Introduction by the Editors

Foreword by Christopher Alexander

Images of Community

Review of Alexander's The Nature of Order

The Architects and City Planners:





Andrés Duany


Léon Krier


Images of Public Buildings


The Scientists:


Philip Ball, Brian  

    Goodwin, Ian



A Response by


    Alexander: New

    Concepts in


    Theory Arising

    from Studies in



Images of Neighbourhood




Built Work of


   Alexander and his



* Examples of






The Kind of


   Architecture is:

   Jane Jacobs,



   and Since


The 1982 Debate



   Alexander and

   Peter Eisenman


Images of Comfort




Nikos Salingaros:   

   Design Methods,

   Emergence and




* Brian Hanson and

   Samir Younes:  

   Reuniting Urban

   Form and Urban



Images of Building Details


* Michael Mehaffy:

   Meaning and the 

   Structure of Things



  Alexander: Our

  New Architecture

  and the Many

  World Cultures


Nikos Salingaros:

   Fractals in the New



Brian Hanson: 

   Architecture and

   the “Science of



Images of Landscape and Gardens


Michael Mehaffy: 

   Codes and the

   Architecture of Life


Nikos Salingaros: 

   Towards a


   Understanding of

   Architecture and



Brian Hanson:   

   Science, Voodoo

   Science and



Images of Houses


* Michael Mehaffy:     The New Modernity



   Alexander:  Sober

   Reflections on

   Architecture in Our



Images of Drawings


Afterword by the Editors


       *       *       *

London Conference

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Discussion Page




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And References




Katarxis Nº 3



The New Modernity

The Architecture of Complexity and The Technology of Life


Michael W. Mehaffy




The “modern” era of the last century and beyond -- the most productive and progressive epoch in human history -- is in an inexorable end-stage crisis.  The last century's unbridled optimism about the rational progress of humanity has given way to a more sober understanding – for some a cynical despair -- about the limitations of human reason, and the insidious imperatives of technology.   At the same time the reductionist science that has propelled the modern era is giving way to another, more advanced kind of science: one reflecting a new understanding of the complex adaptive structure of nature (including human nature) and a recognition of the environmental and cultural damage that the modern era has done.  The “new science” – like the old science that preceded it – carries profound implications for the structure of technological culture and the patterns of life embodied in architecture. But cultural systems, and the architecture and built environment that shape and express them, are lagging behind.  In an environment in which the old century of mechanics is giving way to a new century of biological complexity, it is time to ask deep questions about the implications for the architecture of human culture.  The answers offer a surprisingly hopeful basis for a new and more humane “architecture of our time.”   


I. The “Old Modernity” of Mechanical Science

II. The New Science of Complexity

III. Seven Properties of Complexity

¨      Network Structure

¨      Near Decomposability

¨      Fractal Geometry

¨      Adaptive Iteration

¨      Geometric Holism

¨      Structural Attractors

¨     Connective Symmetries

IV. The Architecture of Complexity

V.  Towards a New Architecture of Life

VI. Notes



I. The “Old Modernity” of Mechanical Science


Modernism's alchemistic promise – to transform quantity into quality through abstraction and repetition – has been a failure, a hoax: magic that didn't work. Its ideas, aesthetics, strategies are finished. Together, all attempts to make a new beginning have only discredited the idea of a new beginning. A collective shame in the wake of this fiasco has left a massive crater in our understanding of modernity and modernization.


                                           - Rem Koolhaas, “Whatever Happened to Urbanism?”



“The future” is mired in the past.


Around the world today an old chimera of modernity still holds us spellbound.  Its rules and assumptions fuel our prodigious industry, our fashions, our vision of ourselves.  It governs our pursuit of endlessly (not to say pointlessly) greater levels of prosperity and wealth.  At a deeper level it lures us with its seductive promise of a final deliverance of humanity from the horrors of nature untamed.  It is – or so we had desperately hoped -- the final achievement of the Enlightenment triumph of human reason.


But the foundation of this quest is crumbling all around us; the signs of its internal contradictions and fallacies are increasingly unmistakable.  Today it has become an ironic parody of its own once-confident quest for advancement.   And yet we remain prisoners of its spell, unable to see where to go next.


In architecture – the realm of art with the greatest impact upon living patterns – today’s “futuristic” jagged crystalline towers are not much different from set pieces from the 1924 movie Metropolis or the 1939 movie The Wizard of Oz.  Skylines take on the quaint spaceship forms of Buck Rogers, or the dazzlingly wacky forms of an old theme park, complete with exploding fireworks.  Interiors have returned to the uncomfortable fashion-victim minimalism of the 1960’s, complete with tacky plastic chairs and un-tacky price tags. Metropolises are still largely planned around passengers in speeding automobiles, whisking far out to suburbs of gleaming corporate office parks set far back from the road – all of it perfectly described (sans congestion, pollution and other dysfunctions) in the utopian drawings of almost a century ago. 


These are but the superficial signs that the “modern” era of roughly the last century -- the most astonishingly productive and politically progressive epoch in human history -- is today in a deepening end-stage crisis.


Let us be clear about the triumphs achieved.  This era, with roots stretching back to Newton and Descartes – and even deeper, into the rational idealism of Plato and even the nature of human thought itself -- has delivered breathtaking advancements for humanity. Its vast wealth has been fuelled by a revolution in science and mathematics, and in particular in our understanding of the structure of nature and the cosmos.  Along with this, as a parallel and interactive phenomenon, has come an explosive revolution in technology, production, wealth, political liberalism, and the means of living.


Today we can fly, heal, dine, in a manner undreamt of by the richest kings of history.  Some of us – members of the industrialised democracies, at least -- operate with unprecedented freedom from the oppressions of history.  We should marvel indeed at this astonishing human achievement.


And yet we know there are costs.  We know there is uncertainty, contradiction, danger.  We struggle to see the next stage, and desperately try to rework the existing regime.  Have we gone deeply enough?  Are we hurtling toward the edge of a precipice?


Architecture has always had a unique place among the arts in shaping the structure of human life within nature.   Often that singular responsibility has meant translating a new technological capability into a mode of living, thereby promoting and accelerating it. At the beginning of the last century, the architecture profession took the new transformation as a challenge to create such a new architecture: more rational, more scientific, more open and more advanced than what came before.  Along with this was a corollary of political liberation from the old aristocracies and the old bourgeois authorities.   We would see the final completion of the grand Enlightenment project.


And in the last century, there was indeed a great explosion of new forms and new ideas, in architecture and in all the arts – propelled by, and in some cases racing to catch up to, the new technological realities.  The era was fuelled by a boundless optimism about the possibilities of a more genuine and more liberating human culture.   The impetus to liberation reached new levels in the wake of the victory over fascism, and an eagerness to cement the final graduation of humanity from such atavist horrors.


There is no doubt that this period, continuing with variations to the present day, has been an exuberant, fascinating and deeply important phase of the history of architecture and the means of living – a grand experiment in the application of once-new scientific and technological ideas toward humane ends.  It has been one of humanity’s great adventures.   This author takes personal pleasure in having been a witness and participant in it. 


But as we enter a new century the signs are unavoidable that the project is moribund and near collapse.   The legacy of almost a century of this modernism, this radical attempt to accommodate the old industrial technology to a fine architecture and design, has been disorder, dysfunction, and a deep complicity in the global threat to life itself.  


Amid the occasional remarkable pieces of fine minimalist art, the effect upon the many thousands of ordinary buildings, public spaces and artefacts, and upon the environment generally around the globe, has been nothing short of devastating. The worthy project of architecture to accommodate the new industrial reality, and to humanise it, has been a quixotic dream.   The technocratic architecture has instead conspired with an increasingly shallow technocratic culture to dehumanise humanity, and nature itself. 


We modernists have a lot to answer for.


Today the old modernist project is in a frantic, desperate search for renewal.  And in this endeavour it is increasingly an embarrassing parody of itself – at one moment acknowledging its relegation to the status of corporate servant creating fashionable  “junkspace,” at the next moment claiming to profound expression of the zeitgeist and sneering at the past, at still the next moment delving shamelessly back into its own retro-modernist version of “insipid nostalgia.” 


Moreover, we do not seem to be able to break away.  The more we try to transcend our old technocratic bonds with one wild damn thing after another, the more we seem trapped in their inescapable grasp.  The more we try to make extravagant singular novelties, the more they all merge into an incoherent white noise of disordered structure. 


We have lost the coherent environmental order and geometric richness that was once the birthright of the human race. 


“Good riddance!”  we may well say.  We are liberated and enlightened; we are modernists.  This is our satisfactory bargain with history, or at any rate our inexorable condition, our fate: to swim in a sea of disordered “complexity.”  We cannot go home again.


But a curious dilemma then poses itself:  how then to secure the theoretical basis of an increasingly antiquated “modernist” architectural art?


Perhaps through an ironic post-modernism we can still recover the symbol and meaning of our roots, while accommodating modern technologies and modern liberation from the oppressions of tradition?  But we recoil in horror at the grotesquely out-scale, mechanically cartoonish forms of such symbolic expressions in a modern context.  Something is creepily out of scale, out of out of place.


Perhaps a post-structural politics can inform our work?  Then we can at least recognise the ways in which privileged elites impose their “narratives” on us, and we can “deconstruct” these impositions and thereby offer a cleansing art of liberation.  But then we ourselves become privileged elites, imposing our own narratives upon cities on a massive scale.  Moreover, we enter a philosophical hall of mirrors in which essential meaning itself is presumed socially constructed – in which, to use Derrida’s phrase, there is nothing outside the text.  Then we find ourselves in a tangle of self-contradictory nihilism, in which the notion of externally-verifiable structure that must lie at the heart of credible science – the foundation of Enlightenment modernism – collapses into absurdity.1


The truth (whether or not anybody constructs it thus) is that architecture has long been marginalized by the hegemony of a rampaging technocracy.  Architects, caught in this Ellulian trap,2 are no longer engaged deeply with the fabric of the culture, as that is now generated autonomously by technocratic imperatives.   Thus they are relegated to the role of macro-sculptors, adding a layer of marketable style to the Empire’s New Clothes.  That they themselves still celebrate this exalted position for grand artistry is a sign of the full extent of their neurotic accommodation. 


The reality is that in most of the building acts throughout the culture, the irrelevance of architects and “designers” is almost total.   They have become part of the entertainment machine, engaged with rendering their own simulacra of culture – no less than the “theme park nostalgia” they so eagerly attack.  Thus are we all relegated to quarrelling with one another over our mutual forgeries.


And so modernism and its progeny remain no less mired in the past – the past of a hegemonic industrial technocracy -- trying ever more desperately to revive and reinvigorate a doomed project of naked apology.   It has not yet understood that the problem cannot be solved at the level at which it was created.


The old modernity was largely a product of the old mechanical science.   If there is indeed a “new science,” we may suspect that it implies a new understanding of nature and of human nature, and it will inexorably produce a new ordering of technological culture.    We have scarcely begun to assess in any depth what that might truly mean.



II. The New Science of Complexity


As science has probed deeper into the mysteries of the universe, we have encountered a strange and wondrous truth. From galaxies to DNA to the nucleus of the atom to superstrings, we see that the universe is a vast assemblage of structures of energy in space and time.   All of the characteristics we can experience, all of the complexities of life and beauty, are structures of smaller structural components.  Though unfathomable in its immensity and intricacy, the universe is, in its essence, a geometric structure.


This structure is vast but far from chaotic.  The precise relationships of its geometries are what make stars shine and flowers grow.  All of the differences between a bacterium and a human being come down to tiny differences in the sequences of molecules of otherwise identical DNA, made from only four molecules.  The structures of the universe are intricately ordered, but in a vastly complex way – and enormously, exceedingly difficult for the human mind to comprehend. 


The history of science and technology is one of rough but improving approximations of these structures of the universe, and the geometries that order them.  For example, the Euclidean plane gave way to the curved geometry of the surface of the earth, and later to the curved fabric of space-time itself.  Similarly, the two-variable mathematics of Newtonian physics gave way to the statistical mathematics of probability, and, only recently, to the non-linear mathematics of organized complexity. 


It is in the nature of scientific understanding – and indeed of all knowledge -- that at any given time we are not aware of the inaccuracies of our current model of reality.  We do not know what we do not know.  Indeed we are often bewitched by the theoretical elegance of scientific theories into thinking that we have the key to nature at last.   This is especially true with modern science – after all, its great precisions have produced breathtaking technological successes.


It is only after a crisis brought on by the discovery of anomalous information that science gradually enters what the philosopher of science Thomas Kuhn famously called a paradigm shift.3  In the last half-century or so  such a shift has indeed occurred in mathematics and in physics, as seemingly complete mathematical descriptions of reality were proven incomplete by the new “limitative” theorems of Gödel, Turing and others.4  In their wake has emerged a new mathematics of complexity. 


The new mathematics and science thus abandoned the expectation of completeness in mathematical description, and embraced instead a recognition of the unavoidability of incompleteness.   It sees formulas as approximations of reality, not as perfect “blueprints.”  Moreover, it understands much more clearly the way nature herself uses codes and generative “algorithms” (or sequences of rule-based processes) to produce vastly complex patterns.  Such patterns may well be fundamentally unanalysable in any perfect sense.5  But they may be, in the memorable phrase of Herbert Simon, “nearly decomposable” into approximate hierarchical schemes.  They may lend themselves to modelling and simulation according to analogous or “isomorphic” processes.   This is the way that such complex and seemingly “irrational” phenomena as weather patterns and stock markets finally yield themselves to deeper understanding.


In this way we are no longer seeking to “distil” reality down to a perfect blueprint of the mechanics of nature -- for we now understand that such a blueprint does not exist.  Rather we are more like “gardeners” of a complex environment.  We control it not by mastery of any “fundamental mechanism”, but through intricate and well-developed knowledge of species, growing conditions, rules of hybridisation.  We deduce the salient features of the deeper structure of things, as genetics pioneer Gregor Mendel did with his peas, through patient observation, modelling, experiment, induction.


Lest the gardening analogy seem too primitive, make no mistake: these are phenomenally powerful new scientific tools.  The new mathematics -- and its algorithmic cousins -- have unlocked many of the secrets of biology and other complex processes.  Stock markets, weather patterns, even the most intricate morphogenetic processes of life itself are finally yielding to human comprehension.  Without doubt, this is a great historic achievement in human history.


Moreover, we understand now that the structures of the universe are not simply additive assemblies of smaller structures, in a grand rational hierarchy.  They are rather structures that are interactive in their totality: they exhibit fields of mutual influence and adaptation, influencing one another as they differentiate in vastly complex ways.  We see that when we isolate some part of the structure, we are abstracting it from its real field of influence, and pretending that the field does not matter.  This is a trick, of course -- one that is very useful up to a point, but in important ways, an inaccurate reflection of reality.  Connectedness, as the mathematician and philosopher Alfred North Whitehead said, is of the essence of all things.


This trick is at the heart of modern science over the last half-millennium.  It is extremely powerful, but equally extremely limited.  And in its limitations lie its dangers. 


The end of the current modernity is the encounter with the dangerous limitations of the usefulness of this trick.


Like science, human culture as a whole has generally developed an increasingly refined understanding of the structure of things.  But human culture is lagging behind.  The gifts of our age have largely been the fruits of analysis and reduction – counting, sorting, dividing into constituents and re-assembling into a prodigious economic machine.  The historic achievements of our times are certainly breathtaking, and should not be underestimated -- sanitation, medicines, agriculture, communication, travel. 


And yet, we have paid a price for this reductionism, this mechanical view of the world.  We have learnt to pull apart the structures of nature and re-assemble them in myriad ways.  But we do not always get them to go back together right – like the mechanic who discovers a few extra parts after the car has gone back together.  Perhaps, we hope, the car will run OK.  We have discovered an immense power, but we poorly understand what our actions have released.  We are like the Sorcerer’s Apprentice, unwittingly unleashing destruction and disorder in our lives and in our environment.  The accelerating pattern suggests that we cannot go on like this; it is an unsustainable enterprise.


And yet going on like this is precisely what we are doing.  We are trying to cobble onto the old technological architecture a few new gadgets to solve the current set of problems – and we are appalled to discover a new set of problems, thanks to the principle of unintended consequences.  That is because we are focussing on the parts, but we are not able to manage the whole.  We cannot solve the problem at the level at which it was created.


We are in paradigm crisis.


The new science offers us a path out.  It implies tools for a new kind of human technology -- with strong echoes of ancient human patterns  – helping us to become more able to adapt to real human needs, more able to comprehend the results of our actions, and hence more able to wield greater responsibility.  But we will have to take some of our attention away from the reductive processes, and toward the inductive and the synthetic.  We will have to supplement the emphasis on combinations with an equal emphasis on differentiation and adaptation.  We will have to embrace the deeper lessons of the new science of complexity.  


This implies a transformation of our culture, and of ourselves.


There is another vital aspect of this transformation.  The trick of the old science relied upon the notion that nature is a “dead” collection of disconnected “things” without meaning.  It was left for other fields like philosophy and religion the question of how meaning and value might get “layered” on to the scheme in some mysterious way.  But the picture of nature itself included the core notion that there is no life or meaning to be had in the physical realm.


As science has advanced into the realm of life sciences, this has become an increasing problem.  How do we explain the evident teleological qualities of life in a “dead” universe?  How do we explain the phenomenon of life at all? 


In answering that question science has found itself in uncomfortable territory, having to acknowledge the place of value in a more complete and more accurate scientific would view.  As the philosopher Whitehead observed, we belie the existence of value at the moment we form a concept of a bit of matter.  It is only “matter” because it “matters” to us – because we can experience it, observe it, feel its impact upon our lives and our structure of meaning as observers.  It is an inescapable a priori of science, and a more complete science must acknowledge it in some way.


Simple, brute “facts” do not underlie the formation of human value;  rather, human value underlies exceedingly abstract and synthetic “facts.”  To reverse this order of concrete and abstract is to commit what Whitehead called “the fallacy of misplaced concreteness.”


In the sciences of life, and in particular the neurosciences, there is emerging today a surprising integration of geometry and human experience – particularly the experience of “meaning”.  This integration of meaning cannot be explained away as a “psychological” phenomenon – for who is experiencing this phenomenon, other than the scientist who feels its value and meaning in the first place?  How can a scientist who begins with a notion of the value of doing science claim that there is no place in the structure of things for value?  That is a rather embarrassing contradiction, after all – an inability to explain matters beyond a certain level of thoroughness.


Thus science is returning however reluctantly to the notion, as the philosopher Whitehead and others have described, that nature is in some primordial sense “alive”.  This is a view that finds no opposition between “matter” and “spirit.”   The geometric arrangement of matter is simply a manifestation, in varying degrees, of what we experience (in the first place, before any knowledge of “matter”) as transcendent value or “spirit”. 


It is the nature of understanding that the meaning and value on which it rests will always remain an impenetrable mystery forever at the heart of things.  It is like the knife that cannot cut itself, or the finger that cannot point to itself, as the Buddhists say.  Nevertheless, science can articulate astonishing patterns of relationship and structure.  They do not “explain away” the mystery, but they deepen and enrich it.


It is important to note that this view of things puts beauty back at the heart of objective reality, as a structural phenomenon.  After all, the most beautiful music – a canon of Bach, an Indian raga – is nothing more, or less, than a pattern of vibrations in the air.  That is all.  And yet for us participating in it, that is everything.  


Our reductionist science wants to see this phenomenon as nothing more than “psychological.”  But as we have seen, that is an alluring philosophical trick that actually explains nothing – for who or what is perceiving the psychology?  We deceive ourselves if we think we can “explain out” our own participation.  We cannot;  it is always there, always mysterious.


We cannot explain the natural world of beauty and meaning in elemental terms of a “dead” collection of structure.  But we can explain the world of structure in terms of beauty and meaning.  It is not meaning and value that is an additive trick of structure, but rather structure that is imbued with meaning and value. 


Thus do we turn the old mechanist world on its head. 


The new science confirms that there is indeed mechanism within the universe.  Phenomena do indeed operate in relative autonomy – but within a totality that is not a mere assemblage of fundamentally discrete phenomena, but a web of interaction.  We ignore this totality when we abstract specific elements, and pretend that they are fundamentally discrete.  But this is a trick – in Whitehead’s words, “nothing less than an omission of part of the truth.”  And it is the trick that makes us believe in a “dead” universe of detached elements that can be recombined in endless ways, as we have done so well in our technological age.  But in this model we have been unable to explain the phenomenon of life.


The new science is able to explain the phenomenon, or at least point to its origin.  The living force is not on an unseen plane, but all around us.  It is not in the details but in the totality, and in us as intelligent beings.  We cannot “explain” it in terms of something “dead” and “atomic” – but we can articulate specific aspects of its structure with greater and greater approximation to the reality.


All of this taken together implies a profound transformation of science -- and a transformation of our current elementary technological culture.  It is time to throw off the crude abstractions of our technological infancy, and step out of the artificial into the rich complex world of nature.  Nothing less than our very survival depends upon it.  



III. Seven Geometric Properties of Complexity


The new science gives us tools to see what has happened in these earlier stages of modern technological culture.  We see that what we mistook for sophistication was in fact a crude and elementary form of machine technology. We see that the obsession with precision has become a pointless fetish.  We see that the effort to strip structures down to their “pure” minimalist form was in fact an accommodation to an elementary and primitive technology, dressed up in the guise of sophistication.   And we see that our ignorant reductionism has done great violence to the adaptive processes on which nature depends. 


This is an enterprise that is unsustainable, in the most fundamental sense.


We can see the failures of the old technological architecture by identifying some of its missing structural qualities.   We can see that while we thought we were being sophisticated in our minimalism, we were in fact only manufacturing incompleteness on a profound scale.  In so doing we did great violence to the biosphere, and to the subtle but essential qualities of human life.  We see, like doctors newly recognising the signs of a disease, that we have created a sickness of place that we could not even recognise in the old model of technological reality.  We were bewitched by our own abstractions.


Following are seven of these missing morphological qualities.   They exist in abundance in nature, and in human nature.  They are ubiquitous in traditional societies, and in the great architecture of history.  They are missing from modern architecture and modern culture – not because this is a desirable state of affairs, but because our modern technology has not been sophisticated enough to generate these qualities, or even to understand them.   We lack them not because we are sophisticated, but because we are backward and ignorant.


In discussing these properties we must remember that it is not enough to simply add in such qualities through some artificial means, but rather that we must understand the processes that generate such morphology.  We will discuss such processes in the next section.


The seven properties are:


¨      Network Structure

¨      Near Decomposability

¨      Fractal Geometry

¨      Adaptive Iteration

¨      Geometric Holism

¨      Structural Attractors

¨     Connective Symmetries


Network Structure


As Christopher Alexander pointed out in his landmark paper of 1964, a city is not a “tree.”6  It is in fact a dense network.


To explain what this means in urban terms, let me offer a specific example.


   From the book Over Europe, Text by Jan Morris (Weldon Owen Inc., 1988)


On the left is a section of Warsaw constructed in the 1970's. On the right is Rynek Starego Miasta, the square at the heart of old Warsaw.  The place on the right is not unlike cities and towns that have been built for many hundreds of years of human history; the place on the left is characteristic of cities all over the world built within the last 50 years.


In comparing these two places, I ask you to forget, for the moment, the semiotic significance or the emotional associations of the two images.  Forget about cuteness and nostalgia, symbolism and memory.  Look at the two places coldly, analytically, as pure mathematical structures.


The structure on the left is a branching hierarchy -- a mathematical “tree.”   Building monads are connected by a branching sequence of linear pathways and entries.  Each entry serves as the sole point of connection for dozens or hundreds of dwelling units.  Each of these units is connected to its neighbours only by elevators or by linear interior corridors.


The connective relationships, the possible number of pathways between units and to the public realm, are much lower than in the example on the right.


Each building's exterior geometry is similarly stiff and hierarchical -- conforming rigidly to relatively simple concepts of line, grid, plane.  The connective relationships are again severely constrained by the simple, fundamental (and quite alien to their context) geometries that are imposed.


The structure on the right exhibits the classic structural characteristics of network.  Residences are for the most part directly connected to the plaza space, and hence to each other via innumerable pathways.  Buildings are physically connected to each other through an iterative process that produces intense variety with a remarkably limited palette of materials and forms.  On many levels of scale, the entire structure is richly connective.


The structure on the right exhibits other connective properties of natural structure that have also been described by mathematical analysis:  the iterative generation of complex form using simple rule-based processes and patterns; the fractal repetition of forms and textures at smaller and larger scales;  the differentiated adaptation of many elements to a complex biological pattern;  the emergence of an overall pattern of coherence and beauty from relatively autonomous elements operating in simple and direct response to their environment.


Note that the structure on the right also has aspects that are strongly hierarchical (the schematic plan of an individual house, the relation of all buildings to the central plaza, etc).  The difference is that the structure on the left is rigidly hierarchical, and lacks the network aspects of the structure on the right.  The structure on the left is generated by a grand abstraction imposed on the site - the ultimate act of hierarchy.  (Readers of Le Corbusier will recognize it as the tower in the park.)


The ignorant conceit of the twentieth century was its belief that the type of structure on the left is actually more sophisticated and "modern" than the type on the right.  We now know that the converse is true.  Technological prodigy is not to be confused  with cultural advancement.


By the way, there is another interesting aspect of the structure on the right, Old Warsaw:  it is not really old at all.  It was entirely rebuilt in the late 1940's from photos and other historic records after being obliterated by WWII bombing.  This is a reminder that structures formed by complex iteration do not have to be old.  They do have to employ the structural processes that in this case took many years to develop.  But there is no reason in principle why such a structure could not be developed during any given time period.


Or look at the urban plans of the two places below.  On the left is a section of the city of Rome; on the right is a typical post-war American suburb.  The structure on the right is a simple tree hierarchy, with limited pathways of connectivity; the structure on the left is vastly more complex.


 (From A New Theory of Urban Design, by Christopher Alexander et al., Oxford University Press, 1987.)


Notice that the structure on the left exhibits many smaller hierarchies; but that they are plugged into a vast overlapping network structure.  The structure on the right almost exclusively conforms to a single hierarchical scheme, with few network properties. 


There is a direct correlation between the kinds of experience in the two structures and their network properties:  the structure on the left has rich interconnectivity, framing of views, variety of sequential experiences.  It is a delight to wander these streets.  It is an engagement of the mind with the deeper complexities of the world.  The structure on the right, however, may be conceptually pleasing in its simplicity; but it is severely limited, lifeless, lacking complexity.  Travelling these streets is, at best, uninteresting.  It is a diminution of the richness of experience.


The richest and most satisfying structures of history consistently exhibit a rich network structure.


Near Decomposability (“Chunks”)


In his landmark paper of 1962, The Architecture of Complexity, Herbert Simon described the properties of complex structures and observed that they tend to contain many “nearly decomposable” hierarchical structures within them.  They are “nearly decomposable” because they are features that can be discerned or “decomposed” from more complex patterns;  they are not pristine hierarchies, but have interactions between the subassemblies that are “weak but not negligible”.  As we saw in the example from the Nolli plan of Rome, the overall structure is dense, interconnected, overlapping.  But within that structure one can make out many local hierarchies.  They are not perfect – there is overlap between hierarchies, and within them – but they are there in abundance.


By contrast, by imposing a grand hierarchical abstraction – say, the rational “Radiant City” plan of Le Corbusier, or the functional plan of an office building, organised like a hierarchical machine – the structures of the “old modernity” blot out these subtler “nearly decomposable” hierarchies.   The result is radically less complex.


Of course the complex processes of nature still generate their own nearly decomposable hierarchies in and around the structure; but they do not fit within the grand abstraction, because it has not been created as part of the same process.  It is external, and artificial.  The result is that the new structures appear as ugly blotches on a formerly perfect (or apparently so, for true perfection is impossible) abstract structure.  Whether they are plants or patinas or wear patterns or cracks or changes made by humans,  they simply “don’t go” with the structure, and they blemish it.


Again by contrast, the structures of history and of nature accommodate such “blemishes” remarkably well, from the patina of stone to the .  The new “nearly decomposable” hierarchies fit in to the structure of the existing ones in an eccentric and often beautiful way. 


A similar tendency to hierarchy was described in human perception by the psychologist George Miller in his remarkable (and playfully named) 1956 paper, The Magical Number Seven, Plus or Minus Two.  In it he described the tendency of the brain to discern what he dubbed “chunks,” or manageable sub-units of perception, arranged in a hierarchical “chunking sequence”. 


It would make eminent sense if the structures of nature tended to contain “nearly decomposable” hierarchies, and human perception was evolved to decode them in “chunks.”  It explains the perception of beauty and order in hierarchies with pleasingly manageable relationships between the parts.  It also explains, however, the way in which the process can become excessively rigid, and the “chunking structure” can be halted arbitrarily through the imposition of rigid hierarchies.  We see this in the experience, for example, of pedestrians up close to an “old modernity” building whose rigid hierarchy does not address that finer scale.  The “chunks” are discontinuous; in cognitive software terms, there is a “chunking violation.”


The structures of the old modernity are shot through with “chunking violations.”


Fractal Geometry


"Fractal" is a geometrical term from the Latin adjective "fractus," or broken. The term was coined by Benoit Mandelbrot, the mathematician who discovered the spectacular and intricate "Mandelbrot Set."7 A fractal is a geometrical fragment that recurs at different scales. For example, the trunk of a tree is like the limbs are like the branches are like the twigs, and so on.

It turns out that the geometry of nature is highly fractal. Trees, clouds, wave patterns, star distributions, and many other structures in nature exhibit fractal patterns.

This structure – and the iterative sequences that generate it, which we will discuss next – comprise one of the central insights of the new geometry. It is a major advance in understanding the mathematical structure of nature. Fractal analysis has applications in many fields.

Many beautiful pieces of art can be shown to be highly fractal. Oriental rugs are well-known examples, and their morphological similarity to the Mandelbrot set is often striking. But there are many others. A recent analysis of the painter Jackson Pollock's work demonstrated it to be highly fractal in structure.

Buildings and cities are also highly fractal -- or they were, that is, until the overwhelming “rational” Euclidean geometries of the twentieth century displaced them.  The reductive processes increasingly took over, largely obliterating the fractal structure, except as a superficial decoration here and there. The overall fractal connectivity does not exist to the same degree.


A central issue of interest to us, I suggest, is the fact that fractals embody a linkage of scales, down to finer and finer levels (and, by implication, up through larger levels). That is, in a fractal-rich structure there are symmetries of forms, or self-similar forms, across many levels of scales. They need not all be conforming to the same regime, however. There can be an overlapping mesh of fractal systems -- and there usually is, especially in nature.


But this quality of self-similar forms linking across scales -- one may call it symmetry across scales, or scalar symmetry for short -- is the key quality that is so richly present in nature, and in the great built environments of the past -- and conspicuously absent in the weaker efforts of contemporary builders across schools and styles. And I suggest this is a very intriguing and important fact.


The discussion of fractal geometry is often a confusing, brain-numbing experience.  But at its core, the idea is very simple:


It is about repeating geometric fragments at smaller levels of scale.


Take for example, one of the simplest fractal structures known, something called a Cantor Set. One takes a line segment and removes the middle third.


---------             ---------


One then takes the two remaining segments, then removes the middle third of each.


---    ---             ---    ---


One now has four line segments, separated by smaller spaces, each pair separated by a larger space. One then removes the middle third of each.


- -    - -              - -     - -


And so on. This process can go on infinitely, at vanishingly small scales. But the algorithm, and the very simple figure it generates, occurs across all scales. It is very simple, but it does not stop. It is continuous, and infinitely varied, in a rather simple way, according to this algorithm.


Now here is where things get very interesting. Extend the Cantor Set into two dimensions, and you will create something called a Cantor Gasket. Take a square region, and remove a big square out of the middle, of dimension 1/3 each side.





XXXXXXXXX                       XXXXXXXXX

XXXXXXXXX                       XXXXXXXXX

XXXXXXXXX                       XXXXXXXXX





Now you can imagine an array of nine squares, one gone from the middle. Of the eight remaining, remove another 1/3 square from each.



XXX       XXXXXX       XXXXXX         XXX


XXXXXXXXX                       XXXXXXXXX

XXX        XXX                       XXX       XXX

XXXXXXXXX                       XXXXXXXXX


XXX       XXXXXX       XXXXXX         XXX



Now repeat the process again, taking away 64 little squares. Continue. Continue.


And you have a pattern that is remarkable similar to the urban plan for Savannah, Georgia, in the USA: 



Or a rough approximation of its grid system of  squares, street intersections, lots, houses, and so on, down to finer levels of outdoor space.


Of course, Savannah is not a perfect Cantor Gasket. There are no microscopic squares on which fleas spend lazy southern afternoons. (Or “littler fleas on their backs to bite 'em, and on ad



The form of a region like Savannah does not exactly conform to a fractal algorithm. As noted, most of nature is a blend of overlapping algorithms, not quite in tune with each other. The important thing is that there is an overall structure of linked algorithms and linked fractal sets, bridging across scales and levels. The process does not stop at one particular level.


Some image compression software has sought to use fractal analysis and synthesis to generate relatively faithful portions of natural images. The software seeks to detect self-similar geometries at different scales and at different regions, and then generate synthetic algorithms. That is what one does in an analysis -- one does not find the "perfect blueprint” – for as we have discussed, such a blueprint does not exist -- but instead one finds a whole series of iterative components that roughly approximate what is seen.  


For us, I suggest that the challenge is not to find the perfect algorithm (as there usually isn't one single algorithm anyway) but to begin a promising skeletal armature on which others can continue the adaptive iterations.


Note that this is not at all inconsistent with the idea of master planning, and we can do this at the master planning stage; the point is that we need to recognize that we are only starting a process. We must not suppose that we are finished.


Clearly Savannah is one great armature, judging by its lovely and richly complex results. But why? Are there others? How can we use them? How do we develop tools of analysis and synthesis? There are many great questions to explore.


In Savannah, the grid system of progressively smaller spaces was a great armature on which to begin the iteration of the rich self-similar detailing of great houses (column, baluster, mullion, muntin) or moulding (roof edge, cornice, ogee trim) or the fractal layering of beautiful moss-covered trees, or so many other fractal systems. (e.g. the powerful self-similar symmetry in the way tree canopies and roof lines echo one another...)


But suppose one took that partial Savannah iteration, and then asked, say, Oscar Niemeyer to come in and do some graceful salad bowls, or got Frank Gehry to do some crumpled napkins. They might be very pleasing sculptural forms indeed. They might, as Gehry's does, have their own internal fractal structure. But they would lack the fractal continuation, the connectivity, that Savannah possesses in such multi-levelled richness. And, I suggest, they would stop the process cold.


Or suppose we just let a typical residential developer come in, with his catalogue plans. What will happen? There would be a loss of fine iteration, a broken symmetry.  There would be a loss of scale in material deflections, textures, grains; there would be aloss of fractal integrity. Savannah would become... the contemporary American suburb.


We imagine this is sophistication. A simple mathematical analysis suggests it is delusion.

This is an intriguing insight. It suggests that we CAN analyze what we thought was not analyzable -- in this case, certain connective geometrical properties of the built environment. It suggests that we can move the discussion beyond the impenetrable world of "what you like" -- much as weather forecasters are moving beyond barometric pressure models, or economists are moving beyond simple equilibrium models, to better understand the secrets of complex structures.8


Adaptive Iteration


One of the key revolutions of recent science has been the recognition of the role of vast numbers of small, adaptive rule-based iterations, or "algorithms", in producing extraordinarily complex structures.  In fact, many of the most complex and previously unfathomable structures of nature have been shown to emerge from such simple rule-based processes.  This in turn has given us a new comprehension of such processes in nature – including human nature -- and an opportunity to engage them with a new degree of understanding and accuracy.


For example, the beautiful intricacy of fractal structures, described earlier, comes from such adaptive iterations, as each step responds to the sequence of steps that have gone before it.  In fact the actual formula for generating a fractal pattern is stunningly simple; yet because each step takes into account all of the steps that came before it, in a particular interactive way, an enormously complex pattern quickly emerges.


Similarly, structures known as “cellular automata” are a collection of independent but interactive “automatons” (or algorithms) operating according to simple algorithmic formulas for responding to their neighbours’ condition.  This state of affairs is common in nature:  examples include molecules in a gas, cells in an organism, traders in a stock market. In spite of the simple rules governing each “automaton,” in practice the resulting pattern can be vastly complex and intricately ordered – but not in a way that could have been predicted according to a simple “blueprint.”


In fact this is a crucial discovery: the process is often irreducible.  That is, there may be no single schematic idea or set of ideas that completely expresses it, that is simpler than the structure itself.  The progression of the iterative process can often be unpredictable, and the only way to fully understand its behaviour is to simply let the iterations run.


The mathematician Steven Wolfram has proposed an entire branch of revolutionary science based on such iterative algorithms.9  For Wolfram, the mathematics of the past has done a wonderful job capturing the essential features of many simpler structures; but it has hit its limits in understanding the vastly complex world of iterative algorithms.  This is because mathematics is by nature an incomplete model of the structure it represents.  (As mentioned previously, this was shown brilliantly by Kurt Gödel, Alan Turing, and other "limitative" theorists of the twentieth century.)  The development of computer science has propelled this work enormously, and in turn has been propelled enormously by it.


This "incompleteness" of mathematics (and indeed of any representative model) is, after all, usually a good thing.  For example, we want our maps to be simpler than the regions they represent -- or else we would be just as lost in the maps as the regions themselves!10   But we get into trouble when we forget the difference -- when we suppose that the abstract "master plan" must be the exact structure of the city, or that the abstract idea of a building should be translated literally into the form of a building.  This "geometrical fundamentalism" can be visually stunning, but it can also be shown to be enormously destructive of the complex patterns of human life.


By contrast, the greatest natural landscapes, and the greatest urban fabrics of history, exhibit abundant patterns of adaptive iteration. 


Many theorists have sought to capture the power of adaptive iteration in building and urban design, but there is much work still to do.  Perhaps most notably, the architect and theorist Christopher Alexander proposed a "new theory of urban design" based on an iterative process, in which individuals respond to each other’s sequential patterns over time to form a larger and more complex whole than any one individual could possibly achieve with one design.  In this way, the structure of wholes is preserved and enhanced in a stepwise process of transformation, following the morphogenetic processes of nature. Alexander is today working on a “generative code” to guide urban design, following similar principles.11


Geometric Holism


The brilliance of Cartesian and Newtonian science -- resulting in an unparalleled era of human prosperity and material progress -- has been its ability to isolate small subassemblies of nature and let them function, independently, as essentially little machine models of reality.  This has been a vastly productive analytical tool, and it has offered astonishingly productive capabilities to re-fashion these reductive mechanisms to our own ends.


But as many authors have noted, there are fundamental limitations to the accuracy and completeness of this kind of science.  In fact, in a key respect, it completely misses a fundamental aspect of reality.  That aspect is one of field effects -- the essential role of connected context in the function of certain processes.  This "systemic" or "organic" quality is summed up in the well-known expression “the whole is greater than the sum of its parts."


As the philosopher and mathematician Alfred North Whitehead once said, "connectedness is of the essence of all things."  By contrast, these little machines are in essence abstractions, defined elegantly by Whitehead as "nothing other than an omission of part of the truth."


This is the brilliance of the human animal -- and precisely its limitation.


We see this essential contextual structure of things perhaps most clearly in the realm of biology and ecology, where organisms do not survive when apparently remote parts of their ecosystem are disrupted.


We see it in very “hard” sciences such as quantum physics, where particles stop behaving like particles, and where a mathematical description of the way in which the whole influences its parts is the only way to explain the behaviour or particles.


And we see it in a particularly powerful way in the realm of aesthetics, where various field structures -- boundaries, proportional regions, and so on -- have a profound effect on the perception of a certain region.


One of the most sensitive examples of this effect can be seen in a human face, when hair is changed, or other features are added.  Even a tiny addition of eyeliner or rouge can cause a dramatic change to the entire appearance of the face. 


Indeed, one could say that fashion and style rely almost exclusively on these kinds of field effects, and not on a mere assembly of objects.


In design, we usually discuss these kinds of field effects with terms like proportion, scale, harmony.  But science today is revealing a far more subtle world of field effects, and one that carries significant new implications, particularly for the understanding of aesthetics.  The new developments point to stunning possibilities; the biologist E.O. Wilson was recently prompted to proclaim that "the field of aesthetics awaits its Mendeleyev."


What is clear is that the strategic use of field effects can greatly increase the experiential power of geometry -- not only in a sculptural viewing perspective, but at many more experiential levels.  The best modernist architects have understood this, although their style was much too abstract to achieve a profound multi-level amplification. Their architecture largely settles for a local amplification -- and cannot capture the rich amplifications of the wider fabric of life.  They are still mired in the architecture of the artificial.


Structural Attractors


In the mathematics of complex or “chaotic” systems, it has been observed that clusters tend to form in certain regions for no apparent reason.   The tendency to such an unexplainable grouping is an “emergent” behaviour of the complex phenomenon.  Such regions are known as “strange attractors.” 


The biologist Brian Goodwin has taken this phenomenon a step further.  He has proposed that in biology, a very similar phenomenon occurs as an emergent phenomenon, having little to do with the accidents of evolutionary history:  for example, the shape of a shark dorsal fin is nearly identical to the shape of a dolphin’s dorsal fin, and yet they are two different orders, with completely different evolutionary histories.  All of the complex forces of turbulence and laminar flow and so on help to shape that structure into something nearly invariant.  And in each case the solution is coded into the DNA, into the collective intelligence of each species. 


It turns out that a similar argument can be made about human environments.  We are all different, but we are all very much the same, our bodies are the same, our human needs are much the same;  and so it should not be surprising that certain regions of “solution-space” should form recurrent patterns, across cultures and across time. And indeed they do – the stable “structural attractors” of classical design, or vernacular design.  These are not stylistic vagaries, or cute sculptural ideas, or artificially imposed “social constructions” by a political elite – they are naturally occurring patterns.  And indeed there is a close relationship to Christopher Alexander’s Pattern Language, and a suggestion that something similar might be taken to the level of architectural element. 


Connective Symmetries


As we noted previously, in its fullest form the architecture of a human place is much more than an experience of fine art.  It is in fact a vastly complex connective structure, creating pathways between physical points and between mental ones too.  In this way it offers rich connective experiences at various levels of a life lived, and a culture shared.  These experiences are, in real geometric terms, connective symmetries.


We use the term “symmetry” not merely in the sense of the more common axial mirroring, but in the deeper sense of the echoes and amplifications that make up the complex fabric of physical and mental life. 


It is important to note that these connective symmetries have a definable geometric structure -- open to description, analysis and adaptive improvement, open to amplification and deepening.  And the symmetries arise, and are amplified, through a process that is equally describable and open to refinement.


This offers the basis for a new kind of humane technology.


Some of these symmetries are clearly biological in origin:  to cite several obvious examples, they may trigger the stirrings of young men at the certain proportions of women’s waist to hips, occurring when they are young and ready to conceive; or the awakenings of powerful maternal instincts in a woman looking at her child’s large doll-like eyes and small chin.


These phenomena are not to be diminished as mere “tricks” of “selfish genes”.12   For the existence of organisms as vehicles for the propagation of genes is no more likely than the existence of genes as vehicles for the propagation of organisms.  Once again, we are falling into the reductionist trap.  We must look at the larger process, and the complex patterns it embodies.  Then we see the symmetries of biological emotion as experiences of meaning and life. 


These experiences cannot be reduced in terms of experience itself.  But they can be reduced –or, more accurately, understood structurally – as geometric phenomena.


For example, what is “blueness?”  What is that quality of blue that we see and enjoy so much?  We may say it is only a certain geometric rippling of light at a certain periodicity, nothing more; and in one sense we would be right.  But the deeper truth is that it is a resonance, a symmetry, an awakening within us of a participation in the structure of the universe.  That particular structure is experienced in a particular way, and in a particularly beautiful way.  It is a deeply resonant symmetry within us.


Thus beauty is brought back to its rightful place – not as a “mere psychological” phenomenon, but as a manifestation of structure, and deep structural symmetry.


Note that “blueness” by itself is not nearly as powerful as it is in an interwoven pattern of, say, blue and gold.  Or a richly interwoven Islamic room of blue and gold tiles and forms.  The more richly connected the symmetries, the more we feel their connections to ourselves and to other parts of our lives, the more intensely do we perceive their beauty.


I suggest that such insights may be the door to a new and powerful theory of aesthetics.


In this way the new science offers us a new “grand unification” between subjectivity and objectivity, and it brings back beauty as a real geometric property of the universe – or of experience, which is all that we really have of the universe in the end anyway.   


Here is where we gain clarity about the aesthetic nature of the modernist project.  For some of these symmetries are synthetic creations of the human mind.  They rely on memory, idea, abstraction.  These mental symmetries are powerful and often very meaningful. 


But they are not the only form of symmetry.  Indeed, they are not the origin of symmetry, but only its echo.  The memory and the abstraction of a form have their origins in the real and concrete form experienced.   Their amplification requires repeated returns to the realm of the concrete.


It is the disease of our age that this connection has been severed, and we wander disconnected as though in a hall of mirrors.  It is a “fun house” of our minds -- severed and alienated from the natural context in which it took root.  The result may be extravagant, clever, imaginative -- but without the return to the concrete, it will not be as richly complex.


And yet we can produce an art that does nothing but celebrate and idolise these abstract symmetries.  There is nothing wrong with this, as long as we are clear about what we are doing.  But as Frank Lloyd Wright put it, “when we ourselves become abstractions, we are lost!”


As the philosopher Alfred North Whitehead said, this discussion “highlights the importance of a right adjustment of the process of abstraction.” Abstraction enriches experience, and amplifies it.  Abstractions can be the powerful servants of field amplification.  But the return to the concrete may be misconceived.  Apart from a balanced emphasis, this misuse of abstraction can end in the triviality of quick-witted people -- and the shallowness of culture.13


Whitehead frequently warned of the danger of becoming lost in abstractions, committing the fallacy that he called "misplaced concreteness".  "Mankind," he said, "is distinguished from animal life by its emphasis on abstractions.  The degeneracy of mankind is distinguished from its uprise by the dominance of chill abstractions, divorced from aesthetic content."


Or, we may add, chill abstractions are divorced from concrete aesthetic content, and supplanted entirely by an artificial aesthetic given by the abstractions themselves.  The result is a disconnection, a severance, from the wider concrete structure of life and nature, and a negligent destruction of the fabric of human life.


We have described the core failure of technological architecture – and indeed of unsustainable technology itself-- in our time.  


Now the challenge is to embrace the larger connective task, of engaging the symmetries of the concrete context, and rooting a new architecture of humanity in these larger symmetries.



IV. The Architecture of Complexity


In the years to come, we should not be surprised that the new sciences will have an enormous impact in the field of human habitat.  This is the arena, after all, where human beings interact most immediately with one another and with their world.   This is the physical form of human civilisation, and arguably the structure that most profoundly shapes it.  As Churchill said -- the truth of which we are beginning to understand with renewed appreciation -- "We shape our buildings, and thereafter they shape us."


The structures of 20th century modernist architecture exhibit a surprisingly elementary, even primitive geometry.14  Supposedly “modern” buildings are in fact conglomerations of lines, planes, cubes embodying many of the most primitive Euclidean forms.  Early modernists like Le Corbusier recognized the inevitability of the machine age and its early elementary mechanical geometries, and sought to make them the basis of their own elegant art form.  Thus Le Corbusier’s pilotis and pipe rails borrowed from ocean liners, his boxes and cylinders from grain silos, and his swooping aerodynamic forms from airplanes. It was a brilliant accommodation, but an accommodation nonetheless.


A more recent school of modernist architecture, represented by architects like Frank Gehry and Rem Koolhas, aims to embrace the new complexity science.  Gehry uses crumpled paper and other “natural” complex forms, while, for example, Peter Eisenman layers angular strips to create energetic compositions, and Koolhas, Libeskind and others, twist and “morph” various forms to create dramatic compositions.


But they are just that – compositions, not reflecting or iteratively engaging the deeper structures around them.  In that respect they are not true examples of complexity at all, but rather the abstract expression of the idea of complexity, celebrating the randomness and disorder of the contemporary city.  As we have seen, this is not at all the same thing.  It is the totemic symbol, not the reality.  And even then, the symbol is a poor simulacrum.15


By contrast, the supposedly humble structures of history – even modest vernacular villages – reveal to the patient analyst a remarkably complex and sophisticated adaptive structure, in some aspects rivalling the morphogenetic complexity of nature.16   The new science and mathematics is awakening in us a new appreciation for the marvellous degree of adaptation and sophistication in traditional societies, even in the face of comparative technological poverty.  We are teased by the possibility of such adaptive sophistication with contemporary resources, in a contemporary setting.


We are teased by the notion of an architecture of deeply adapted connection, in place of an architecture of superficially imposed ideas.


Of course few would suggest that it would be a good idea to go back to a pre-technological time, with its disease, its repression, its brutish standards of health and sanitation.  But at the same time, as this discussion reveals, we can learn “geometry lessons” from these cultures -- from their adaptive processes, and the marvellously subtle and exquisitely adapted forms that have resulted.  In their adaptation these forms have the morphogenetic stability of nature itself.  Their endurance must be a lesson to us in an age that recognizes the need for “sustainability.”


These lessons have been further elucidated in anthropology, where researchers have described the remarkable adaptive complexity of traditional societies.  Some anthropologists have called for us to embrace the lessons of these societies in our own culture.17  Their call has been dismissed as an impossible return to another time and place, and a rigid political authoritarianism that is not compatible with contemporary science or contemporary open society. 


But it is a fallacy to presume that a given class of beneficial morphology can only result from a given socio-political history.18  On the contrary nature, including human nature, offers abundant examples of isomorphism, transplants, adaptations, migrations.  Amid the myriad geometries and properties around the world’s cultures, there is simply no evidence for a “morphogenetic determinism” in politics. 


There is, however, evidence for a more direct relationship between a primitive reductionist technology and a primitive reductionist architecture.  That exists in no other culture than Western “modern” industrial society.18  And it is a core argument of this paper that as the earlier technology did indeed imply a concomitant elementary mechanical geometry, the new biological science and technology implies a new geometry and a new deeper ordering of culture, in many ways incorporating some of the morphogenetic lessons of other cultures. 


This, we assert, will be a new and necessary dialectical advancement.


How then can we translate these lessons into action in our own age?  How can we achieve a true integration and regeneration of such beneficial morphologies, and not an artificial graft or “pastiche”?  The ideas discussed here suggest that such a thing is entirely possible.  In fact it may be inevitable and necessary, as we have argued.


The five geometric properties outlined here give us a clearer idea about the properties of such a “new” (regenerated) architecture.  Significantly, it would embody the structural richness of the greatest architecture of history, but also incorporate new technologies and new innovations -- as the best architecture has always done.  


Most significantly, it would cease to exist in an artificial, isolated realm of abstract art -- or the equally artificial realm of abstract technocratic economic game theory, the realm of schlock and crude primitivism.  It would reflect again, as the best work of humanity has always done, the complex adaptive structure of nature.  It would be integrative into human culture, and cultural processes.


This implies a modification to the economic game theory around which artistic culture now revolves as a mere epiphenomenon, and a return of cultural valuation to its rightful place at the centre of human life.   We have not yet begun to assess the changes to economic and artistic institutions that this implies.  But we can predict with some confidence that it is in the nature of the evolution of more intelligent human structures that they will inevitably move in this direction.  We, as intelligent actors and participants, need to recognise and hasten this process.  Indeed, our intervention as allegedly intelligent beings may well be necessary to avert disaster.


There is a huge amount of work to be done.


Meanwhile, we can describe – as a preliminary step – the kinds of processes and the morphologies they produce.  Again, the key distinction is that the morphogenesis occurs not as an artistic idea applied over a technological reality and shaping it, but as a deep process engaged with a deeper and more biological kind of technology.  That is, the new architecture would take the complex adaptive form of nature not as a result of ideas alone, but as a result of an iterative morphogenetic process. 


The most salient trait of this architecture – in contrast to the architecture of elementary modernity -- is its process of natural connections, formed across many scales.   The connections are both structural and symmetric: that is, they are physical linkages, and linkages between symmetrical structures at many scales.


These are the characteristics of such an “architecture of complexity”:


1.    The form arises through a deep process

2.    The process engages human and natural patterns of activity

3.    The process uses adaptive iteration, building up a complex structure over time

4.    The iteration includes patterns of collective intelligence formed over centuries

       of adaptation and refinement

5.    The iteration continues forward in time, integrating natural patinas, new patterns of

       human activity and adaptive re-use

6.    The process adapts technology to life, and not the reverse

7.    The process results in a rich differentiation across scales

8.    The process results in a dense network of connections

9.    The process creates deep symmetries throughout levels of daily experience

10.  Artistic expression and ornament is integrated seamlessly into the process, 

       expressing to human consciousness the rich underlying connective order and beauty 

       in which the experiencing individual participates


Now let us consider the morphogenetic process of what we have here called “elementary” modernity:


1.    The form arises from an artistic concept or visual idea

2.    The concept celebrates the artificial and the abstract in isolation from “messy” nature

3.    The concept is a singular entity, from a single “heroic” artist

4.    The concept celebrates radical novelty and eschews "old-fashioned" knowledge

5.    The concept exists outside of time (while the real artefact therefore ages poorly)

6.    The concept accepts elementary mechanical technology as a required basis of art and an unchallenged condition of “modern” life

7.    The concept halts at arbitrary scales and leaves large scale-gaps, particularly at finer scales

8.    The concept forgoes connectivity for clarity of conception

9.    The concept has limited symmetries based upon gallery experience

10.  Artistic expression is a segregated function: an artificially added layer to an underlying technological game process (almost entirely after the fact)


In the latter case, an initial symbolic impact is exchanged for long-term poverties of experience.  The form becomes prisoner of the symbolic rule-based game of modern fashion economics, in which a legacy of deep traditional refinement is exchanged for shallow novelties and easily exchanged simulacra. 


Thus is “modern” architecture deeply implicated in the larger cancer of economic and technological reductionism, a powerful force destroying the deeper differentiation on which life itself depends.


As we have noted, this enterprise is self-consuming by nature and therefore fundamentally unsustainable. It is doomed to collapse.  Its correction will require a deep re-evaluation of the relationship between commerce, politics and culture.  It will require a new technological and cultural reality.



V. Towards a New Architecture of Life


In our age it is our great privilege to witness the development of new and revolutionary forms of science, and in particular those based on the new understanding of complex iterative processes and the connective geometries they create.  We have seen the way that nature itself uses such processes in the morphogenetic transformations of life itself.  We have seen tantalizing hints at the potential to develop tools for a much richer architecture for the future, and even a richer and more genuine kind of culture.


In this light we can view with some scepticism and even bemusement – to put it charitably -- the claims by the current leading architects, that theirs is the new paradigm in architecture.


For all their claims of a new paradigm, we see that these neo-modernists are still very much creatures of the old technocratic modernist paradigm that they so willingly discredit.  They still do not let go of the central conceit of modernism, its naïve chronocentrism -- its belief that we are now and forever divorced from the past, in all its bourgeois irrationality; and that we have created an entirely new artificial reality, based upon current technological culture, in place of the old.  They do not surrender their faith in perpetual novelty as supreme value, no matter how shallow.  They still cling to an isolated architecture of simplistic mental constructs, inspired by a crude and ignorant phase of industrialism, stripped bare of the complexities of nature and of history.  They harshly criticize an increasingly shallow corporate culture of architectural simulacra, and yet they make themselves its willing victims and co-conspirators.  They sneer at the vast quantity of crude and artless pseudo-traditional construction across the globe, and yet they offer no meaningful leadership for its builders.


And they hold fast to the curious ideological faith that even to consider any other basis of architecture is to descend into bourgeois decadence, to become the tool of social discipline, to serve as apologist for power.   In so doing they deny themselves a rational exit.  They offer not the reform of rationality, but its absurdist end.


But the central lesson of our time is this: history is far from over. As the twentieth century recedes, we are left humbled by the lessons of the new sciences, and we see our unwarranted arrogance and hubris for what it was.  We see that traditional societies of the past will not go quietly into that good night -- and may well come raging at modernity and its symbols.  We see that power is a human universal, and the best weapon yet found against it is openness and pluralism -- not the end of traditionalism, but the diversification of it.


In this way, we recognise that human tradition cannot be eradicated, but it can certainly be transformed.  It can be subverted into an oppressive technocratic economy in which human understanding and choice are marginalised.  Or it can be more artfully engaged in a more open and pluralistic society using the new tools and insights of complexity.  It can become a rule-based game under our own intelligent control. 


In so doing we see that tradition in itself is not the enemy, but nothing other than the collective intelligence of human life itself – there to be shaped in more or less intelligent and humane ways.  


And we see that the vast world of nature and of human history, stretching far beyond our historically tiny modernist era, holds untold riches, there for future generations to mine with the new tools.  We see tantalising hints of a waiting renaissance, or perhaps many more renaissances to come.


The new sciences show us a picture of a vast world beyond the deconstructivists' entertaining mishmash of mental constructs:  a world rather that is densely connected, intricately ordered, full of emergent life.  It is a world in which the genius of human culture is manifested in an articulation of varied contexts, the sheer vast geometric complexity of order achieved by time and connectivity.


The new sciences show us how simple rules and patterns generate unending variety, how codes and other abstractions create an architecture of possibility.  We are teased with the possibility that we can learn to be better masters of this game.  They also warn against the human habit of misusing over-rigid abstractions -- what Whitehead called "misplaced concreteness" -- to remove ourselves from the truth.


And the truth of our human existence today is that all around the world we have learnt very well to make horrible, inhuman, disconnected places, sprawling places serving only our machines, moderately interesting and superficially entertaining experimental places that are, in the end, grossly dysfunctional, and terminally incomplete.  In spite of all efforts at art, they are only more output of a prodigious, unsustainable machine.  Koolhas’ term is apt:  this is junkspace.


But we scarcely know anymore how to make places worthy of our humanity. 


Responding to these revelations, a new crop of architects and scientists is emerging, as surely as the new sciences of complexity are emerging from the broken pieces of deconstructed rubbish left by the old rationalism.   These designers and theorists are not simply trendy giant sculptors, or philosophers of despair.  They are the real heirs to the Enlightenment, because they believe that humanity is intelligent, and that intelligence means the shaping of our own destiny.  They are anthropologists, philosophers, mathematicians, biologists, physicists.  They are historians. 


They are connectors.


The emerging architects and scientists are much more than romantic reactionaries, as the rear guard of modernist critics find it comforting to suppose.  Indeed some do fall into the old dualist trap, quixotically advocating a reversal of the Enlightenment project.  But of course the modernists are right about one thing: a synthesis is not a mere re-statement of an old thesis. Rather, most of the new visionaries have faith in progress and in the Enlightenment, but no longer in its inexorable path to reduction.  They have a desire to temper power with pluralism, openness and progress, but not with disintegration.  They believe that to end a throwaway society and to build a more sustainable human future, we must build a world that is not designed to be thrown away, like last year's novel fashions.  They know that in spite of the formidable difficulty of a modern revival of traditional practice, and the halting efforts so far, we still exist in time and place, connected to our common past.  They believe that we must recognise and embrace again the timeless structures within our own time.


In this way, we will cease to be consumers of an unsustainable capital, and we will begin adding back to the deep capital of the species, and the biosphere.  We will cease being floral arrangers of dying cuttings, drawn from around a dying world.  We will begin again to be expert gardeners.  It will change nothing, and everything.


This, we assert, is the new modernity.


VI. Notes

  1. There is a famous episode in which physicist Alan Sokal successful had published an absurd spoof paper, “Transgressing the Boundaries:  Toward a Hermeneutics of Quantum Gravity” in the journal Social Text (46/47 vol. 14 , 1996). Beneath its merciless satire was a serious demonstration of the impossibility of credible science under a philosophical regime in which veracity is an entirely artificial social construct.  This Post-structuralist position on truth is to be distinguished from that of Structuralism, which describes the social constructions of reality without making self-contradictory ontological claims (of the sort made famous by Derrida when he said “there is nothing outside the text”). 

  2. This argument was spelled out clearly by Jacques Ellul in his landmark book The Technological Society (Vintage Books, 1964).

  3. See Thomas Kuhn. The Structure of Scientific Revolutions, 2nd. Edition (University of Chicago Press, Chicago, 1970).

  4. See e.g. Kurt Godel, “On the Undecidability of Principia Mathematica and Related Systems,” `1931.  Verify

  5. See the more extensive discussion of this idea under the section on adaptive iterations.

  6. See Christopher Alexander, “A City is Not A Tree,” www.rudi.net/bookshelf/classics/ city/alexander/alexander1.shtml

  7. See Mandelbrot, Benoit B. The Fractal Geometry of Nature (Freeman, New York, 1983).

  8. My colleague Professor Nikos Salingaros has discussed the fractal structure of architecture in a number of significant papers.  See e.g. Fractals in the New Architecture, www.archimagazine.com/afrattae.htm

  9. See Steven Wolfram, A New Kind of Science,

  10. There is a marvellous story by Lewis Carroll about a group of mapmakers who, disturbed by all the omissions in their maps, proceed to make them larger and larger.  Finally their maps are as large as the regions they represent, and so the mapmakers decide to simply use the regions as their own maps and they do “well enough.”  This delicious anecdote highlights the fact, of course, that it is precisely the incompleteness of maps (and indeed of any abstraction) that is their value.  We would be just as lost in a “complete” map as in the region itself!  See Lewis Carroll, “Mein Herr” in Sylvie and Bruno Concluded.

  11. See Alexander, Christopher. The Nature of Order (Center for Environmental Structure, 2003).

  12. The argument for the “selfish gene” was made commendably by Richard Dawkins in his book by the same name.  The only problem is the one we have noted: it is a fully symmetrical relationship and a kind of “chicken-and-egg” conundrum that can be just as well answered – or, we fear, poorly answered – by the opposite analysis.  Such single-variable teleology is not sufficiently meaningful, and one must look at a deeper level of morphogenesis to understand the teleological aim of the system as a whole.  But the Dawkins argument does show the mire in which such reductive exercises tend to land the reasoning.

  13. See the landmark work Modes of Thought, Alfred North Whitehead (MacMillan Free Press, New York, 1938)..

  14. See e.g. “Geometrical Fundamentalism,” Michael Mehaffy and Nikos Salingaros, 2001.  In Plan Net, www.plannet.com/ features/geometricalfundamentalism.html

  15. See for example Nikos Salingaros and Brian Hanson, “Death, Life and Libeskind.” In Architexturez, http://www.architexturez.net/sub.gate/subject-listing/000122.shtml

  16. This has been elegantly shown by a number of authors; see for example Bernard Rudofsky, Architecture Without Architects.  We believe a few more PhDs could be earned in this subject…

  17. For example, see Edward Sapir’s classic paper, Culture: Genuine and Spurious.   It is one of the most incisive critiques of modern technocratic culture, written rather too presciently in 1933.   Today we are seeing an acceleration of the erosion of genuine culture and its increasing replacement by simulacra, be it the world of consumer goods, fashion, newspapers and books, art, politics, the law – no field, it seems, is immune.    We are rather too much like the proverbial boiling frogs, unaware of the slow death of our collective intelligence and its substitution with a virus of technocratic mindlessness.   The new science suggests a profound re-evaluation of our institutions and rule-based economic processes, implying radically new kinds of institutions and processes. 

  18. The fallacy reaches its absurdist extreme in the arguments of some modernists that Greco-Roman Classical Revival is a de-facto concomitant of political tyrannies:  the empires of Greece and Rome, or the monarchies of the Renaissance, or the 20th century Fascist regimes.  This overlooks the popularity of the revival within the culture of 18th century Enlightenment liberals Jefferson, Franklin and others.   Also anomalous for such a curious notion were the many pro-Fascist proponents of early modernism itself, including Johnson, xxx.

  19. Again, see “Geometrical Fundamentalism,” Michael Mehaffy and Nikos Salingaros, 2001.



VII. Bibliography


Alexander, Christopher. The Nature of Order (Center for Environmental Structure, 2003).

Alexander, Christopher et al. A New Theory of Urban Design (Oxford University Press, New York, 1987).

Bovill, Carl. Fractal Geometry in Architecture and Design (Boston: Birkhäuser, 1996).

Carroll, Lewis, The Man in the Moon, in Sylvie and Bruno Concluded.  http://www.bibliomania.com/0/0/11/1946/frameset.html

Coveney, Peter and Highfield, Roger, Frontiers of Complexity:  The Search for Order in a Chaotic World.  (Fawcett Columbine, 1995).

Doczi, Gyorgi.  The Power of Limits:  Proportional Harmonies in Nature, Art, and Architecture. (Shambhala Publications, 1994).

Ellul, Jacques, The Technological Society (Vintage Books, 1964).

Ghyka, Matila.  The Geometry of Art And Life (Paperback, 1988).

Gleick, James Chaos. (Penguin USA, 1988).

Hofstader, Douglas R. Gödel, Escher, Bach:  An Eternal Golden Braid.  (Basic Books, 1979).

Jencks, Charles. The New Paradigm in Architecture (Yale University Press, New Haven 2002).

Johnson, Steven.  Emergence:  The Connected Lives of Ants, Brains, Cities, and Software.  (Scribner, 2001).

Thomas Kuhn. The Structure of Scientific Revolutions, 2nd. Edition (University of Chicago Press, Chicago, 1970).

Le Corbusier, Towards a New Architecture (Architectural Press, London, 1927).

Mandelbrot, Benoit B. The Fractal Geometry of Nature (Freeman, New York, 1983).

Miller, George, The Magical Number Seven, Plus or Minus Two, Psychological Review, 63, 81-97 (1956).

Morris, Jan et al., Over Europe (Weldon Owen Inc., 1988).

Simon, Herbert, “The Architecture of Complexity,”  Proceedings of the American Philosophical Society 106 1962 pp 467-482

Sokal, Alan, “Transgressing the Boundaries: Toward a transformative hermeneutics of Quantum Gravity,” Social Text 46/47 vol. 14 , 1996

Waldrop, M. Mitchell, Complexity. (Touchstone Books, 1992).

Whitehead, Afred North, Modes of Thought. (MacMillan Free Press, New York, 1938).

Whitehead, Afred North, Process and Reality.   (MacMillan Free Press, New York, 1929).

Whitehead, Alfred North, Adventures of Ideas.  (MacMillan Free Press, New York, 1933).

Wolfram, Steven, A New Kind of Science (Wolfram Media (2002).