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The Next Architecture

Lessons from the New Sciences for the Shape of Things to Come



The modern era – the most astonishingly productive epoch in human history -- is showing dramatic signs of end-stage crisis.  The last century's optimism about the rational progress of humanity has given way to a more sober understanding of the limitations of reason and technology, in the face of daunting human challenges.  


Out of this recognition, a post-modernist movement in architecture and the arts has been born.  But although this post-modernism often symbolically acknowledges the new science, in actual process it can be seen to offer little more than stylish retrofitting of the old elements of modernism.  In its methodology and its world view, it in fact owes more to the science of 1900 than that of 2000.


Meanwhile, the new science continues to provide startling new insights into the complex adaptive structure of nature -- including human nature -- and a deeper understanding of the environmental and cultural damage that the modern era has done.  It does indeed suggest rich possibilities for a more humane architecture.  The implications go far beyond the technological manipulations of the post-modernists, to challenge the very foundations of architectural and building practice in the modern era.  


Today we can begin to describe the implications of the new science for a new architecture, and for the broader culture of building.  Most notably, we can now describe a key feature of the greatest architecture, a feature conspicuously lacking in the impoverished work of the modernist era.  That feature, outlined in detail here, is its evolutionary structure of adaptive connections.


I. Introduction

II. Lessons of the New Complexity Science

III. Five Properties of the New Geometry of Complexity

¨      Network Structure

¨      Fractal Order (also called Scaling Symmetry)

¨      Adaptive Iteration (also called Adaptive Algorithm)

¨      Field Amplification

¨      Connective Symmetry

IV. Characteristics of a Connective Architecture

V.  Towards a Revived Connective Architecture in a Technological Age

VI. Bibliography


I. Introduction


As we are all aware, in the last century there has been 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 secondary phenomenon, has come an explosive revolution in technology, production, and the means of living.


Now the architecture profession has taken this as a challenge to create a new architecture -- more rational, more scientific, more open and more advanced than what came before.  And in the last century, in architecture and in all the arts, there has indeed been an explosion of new forms and new ideas, reflecting the new industrial technologies.  


I personally do not doubt that this has been an exuberant, fascinating, occasionally compelling phase of architecture -- or at least, one could say, of a kind of sleek architectural sculpture.  But now we must ask, what is the legacy of almost a century of this once-new architecture, and its leadership for other parts of the built environment? 


The unhappy evidence is that it is a long trail of disasters and wrecked places, failed sterile modernism and failed build-by-numbers sprawling subdivisions.  It is a legacy of throwaway buildings.


Yet the heirs to this earlier Modernism today still maintain the majority of leadership positions in the universities and in the circles of critics.  Like defenders of a dying paradigm, they want to assure us that this is the only valid art of our time; and that now they can correct the earlier mistakes with a new wave of innovation, that this was not free enough or that was not daring enough, that now we have even more advanced scientific ideas to propel us.  They cling to the belief that only the severe reductive geometries of the machine are sufficiently sophisticated in this new age, and that the great patterns and gorgeous geometries of history could not ever possibly be valid again, for we are now “modern.”  


But I want to argue that science now shows us something surprisingly different:  it shows us our naïveté, our arrogance, our blind trust in an earlier and cruder age of machines -- something, in fact, that we only mistook for sophistication.  It shows us the very dangers of a system that over-promotes architects as abstract form-givers.  Such abstractions, we now know, are artificially simple, and destructive of the evolved complexity of a real human place.


And so I want to argue that this period is in fact not a "modern" period of advanced architecture at all, but in important ways a primitive period -- a period in which a technology of abstractions has bewitched us, and created for us a great distraction: a focus on buildings as technological objects.  We have been distracted away from what it is that truly constitutes good human habitat -- rich, complex, life-supporting human habitat -- at its core.  There has been an emphasis on consciously perceived form, indeed on abstractly conceived form, to the exclusion of something much more primary and more essential to architecture.  One may say that this something is in fact the essence of architecture. 


And this is in fact being revealed to us now by the new science, in startling clarity. 


I want to argue that this essence is the evolutionary structure of adaptive connections. It is this connective structure that engages us, not only at the level of gallery viewer of art, but at the myriad levels of our fully lived and fully connected lives. It is this structure that allows us joyful sequences of experiences, interactions of views, perception of beauty at the finest and greatest levels, enrichment of experience -- ultimately a sense of rich connectedness with our own lives and with our world.


And further, we now see that this structure is entirely comprehensible, analyzable, reproducible.  Indeed, in recent years, marvelous new mathematical and scientific insights have been developed that hold out the possibility to do exactly that.


I want to venture further to suggest that the ultimate purpose of architecture is the deepening experience of connective symmetry.  Symmetry here is meant in the full sense of the word, the Greek same-measure, or reflected relationship.  It is used here more in the mathematicians' sense of the word, not just the conventional notion of something on one side mirroring that on the other, but the recurrence of a pattern or a relationship in space, or in time, or both.    And so I want to talk about a new architecture based on these insights – what one might call an architecture of connectivism -- which I will discuss in more detail presently.  But first let me describe in more detail, by way of contrast, what has happened to produce the current state of affairs in architecture.


Today we see that the modernists and their progeny have been engaged for some years in a kind of sculptural dialogue, using elemental abstractions -- one may even say, primitive abstractions, wrought on a grand scale.  As we said, this was done with good intentions; the architects were responding to and seeking to integrate an industrial fait accompli, with the aim of a purer, more rational architecture, more befitting a technological age.  And these abstract forms included rigid grids, boxes, razor-precise lines, simple mechanistic volumes.  These were organized in rigidly hierarchical schemes, with none of the supposed "messiness" of traditional architecture.  This was considered a "rational" approach to the problems of cities, befitting an age in which medicine and science seemed to offer the promise of a final conquest of disease and irrationality. 


We have seen the sterile, disastrous results of this early twentieth century radicalism, and they have been well-documented. 


In more recent times, the neo-modernists, the deconstructivists and others have attempted to incorporate the new lessons of mathematics and fractals into their work.  For example, the work of Frank Gehry (who it should be noted eschews the term “deconstructivism”) is known to attempt fractal repetition and interactive complexity, with very interesting and sculpturally pleasing results.  


I suggest that these efforts should be applauded for moving in the direction of greater geometric complexity; but that they still fall woefully short of addressing the core problem of architecture, the overall structure of experiential connections, and the evolutionary process that achieves it.  These artists -- and that is a better word than architect -- these artists are concerned with the structure of connections within their objects, and their relation to the conscious mind of the viewer.  But they overlook the deeper network of connections to the urban fabric, and to the larger environment, to history, to the daily lives of users.  And they often overlook the scaling relationships at the smaller scales, because they are focused on a single, consciously defined scale of view. 


And that is why what they are doing has more to do with sculpture than architecture.


Theirs is an architecture of conscious, informed apprehension.  The best architecture of history has also been a deeply rooted architecture of prehension -- not only at the level of an informed viewer, but at myriad levels of experience and connection.  Its architects occasionally imposed cerebral form, but always in service to the evolutionary process.  The result has been a far more complex architecture, with richer poetic layering across the scales of experience. 


The question for us now is how we can restore this level of rich connectivity to a technological age.


II. Lessons of the New Complexity Science


As science in our age has probed ever deeper into the mysteries of the universe, we have increasingly confronted an astonishing 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.   All of the characteristics we can experience, all of the complexities of life and beauty, are structures made 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 an exceedingly 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 mathematics of probability and statistics, and, only recently, to the multiple-variable mathematics of organized complexity. 


This 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 processes of life itself are finally yielding to human comprehension.  This is a historic achievement in human history.


We see 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 exhibit fields of mutual influence and adaptation -- that influence 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, but in important ways, not accurate.  Connectedness, as the mathematician and philosopher Alfred North Whitehead said, is of the essence of all things.


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.  We have learned 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 this power that 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.


The new science holds the promise of a new stage of human technology – 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 lessons of the new science of complexity.  


Perhaps the most visible changes will come 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 civilization, and the structure that 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."


This arena today is dominated by developers, architects and planners. Developers see their work as the generation of sales, rents and income. Architects see their work as a kind of isolated fine art to be applied over the developers’ program -- an abstract sculpture to be experienced, as they promote their identities and their careers -- that is, when they are allowed to participate at all.  Planners see their work as the regulation of the activities of the other two specialists, controlling their negative effects for the welfare of the general public. All are engaged in primarily reductive activities.


None of them has devoted their full attention to the adaptive synthesis of fitting human habitat -- the differentiation of spatial character.  None of them is applying the lessons of complexity.


The structures of the contemporary world exhibit a surprisingly elementary, even a primitive geometry.  The supposed “modern” buildings are in fact conglomerations of lines, planes, cubes – many of the most primitive Euclidean forms.  Early modernists like Le Corbusier recognized the inevitability of the early reductive machine age, and sought to make its elemental geometries the basis of their own art form.  The negative consequences of this well-intended effort have been exhaustively documented.


Another more recent school of contemporary architecture, represented by architects like Frank Gehry and Rem Koolhas, aims to embrace complexity.  But in fact, it embraces only the abstract idea of complexity, or else only the randomness and disorder of the contemporary city.  As we have seen, this is not at all the same thing.  Complexity is not merely a pile of disorganized fragments.


By contrast, the supposedly humble structures of history – even modest vernacular villages – reveal to the patient analyst a remarkably complex and sophisticated adaptive structure.   The new science and mathematics is awakening in us a new appreciation for the marvelous 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.


Of course few would suggest it would be a good idea to go back to a pre-technological time, with its disease and its brutish standards.  But at the same time we can learn history lessons from these cultures -- from their adaptive processes, and the marvelously subtle forms that have resulted.  We can learn from the surprising sophistication of some of their processes, and make our own technology more sophisticated.


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.  But their call has been dismissed as an impossible return to another time and place, and a rigid authoritarianism that is not compatible with contemporary science or contemporary open society.  The most recent insights suggest that this skepticism is fundamentally mistaken, and that the adaptive evolution of these societies is quite independent of their authoritarian structure or their relatively primitive technological condition.  There is an apparent “collective intelligence” in the cultural traditions of these societies whose sophistication we would do well to emulate. 


III. Five Properties of the New Connective Geometry


What are the properties of this new geometry as they apply to human habitat?  Here is a brief overview of five properties, and how they have been applied – and could be applied again in a contemporary context -- to the built environment.  This overview is not meant to be exhaustive (other authors have treated each topic in far greater detail) but rather to give some sense of the application of these topics in specific forms, and the transformation that they make possible for the building arts in our time.


The five properties are:


¨      Network Structure

¨      Fractal Order (also called Scaling Symmetry)

¨      Adaptive Iteration (also called Adaptive Algorithm)

¨      Field Amplification

¨      Connective Symmetry


Network Structure


To illustrate the nature of this kind of structure and how it applies to urbanism, 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 emotional associations of the two images.  Forget about cuteness and nostalgia, symbolism and memory -- forget all that.  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 neighbors 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 complex iterative structures 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.


Here is another example of a connective network at a smaller scale.


Consider a simple modern building with a supposedly "rational" plan -- a hallway down the center, leading to various rooms.  The flow of connections -- of views, of movement, of experience -- must follow this one rigid tree-like hierarchy:




Consider by comparison another building, this one with a number of additional connections between rooms, and between several of the rooms and the outdoors.  Although there is still an overall hierarchical character, the number of connective pathways is much greater.  There are overlapping pathway connections between the elements.



In the top example, the sequence of connections through rooms is highly constrained:  Room A, hallway, Room B, hallway, Room C, hallway, etc.  In the bottom example, the possible number of sequence is vast:  Room A, Room B, Room C, Room F, Room B, etc.


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 postwar 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 Alexader 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 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.  The structure on the right, however, may be conceptually pleasing in its simplicity; but it is severely limited, lifeless, lacking complexity.  Traveling these streets is, at best, unpleasant and uninteresting.


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


Fractal Order


"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." 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, myriad structures in nature exhibit fractal patterns.

This insight has revolutionized geometry. It is one of the key insights of the revolution in understanding the mathematical structure of nature, a revolution that has shaped the new science of complexity. Practical results can be seen for example in image compression software that commonly uses fractal analysis to reproduce images more efficiently, using less information. Fractal analysis also has applications in many other fields.

Many beautiful pieces of art can be shown to be highly fractal. Oriental rugs are well-known examples (and they often have intriguing geometric similarities to the Mandelbrot set). But there are many others. I recently saw an interesting analysis of Jackson Pollock's work showing it to be highly fractal in structure.

Buildings and cities are also highly fractal -- or they were, that is, until the elementary 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.


Please bear with me for a bit of elementary discussion of what this fractal structure is all about. Let me put it simply, again:


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.  It goes like this:


Take a square, and remove a smaller square out of the middle, of dimension 1/3 each side.





XXXXXXX                    XXXXXXX

XXXXXXX                    XXXXXXX

XXXXXXX                    XXXXXXX





In effect you now have an array of nine squares, three rows of three, the middle one gone from the middle row.


Now of the eight remaining, remove another 1/3 square from each.



XX        XXXX       XXXX          XX


XXXXXXX                   XXXXXXX

XX        XX                   XX         XX

XXXXXXX                   XXXXXXX


XX        XXXX       XXXX          XX



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, GA.



Or a rough approximation of its grid system of squares, street intersections, lots, houses, etc., 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 infinitum...) 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.


Reproducing this overall fractal structure is the key to some image compression software. One can 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", the key to the black box, but 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 molding (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. 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-leveled richness. And, I suggest, they would stop the process cold.


Or suppose we just let some garden-variety condo developer come in, with his catalog plans. What will happen? Loss of fine iteration, broken symmetry. Loss of scale in material deflections, textures, grains. Loss of fractal integrity. Savannah becomes... 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 crack the secrets of complex structures.

Adaptive Iteration


One of the key revolutions of recent science has been the recognition of the role of vast numbers of small, adaptive step-based routines, or "iterations", 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 a process.


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 often 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.


The significant point is that the process is often irreducible.  That is, there can be no "blueprint" capturing the structure that emerges -- no single schematic idea or set of ideas that completely expresses it.  The progression of the iterative process can often be unpredictable, and the only way to fully understand it to any real degree is to simply let the iterations run.


Computer programs often include such iterations, in repetitive sequences called “algorithms”.  For example, the particular fractal structure called a Mandelbrot set is generated on a computer, using a very simple algorithm repeated many millions of times.  As each step takes into account all the steps before it, a vastly complex interactive pattern quickly emerges.


The mathematician Steven Wolfram has proposed an entire branch of revolutionary science based on such algorithms.  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.  (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 as well.


This "incompleteness" of mathematics (and of any representative model) is precisely what makes it useful.  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!    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 result in visually stunning structures, but often at the price of enormously destruction to the complex patterns of human life.


This is the problem of the modern build environment – whether created by the modernist architect, or the modern procution builder, or the modern highway engineer.  It is the problem of simple imposed abstractions.


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.


Field Amplification


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 machines.  This has been a vastly productive analytical tool, with enormously productive results as these reductive mechanisms are re-fashioned 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, which Whitehead called "nothing other than an omission of part of the truth."


As we saw earlier, this is the brilliance of the human animal -- and at the same time, precisely its limitation.


We see the essential contextual structure of things perhaps most clearly in the realm of biology and ecology, where organisms cease to survive when apparently remote parts of their ecosystem are disrupted.


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.


Connective Symmetry


As we noted previously, architecture in its fullest form is more than a momentary visual experience.  It must be a kind of complex connective experience, echoed at various levels of a life lived, and a culture shared.  We posit that this is the experience of connective symmetries -- symmetries not only in the sense of the usual axial mirroring, but in the sense of the deeper echoes and amplifications that make a complex fabric of lived experiences. 


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. 


Some of these symmetries are clearly biological in origin:  they 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.


Some of these symmetries are purely mental.  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, 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.


As the philosopher Alfred North Whitehead said, the 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. (For more of this discussion see Modes of Thought, by Alfred North Whitehead.)


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 architecture 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. Characteristics of a Connective Architecture


These five properties offer powerful new tools to create a new architecture, embodying the structural richness of the greatest architecture of history, but also incorporating new technologies and new innovations -- as the best architecture has always done.   The defining trait of this architecture, the trait that distinguishes it from so much of what is done today, is its system of connections, formed across many scales.  


Following are the characteristics of this new architecture, and its differences from the dominant paradigm of architecture in our time – a paradigm in crisis, and searching for such a basis to advance.


1.      The form is inseparable from the network of connections, and arises in large part from it;

2.      The connections include human activities and processes, actual and potential;

3.      The connections are embedded in time and history, and necessarily reflect a traditional evolution;

4.      The expressive details are not superfluous ornament, but in fact express to human consciousness the rich underlying connective order in which the experiencing individual participates;

5.      Symbolic expression takes its place within this connective system, and is subservient to it


By contrast, following are the comparative properties of the architectural design process that dominated in the 20th century:


1.      The form is detached from the connective systems of human life;

2.      The form is derived from the conceptions of a singular human being, in the form of a singular abstract complex of ideas;

3.      The form is conceived as a regarded sculptural artifact, to be consciously viewed and admired;

4.      The form is derived in large part from the quest for abstract aesthetic qualities;

5.      The form is largely imposed upon the site, and does not emerge from it except in trivial programmatic aspects

6.      The form exhibits a vastly simpler network of connections

7.      The range of human experiences is correspondingly simpler, exchanging initial dramatic impact for long-term poverties of experience.


V. Towards a New Architecture


In our age we are witnessing the development of a breathtaking new and perhaps revolutionary form of science, based on the new understanding of complex iterative processes.  We have seen tantalizing hints at the potential to develop tools for a much richer architecture for the future.


And we have seen claims by the deconstructivists and related post-modernists, that theirs is the new paradigm in architecture.


But for all their claims of a new paradigm, we see that these post-modernists are still very much creatures of the old modernist paradigm that they so willingly discredit.  They still do not let go of the central conceit of modernism, its chronocentrism -- its belief that we are now and forever divorced from the past, in all its bourgeois irrationality.  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. 


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.


But the central lesson of our time is this: history is not over. We have not arrived in a final “modern” era, in which everything is different from all previous eras. As the twentieth century recedes, we are left humbled by the lessons of the new sciences, and we see our unwarranted arrogance 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. 


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 tantalizing evidence that perhaps another renaissance -- or renaissances -- await.


The new sciences show us a picture of a vast world beyond the deconstructivists' 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 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, under the right adaptive circumstances.  They also illustrate the human habit of misusing 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 learned very well to make horrible, inhuman, disconnected places, sprawling places serving only our machines, moderately interesting experimental places that are grossly dysfunctional.


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


Responding to these revelations, a new crop of architects and planners is emerging, as surely as the new sciences of complexity are emerging from the broken pieces of deconstructed debris left by rationalism.   These designers and theorists are not simply trendy giant sculptors.  They are anthropologists, philosophers, mathematicians, physicists.  They are historians. 


They are connectors.


Some, like Christopher Alexander, bring a professional understanding of the new lessons of mathematics and physics to the problem of architecture, and the broader culture of building in which it is only one part.  Some, like Leon Krier, bring a deep understanding of the universal human solutions embodied in the designs of antiquity.  And some, like Andres Duany, bring a tactician's understanding of the workings of culture and the ways to effect the broad changes that will be needed.


The emerging architects are much more than romantic reactionaries, as the fashionable critics imagine.  They 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 recognize and embrace again the timeless within our own time.


This, we assert, is the coming "modern" paradigm.


VI. Bibliography


Alexander, Christopher. The Nature of Order (Oxford University Press, New York, in press).

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).

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).

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).

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

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).