Junkspace, extracted.

July 16, 2012 § Leave a comment

Some years after “The Generic City” Koolhaas published

a further essay on the problematic field of identity: “Junkspace” (JS).[1] I think it is a good idea to introduce both of them and to relate them before discussing the issues of this field by ourselves.

Unlike “The Generic City” (TGC), which was constructed as kind of a report about a film script, JS is more like a “documentary manifesto,” certainly provocative (for thought?), but also not a theory. “Junkspace” throws a concept in/out, according to its message, one could say. As in TGC, Koolhaas tries to densify and to enhance contrasts in order to render the invisible visible. Its language thus should not be misunderstood as “apocalyptic” or the like, or as a reference to actual “facts”. We else must consider that even documentations are inevitably equipped with theories and models, intentions and expectations. The biggest difference between the two essays is probably the fact that in JS Koolhaas does not try to keep distance through the formal construction of the writing. Hence, it may be legitimate to read his essay indeed as kind of a seriously taken diagnosis.

In many ways, JS reads as a critique of modernism and of post-modernism, not just as attitudes in architecture, but rather concerning the whole culture, ending in a state where the “cosmetic is the new cosmic.” Albeit critique is not made (too) explicit, trying to avoid bringing in explicit value statements, the tone of JS appears negative. Yet, it does so only upon the reader’s interpretation. “Junkspace is a low-grade purgatory.” In Christian mythology, everybody had to pass it, the good ones and the evil ones, except the bravest saints, perhaps. Failure is expressed, but by referring to a certain otherworldliness: “We do not leave pyramids.”

The style of JS is ambiguous itself, presumably intentionally so. On the one hand, it reminds to mathematical, formal series of sentences. Sections often start with existential proposals: “Junkspace is …”. Together, as a series, or a hive, these imply  unspoken axioms. On the other hand it seems as if Koolhaas hesitates to use the figure of logic, or accordingly of cause and effect, with regard to the Junkspace itself. Such, Koolhaas exhibits performatively a clear-cut non-modern, or should we say “meta-modern”, attitude. By no means this should be taken as kind of some irrationality, though. We just find lines of historical developments, often even only historizing contrasts. This formal structure is anything but a self-righteous rhetoric game, it’s more like a necessary means to maintain some distance to modernism. The style of JS could be considered as (empty) rhetoric only from within  a modernist attitude.

Before we deal further with modernism (below, and more extensively here), I first want to list my selection of core passages. The sections in Koolhaas’ text are neither enumerated nor divided by headlines (no hierarchies! many “…”! a Junkspace…), so I provide the page numbers in order to facilitate reference. Additionally, I enumerated the pieces for referencing them from within our own writing.

Here is the extract from Junkspace; it is of  course hard to do such a selection—even if we allow for a total of 59 passages—, as JS is rather densely written. Koolhaas begins with some definitions before turning to its properties, readings and implications:

Précis of “Junkspace”


1. “Identity” is the new junk food for the dispossessed, globalization’s fodder for the disenfranchised … […] Junk-Space is the residue mankind leaves on the planet. The built […] product of modernization is not modern architecture but Junkspace. Junkspace is what remains after modernization has run its course, or, more precisely, what coagulates while modernization is in progress, its fallout. Modernization had a rational program: to share the blessings of science, universally. Junkspace is its apotheosis, or meltdown.

2. Junkspace is the sum total of our current achievement;

3. It was a mistake to invent modern architecture for the twentieth century. Architecture disappeared in the twentieth century; we have been reading a footnote under a microscope hoping it would turn into a novel;

4. […] our concern for the masses has blinded us to People’s Architecture. Junkspace seems an aberration, but it is the essence, the main thing. the product of an encounter between escalator and air-conditioning.

5. Continuity is the essence of Junkspace.


6. Junkspace is sealed, held together not by structure but by skin, like a bubble.

7. Junkspace is a Bermuda Triangle of concepts, an abandoned petri dish: it cancels distinctions, undermines resolve, confuses intention with realization. It replaces hierarchy with accumulation, composition with addition. […] A fuzzy empire of blur, it […] offer[s] a seamless patchwork of the permanently disjointed. […] Junkspace is additive, layered, and lightweight, not articulated in different parts but subdivided, […].

8. Junkspace’s iconography is 13 percent Roman, 8 percent Bauhaus and 7 percent Disney (neck and neck), 3 percent Art Nouveau, followed closely by Mayan.


9. Junkspace is beyond measure, beyond code … Because it cannot be grasped, Junks pace cannot be remembered. It is flamboyant yet unmemorable, like a screen saver;

10. Junkspace’s modules are dimensioned to carry brands;

11. Junkspace performs the same role as black holes in the universe: they are essences through which meaning disappears.

12. Junkspace is best enjoyed in a state of post-revolutionary gawking. Polarities have merged.

13. Modern architecture […] exposes what previous generations kept under wraps: structures emerge like springs from a mattress.

14. Junkspace thrives on design, but design dies in Junkspace […] Regurgitation is the new  creativity.

15. Superstrings of graphics, […] LEDs, and video describe an authorless world beyond anyone’s claim, always unique, utterly unpredictable, yet intensely familiar.


16. Junkspace sheds architectures like a reptile sheds skins, is reborn every Monday morning.

17. Architects thought of Junkspace first and named it Megastructure, the final solution to transcend their huge impasse.

18. In Junkspace, the tables are turned: it is subsystem only, without superstructure, orphaned particles in search of a framework or pattern.

19. Each element performs its task in negotiated isolation.

20. Instead of development, it offers entropy.

21. Change has been divorced from the idea of improvement. There is no progress; like a crab on LSD, culture staggers endlessly sideways …

22. Everywhere in Junkspace there are seating arrangements, ranges of modular chairs, even couches, as if the experience Junkspace offers its consumers is significantly more exhausting than any previous spatial sensation;


23. Junkspace is fanatically maintained, the night shift undoing the damage of the day shift in an endless Sisyphean replay. As you recover from Junkspace, Junkspace recovers from you.

24. Traditionally, typology implies demarcation, the definition of a singular model that excludes other arrangements. Junkspace represents a reverse typology of cumulative, approximative identity, less about kind than about quantity. But formlessness is still form, the formless also a typology.

25. Junkspace can either be absolutely chaotic or frighteningly aseptic-like a best-seller-overdetermined and indeterminate at the same time.

26. Junkspace is often described as a space of flows, but that is a misnomer; flows depend on disciplined movement, bodies that cohere. Junkspace is a web without a spider; […] It is a space of collision, a container of atoms, busy, not dense …


27. Junkspace features the tyranny of the oblivious: sometimes an entire Junkspace comes unstuck through the nonconformity of one of its members; a single citizen of an another culture-a refugee, a mother-can destabilize an entire Junkspace, […]

28. Flows in Junkspace lead to disaster: department stores at the beginning of sales; the stampedes triggered by warring compartments of soccer fans;

29. Traffic is Junkspace, from airspace to the subway; the entire highway system is Junkspace […]

30. Aging in Junkspace is nonexistent or catastrophic; sometimes an entire Junkspace—a department store, a nightclub, a bachelor pad-turns into a slum overnight without warning.


31. Corridors no longer simply link A to B, but have become “destinations.” Their tenant life tends to be short: the most stagnant windows, the most perfunctory dresses, the most implausible flowers. All perspective is gone, as in a rainforest (itself disappearing, they keep saying … ).

32. Trajectories are launched as ramp, turn horizontal without any warning, intersect, fold down, suddenly emerge on a vertiginous balcony above a large void. Fascism minus dictator.


33. There is zero loyalty—and zero tolerance—toward configuration, no “original” condition; architecture has turned into a time-lapse sequence to reveal a “permanent evolution.” … The only certainty is conversion-continuous-followed, in rare cases, by “restoration,” the process that claims ever new sections of history as extensions of Junkspace.

34. History corrupts, absolute history corrupts absolutely. Color and matter are eliminated from these bloodless grafts.

35. Sometimes not overload but its opposite, an absolute absence of detail, generates Junkspace. A voided condition of frightening sparseness, shocking proof that so much can be organized by so little.

36. The curse of public space: latent fascism safely smothered in signage, stools, sympathy … Junkspace is postexistential; it makes you uncertain where you are, obscures where you go, undoes where you were. Who do you think you are? Who do you want to be? (Note to architects: You thought that you could ignore Junkspace, visit it surreptitiously, treat it with condescending contempt or enjoy it vicariously … because you could not understand it, you’ve thrown away the keys … But now your own architecture is infected, has become equally smooth, all-inclusive, continuous, warped, busy, atrium-ridden …)


37. Restore, rearrange, reassemble, revamp, renovate, revise, recover, redesign, return-the Parthenon marbles-redo, respect, rent: verbs that start with re-produce Junkspace …

38. Junkspace will be our tomb.

39. Junkspace is political: It depends on the central removal of the critical faculty in the name of comfort and pleasure.

40. Not exactly “anything goes”; in fact, the secret of Junkspace is that it is both promiscuous and repressive: as the formless proliferates, the formal withers, and with it all rules, regulations, recourse …

41. Junkspace […] is the interior of Big Brother’s belly. It preempts people’s sensations. […] it blatantly proclaims how it wants to be read. Junkspace pretends to unite, but it actually splinters. It creates communities not out of shared interest or free association, but out of identical statistics and unavoidable demographics, an opportunistic weave of vested interests.


42. God is dead, the author is dead, history is dead, only the architect is left standing … an insulting evolutionary joke … A shortage of masters has not stopped a proliferation of masterpieces. “Masterpiece” has become a definitive sanction, a semantic space that saves the object from criticism, leaves its qualities unproven, its performance untested, its motives unquestioned.

43. Junkspace reduces what is urban to urbanity. Instead of public life, Public SpaceTM: what remains of the city once the unpredictable has been removed …

44. Inevitably, the death of God (and the author) has spawned orphaned space; Junkspace is authorless, yet surprisingly authoritarian … At the moment of its greatest emancipation, humankind is subjected to the most dictatorial scripts.: […] The chosen theater of megalomania—the dictatorial—is no longer politics, but entertainment.

45. Why can’t we tolerate stronger sensations? Dissonance? Awkwardness? Genius? Anarchy? … Junkspace heals, or at least that is the assumption of many hospitals.


46. Often heroic in size, planned with the last adrenaline of modernism’s grand inspiration, we have made them (too) human;

47. Junkspace is space as vacation;


48. Junkspace features the office as the urban home, a meeting-boudoir. […] Espace becomes E-space.

49. Globalization turns language into Junkspace. […] Through the retrofitting of language, there are too few plausible words left; our most creative hypotheses will never be formulated, discoveries will remain unmade, concepts unlaunched, philosophies muffled, nuances miscarried … We inhabit sumptuous Potemkin suburbs of weasel terminologies. Aberrant linguistic ecologies sustain virtual subjects in their claim to legitimacy, help them survive … Language is no longer used to explore, define, express, or to confront but to fudge, blur, obfuscate, apologize, and comfort … it stakes claims, assigns victimhood, preempts debate, admits guilt, fosters consensus. […] a Satanic orchestration of the meaningless …

50. Intended for the interior, Junkspace can easily engulf a whole city.


51. Seemingly at the opposite end of Junkspace, the golf course is, in fact, its conceptual double: empty, serene, free of commercial debris. The relative evacuation of the golf course is achieved by the further charging of Junkspace. The methods of their design and realization are similar: erasure, tabula rasa, reconfiguration. Junkspace turns into biojunk; ecology turns into ecospace. Ecology and economy have bonded in Junkspace as ecolomy.

52. Junkspace can be airborne, bring malaria to Sussex;


53. Deprivation can be caused by overdose or shortage; both conditions happen in Junkspace (often at the same time). Minimum is the ultimate ornament, a self-righteous crime, the contemporary Baroque.

54. It does not signify beauty, but guilt.

55. Outside, in the real world, the “art planner” spreads Junkspace’s fundamental incoherence by assigning defunct mythologies to residual surfaces and plotting three-dimensional works in leftover emptiness. Scouting for authenticity, his or her touch seals the fate of what was real, taps it for incorporation in Junkspace.

56. The only legitimate discourse is loss; art replenishes Junkspace in direct proportion to its own morbidity.


57. […] maybe the origins of Junkspace go back to the kindergarten …

58. Will Junkspace invade the body? Through the vibes of the cell phone? Has it already? Through Botox injections? […] Is each of us a mini-construction site? […]


59. Is it [m: mankind] a repertoire of reconfiguration that facilitates the intromission of a new species into its self-made Junksphere? The cosmetic is the new cosmic… ◊


JS is about the consequences of modernism for architecture and for urbanism. Koolhaas does not hesitate to explicate it: Modernization, modernism ends in a “meltdown”. As an alternative he offers the “apotheosis”, a particular quality as a Golden Calf of modernization. Within the context of urban life and architectural activities, this outcome shows up as “Junkspace”. The essence of it is emptiness, isolation, splintering, arbitrariness. Its “victory” is named by its offer, entropy, and its essence is continuity. Probably it is meant as kind of a tertiary chaos, vanishing any condition for the possibility of discernability, unfortunately as the final point attractor. We will see.

Koolhaas describes Junkspace as an unintended outcome of a global collective activity. Obviously, Koolhaas is struggling with that, or with the unintendedness of the effect, in other words with emergence and self-organization. Emergence and self-organization can be understood exclusively in the wider context of complexity as we have outlined it previously (see this piece). The concept of complexity as we have constructed it is by no means anti-scientific in a fundamental sense. Yet, it is a severe challenge to scientism as it is practiced today, as our concept explicitly refers to a reflected conceptual embedding, something that is still excluded from natural science today. Anyway, complexity as an explicated concept must be considered as a necessary part of architectural theory, if we take Koolhaas and his writings such as “Junkspace” serious. Without it, we could not make sense of the difference between standardization and homogenization, between uniqueness and singularity, between history and identity, between development and evolution, or between randomness and heterotopia.

Modernism and its effects is the not so hidden agenda of JS. We have to be clear about this concept—at least concerning its foundations, albeit we will not find space enough here for discussing or even just listing its branches that reach not only till Marcuse’s office in Frankfurt—if we want to understand neo-leftist interpretations of JS as that by Jameson (“Future City” [2]), and the not so hidden irony expressed by the resonating label “Future Cities Lab” that denotes the urbanism project of the Department of Architecture (one of the biggest in Europe) of the Swiss Federal Institute of Technology (ETHZ). It is also the name of a joint venture between National University of Singapore (NUS) and ETHZ. Yes, they indeed call it Lab(oratory), a place usually producing hives of “petri dishes,” either abandoned (see 7. above) or “containing” the city itself (see section 8.1. of “The Generic City”), and at the same time still, and partially contradictory to its practices, an oratory of modernism. Perhaps. (more about that later).

Latest here we have to address the question:
What is the problem with modernism?

This will be the topic of the next post.

  • [1] Rem Koolhaas (2002). Junkspace. October, Vol. 100, “Obsolescence”, pp. 175-190. MIT Press. available here
  • [2] Fredric Jameson, Future City, New Left Review NLR 21, May-June 2003, pp. 65-79. available here


Elementarization and Expressibility

March 12, 2012 § Leave a comment

Since the beginnings of the intellectual adventure

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

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

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

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

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

The Roots1

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

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

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

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

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

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

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

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

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

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

2. Examples

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

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

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

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

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

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

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

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

Characterizing the Concept of “Element”

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

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

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

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

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

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

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

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

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

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

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

4. Expressibility

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

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

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

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

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

Spaces and Dimensions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Aspectional Space

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

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

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

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

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

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

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

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

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

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

Aspections, Dimensions

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

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

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

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

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

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

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

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

A brief Example

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

5. Conclusion

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

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

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

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

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

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

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

Part 3: A Pragmatic Start for a Beautiful Pair

Part 5: Relations and Symmetries (forthcoming)


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

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

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

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

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


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