we can overcome the existential fallacy as it has been purported and renewed over and over again by the dual pair of material and immaterial. The language game that separates the material and immaterial inevitably leads into the nonsensical abyss of existentialism. Dual concepts always come with tremendous costs, as they prevent any differentiated way of speaking about the matter. For instance, it prevents to recognize the materiality of symbols, or more precisely, the double-articulation of symbols between the more material and the more immaterial aspects of the world.

The following series of images may be taken as a metaphorical illustration of that semio-behavioral field. We call it the zona extima of the behavioral coating of entities.

Figure 2a: The semio-behavioral field around an entity.

Figure 2b: The situation as another entity approaches perceptively.

Figure 2c: Mutual penetration of semio-behavioral fields.

Taken together we may say, that whenever {sb,sth} gets into contact with {sb, sth}, we do so through the behavioral coating. This zone is of contact is not intimate (as Peter Sloterdijk describes it), it is rather extimate, though there is a smooth and graded change of quality from extimacy to intimacy as the distance decreases. The zona extima is a borderless (topological) field, driven by purposes (due to modelling), it is medial, behaviorally  choreographed as negotiation, exposure, call & request.

The concept of extimation, or also the process of extimating, is much more suitable than “interaction” to describe what‘s going on when we act, behave, engage, actively perceive, encounter with or towards the other. The interesting thing with the web-based media is that some aspects of zona extima can be transferred.

10. Conclusion

In this essay we try to argument in favor of a behavioral turn as a general attitude when it comes to conceive the interaction of any kind of two entities. The behavioral turn is a consequence of three major and interrelated assumptions:

  • – primacy of interpretation in the relation to the world;s;
  • – primacy of process and relation against matter and point;
  • – complexity and associativity in strongly mediatized environments.

All three assumptions are strictly outside of anything that phenomenological, positivist or modernist approaches can talk about or even practice.

It particularly allows to overcome the traditional and strict separation between the material and the immaterial, as well as the separation between the active and the passive. These shifts can’t be underestimated; they have far-reaching consequences upon the way we practice and conceive our world.

The behavioral turn is the consequence of a particular attitude that respects the bi-valency of world as a dynamic system of populations of relations. It is less the divide between the material and the immaterial, which anyway is somewhat an illusion deriving from the metaphysical claim of the possibility of essences. For instance, the jump that occurs between the realms of the informational and the causal establishes as a pair of two complimentary but strictly and mutually exclusive modes of speaking about the orderliness in the world. In some way, it is also the orderliness in the behavior of the observer—as repetition—that creates the informational that the observer than may perceive. The separation is thus a highly artificial one, in either direction. It is simply silly to discuss the issue of causality without referring to the informational aspects (for a full discussion of the issue see this essay). In any real-world case we always find both aspects together, and we find it as behavior.

Actually, the bi-valent aspect that I mentioned before refers to something quite different, in fact so different that we even can’t speak properly about it. It refers to these aspects that are apriori to modeling or any other comprehension, that are even outside to the performance of the individual itself. What I mean is the resistance of existential arrangements, inclusive the body that the comprehending entity is partially built from. This existential resistance introduces something like outer space for the cultural sphere. Needless to say that we can exist only within this cultural sphere. Yet, any action upon the world enforces us to take a short trip into the vacuum, and if we are lucky the re-entrance is even productive. We may well expect an intensification of the aspect of the virtual, as we argued here. Far from being suitable to serve as a primacy (as existentialism misunderstood the issue), the existential resistance, the absolute outside, enforces us to bark on the concept of behavior. Only “behavior” as a perceptional and performative attitude allows to extract coherence from the world without neglecting the fact of that resistance or contumacy.

The behavioral turn triggers a change in the methodology for empiric investigations as well. The standard set of methods for empiric descriptions changes, using the relation and the coherent series always as the starting point, best in its probabilized form, that is, as generalized probabilistic context. This also prevents the application of statistical methods directly to raw data. There should always be some kind of grouping or selection preceding the statistical reasoning. Otherwise we would try to follow the route that Wittgenstein blocked as a “wrong usage of symbols” (in his rejection of the reasonability of Russel/Whitehead’s Principia Mathematica). The concept of abstract behavior inclusive the advanced methodology that avoids to start with representational symbolification is clearly a sound way out of this deep problem from which any positivist empiric investigation suffers.

Interaction, including any action upon some other entity, when understood within the paradigm of behavior, becomes a recurrent, though not repetitive, self-adjusting process. During this process means and symbols may change and be replaced all the way down until a successful handshake. There is no objectivity in this process other than the mutual possibility for anticipation. Despite the existential resistance and contumacy that is attached to any re-shaping of the world, and even more so if we accomplish it by means of tools, this anticipation is, of course, greatly improved upon the alignment to cultural standards, contributing to the life-world as a shared space of immanence.

This provides us finally a sufficiently abstract, but also a sufficiently rich or manifold perspective on the issue of the roles of symbols regarding the text, the urban and the anime, the animal-like. None of those could be comprehended without first creating a catalog or a system of symbols. These symbols, both material and immaterial and thus kind of a hinge, a double-articulation, are rooted both in the embedding culture (as a de-empirifying selective force) and the individual, which constitutes another double-articulation. The concept of abstract behavior, given as a set of particular conditions and attitudes, allows to respond appropriately to the symbolic.

The really big question concerning our choreostemic capabilities—and those of the alleged machinic—therefore is: How to achieve the fluency in dealing with the symbolic without presuming it as a primary entity? Probably by exercising observing. I hope that the suggestions expressed so far in these essay provide some robust starting points. …we will see.


1. Here we simply cite the term of “information retrieval”, we certainly do not agree that the term is a reasonable one, since it is deeply infected by positivist prejudices. “Information” can’t be retrieved, because it is not “out there”. Downloading a digitally encoded text is neither a hunting nor a gathering for information, because information can’t be considered to be an object. Information is only present during the act of interpretation (more details about the status of information you can find here). Actually, what we are doing is simply “informationing”.

2. The notion of a “behavioral turn” is known from geography since the late 1960ies [22][23], and also from economics. In both fields, however, the behavioral aspect is related to the individual human being. In both areas, any level of abstraction with regard to the concept of behavior is missing. Quite in contrast to those movements, we do not focus on the neglect of the behavioral domain when it comes to human society, but rather the transfer of the abstract notion of behavior to non-living entities.

Another reference to “behavioral sciences” can be found in social sciences. Yet, in social sciences “behavioral” is often reduced to “behaviorist”, which of course is nonsense. A similar misunderstanding is abundant in political sciences.

3. Note that the proposed „behavioral turn“ should not be mistaken as a “behavioristic” move, as sort of a behaviorism. We strictly reject the stimulus-response scheme of the behaviorism. Actually, behaviorism as it has been developed by Watson and Pavlov has only little to do with behavior at all. It is nothing else than an overt reductionist program, rendering any living being into a trivial machine. Unfortunately, the primitive scheme of behaviorism is experiencing kind of a come-back in so-called “Behavioral Design”, where people talk about “triggers” much in the same way as Pavlov did (c.f. BJ Fogg’s Behavior Model).


  • [1] Michael Epperson (2009). Quantum Mechanics and Relational Realism: Logical Causality and Wave Function Collapse. Process Studies, 38(2): 339-366.
  • [2] G. Moran, J.C. Fentress (1979). A Search for Order in Wolf Social Behavior. pp.245-283. in: E. Klinghammer (ed.), The Behavior and Ecology of Wolves. Symp. held on 23-24.5.1975 in Wilmington N.C.), Garland STPM Press, New York..
  • [3] Gilles Deleuze, Difference and repetitionGilles Deleuze, Difference and Repetition.
  • [4] J.A.R.A.M. Van Hooff (1982). Categories and sequences of behaviour: methods of description and analysis. in: Handbook of methods in nonverbal behavior research (K.R. Scherer& P. Ekman, eds). Cambridge University Press, Cambridge.
  • [5] P.G.M. van der Heijden, H. de Vries, J.A.R.A.M. van Hooff (1990). Correspondence analysis of transition matrices, with special attention to missing entries and asymmetry. Anim.Behav. 40: 49-64.
  • [6] Teuvo Kohonen, Samuel Kaski, K. Lagus und J. Honkela (1996). Very Large Two-Level SOM for the Browsing of Newsgroups. In: C. von der Malsburg, W. von Seelen, J. C. Vorbrüggen and B. Sendhoff, Proceedings of ICANN96, International Conference on Artificial Neural Networks, Bochum, Germany, July 16-19, 1996, Lecture Notes in Computer Science, Vol. 1112, pp.269-274. Springer, Berlin.
  • [7] Hecht-Nielsen (1994).
  • [8] Javier Rojo Tuan, S. Nguyen (2010). Improving the Johnson-Lindenstrauss Lemma. available online.
  • [9] Sanjoy Dasgupta, Presentation given about: Samuel Kaski (1998), Dimensionality Reduction by Random Mapping: Fast Similarity Computation for Clustering, Helsinki University of Technology 1998. available online.
  • [10] Michel Serres, Nayla Farouki. Le trésor. Dictionnaire des sciences. Falmamrion, Paris 1998. p.394.
  • [11] Bill Hillier, Space Syntax. E-edition, 2005.
  • [12] Bill Hillier (2009). The City as a Socio-technical System: a spatial reformulation in the light of the levels problem and the parallel problem. Keynote paper to the Conference on Spatial Information Theory, September 2009.
  • [13] Alan Hájek (2007). The Reference Class Problem is Your Problem Too. Synthese 156 (3):563-585.
  • [14] Vera Bühlmann (2012). In the Quantum City – design, and the polynomial grammaticality of artifacts. forthcoming.
  • [15] David G. Shane. Recombinant Urbanism. 2005.
  • [16] Klaus Wassermann (2010). SOMcity: Networks, Probability, the City, and its Context. eCAADe 2010, Zürich. September 15-18, 2010. available online.
  • [17] Klaus Wassermann, Vera Bühlmann, Streaming Spaces – A short expedition into the space of media-active façades. in: Christoph Kronhagel (ed.), Mediatecture, Springer, Wien 2010. pp.334-345. available here. available here.
  • [18] D.J. Hopkins, Shelley Orr and Kim Solga (eds.), Performance and the City. Palgrave Macmillan, Basingstoke 2009.
  • [19] Roland Barthes, From Work to Text. in: Image, Music, text: Essay Selected and translated. Transl. Stephen Heath, Hill&Wang, New York 1977. also available online @ google books p.56.
  • [20] Henri Lefebvre, The Production of Space. 1979.
  • [21] Vera Bühlmann. Inhabiting media. Thesis, University of Basel (CH) 2009.
  • [22] Kevin R Cox, Jennifer Wolch and Julian Wolpert (2008). Classics in human geography revisited. “Wolpert, J. 1970: Departures from the usual environment in locational analysis. Annals of the Association of American Geographers 50, 220–29.” Progress in Human Geography (2008) pp.1–5.
  • [23] Dennis Grammenos. Urban Geography. Encyclopedia of Geography. 2010. SAGE Publications. 1 Oct. 2010. available online.


The Text Machine

July 10, 2012 § Leave a comment

What is the role of texts? How do we use them (as humans)?

How do we access them (as reading humans)? The answers to such questions seem to be pretty obvious. Almost everybody can read. Well, today. Noteworthy, reading itself, as a performance and regarding its use, changed dramatically at least two times in history: First, after the invention of the vocal alphabet in ancient Greece, and the second time after book printing became abundant during the 16th century. Maybe, the issue around reading isn’t so simple as it seems in everyday life.

Beyond such accounts of historical issues and basic experiences, we have a lot of more theoretical results concerning texts. Beginning with Friedrich Schleiermacher who was the first to identify hermeneutics as a subject around 1830 and formulated it in a way that has been considered as more complete and powerful than the version proposed by Gadamer in the 1950ies. Proceeding of course with Wittgenstein (language games, rule following), Austin (speech act theory) or Quine (criticizing empirism). Philosophers like John Searle, Hilary Putnam and Robert Brandom then explicating and extending the work of the former heroes. And those have been accompanied by many others. If you wonder about linguistics missing here, well, then because linguistics does not provide theories about language. Today, the domain is largely caught by positivism and the corresponding analytic approach.

Here in his little piece we pose these questions in the context of certain relations between machines and texts. There are a lot of such relations, and even quite sophisticated or surprising ones. For instance, texts can be considered as kind of machines. Yet, they bear a certain note of (virtual) agency as well, resulting in a considerable non-triviality of this machine aspect of texts. Here we will not deal with this perspective. Instead, we just will take a look on the possibilities and the respective practices to handle or to “treat” texts with machines. Or, if you prefer, the treating of texts by machines, as far as a certain autonomy of machines could be considered as necessary to deal with texts at all.

Today, we can find a fast growing community of computer programmers that are dealing with texts as kind of unstructured information. One of the buzz-words is the so-called “semantic web”, another one is “sentiment analysis”. We won’t comment in any detail about those movements, because they are deeply flawed. The first one is trying to formalize semantics and meaning apriori, trying to render the world into a trivial machine. We repeatedly criticized this and we agree herein with Douglas Hofstadter. (see this discussion of his “Fluid Analogy”). The second is trying to identify the sentiment of a text or a “tweet”, e.g. about a stock or an organization, on the basis of statistical measures about keywords and their utterly naive “n-grammed” versions, without actually paying any notice to the problem of “understanding”. Such nonsense would not be as widespread if programmers would read only a few fundamental philosophical texts about language. In fact, they don’t, and thus they are condemned to visit any of the underdeveloped positions that arose centuries ago.

If we neglect the social role of texts for a moment, we might identify a single major role of texts, albeit we have to describe it then in rather general terms. We may say that the role of a text, as a specimen of many other texts from a large population, is its functioning as a medium for the externalization of mental content in order to serve the ultimate purpose, which consists of the possibility for a (re)construction of resembling mental content on the side of the interpreting person.

This interpretation is a primacy. It is not possible to assign meaning to text like a sticky note, then putting the text including the yellow sticky note directly into the recipients brain. That may sound silly, but unfortunately it’s the “theory” followed by many people working in the computer sciences. Interpretation can’t be controlled completely, though, not even by the mind performing it, not even by the same mind who seconds before externalized the text through writing or speaking.

Now, the notion of mental content may seem both quite vague and hopelessly general as well. Yet, in the previous chapter we introduced a structure, the choreostemic space, which allows to speak pretty precise about mental content. Note that we don’t need to talk about semantics, meaning or references to “objects” here. Mental content is not a “state” either. Thinking “state” and the mental together is much on the same stage as to seriously considering the existence of sea monsters in the end of 18th century, when the list science of Linnaeus was not yet reshaped by the upcoming historical turn in the philosophy of nature. Nowadays we must consider it as silly-minded to think about a complex story like the brain and its mind by means of “state”. Doing so, one confounds the stability of the graphical representation of a word in a language with the complexity of a multi-layered dynamic process, spanned between deliberate randomness, self-organized rhythmicity and temporary thus preliminary meta-stability.

The notion of mental content does not refer to the representation of referenced “objects”. We do not have maps, lists or libraries in our heads. Everything which we experience as inner life builds up from an enormous randomness through deep stacks of complex emergent processes, where each emergent level is also shaped from top-down, implicitly and, except the last one usually called “consciousness,” also explicitly. The stability of memory and words, of feelings and faculties is deceptive, they are not so stable at all.  Only their externalized symbolic representations are more or less stable, their stability as words etc.  can be shattered easily. The point we would like to emphasize here is that everything that happens in the mind is constructed on the fly, while the construction is completed only with the ultimate step of externalization, that is, speaking or writing. The notion of “mental content” is thus a bit misleading.

The mental may be conceived most appropriately as a manifold of stacked and intertwined processes. This holds for the naturalist perspective as well as for the abstract perspective, as he have argued in the previous chapter. It is simply impossible to find a single stable point within the (abstract) dynamics between model, concept, mediality and virtuality, which could be thought of as spanning a space. We called it the choreostemic space.

For the following remarks about the relation between text and machines and the practitioners engaged in building machines to handle texts we have to keep in mind just those two things: (i) there is a primacy of interpretation, (ii) the mental is a non-representative dynamic process that can’t be formalized (in the sense of “being represented” by a formula).

In turn this means that we should avoid to refer to formulas when going to build a “text machine”. Text machines will be helpful only if their understanding of texts, even if it is a rudimentary understanding, follows the same abstract principles as our human understanding of texts does. Machines pretending to deal with texts, but actually only moving dead formal symbols back and forth, as it is the case in statistical text mining, n-gram based methods and similar, are not helpful at all. The only thing that happens is that these machines introduce a formalistic structure into our human life. We may say that these techniques render humans helpful to machines.

Nowadays we can find a whole techno-scientific community that is engaged in the field of machine learning, devised to “textual data”. The computers are programmed in such a way that they can be used to classify texts. The idea is to provide some keywords, or anti-words, or even a small set of sample texts, which then are taken by the software as a kind of template that is used to build a selection model. This model then is used to select resembling texts from a large set of texts. We have to be very clear about the purpose of these software programs: they classify texts.

The input data for doing so is taken from the texts themselves. More precisely, they are preprocessed according to specialized methods. Each of the texts gets described by a possibly large set of “features” that have been extracted by these methods. The obvious point is that the procedure is purely empirical in the strong sense. Only the available observations (the texts) are taken to infer the “similarity” between texts. Usually, not even linguistic properties are used to form the empirical observations, albeit there are exceptions. People use the so-called n-gram approach, which is only little more than counting letters. It is a zero-knowledge model about the series of symbols, which humans interpret as text. Additionally, the frequency or relative positions of keywords and anti-words are usually measured and expressed by mostly quite simple statistical methods.

Well, classifying texts is something that is quite different from understanding texts. Of course. Yet, said community tries to reproduce the “classification” achieved or produced by humans. Such, any of the engineers of the field of machine learning directed to texts implicitly claims kind of an understanding. They even organize competitions.

The problems with the statistical approach are quite obvious. Quine called it the dogma of empiricism and coined the Gavagai anecdote about it, which even provides much more information than the text alone. In order to understand a text we need references to many things outside the particular text(s) at hand. Two of those are especially salient: concepts and the social dimension. Straightly opposite to the believe of positivists, concepts can’t be defined in advance to a particular interpretation. Using catalogs of references does not help much, if these catalogs are used just as lists of references. The software does not understand “chair” by the “definition” stored in a database, or even by the set of such references. It simply does not care whether there are encoded ASCII codes that yield the symbol “chair” or the symbol “h&e%43”. Douglas Hofstadter has been stressing this point over and over again, and we fully agree to that.

From that necessity to a particular and rather wide “background” (notion by Searle) the second problem derives, which is much more serious, even devastating to the soundness of the whole empirico-statistical approach. The problem is simple: Even we humans have to read a text before being able to understand it. Only upon understanding we could classify it. Of course, the brain of many people is trained sufficiently as to work about the relations of the texts and any of its components while reading the text. The basic setup of the problem, however, remains the same.

Actually, what is happening is a constantly repeated re-reading of the text, taking into account all available insights regarding the text and the relations of it to the author and the reader, while this re-reading often takes place in the memory. To perform this demanding task in parallel, based on the “cache” available from memory, requires a lot of experience and training, though. Less experienced people indeed re-read the text physically.

The consequence of all of that is that we could not determine the best empirical discriminators for a particular text in-the-reading in order to select it as-if we would use a model. Actually, we can’t determine the set of discriminators before we have read it all, at least not before the first pass. Let us call this the completeness issue.

The very first insight is thus that a one-shot approach in text classification is based on a misconception. The software and the human would have to align to each other in some kind of conversation. Otherwise it can’t be specified in principle what the task is, that is, which texts should actually be selected. Any approach to text classification not following the “conversation scheme” is necessarily bare nonsense. Yet, that’s not really a surprise (except for some of the engineers).

There is a further consequence of the completeness issue. We can’t set up a table to learn from at all. This too is not a surprise, since setting up a table means to set up a particular symbolization. Any symbolization apriori to understanding must count as a hypothesis. Such simple. Whether it matches our purpose or not, we can’t know before we didn’t understand the text.

However, in order to make the software learning something we need assignates (traditionally called “properties”) and some criteria to distinguish better models from less performant models. In other words, we need a recurrent scheme on the technical level as well.

That’s why it is not perfectly correct to call texts “unstructured data”. (Besides the fact that data are not “out there”: we always need a measurement device, which in turn implies some kind of model AND some kind of theory.) In the case of texts, imposing a structure onto a text simply means to understand it. We even could say that a text as text is not structurable at all, since the interpretation of a text can’t never be regarded as finished.

All together, we may summarize the issue of complexity of texts as deriving from the following properties in the following way:

  • – there are different levels of context, which additionally stretch across surrounds of very different sizes;
  • – there are rich organizational constraints, e.g. grammars
  • – there is a large corpus of words, while any of them bears meaning only upon interpretation;
  • – there is a large number of relations that not only form a network, but which also change dynamically in the course of reading and of interpretation;
  • – texts are symbolic: spatial neighborhood does not translate into reference, in neither way;
  • understanding of texts requires a wealth of external, and quite abstract-concepts, that appear as significant only upon interpretation, as well as a social embedding of mutual interpretation,.

This list should at least exclude any attempt to defend the empirico-statistical approach as a reasonable one. Except the fact that it conveys a better-than-nothing attitude. These brings us to the question of utility.

Engineers build machines that are supposedly useful, more exactly, they are intended to be fulfill a particular purpose. Mostly, however, machines, even any technology in general, is useful only upon processes of subjective appropriation. The most striking example for this is the car. Else, computers have evolved not for reasons of utility, but rather for gaming. Video did not become popular for artistic reasons or for commercial ones, but due to the possibilities the medium offered for the sex industry. The lesson here being that an intended purpose is difficult to achieve as of the actual usage of the technology. On the other hand, every technology may exert some gravitational forces to develop a then unintended symbolic purpose and regarding that even considerable value. So, could we agree that the classification of texts as it is performed by contemporary technology is useful?

Not quite. We can’t regard the classification of texts as it is possible with the empirico-statistical approach as a reasonable technology. For the classification of texts can’t be separated from their understanding. All we can accomplish by this approach is to filter out those texts that do not match our interests with a sufficiently high probability. Yet, for this task we do not need text classification.

Architectures like 3L-SOM could also be expected to play an important role in translation, as translation requires even deeper understanding of texts as it is needed for sorting texts according to a template.

Besides the necessity for this doubly recurrent scheme we haven’t said much so far here about how then actually to treat the text. Texts should not be mistaken as empiric data. That means that we have to take a modified stance regarding measurement itself. In several essays we already mentioned the conceptual advantages of the two-layered (TL) approach based on self-organizing maps (TL-SOM). We already described in detail how the TL-SOM works, including the the basic preparation of the random graph as it has been described by Kohonen.

The important thing about TL-SOM is that it is not a device for modeling the similarity of texts. It is just a representation, even as it is a very powerful one, because it is based on probabilistic contexts (random graphs). More precisely, it is just one of many possible representations, even as it is much more appropriate than n-gram and other jokes. We even should NOT consider the TL-SOM as so-called “unsupervised modeling”, as the distinction between unsupervised vs. supervised is just another myth (=nonsense if it comes to quantitative models). The TL-SOM is nothing else than an instance for associative storage.

The trick of using a random graph (see the link above) is that the surrounds of words are differentially represented as well. The Kohonen model is quite scarce in this respect, since it applies a completely neutral model. In fact, words in a text are represented as if they would be all the same: of the same kind, of the same weight, etc. That’s clearly not reasonable. Instead, we should represent a word in several, different manners into the same SOM.

Yet, the random graph approach should not be considered just as a “trick”. We repeatedly argued (for instance here) that we have to “dissolve” empirical observations into a probabilistic (re)presentation in order to evade and to avoid the pseudo-problem of “symbol grounding”. Note that even by the practice of setting up a table in order to organize “data” we are already crossing the rubicon into the realm of the symbolic!

The real trick of the TL-SOM, however, is something completely different. The first layer represents the random graph of all words, the actual pre-specific sorting of texts, however, is performed by the second layer on the output of the first layer. In other words, the text is “renormalized”, the SOM itself is used as a measurement device. This renormalization allows to organize data in a standardized manner while allowing to avoid the symbolic fallacy. To our knowledge, this possible usage of the renormalization principle has not been recognized so far. It is indeed a very important principle that puts many things in order. We will deal later in a separate contribution with this issue again.

Only based on the associative storage taken as an entirety appropriate modeling is possible for textual data. The tremendous advantage of that is that the structure for any subsequent consideration now remains constant. We may indeed set up a table. The content of this table, the data, however is not derived directly from the text. Instead we first apply renormalization (a technique known from quantum physics, cf. [1])

The input is some description of the text completely in terms of the TL-SOM. More explicit, we have to “observe” the text as it behaves in the TL-SOM. Here, we are indeed legitimized to treat the text as an empirical observation, albeit we can, of course, observe the text in many different ways. Yet, observing means to conceive the text as a moving target, as a series of multitudes.

One of the available tools is Markov modeling, either as Markov chains, or by means of Hidden Markov Models. But there are many others. Most significantly, probabilistic grammars, even probabilistic phrase structure grammars can be mapped onto Markov models. Yet, again we meet the problem of apriori classification. Both models, Markovian as well as grammarian, need an assignment of grammatical type to a phrase, which often first requires understanding.

Given the autonomy of text, their temporal structure and the impossibility to apply apriori schematism, our proposal is that we just have to conceive of the text like we do of (higher) animals. Like an animal in its habitat, we may think of the text as inhabiting the TL-SOM, our associative storage. We can observe paths, their length and form, preferred neighborhoods, velocities, size and form of habitat.

Similar texts will behave in a similar manner. Such similarity is far beyond (better: as if from another planet) the statistical approach. We also can see now that the statistical approach is being trapped by the representationalist fallacy. This similarity is of course a relative one. The important point here is that we can describe texts in a standardized manner strictly WITHOUT reducing their content to statistical measures. It is also quite simple to determine the similarity of texts, whether as a whole, or whether regarding any part of it. We need not determine the range of our source at all apriori to the results of modeling. That modeling introduces a third logical layer. We may apply standard modeling, using a flexible tool for transformation and a further instance of a SOM, as we provide it as SomFluid in the downloads. The important thing is that this last step of modeling has to run automatically.

The proposed structure keeps any kind of reference completely intact. It also draws on its collected experience, that is, all texts it have been digesting before. It is not necessary to determine stopwords and similar gimmicks. Of course, we could, but that’s part of the conversation. Just provide an example of any size, just as it is available. Everything from two words, to a sentence, to a paragraph, to the content of a directory will work.

Such a 3L-SOM is very close to what we reasonably could call “understanding texts”. But does it really “understand”?

As such, not really. First, images should be stored in the same manner (!!), that is, preprocessed as random graphs over local contexts of various size, into the same (networked population of) SOM(s). Second, a language production module would be needed. But once we have those parts working together, then there will be full understanding of texts.

(I take any reasonable offer to implement this within the next 12 months, seriously!)


Understanding is a faculty to move around in a world of symbols. That’s not meant as a trivial issue. First, the world consists of facts, where facts comprise an universe of dynamic relations. Symbols are just not like traffic signs or pictograms as these belong to the more simple kind of symbols. Symbolizing is a complex, social, mediatized diachronic process.

Classifying, understood as “performing modeling and applying models” consists basically of two parts. One of them could be automated completely, while the other one could not treated by a finite or apriori definable set of rules at all: setting the purpose. In the case of texts, classifying can’t be separated from understanding, because the purpose of the text emerges only upon interpretation, which in turn requires a manifold of modeling raids. Modeling a (quasi-)physical system is completely different from that, it is almost trivial. Yet, the structure of a 3L-SOM could well evolve into an arrangement that is capable to understand in a similar way as we humans do. More precisely, and a bit more abstract, we also could say, that a “system” based on a population of 3L-SOM once will be able to navigate in the choreostemic space.

  • [1] B. Delamotte (2003). A hint of renormalization. Am.J.Phys. 72 (2004) 170-184, available online: arXiv:hep-th/0212049v3.


Dealing with a Large World

June 10, 2012 § Leave a comment

The world as an imaginary totality of all actual and virtual

relationships between assumed entities can be described in innumerable ways. Even what we call a “characteristic” forms only in a co-dependent manner together with the formation processes of entities and relationships. This fact is particularly disturbing if we encounter something for the first time, without the guidance provided by more or less applicable models, traditions, beliefs or quasi-material constraints. Without those means any selection out of all possible or constructible properties is doomed to be fully contingent, subject to pure randomness.

Yet, this does not result in results that are similarly random. Given that the equipment with tools and methods is given for a task or situation at hand, modeling is for the major part the task to reduce the infiniteness of possible selections in such a way that the resulting representation can be expected to be helpful. Of course, this “utility” is not a hard measure in itself. It is not only dependent on the subjective attitude to risk, mainly the model risk and the prediction risk, utility is also relative to the scale of the scope, in other words, whether one is interested in motor or other purely physical aspects, tactical aspects or strategic aspects, whether one is interested in more local or global aspects, both in time and space, or whether one is interested in any kind of balanced mixture of those aspects. Establishing such a mixture is a modeling task in itself, of course, albeit one that is often accomplished only implicitly.

The randomness mentioned above is a direct corollary of the empirical underdetermination1. From a slightly different perspective, we also may say that it is an inevitable consequence of the primacy of interpretation. And we also should not forget that language and particularly metaphors in language—and any kind of analogical thinking as well—are means to deal constructively with that randomness, turning physical randomness into contingency. Even within the penultimate guidance of predictivity—it is only a soft guidance though—large parts of what we reasonably could conceive as facts (as temporarily fixed arrangement of relations) is mere collaborative construction, an ever undulating play between the individual and the general.
Even if analogical thinking indeed is the cornerstone, if not the Acropolis, of human mindedness, it is always preceded by and always rests upon modeling. Only a model allows to pick some aspect out of the otherwise unsorted impressions taken up from the “world”. In previous chapters we already discussed quite extensively the various general as well as some technical aspects of modeling, from an abstract as well as from a practical perspective.2  Here we focus on a particular challenge, the selection task regarding the basic descriptors used to set up a particular model.

Well, given a particular modeling task we have the practical challenge to reduce a large set of pre-specific properties into a small set of “assignates” that together represent in some useful way the structure of the dynamics of the system that we’d observed. How to reduce a set of properties created by observation that comprises several hundreds of them?
The particular challenge arises even in the case of linear systems if we try to avoid subjective “cut-off” points that are buried deeply into the method we use. Such heuristic means are wide-spread in statistically based methods. The bad thing about that is that you can’t control their influence onto the results. Since the task comprises the selection of properties for the description of the entities (prototypes) to be formed, such arbitrary thresholds, often justified or even enforced just by the method itself, will exert a profound influence on the semantic level. In other words it corroborates its own assumption of neutrality.

Yet, we also never should assume linearity of a system, because most of the interesting real systems are non-linear, even in the case of trivial machines. Brute force approaches are not possible, because the number of possible models is 2^n, with n the number of properties or variables. Non-linear models can’t be extrapolated from known ones, of course. The Laplacean demon3 became completely wrapped by Thomean folds4, being even quite worried by things like Turing’s formal creativity5.

When dealing with observations from “non-linear entities”, we are faced with the necessity to calculate and evaluate any selection of variables explicitly. Assuming a somewhat phantastic figure of 0.0000001 seconds (10e-6) needed to calculate a single model, we still would need 10E15 years to visit all models if we would have to deal with just 100 variables. To make it more palpable: It would take 80 million times longer than the age of the earth, which is roughly 4.8 billion years…

Obviously, we have to drop the idea that we can “proof” the optimality of a particular model. The only thing we can do is to minimize the probability that within a given time T we can find a better model. On the other hand, the data are not of unbounded complexity, since real systems are not either. There are regularities, islands of stability, so to speak. There is always some structure, otherwise the system would not persist as an observable entity. As a consequence, we can organize the optimization of “failure time probability”, we may even consider this as a second-order optimization. We may briefly note that the actual task thus is not only to select a proper set of variables, we also should identify the relations between the observed and constructed variables. Of course, there are always several if not many sets of variables that we could consider as “proper”, precisely for the reason that they form a network of relations, even if this network is probabilistic in nature and itself being kind of a model.

So, how to organize this optimization? Basically, everything has to be organized as nested, recurrent processes. The overall game we could call learning. Yet, it should be clear that every “move” and every fixation of some parameter and its value is nothing else than a hypothesis. There is no “one-shot-approach”, and no linear progression either.
If we want to avoid naive assumptions—and any assumption that remains untested is de facto a naive assumption—we have to test them. Everything is trial and error, or expressed in a more educated manner, everything has to be conceived as a hypothesis. Consequently we can reduce the number of variables only by a recurrent mechanism. As a lemma we conclude that any approach that reduces the number of variables not in a recurrent fashion can’t be conceived as a sound approach.

Contingent Collinearities

It is the structuredness of the observed entity that cause the similarity of any two observations across all available or apriori chosen properties. We also may expect that any two variables could be quite “similar”6 across all available observations. This provides the first two opportunities for reducing the size of the problem. Note that such reduction by “black-listing” applies only to the first steps in a recurrent process. Once we have evidence that certain variables do not contribute to the predictivity of our model, we may loosen the intensity of any of the reductions! Instead of removing it from the space of expressibility we may preferably achieve a weighted preference list in later stages of modeling.
So, if we find n observations or variables being sufficiently collinear, we could remove a portion p(n) from this set, or we could compress them by averaging.
R1: reduction by removing or compressing collinear records.
R2: reduction by removing or compressing collinear variables.
A feasible criterion for assessing the collinearity is the monotonicity in the relationship between two variables as it is reflected by Spearman’s correlation. We also could apply K-means clustering using all variables, then averaging all observations that are “sufficiently close” to the center of the clusters.
Albeit the respective thresholding is only a preliminary tactical move, we should be aware of the problematics we introduce by such a reduction. Firstly, it is the size of the problem that brings in a notion of irreversibility, even if we are fully aware of the preliminarity. Secondly, R1 is indeed critical because it is in some quite obvious way a petitio principii. Even tiny differences in some variables could be masked by larger differences in such variables that penultimately are recognized as irrelevant. Hence, very tight constraints should be applied when performing R1.
When removing collinear records we else have to care about the outcome indicator. Often, the focused outcome is much less frequent than its “opposite”. Preferably, we should remove records that are marked as negative outcome, up to a ratio of 1:1 between positive and negative outcome in the reduced data. Such “adaptive” sampling is similar to so-called “biased sampling”.

Directed Collinearities

Additionally to those two collinearities there is a third one, which is related to the purpose of the model. Variables that do not contribute to the predictive reconstruction of the outcome we could call “empirically empty”.

R3: reduction by removing empirically empty variables

Modeling without a purpose can’t be considered to be modeling at all7, so we always have a target variable available that reflects the operationalization of the focused outcome. We could argue that only those variables are interesting for a detailed inspection that are collinear to the target variable.

Yet, that’s a problematic argument, since we need some kind of model to draw the decision whether to exclude a variable or not, based on some collinearity measure. Essentially, that model claims to predict the predictivity of the final model, which of course is not possible. Any such apriori “determination” of the contribution of a variable to the final predictivity of a model is nothing else than a very preliminary guess. Thus, we indeed should treat it just as a guess, i.e. we should consider it as a propensity weight for selecting the variable. In the first explorative steps, however, we could choose an aggressive threshold, causing the removal of many variables from the vector.


R1 removes redundancy across observations. The same effect can be achieved by a technique called “bagging”, or similarly “foresting”. In both cases a comparatively small portion of the observations are taken to build a “small” model, where the “bag” or “forest” of all small models then are taken to build the final, compound model. Bagging as a technique of “split & reduce” can be applied also in the variable domain.

R4: reduction of complexity by splitting


Once an acceptable model or set of models has been built, we can check the postponed variables one after another. In the case of splitting, the confirmation is implicitly performed by weighting the individual small models.

Compression and Redirection

Elsewhere we already discussed the necessity and the benefits of separating the transformation of data from the association of observations. If we separate it, we can see that everything we need is an improvement or a preservation of the potential distinguishability of observations. The associative mechanism need not to “see” anything that even comes close to the raw data, as long as the resulting association of observations results in a proper derivation of prototypes.8

This opens the possibility for a compression of the observations, e.g. by the technique of random projection. Random projection maps vector spaces onto each other. If the dimensionality of the resulting vector of reduced size remains large enough (100+), then the separability of the vectors is kept intact. The reason is that in a high-dimensional vector space almost all vectors are “orthogonal” to each other. In other words, random projection does not change the structure of the relations between vectors.

R5: reduction by compression

During the first explorative steps one could construct a vector space of d=50, which allows a rather efficient exploration without introducing too much noise. Noise in normalized vector space essentially means to change the “direction” of the vectors, the effect of changing the length of vectors due to random projection is much less profound. Else note that introducing noise is not a bad thing at all: it helps to avoid overfitting, resulting in more robust models.

If we conceive of this compression by means of random projection as a transformation, we could store the matrix of random numbers as parameters of that transformation. We then could apply it in any subsequent classification task, i.e. when we would apply the model to new observations. Yet, The transformation by random projection destroys the semantic link between observed variables and the predictivity of the model. Any of the columns after such a compression contains information from more than one of the input variables. In order to support understanding, we have to reconstruct the semantic link.
That’s fortunately not a difficult task, albeit it is only possibly if we use an index that allows to identify the observations even after the transformation. The result of the building the model is a collection of groups of records, or indices, respectively. Based on these indices we simply identify those variables, which minimize the ratio of variance within the groups to the variance of the means per variable across the groups. This provides us the weights for the list of all variables, which can be used to drastically reduce the list of input variables for the final steps of modeling.

The whole approach could be described as sort of a redirection procedure. We first neglect the linkage between semantics of individual variables and prediction in order to reduce the size of the task, then after having determined the predictivity we restore the neglected link.
This opens the road for an even more radical redirection path. We already mentioned that all we need to preserve through transformation is the distinguishability of the observations without distorting the vectors too much. This could be accomplished not only by random projection though. If we’d interpret large vectors as a coherent “event” we can represent them by the coefficients of wavelets, built from individual observations. The only requirement is that the observations consist from a sufficiently large number of variables, typically n>500.

Compression is particularly useful, if the properties, i.e. the observed variables do not bear much semantic value in itself, as it is the case in image analysis, analysis of raw sensory data, or even in case of the modeling of textual information.


In this small essay we described five ways to reduce large sets of variables, or “assignates” (link) as they are called more appropriately. Since for pragmatic reasons a petitio principii can’t be avoided in attempting such a reduction, mainly due to the inevitable fact that we need a method for it, the reduction should be organized as a process that decreases the uncertainty in assigning a selection probability to the variables.

Regardless the kind of mechanism to associate observations into groups and forming thereby the prototypes, a separation of transformation and association is mandatory for such a recurrent organization being possible.


1. Quine  [1]

2. see: the abstract model, modeling and category theory, technical aspects of modeling, transforming data;

3. The “Laplacean Demon” refers to Laplace’s belief that if all parts of the universe could be measured the future development of the universe could be calculated. Such it is the paradigmatic label for determinism. Today we know that even IF we could measure everything in the universe with arbitrary precision we (what we could not, of course) we even could NOT pre-calculate the further development of the universe. The universe does not develop, it performs an open evolution.

4. Rene Thom [2] was the first to explicate the mathematical theory of folds in parameter space, which was dubbed “catastrophe theory” in order to reflect the subjects experience moving around in folded parameter spaces.

5. Alan Turing not only laid the foundations of deterministic machines for performing calculations; he also derived as the first one the formal structure of self-organization [3]. Based on this formal insights we can design the degree of creativity of a system.

impossibility to know for sure is the first and basic reason for culture.

6. note that determining similarity also requires apriori decisions about methods and scales, that need to be confirmed. In other words we always have to start with a belief.

7. Modeling without a purpose can’t be considered to be modeling at all. Performing a clusterization by means of some algorithm is not creating a model until we do not use it, e.g. in order to get some impression. Yet, as soon as we indeed take a look following some goal we imply a purpose. Unfortunately, in this case we would be enslaved by the hidden parameters built into the method. Things like unsupervised modeling, or “just clustering” always implies hidden targets and implicit optimization criteria, determined by the method itself. Hence, such things can’t be regarded as a reasonable move in data analysis.

8. This sheds an interesting light to the issue of “representation”, which we could not follow here.

  • [1] WvO Quine. Two Dogmas of Empiricism.
  • [2] Rene Thom. Catastrophe Theory
  • [3] Alan Turing (1956) Chemical basis of Morphogenesis



November 19, 2011 § Leave a comment

Without context, there is nothing.

Without context, everything would be a singularized item without relations. There wouldn’t be any facts or events, there would be no information or understanding. The context provides the very basic embedding for events, the background for figures, and also hidden influences to the visible. Context could be the content-side of the inevitable mediality of being. Such, context appears as an ontological term.

Yet, context is a concept as little as ontological as any other concept. It is a matter of beliefs, cognitive capacity and convention where one draws the border between figure and ground. Or even a manifold of borders. Their is no necessity in setting a particular border, even if we admit that natural objects may form material compartments without any “cognitive” activity. Additionally, a context not only does not have borders at all, much like in topology the borderless sets, context is also a deeply probabilistic concept. In an important sense, contexts can be defined as positively definite entities only to some extent. The constraint as a way to express the context ex negativo is an important part of the concept of context. Yet, even the constraints have to be conceived as a  probabilistic actualization, as their particular actualization could be dependent on the “local” history or situation.

After all, the concept of context shares a lot with texts and writing, or, even more appropriate, with stories and narrating. As a part of a text, the context becomes subject to the same issues as the text itself. We may find grammaticality, the implied issue of acting as in the speech-act-theory, style and rhetoric, and a runaway interpretive vortex, as in Borges, or any poem. We have to consider this when we are going to choose the tools for modeling and comparing texts.

The neighborhood of texts and contexts points to the important issue of the series, and hence of time and memory. Practically spoken, in order to possibly serve as part of a context synchronicity of signs (not: signals!) have to be established. The degree of the mutual influence as well as the salience of signs is neither defined nor even definable apriori. It is the interpretation itself (understood as streaming process) that eventually forms groups of signs, figures and background by similarity considerations. Before the actual interpretation, but still from the perspective of the interpreting entity, a context is defined only in probabilistic terms. Within the process of an interpretation, now taken the position inside that process itself, the separation of signals into different signs, as well as the separation of signs into different groups, figures or background necessarily needs other “signs” as operable and labeled compounds of rules and criteria. Such “compound” entities are simply (abstract) models, brought in as types.

This result is quite important. In the definition of the concept of context it allows us to refer to signs without committing the symbolic fallacy, if the signs are grounded as operable models outside of the code of the software itself. Fortunately, self-organizing maps (SOM) are able to provide exactly this required quality.

The result provides also hints to issues in a quite different area: the understanding of images. It seems that images can not be “understood” without the use of signs, where those signs have been acquired outside of the actual process of interpreting the pixel information of an image (of course, that interpretation is not limited to descriptions on the level of pixels, despite the fact that any image understanding has to start there)

In the context of our interests here, focusing on machine-based epistemology, the concept of context is important with regard to several aspects. Most generally spoken, any interpretation of data requires a context. Of course, we should neither try to exactly determine the way of dealing with context,  nor even to define the criteria to define a particular context. In doing so, we would commit the symbolic fallacy. Any so-called ontology in computer sciences is a direct consequence of getting victimized by this fallacy.

Formalizing the concept of context does not (and can not) make any proposals about how a context has been formed or established. The formalization of context is a derived, symbolic, hence compressed view of the results of context formation. Since such a description of a context can be exported itself, the context exerts normative power. This normative power can be used, for example, to introduce a signal horizon in the population of self-organized maps (SOMs): not any SOM instance can get any message from another such instance, if contexts are used for organizing messaging between SOM instances. From a slightly shifted perspective we also could say that contexts provide the possibility to define rules that organize affectability.

In order to use that possibility without committing the symbolic fallacy we need a formalization on an abstract level. Whatever framework we use to organize single items—we may choose from set theory, topology or category theory— we also have to refer to probability theory.

A small Example

Before we start to introduce the formalization of context, we would like to provide a small example.

Sometimes, and actually more often than not, a context is considered to embed something. Let us call this item z. The embedding of z together with z then constitutes a context 𝒵, of which z is a part.Let us call the embedding E, then we could write:

𝒵 = {z, E}

Intuitively, however, we won’t allow any embedding. There might be another item p, or more generally p out of a set P, that prohibits to consider  {z, E} as 𝒵.

So we get

𝒵 ≠ {z, E, P}

or, equivalently,

𝒵 = {z, E, ¬P}

Again intuitively, we could think about items that would not prohibit the establishment of a context as a certain embedding, but if there are too much of them, we would stop to consider the embedding as a particular context. Similarly, we can operationalize the figure-ground phenomenon by restricting the length of the embedding that still would be considered as 𝒵. Other constraints could come as mandatory/probabilistic rules addressing the order of the items. Finally, we could consider a certain arrangement of items as a context even without a certain mandatory element z.

These intuitions can now be generalized and written down in a more formal way, e.g. to guide an implementation, or as we will see below, to compare it to other important formal ideas.

Components by Intuition

A context consists of four different kinds of sets, the threshold values associated them, and order relations between pairs of items of those sets. Not all of the components need to be present at the same time, of course. As we have seen, we even may drop the requirement of a particular mandatory item.

The sets are

  • – mandatory items
  • – normal items
  • – facultative items
  • – stopping items

Context, formalized

In the formal definition we do not follow the distinction of different sets as guided by intuition. A proper generalization moves the variability into mappings, i.e. functions. We need then two different kinds of mappings. The first one controls the actualization function, which reflects the relation between presence of an item and the assignment of a context. In some respect, we could call it also a “completeness function.” The second mapping describes order relations.

Such, we propose to start with three elements for a definition of the generalized context. On the upmost level we may say that a context is a collection of items, accompanied by two functions that establish the context by a combination of implying a certain order and demanding a particular completeness.

So, starting with the top level we introduce the context 𝒞 as the 3-tupel

  • 𝒞 = { Ci, A, R }

where Ci is the collection of items, A denotes the actualization function, and finally  R is a function that establishes certain relations between the item c of Ci. The items i need not be items in the sense of set theory. If a more general scope needs to be addressed, items could also be conceived as generic items, e.g. representing categories.
𝒞 itself may be used as a simple acceptance mapping

  • 𝒞: F{0,1}

or as a scalar

  • 𝒞: F { x | 0>=x>=1 }

In the second form we may use our context as basis for similarity measure!

The items c of the collection Ci have a weight property. The weight of an item is simply a degree of expectability. We call it w.

The actualization (completeness) function A describes the effect of three operations that could be applied to the collection Ci. All of those operations can be represented by thresholds.

Items c could be either

  • (i) removed,
  • (ii) non-C-items could be inserted to (or appear in) a particular observation,
  • (iii) C-items could be repeated, affecting the actual size of an observation.
  • A(1): The first case is a deterioration of the “content” of the context. This operation is modulated by the weight w of the items c. We may express this aspect as a degree of internal completeness over the collection Ci. We call it pi.
  • A(2): The second case represents a “thinning” or dilution. This affects the density of the occurrence of the items c within a given observation. We call it px.
  • A(3): The third operation of repeating items c of Ci affects the size of the observation. A context is a context only if there is some other thing than the context. Rather trivially, if the background—by definition the context—becomes figure—by definition not the context—, it is not a context any more. We may denote it simply by the symbol l. l could be given as a maximum length, or as a ratio invoking the size of C.
  • A(4) : The contrast function K, describing the differential aspect of the item sets (of the same type) between two patterns, defined as
    𝒦(x,y) = F(X ∩ Y, α(X-Y), β(Y-X)), α, β ≥ 0,
    with the possible instantiation as a ratio model
    K(a,b) = f(A ∩ B) / f(A ∩ B)+ αf(A-B)+ βf(B-A)

The last aspect of a context we have to consider is the relation R between items c. These relations are described by two functions S and D, the neighborhood function S, the dependency function D.

  • R(1) : The set of all neighborhood function S upon items c results in a partial and probabilistic serial order. One might think for instance about a context with items (v,w,x,y), where S determines a partial order such that the context gets established only if v follows x.
  • R(2) : The dependency function D(ck) imposes a constraint on pi, since it demands the actual co-occurrence of the argumented items ck.

Any formalism to express the serial order of symbolic items is allowed here, whether it is an explicit formalism like a grammar or a finite-state-automaton, or an implicit formalism like a probabilistic associative structure (ANN or SOM) accepting only particular patterns. Imposing a serial order also means to introduce asymmetries regarding the elements.

So we summarize our definition of the concept of context:

  • 𝒞 = { Ci, A, R } eq.1

where the individual terms unfold to:

  • Ci = { c (w) } eq.2, “sets, items & weights”
  • A = f( pi, px, l, K) eq.3, “actualization”
  • R = S ∩ D  eq.4, “relations”

This formal definition of the concept of context is situated on a very general level. Most important, we can use it to represent contextual structures without defining the content or the actualization of a particular instance of the concept at implementation time. Decisions about passing or accepting messages have been lifted to the operable, hence symbolic level. In terms of software architecture we can say, much like it is the case for SOM, that conditions are turned into data. In category theory we meet a similar shift of perspective, as the representability of a transformation (depictable by the “categorial triangle”) is turned into a symbol.

The items forming a context need not to be measurable on the elementary symbolic level, i.e. the items need not to form an alphabet 𝒜. We could think of pixels in image processing, for instance, or more general, any object that could be compared along a simple qualitative dimension (which could be the result of a binary mapping, of course). Yet, in the end a fixation of the measurement of the respective entity has to result in at least one alphabet, even if the items are abstract entities like categories in the mathematical sense. In turn, whenever one invokes the concept of context, this also implies any arbitrary mode of discretization of the measured “numerical” signal. Without letters, i.e. quasi-material symbols, there is no context. Without context, we would not need “letters”.

In the scientific literature, especially about thesauri, you may find similar attempts to formalize the notion of context. We have been inspired by those, of course. Yet, here we introduced it for a different purpose… and in a different context. Given the simple formalization above, we now can implement it.

Random Contexts, Random Graphs

A particular class of concepts we would like to mention here briefly, because they are essential for a certain class of self-organizing maps that have been employed in the so-called WebSom project. This class of SOMs could be described as two-layered abstracting SOM. For brevity, let us call them 2A-SOM here.

2A-SOM are used for the classification of texts with considerable success. The basic idea is to conceive of texts as a semi-ordered set of probabilistic contexts. The 2A-SOM employs random contexts, which are closely related to random graphs.

A particular random context is centered around a selected word that occurs several times in a text (or a corpus of texts). The idea is quite simple. Any of the words in a text gets a fingerprint vector assigned, consisting of random values from  [0..1], and typically of a minimal length of 80..100 positions. To build a random context one measures all occurrences of the targeted word. The length of the random context, say L(rc), is set as an odd number, i.e. L(rc) = 2*n+1, where the targeted word is always put to the center position. “n” then describes the number of preceding/succeeding positions for this word. The random context then is simply the superposition of all fingerprint vectors in the neighborhood of the targeted word. So it should be clear that a random context describes all neighborhoods of a text (or a part of it) in a single set of values.

With respect to our general notion of context there are some obvious differences to the random context as used in 2A-SOM:

  • – constant length
  • – assumption of zero knowledge: no excluding items can be represented, no order relations can be represented;

An intermediate position between the two concepts would introduce a separate weighting function W(0,1) ↦ {0,1}, which could be used to change the contribution of a particular context to the random context.

The concept of context as defined here is a powerful structure that provides even the possibility of a translation into probabilistic phrase structure grammar, or equivalently, into a Hidden-Markov-Model (HMM).

Similarity and Feature Vectors

Generalized feature vectors are an important concept in predictive modeling, especially for the task of calculating a scalar that represents a particular similarity measure. Generalized feature vectors comprise both (1) the standard vector, which basically is a row extracted from a table containing observational data about cases (observations), and (2) the feature set, that may differ between observations. Here, we are interested in this second aspect.

Usually, the difference of the set of features taken from two different observations is evaluated under the assumption that all the features are equally important. It is obvious that this is not appropriate for many cases. One possibility to replace the naive approach that treats all items in the same way is the concept of concept as developed here. Instead of simple sets without structure it is possible to use weights and order relations, both as dynamic parameters that may be adjusted during modeling. In effect, the operationalization of similarity can be changed while searching for the set of appropriate models.

Concerning the notion of similarity, our concept of context shares important ideas with the concept proposed by Tversky [1], for instance the notion of asymmetry. Tversky’s approach is, however, much more limited as compared to ours.

Modeling and Implementation

Random contexts as well as structured probabilistic contexts as defined above provide a quite suitable tool for the probabilization of the input for a learning SOM. We already have reasoned in the chapter about representation that such probabilization is not only mandatory, it is inevitable: words can’t be presented (to the brain, the mind or a SOM) as singularized “words”: they need context, the more the better, as philosophical theories about meaning or those about media suggest. The notion of context (in the way defined above) is also a practicable means to overcome the positivistic separation of syntax, semantics and pragmatics, as it has been introduced by Morris [2]. Robert Brandom in his inferentialist philosophy labeled “expressive reason” denies such a distinction, which actually is not surprising. His work starts with the primacy of interpretation, just as we do [3].

It is clear that any representation of a text (or an image) should always be started as a context according to our definition. Only in this case a natural differentiation could take place from symmetric treatment of items to their differentiated treatment.

A coherent object that consists of many parts, such like a text or an image, can be described as a probabilistic “network” of overlapping (random) contexts. Random contexts need to be used if no further information is available. Yet, even in the case of a first mapping of a complicated structure there is more information available than “no information.” Any further development of a representation beyond the zero-knowledge approach will lead to the context as we have defined it above.

Generalized contexts may well serve as a feasible candidate for unifying different approaches of probabilistic representation (random graphs/contexts) as well as operationalizations of similarity measures. Tversky’s feature-set-based similarity function(al) as well as feature-vector-based measures are just particular instances of our context. In other words, probabilistic representation, similarity and context can be handled using the same formal representation, the difference being just one of perspective (and algorithmic embedding). This is a significant result not only for the practice of machine-based epistemology, but also for philosophical questions around vagueness, similarity and modeling.

This article was first published 19/11/2011, last revision is from 30/12/2011

  • [1] Amos Tversky (1977), Features of Similarity. Psychological Review, Vol.84, No.4. available online
  • [2] Charles Morris,
  • [3] Robert Brandom, Making it Explicit, chp.8.6.2



October 24, 2011 § Leave a comment

Representation always has been some kind of magic.

Something could have been there—including all its associated power—without being physically there. Magic, indeed, and involving much more than that.

Literally—if we take the early Latin roots as a measure—it means to present something again, to place sth. again or in an emphasized style before sth. else or somebody, usually by means of placeholder, the so-called representative. Not surprising then it is closely related to simulacrum which stands for “likeness, image, form, representation, portrait.”

Bringing the notion of the simulacrum onto the table is dangerous, since it refers not only to one of the oldest philosophical debates, but also to a central one: What do we see by looking onto the world? How can it be that we trust the images produced by our senses, imaginations, apprehensions? Consider only Platon’s famous answer that we will not even cite here due to its distracting characteristics and you can feel the philosophical vortices if not twisters caused by the philosophical image theory.

It is impossible to deal here with the issues raised by the concepts of representation and simulacrum in any more general sense, we have to focus on our main subject, the possibility and its conditions for machine-based epistemology.

The idea behind machine-based epistemology is to provide a framework for talking about the power of (abstract and concrete) machines to know and to know about the conditions of that (see the respective chapter for more details). Though by “machine” we do not understand a living being here, at least not apriori, it is something produced. Let us call the producer in a simplified manner a “programmer.” In stark contrast to that, the morphological principles of living organisms are the result of a really long and contingent history of unimaginable 3.6 billion years. Many properties, as well as their generalizations, are historical necessities, and all properties of all living beings constitute a miraculous co-evolutionary fabric of dynamic relations. In case of the machine, there are only little historic necessities, for the good and the bad. The programmer has to define necessities, the modality of senses, the chain of classifications, the kind of materiality etc.etc. Among all these decisions there is one class that is predominantly important:

How to represent external entities?

Quite naturally, as “engineers” of cognitive machines we can not really evade the old debate about what is in our brains and minds, and what’s going on there while we are thinking, or even just recognizing a triangle as a triangle. Our programmer could take a practical stance to this question and reformulate it as: How could she or he achieve that the program will recognize any triangle?

It needs to be able to distinguish it from any other figure, even the program never has been confronted with an “ideal” template or prototype. It also needs to identify quite incorrect triangles, e.g. from hand drawings, as triangles. It even should be able to identify virtual figures, which exist only in their negativity like the Kanizsa-triangle. For years, computer scientists proposed logical propositions and shape grammars as a solution—and failed completely. Today, machine learning in all its facets is popular, of course. This choice alone, however, is not yet the solution.

The new questions then have been (and still are): What to present to the learning procedure? How to organize the learning procedures?

Here we have to care about a threatening misunderstanding, actually of two misunderstandings, heading from opposite directions to the concept of “data.” Data are of course not “just there.” One needs a measurement device, which in turn is based on a theory, then on a particular way to derive models and devices from that theory. In other words, data are dependent on the culture. So far, we agree with Putnam about that. Nevertheless, given the body of a cognitive entity, that entity, whether human, animal or machine, finds itself “gestellt” into a particular actuality of measurement in any single situation. The theory about the data is apriori, yet within the particular situation the entity finds “raw data.” Both, theory and data impose severe constraints on what can be perceived by or even known to the cognitive entity. Given the data, the cognitive entity will try to construct diagnostic / predictive models, including schemes of interpretations, theories, etc.  The important question then is concerned about the relationship between apriori conditions regarding the cognitive entity and the possibly derived knowledge.

On the other hand, we can defend us against the second misunderstanding. Data may be conceived as (situational) “givens”, as the Latin root of the word suggests. Yet, this givenness is not absolute. Somewhat more appropriate, we may conceive data as intermediate results of transformations. This renders any given method into some kind of abstract measurement device. The label of “data” we usually just use for those bits whose conditions of generation we can not influence.

Consider for instance a text. For the computer a text is just a non-random series of graphemes. We as humans can identify a grammar in human languages. Many years, if not decades, people thought that computers will understand language as soon as grammar has been implemented. The research by Chomsky [1], Jackendoff [2] and Pinker [3], among others, is widely recognized today, resulting in the concepts of phrase structure grammar, x-bar syntax or head-driven syntax. Yet, large research projects with hundreds of researchers (e.g. “verbmobil”) did not only not reach the self-chosen goals, they failed completely on the path to implement understanding of language. Even today, for most languages there is no useful parser available, the best parser for German language achieves around 85-89% accuracy, which is disastrous for real applications.

Another approach is to bring in probabilistic theories. Particularly n-grams and Markov-models have been favored. While the first one is an incredibly stupid idea for the representation of a text, Markov-models are more successful. It can be shown, that they are closely related to Bayes belief networks and thus also to artificial neural networks, though the latter employ completely different mechanism as compared to Markov-models. Yet, from the very mechanism and the representation that is created as/by the Markov-model, it is more than obvious that there is no such thing as language understanding.

Quite obviously, language as text can not be represented as a grammar plus a dictionary of words. Doing so one would be struck by the “representational fallacy,” which not only has been criticized by Dreyfus recently [4], it is a matter of fact that representationalist in machine learning approaches failed completely. Representational cognitivism claims that we have distinct image-like engrams in our brain when we are experiencing what we call thinking. They should have read Wittgenstein first (e.g. About Certainty), before starting expensive research programs. That experience about one’s own basic mental affairs is as little directly accessible as any other thing we think or talk of. A major summary of many subjections against the representationalist stance in theories about the mind, as well as a substantial contribution is Rosenfield’s “The Invention of Memory” [6]. Rosenfield argues strongly against the concept of “memory as storage,” in the same venue as Edelman, to which we fully agree.

It does not help much either to resort to “simple” mathematical or statistical models, i.e. models effectively based on an analytical function, as apposed to models based on a complex system. Conceiving language as a mere “random process” of whatsoever kind simply does not work, let it be those silly n-grams, or sophisticated Hidden Markov Models. There are open source packages in the web you can use to try it yourself.

But what then “is” a text, how does a text unfold its effects? Which aspects should be presented to the learning procedure, the “pattern detection engine,” such that the regularities could be appropriately extracted and a re-presentation could be built? Taking semiotics into account, we may add links between words. Yet, this involves semantics. Peter Janich has been arguing convincingly that the separation of syntax and semantics should be conceived of as just another positivist/cyberneticist myth [5]. And on which “level” should links be regarded as significant signals? If there are such links, any text renders immediately into a high-dimensional non-trivial and above all dynamic network…

An interesting idea has been proposed by the research group around Teuvo Kohonen. They invented a procedure they call the WebSom [7]. You can find material in the web about it, else we will discuss it in great detail within our sections devoted to the SOM. There are two key elements of this approach:

  • (1) It is a procedure which inherently abstracts from the text.
  • (2) the text is not conceived—and (re-)presented—as “words”, i.e. distinct lexicographical primitives; instead words are mapped into the learning procedure as a weighted probabilistic function of their neighborhood.

Particularly seminal is the second of the key properties, the probabilization into overlapping neighborhoods. While we usually think that words a crisp entities arranged into a structured series, where the structure follows a grammar, or is identical with it,  this is not necessarily appropriate, even not for our own brain. The “atom” of human language is most likely not the word. Until today, most (if not all people engaged in computer linguistics) think that the word, or some very close abstraction of it, plus some accidentia, forms the basic entities, the indivisible of language.

We propose that this attitude is utterly infected by some sort of pre-socratic and romantic cosmology, geometry and cybernetics.We even can’t know which representation is the “best”, or even an appropriate one.  Even worse, the appropriateness of the presentation of raw data to the learning procedure via various pre-processors and preparation of raw data (series of words) is not independent from the learning procedure. We see that the problems with presentation and representation reach far into the field of modeling.

Despite we can’t know in principle how to perform measurements in the most appropriate manner, as a matter of fact we will perform some form of measurement. Yet, this initial “raw data” does not “represent” anything, even not the entity being subject of the measurement. Only a predictive model derived from those observations can represent an entity, and it does so only in a given context largely determined by some purpose.

Whatsoever such an initial and multiple presentation of an entity will look like, it is crucial, in my opinion, to use a proababilized preparation of the basic input data. Yet, components of such preparations not only comprise the raw input data, but also the experience of the whole engine, i.e. a kind of semantic influence, acquired by learning. Further (potential) components of a particular small section of a text, say a few words, are any kind of property of the embedding text, of any extent. Not only words as lexemes, but also words as learned entities, as structural elements, then also sentences and their structural (syntactical)) properties, semantic or speech-pragmatic markers, etc.etc. and of course also including a list of properties as Putnam proposed already in 1979 in “The meaning of “Meaning” [8].”

Taken together we can state that the input to the association engine are probabilistic distributions about arbitrarily chosen “basic” properties. As we will see in the chapter on modeling, these properties are not to be confused with objective facts to be found in the external world. There we also will see how we can operationalize these insights into implementation. In order to enable a machine to learn how to use words as items of a language, we should not present words in their propositional form to it. Any entity has to be measured as a entity from a random distribution and represented as a multi-dimensional probability distribution. In other words, we deny the possibility to transmit any particular  representation into the machine (or another mind as well). A particular manifold of representations has to built up by the cognitive entity itself in direct response to requirements of the environment, which is just to be conceived as the embedding for “situations.” In the modeling chapter we will provide arguments for the view that this linkage to requirements does not result in behavioristic associativism, the simple linkage between simulus and response according to the framework proposed by Watson and Pawlow. Target-oriented modeling in the multi-dimensional case necessarily leads to a manifold of representations. Not only the input is appropriately described by probability distributions, but also the output of learning.

And where is the representation of the learned subject? How does it look like? This question is almost sense-free, since it would require to separate input, output, processing, etc. it would deny the inherent manifoldness of modeling, in short, it is a deeply reductionist question. The learning entity is able to behave, react, anticipate, and to measure, hence just the whole entity is the representation.

The second important anatomical property of an entity able to acquire the capability to understand texts is the inherent abstraction. Above all, we should definitely not follow the flat world approach of the positivist ideology. Note, that the programmer should not only not build a dictionary into the machine; he also should not pre-determine the kind of abstraction the engine develops. This necessary involves internal differentiation, which is another word for growth.

  • [1] Noam Chomsky (to be completed…)
  • [2] Jackendoff
  • [3] Steven Pinker 1994?
  • [4] Hubert L Dreyfus, How Representational Cognitivism Failed and is being replaced by Body/World Coupling. p.39-74, in: Karl Leidlmair (ed.), After Cognitivism: A Reassessment of Cognitive Science and Philosophy, Springer, 2009.
  • [5] Peter Janich. 2005.
  • [6] Israel Rosenfield, The Invention of Memory: A New View of the Brain. New York, 1988.
  • [7] WebSom
  • [8] Hilary Putnam, The Meaning of “Meaning”. 1979.


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