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Perceptual Orientation and Spatial navigation in Dense Urban Environments
Patrik Schumacher, Cham, Switzerland 2016
Published in: Jan Knippers, Klaus G. Nickel, Thomas Speck (Editors), Biomimetic Research for Architecture and Building Construction – Biological Design and Integrative Systems, Springer Nature, Springer International Publishing


This paper poses the problem of perceptual orientation and spatial navigation in dense urban environments and proposes a scenario and methodology of urbanisation in analogy to natural ecologies where land formation, streams and rivers, flora and fauna come together according to rules of interdependency that build up a complex variegated order. Despite their complexity such natural environments are eminently legible and navigable. The vision of a perceptually tractable complex urban order contrasts with the urban disarticulation that has resulted from the urbanisation processes of the last 40 years, since the demise of modernism and modernist urban planning.

Postfordism - Network society - Communicative density - Agglomeration economies - Urban planning – Entrepreneurial freedom - Stylistic pluralism - Parametricism - Associative logics - Deconstructivism - Postmodernism - Modernism – Urban neg-entropy - Multi-species ecologies - Multi-author urbanism - Garbage-spill urbanisation - Beauty


Historical Socio-economic Condition of Urban Planning’s Demise

We are witnessing a sustained drive towards urban concentration in global hub cities like London, New York, Tokyo, Shanghai, Sao Paulo etc. Within contemporary network society one’s productivity depends on being plugged into urban professional and cultural networks that exist only in the big cities. What each of us is doing needs to be continuously re-calibrated with what everybody else is doing. That’s what all further productivity gains depend on. This requires a new level of communicative density that is only available in the metropolis. This underlies what economists measure as ‘agglomeration economies’. In the provinces you are cut off and thus unproductive. We all feel this and that’s why we rightly pile into the city, and the more central we can locate, the better. Since the neat division into work and leisure has disappeared and we feel the vital urge to remain plugged into the network 24/7 it is as important for us to live in the city as it is inevitable for us to work in the city. Everything presses into the centre, the more the better. This spells a new desire for an unprecedented degree of urban intensification and mixity, a desire which is currently frustrated by outmoded planning restrictions. This new urban dynamic is not only a fascinating challenge and task for architects but first of all requires new degrees of freedom for urban entrepreneurs who need this freedom to experiment, discover and create the best ways to weave the new urban texture and to garner the potential synergies through new intricate programmatic juxtapositions. Only an unhampered market process can be such a discovery process and has the information processing capacity and agility to weave a viable complex variegated urban programmatic order for this new dynamic societal context. The planning brakes had to be released in terms of land use and density restrictions. The power of urban planning and control has been eroded accordingly. If we take a global glance at our big cities it is amazing that there should be any planning systems in place at all. The amorphous urban agglomerations our cities have become certainly don’t allow us to see any trace of these regulatory efforts.  Planning fights a losing rear-guard battle. The thesis elaborated in this paper not only accepts this fact but moreover extrapolates to municipal urban planning’s final demise as logical and desirable culmination of the current socio-economic trend towards what we might call Post-fordist Network Society. Cities are our civilisation’s the ‘super brains’ continuously brainstorming and elaborating innovations that lead to the continuous re-programming of the manufacturing and agricultural production robots churning out our means of life in emptied out production landscapes (which are then sorted in robotic warehouses and shipped back to us city dwellers). The most crucial information processing and ideation in the ‘super brain’ is happening in face-to-face communications. The myriad ordered spaces of the city operate as an integrated system of communication interfaces that needs to be browsed and navigated by all to maximise interaction density and relevancy, generating more productivity enhancing ‘brain power’. This network cannot be planned. It must be given plenty of freedom to evolve via negative and positive feedback loops. Plasticity is here as much a precondition of learning and intelligence upgrading as in the case of our brains proper. Cities are our civilization’s ‘super brains’, continuously brainstorming and elaborating innovations that lead to the ongoing re-programming of the manufacturing and agricultural production robots churning out our means of life in 'inhuman' production landscapes. (The products are then sorted in robotic warehouses and shipped back to us city dwellers). The most crucial information processing and ideation in the ‘super brain’ is happening in face-to-face communications. The myriad ordered spaces of the city operate as an integrated system of communication interfaces that needs to be browsed and navigated by all to maximise interaction density and relevancy, generating more productivity enhancing ‘brain power’. This network cannot be planned. It must be given plenty of freedom to evolve via negative and positive feedback loops. Plasticity is here as much a precondition of learning and intelligence upgrading as in the case of our brains proper. (It’s only the big cities that evolve brain power and brain-drain all else.)

Large scale city planning first started to recede during the second half of the 1970s and since then urbanism as a discourse, discipline, and profession has all but disappeared. The disappearance of urbanism coincides with the crisis of Modernism which can be interpreted as the way in which the crisis of the Fordist planned economy manifested itself within architecture. The 50 core years of architectural modernism (1925 – 1975) were also the golden era of urbanism. During this period the advanced industrial nations urbanized on a massive scale. This was also the era of Fordism, i.e. the era of mechanical mass production and the era of the planned/mixed economy. The state dominated much of the city building via big public investments in infrastructure, social housing, schools, hospitals, universities etc. This made large scale, long term physical planning possible. In Western Europe energy, utilities, broadcasting, railways, as well as many large scale industries had been nationalized. This further enhanced the feasibility of large scale, long term urban planning. The most congenial societal context for modernist urbanism existed within the socialist block with its centrally planned economy. Socialism delivered the logical conclusion of the tendencies of the era, rolling out the technological achievements of the era in a predictable, centrally planned manner, literally delivering the uniform consumption standard made possible by Fordist mass production to every member of society. Consequently, we find the fullest expression of modernist urbanism in the Eastern Block.  Civilization evolved further. The crisis of Fordism, Post-fordist restructuring, the neo-liberal turn in economic policy (privatization, deregulation), and the collapse of the Eastern Block system all coincide with the crisis of modernism in architecture and urbanism. The bankruptcy of Modernist planning gave way everywhere to the same visual chaos of laissez faire urban expansion and agglomeration under the auspices of stylistic pluralism and the anti-method of collage. Our contemporary cities exude vitality but they are no longer symbols of order, but rather poised to tip over into a menacing disorder.

London’s shapeless expansion
Like all urban agglomerations, London expands without bounds and without shape. The only features that give otherwise amorphous mega-cities  a recogniseable shape are natural landscape features like rivers, hills and valleys etc.

City of London: Communication density becomes physically manifest.
London is paradigmatic exemplar of the urban concentration process in global hub cities. As more and more large iconic structures pile into the financial district the urban scape becomes more and more chaotic, an uninentional bricolage. The planning process is evidently failing to stem the visual chaos and unable to establish any semblance of urban order.

Left: Shanghai, right: Moscow City


Concepts of Order: The Dialectic of Urban and Conceptual Order

Architecture and the city used to be the ultimate incarnations and indeed models of all concepts of order: Ancient cities like Babylon, ancient Roman cities, the ideal and built cities of the Renaissance, the Baroque cities.  Architectural figures and urban ordering patterns offer the archetypical paradigm of any concept or order: A place for everything and everything in its place, within a bounded realm, subdivided by an orderly geometric arrangement.
The built environment does indeed provide the historical/material conditions for the emergence and transformation of those deep-seated conceptual ‘architectures’ that are constitutive of our abstract thinking in general. The Classical architectural canon that developed following the rebirth of architecture in the Italian Renaissance served as the source domain for the transference of analogies of order within all domains of abstract, conceptual thinking, including the most sophisticated philosophies of the Enlightenment.

Renaissance Ideal City as model of order: social, spatial and conceptual order.

Spatialized conceptual orders: system of vices and system of virtues, Cosmas Rossellius, Thesaurus Artificiosae Memoriae, Venice, 1579

The two diagrams depicted here are trying to conceptualize the moral universe of vices and virtues. The diagrams construct an abstract conceptual order. Diagrammatic conceptualizations became prevalent during the Renaissance and continued to be prominent until the end of the 18th century. However, there was but one schema for such conceptualizations: the organizational schema of the ideal city, as a concentric and radially segmented order, representing the classificatory pyramid as only tool of abstract thinking of this era (and still prevalent today). This schema of an ideal city was itself abstracted from the prior material reality of the unplanned, medieval walled city which evolved by a quasi-material (economic) process with the ring as most efficient boundary and with growth via concentric (ring upon ring) expansion. Thus at the root of this universal conceptual structure –– lies the spontaneous, evolutionary morphogenesis of the concentrically growing walled city.

Left: Renaissance Ideal City built; right: Baroque Ideal City built

Brasilia: Modernist “Ideal City” - simple order based on separation, specialisation, repetition

The spatial order of the built environment constitutes one of the primary analogical source domains for schemata of thinking. This phenomenon is not restricted to prehistoric times, but remains an active force all along. The permanent possibility and immediacy of architectural/spatial analogies as resource of our thinking are reinforced and confirmed through our daily navigation of architectural orders. Order might still be defined as ‘everything in its place and a place for everything’. ‘Architecture’ is still at the root of most of the conceptual schemata we rely on today: sequences, branching graphs, grids, concentric nesting etc. This deep-seated power of architectural tropes, embedded in the most general operations of logic and language, poses a formidable barrier to radical innovation. The transcendence of these tropes is so difficult because the very patterns of conception (clear and distinct thinking) are locked within these tropes. An architecture that today is self-conscious of its formative role within the domain of conceptual order should be able to challenge deeply ingrained patterns of thought by effective spatial intervention.

Renaissance, Baroque as well as planned modernist cities like Brasilia delivered further recognisable paradigms of order. The Baroque used primary and secondary axes and ever ramifying symmetries as new ordering structures. Modernism added the principles of separation, specialization and repetition. Brasilia was perhaps the last sizeable city or urban district that projects a clear visual urban order: the last beautiful city development.
Symmetry has been made the norm in Classical architecture. Conceptual symmetries inform all Classical conceptual formalisms within science and philosophy up to the end of the 18th century: for instance the Kantian table of categories is marked by an insistence upon symmetric order – signifying completeness. This insistence on symmetry, which was for Kant an unreflected a priori of his theory, strikes us today as an irrational formalism. Modernism had since established the possibility of designing architectural orders without symmetry, but was still based on orthogonal grids and seriality.  Relations of exclusion, inclusion, subsumption and subdivision, as well as lists and sequences, are operating in all modernist architectural and urban orders. These ordering devices are ubiquitous in modern civilization. These abstracted architectural tropes have recycled back from thinking to building, i.e. to concrete architectural construction, thus perpetuating their hold over our conceptual, social and spatial order. Deconstructivism was trying to cut this loop. It was the vehicle by which philosophy returned to its roots in architecture in an effort to break this circle of repetition through direct action in space. Deconstructivism did indeed violate longstanding conceptions of clear and distinct order. Initially this work was limited to the creative destruction of order, producing gestures of disruption and disorder. However, a new repertoire of ordering principles emerged that was able to increase the capacity of architecture to organize and articulate the more complex life-processes and social institutions that had started to emerge. For instance, Deconstructivism elaborated a capacity for spatial overlap and interpenetration of domains. This capacity recognizes a salient trend in contemporary social institutions whereby conditions of multivalency become more and more widespread.  The main point here is to increase the repertoire of both conceptual and spatial ordering principles and to upgrade their capacity to structure complexity. The contemporary style of Parametricism is well prepared to continue the Deconstructivist project of expanding architecture's repertoire of conceptual and spatial ordering way beyond the capacity of Deconstructivism or any prior style.

All urbanisation at since 1980 has produced “ugly”, amorphous urban agglomerations without recognisable order and identity. However, if real estate and rental markets are able to deliver synergetic programme mixes, i.e. programmatic order, then the hypothesis might be ventured that the disorder we perceive in our contemporary urban agglomerations is only apparent, only visual. The urban morphological cacophony obscures the underlying programmatic order, i.e. the evolved urban system of interaction offerings. This obscurity is not only due to the disarticulation produced by the prevalent pluralism of styles but also partly due to our limited conceptual repertoire of recognizing more complex systems of order.
Le Corbusier insists that: ‘the house, the street, the town … should be ordered; … if they are not ordered, they oppose themselves to us.’1 Le Corbusier's limitation is not his insistence upon order but his limited concept of order in terms of Classical geometry. Complexity theory (or chaos theory) in general, and the research of Frei Otto in particular, have since taught us to recognize, measure and simulate the complex patterns of order that emerge from processes of self-organization. Phenomena like the ‘donkey's path’ and the urban patterns resulting from unplanned settlement processes can now be analysed and appreciated in terms of their underlying logic and rationality, i.e. in terms of their hidden regularity and related performative power that result from the consistent constraining pressures that have been underlying their process of formation. Le Corbusier realized that although ‘nature presents itself to us as a chaos … the spirit which animates nature is a spirit of order’.2 However, his understanding of nature's order was limited by the science of his day. He lacked the concepts and computational tools that can now reveal the complex order of those apparently chaotic patterns by means of simulating their lawful ‘material computation’. Parametricist sensibility gives more credit to the ‘pack-donkey's path’ as a form of adaptive material computation than to the simplicity of clear geometries that can be imposed in one sweeping move. Frei Otto's pioneering work on natural structures included work on settlement patterns. His starting point was the distinction and interplay of occupying and connecting as the two fundamental processes that are involved in all processes of urbanization.3 His mapping of existing patterns and their geometric analyses was paralleled by physical experiments that were conceived as analogues modelling crucial features of the settlement process. In terms of occupation, he distinguished distancing and attractive occupations. For distancing occupation he used magnets floating in water and for attractive occupation he used floating polystyrene chips. A more complex model integrates both distancing and attractive occupation whereby the polystyrene chips cluster around the floating magnetic needles that maintain distance among themselves.4 The result closely resembles the typical settlement patterns found in real urban landscapes.

Frei Otto, Occupation with simultaneous distancing and attracting forces,
Institute for Lightweight Structures (ILEK), Stuttgart, Germany, 1992

Analogue models for the material computation of structural building forms (form-finding) are the hallmark of Frei Otto’s research institute. The same methodology has been applied to his urban simulation work. The model shown integrates both distancing and attractive occupations by using polystyrene chips that cluster around the floating magnetic needles that maintain distance among themselves.

This suggests that there are potentially discernible patterns in the apparent visual chaos of contemporary urban agglomerations. The assumption here is that these patterns can be clarified and accentuated by architectural articulation. There are underlying rules – economic rules – which guide individual decisions that form the (so far mostly obscure) patterns. The proposition put forward here is that these economic-programmatic rules should be aligned with rules of architectural translation that make the intricately ordered complexity of the urban life processes visually legible and avoid the visual pollution and obfuscation that stems from the current, unprincipled cacophony of disparate architectural translations. The processes of architectural translation do not need to follow a uniform script as if conducted by a single hand, but could be delivered on the basis of multiple authors working within a shared language, with the shared ethos of making and maintaining connections, resonances and continuities across a field of diverse urban riches.


Beauty and the Evolution of Concepts of Order

What is beauty, including urban beauty? Whatever appeals at first sight. Being impressed by beauty is a gut reaction, triggered by a perceptual encounter. This immediate gut reaction operates according to an underlying rationality. The recognition of beauty within a built environment is the recognition of the vitality of this environment, on the basis of its mere appearance, prior to a more in-depth experience and verification of its functionality. This works due to the extent to which subjects are conditioned by prior experience. However, as society evolves what was once vital might have become dysfunctional. Aesthetic sensibilities have to be adapted via aesthetic revolutions. New vital societal processes might be unduly constrained by the established order of beauty. They break out of this order and the environments they find or bring forth appear ugly. Their aesthetic rejection becomes a fetter on their further progress. A contradiction develops that can only be solved by an aesthetic revolution. Sensibilities need to be (periodically) brought in line with the morphological conditions of the most vital social life-processes. In this sense beauty keeps changing its physiognomy. But is the category of beauty really devoid of any features that persist across its different, concrete historical manifestations? If this were so we would not be able to see the beauty of earlier styles. However, contemporary society – inclusive of contemporary architects – is still touched by the beauty (filigree order) of the Gothic, by the beauty (simple elegance) of the Renaissance, by the beauty (intense plasticity) of the Baroque etc. Contemporary architects recognize the beauty of past eras (although they would not find it appropriate to use any of these older styles to frame contemporary institutions). Is it possible to identify an invariant characteristic, a universally applicable condition that must be met by all environments, and even by all phenomena, that is recognized as beautiful? Yes, there is an invariant aspect that guides all discriminations of beauty versus ugliness: the sensation of beauty is always bound to a sense of order as distinct from chaos. Order as the universal and invariant aspect of beauty has been alluded to by many classical definitions of beauty. For instance Leon Battista Alberti's famous definition reads as follows: ‘Beauty is that reasoned harmony of all the parts within a body, so that nothing may be added, taken away, or altered, but for the worse.’5 The positive principle of harmony/order is emphasized by reference to an ‘integral body’ and contrasted with a mere agglomeration: ‘The harmony is such that the building appears a single, integral, and well-composed body, rather than a collection of extraneous and unrelated parts.’6 The same point is further explicated by negating its opposite which might thus be taken as the implicit definition of the ugly: a composition should be ‘neither jumpy, nor confused, nor disorganized, nor disconnected, nor composed of incongruous elements, … nor too disjointed or distant from the rest of the body.’7 Alberti references order via the phrase ‘harmony of all the parts’. However, his insistence on completeness, ie, that nothing may be added, taken away or altered, is specific to Classical architecture and can no longer be considered a universal and invariant feature of beauty. Alberti's concept of an organic whole, with symmetry and strict rules of proportion, with a state of completeness or perfection that tolerates neither additions nor subtractions, describes a general ideal of beauty that remained in force from the Renaissance until the Historicism of the 19th century. The restrictions of symmetry, proportion and wholeness/completeness were abandoned within 20th-century Modernism. Instead, order was maintained via the order of the module, the grid and via the order of dynamic equilibrium. In addition features like simplicity and lightness were pursued, further specifying the Modernist sense of beauty. The formal heuristics of Parametricism call for order via lawful differentiation and correlation. These concepts are implemented via rule-based (algorithmic) design processes. A sense of order as distinct from chaos is maintained in all historical concretizations of the code of beauty. Order vs chaos is thus the invariant criterion of beauty. However, the criterion of order vs chaos is insufficient to give an operational definition of beauty that could fully guide the concrete application of the code values beautiful vs ugly. The order vs chaos criterion is still too abstract and leaves too many possibilities open. There can be many different forms of ordering, of relating non-arbitrarily. Order is a necessary but not a sufficient condition of beauty. Being attracted to order and repulsed by chaos might be a biologically hardwired response, i.e. the rationality of this response might be based on biological evolution rather than on cultural evolution or on conditioning on the basis of individual experience. Chaos, the absence of any perceived order, is disorienting and thus threatening, especially if the whole environment lacks order. If the environment is partially ordered and partially configured randomly, then it makes sense that attention is drawn towards the ordered aspects, ignoring the less ordered or accidental configurations. The probability that a random configuration of entities constitutes an interrelated, functioning assemblage is very low. Where entities are configured into an order, the presumption is justified that these entities somehow add up to a unit of interaction. Ordered configurations are thus more likely to constitute a force than random configurations, a force that should be reckoned with. Complex order inspires curiosity and awe, random configurations – like a heap of garbage or the disarticulated agglomerations of suburbia – are usually taken no notice of, except negatively for their ugliness and thus absence of interest. All natural systems are ordered in some way. However, the complexity of many natural phenomena prevented the recognition of their order and beauty in earlier times. Animal forms (and animal formations like flocks) are more organized than plant forms. Attention to animals is of higher evolutionary importance than attention to plants. Cultural evolution further confirmed the privileging of order over disorder. The more ordered appearance of the early city-based civilizations (Babylon, Maya Civilization etc.), compared with village-based clan societies, correlates with the superiority of these civilizations. The effort to give order to the built environment has been a constant feature of the process of civilization.


Evolving Multi-species Ecologies as Model for an Evolving Multi-author Urban Order

The market process is an evolutionary process that operates via mutation (trial and error), selection and reproduction. It is self-correcting, self-regulation, leading to a self-organized order. Thus we might presume that the land use allocation and thus the programmatic dimension of the urban and architectural order is to be determined by architecture’s private clients within a market process that allocates land resources to the most valued uses. However, in the absence of stylistic and methodological coherence we cannot expect the underlying programmatic order to become legible as a spatio-morphological order. For this to happen we must presume a hegemonic stylistic and methodological paradigm that has the versatility and ordering capacity to translate the social order into a complex variegated spatial order. A shared paradigm offers the prospect of coherence across multiple authors working for multiple clients. No controlling hand needs to be presupposed.

The thesis presented here proposes the analogy of an unplanned multi-author parametric urbanism with a multi-species ecology. Consider the way the various features and creatures within a natural environment coalesce to create a complex variegated order on the basis of rules  - in turn based on the complex interaction of multiple laws of nature – that establish systematic correlations between the various organic and anorganic subsystems that make up a natural landscape. The topography correlates with the path of the river, the river together with topography and sun orientation differentiate the flora and the differentiation of the flora – together with river and topography - shape the differentiation and distribution of the fauna, which in turn impacts back on the fauna and thus often also on rivers and even the topography. While thus causality is complex and not easy to unravel, correlations and thus inference potentials are being established in all directions, and give information to those who want to navigate such a landscape. The key here is the build-up of correlations and associations (irrespective of the underlying causality). Each new species of plant or animal proliferates according to its own rules of adaptation and survival. For instance, the moss grows differentially on the terraced rock surface in certain shaded slopes, i.e. depending on surface pattern, sun orientation, self-shading rock formation etc. A population of a certain species of birds then might settle on these slopes accordingly etc. In the same way parametricism envisions the build-up of a densely layered urban environment via differentiated, rule-based architectural interventions, that are designed via scripts that form the new architectural sub-systems, just like a new species settles into a natural environment. This process delivers rich diversity, yet fully correlated, if designed according to the heuristics of parametricism. Each new architect/author can be uniquely creative in inventing and designing the rules/scripts of his/her project and participate in its own unique way in the build-up of a variegated, information-rich urban order. The analogy also extends to the navigation in rule-based environments: the urbanite’s intuitive orientation within a parametric urban environment functions analogous to animal cognition/navigation in a natural environment.

Multi-species Ecologies as Model for an Evolving Multi-author Urban Order

Complex Variegated Order via multi-author coherence, Istanbul Cultural District, Studio Hadid/Schumacher, Yale University, 2013
This design experiment in un-planned multi-author urban order demonstrates how coherence, interarticulation and resonnance can emerge if independent authors work from within the shared paradigm of parametricism that enables and calls for mutually adaptive, affiliative and resonate design moves.

Parametricism Delivers Urban Neg-entropy

The only viable candidate for the next hegemonic epochal style is parametricism. Neither a hegemonic Postmodernism, nor a hegemonic Deconstructivism could overcome the visual chaos that allows the proliferation of differences to collapse into global sameness (white noise). Both Postmodernism and Deconstructivism operate via collage, i.e. via the unconstrained agglomeration of differences. Deconstructivism can be looked at as the aesthetic sublimation of the urban process of “garbage spill” collage. Only Parametricism has the capacity to combine an increase in complexity with a simultaneous increase in order, via the principles of lawful differentiation and multi-system correlation. Only parametricism can overcome the visual chaos and white noise sameness that laissez faire urbanisation produces everywhere. Parametricism holds out the possibility of a free market urbanism that produces an emergent order and local identity in a bottom up process, i.e. without relying on political or bureaucratic power. The values and methodological principles of parametricism are prone to produce path-dependent, self-amplifying local identities, starting with the given natural features and settlements. Its ethos of contextual affiliation and ambition to establish or reinforce continuities allows for the development of unique urban identities on the basis of local contexts, topography, climate etc.
Parametricist order does not rely on the uniform repetition of patterns as Modernist urbanism does. In contrast to Baroque or Beaux Arts master-plans, Parametricist compositions are inherently open ended (incomplete) compositions. Their order is relational rather than geometric. They establish order and orientation via the lawful differentiation of fields, via vectors of transformation, as well as via contextual affiliations and subsystem correlations. This neither requires the completion of a figure, nor - in contrast to Modernist master-plans - the uniform repetition of a pattern. There are always many (in principle infinitely many) creative ways to transform, to affiliate, to correlate. A unique, unpredictable, but recognisable and legible order (which allows for orienting inferences) will emerge, as long as all architects acquire the required skills and create within the parametrist paradigm and ethos that calls for continuities and affiliations, under the critical eye and peer pressure of each other.  A hegemonic parametricism thus holds out the prospect of a free market urban order.


Progression of Styles: Freedom vs Order,  graph by Patrik Schumacher
Parametricism achieves an inversion of architecture’s entropy law. Freedom must be bought by giving up order until the techniques of parametricism give a new, powerful ordering capacity to the discipline of architecture, a capacity that delivers a simultaneous enhancement of freedom and order.

If we look at the historical progression of styles we find that the last 300 years established what we might call architecture’s entropy law: all gains in terms of design freedom and versatility have been achieved at the expense of urban and architectural order, i.e. increases in versatility had to be bought by a progressive degeneration of architecture’s ordering capacity. The increase of the designer’s degrees of freedom was established via the enrichment of architecture’s formal-compositional repertoire. This increase in freedom/versatility was the paramount criterion of progress in architecture’s pursuit of matching the requisite variety of societal complexity.  Like the move from classical architecture to modernism, the move from modernism via postmodernism to deconstructivism delivered an expansion of degrees of freedom and versatility (to accommodate a more complex society) that was paid for by a relaxation or rejection of rules of composition, i.e. of means of ordering, and thus a resultant degeneration of the visual order.
Order was progressively eroded. This long trend of a negative correlation of freedom and order can be reversed under the auspices of parametricism. Parametricism offers the simultaneous increase in freedom and order and thus inaugurates a new phase of architectural neg-entropy. Parametricism’s radical ontological and methodological innovation translates into a massive leap in both dimensions of architectural progress considered here, i.e. it entails an unprecedented expansion of architecture’s compositional freedom and an unprecedented leap in architecture’s ordering capacity through the deployment of algorithms and associative logics.

Parametricism is the first style that delivers further degrees of freedom and versatility in conjunction with a simultaneous increase in its ordering capacity via new compositional rules like affiliations, gradients and associative logics. In principle all design moves are now rule based and thus with the potential to enhance the visual order and thus legibility of the built environment in the face of an increased complexity.

Classicism: High Level of Order – Limited Degrees of Freedom, Versailles
The ordering principles of symmetry and proportion gave classical architecture the capacity to compose potent unities by ordering the city around the institutional ensemble of church and palace.


Modernism: Increased Degrees of Freedom – Lower level of Order, Nicolai Kusmin, Miners Housing 1930
Modernism did let go of the constraints of symmetry and proportion and gained the freedom of radical abstarction. It maintained orthogonality and worked with the ordering principles of separation, specialisation and limitless repetition.


Postmodernism: Further Increases in Degrees of Freedom – Further Loss of Order, OMA, 1976
Postmodernism rejected the monotony of modernist separation and repetition and opened itself up for an unconstrained juxtaposition and collage of architectural forms and motifs from all other periods of architecture.


Deconstructivism: Further Degrees of Freedom -  Further Degeneration of Order
Daniel Libeskind Micro-megas (1981)
Deconstructivism abandons orthogonality and all historical motifs to regain the freedom of abstraction and intensifies the principle of collage by allowing superimposition and interpenetration as much as juxtaposition.


Parametricism: Pronounced Increase in Freedom -  Sharp Increase in Order, AADRL 2008/09
Parametricism expands the repertoire and thus freedom with spline/nurb based curvelinearity as well as gradient swarm formations. Parametricism hugely expanded architecture’s ordering capacity via the scripting or agent-based emergence of associative logics.


Parametricism is by now manifestly superior to all other styles that are still pandered and pursued. This implies that parametricism should sweep the market and put an end to the current pluralism of styles (that resulted from modernism’s crisis and) that has been going on for far too long due to ideological inertia. The plurality of styles must make way for a sweeping, universal, i.e. hegemonic parametricism, to allow architecture to finally make once more a vital, decisive, transformative impact on the built environment, the way modernism had done in the 20th century.



1 Le Corbusier, The City of Tomorrow and its Planning, Dover Publications (New York), 1987, translated from French original Urbanisme, Editions Crès & Cie (Paris), 1925, p.15; 1st English publication Payson & Clarke, New York 1929

2 Ibid, p.18

3 Frei Otto, Occupying and Connecting – Thoughts on Territories and Spheres of Influence with Particular Reference to Human Settlement, Edition Axel Menges (Stuttgart/London), 2009.

4 Ibid, p 45.

5 Leon Battista Alberti, On the Art of Building in Ten Books, translated by Joseph Rykwert, Neil Leach & Robert Tavernor, MIT Press (Cambridge, MA/London), 1988, p 156.

6 Ibid, p.24

7 Ibid, p.163











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