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

Information  - NEW


Discussion Page




Previous Issues


Contact Us


Additional Links

And References



Katarxis Nº 3


A Conversation with Three Scientists:

Physicist Philip Ball, Biologist Brian Goodwin and Mathematician Ian Stewart



The Imitation of Nature


Order and Power

Quality and Wholeness

Contradictory Uses of the New Sciences

Subjectivity and Objectivity

Wider Implications for Architecture and Urbanism


About the Scientists 

Philip Ball was for a decade physical science editor of the influential magazine Nature. Since then he has been consultant editor to the magazine, author of many well-received popular books on science, and broadcaster. His abiding interest in pattern, and in the relevance of scientific ideas to social problems, is clear from books such as The Self-Made Tapestry: Pattern Formation in Nature, 1998; and Critical Mass: How One Thing Leads to Another, 2004. He recently presented a series of programmes on nanotechnology – Small Worlds – on BBC Radio 4.

Ian Stewart FRS is Professor of Mathematics at the University of Warwick, and Director of the Mathematics Awareness Centre there. He has been the most active among UK mathematicians in bringing new scientific concepts – particularly to do with geometry, symmetry, order and chaos – before a wider audience. His books include Life’s Other Secret: The New Mathematics of the Living World, 1998; and (with Jack Cohen) The Collapse of Chaos: Discovering Simplicity in a Complex World, 2000.

Brian Goodwin is Professor of Biology at Schumacher College in Devon. He sees the “new biology” as sharing with physics an interest in principles of order. He is implacably opposed to reductionist science, and is a member of the Board of Directors of the Santa Fe Institute, an influential "think tank" devoted to the study of complexity in various fields. His books include How the Leopard Changed Its Spots: The Evolution of Complexity, 1994; and Form and Transformation: Generative and Relational Principles in Biology, 1996.

About the Interviewer

Dr. Brian Hanson is Research Fellow, Centre for the Study of Religion, Ideas and Society at London University.  He is author of a number of books including Architects and the "Building World" from Chambers to Ruskin: Constructing Authority (Cambridge University Press, 2003).

The following exchange was edited to read as a single Question & Answer session, with discussion not only between the interviewer (Brian Hanson) and his subjects (Messrs. Ball, Stewart and Goodwin), but also between the interviewees themselves. To achieve this three separate interviews were conducted by email, in two stages each. At the second stage – of “supplementary” questions – interviewees were able to respond to points made earlier by their fellows.

The Imitation of Nature


Current developments in the natural sciences prompt us to look again at an old question – or rather, two questions. The first – “is nature an appropriate model for architecture?”; the second – “if so, in what ways should architecture imitate nature?”. These questions have divided architects and theorists for centuries, and continue to do so today[1]. I wondered how scientists themselves viewed the subject.


Brian Hanson: Philip Ball, do you think that nature provides a good model for architecture?


Philip Ball: I see no reason automatically to conclude that ‘nature equals good’, or that nature always does things in a way that will best suit our own objectives … I feel quite strongly about it; there is often a far too rose-tinted view taken of nature …

[Yet] one might suggest that our aesthetic choices are likely to be influenced by what we find in nature, and I think there is likely to be some truth in that. I do think we often find a certain level of complexity interesting and pleasing (for example, complex but discernible structure in music, rather than monotones or random noise[2]). But it seems to me that we can also enjoy [more artificial qualities such as] simplicity, spaces that are easy to ‘read’, certain types of proportion, and so on.


BH: The way your work has proceeded from the physical sciences, through the physical aspects of nature, and finally to social issues, reminds me strongly of that great Victorian, John Ruskin. Indeed, the art critic Peter Fuller once said that “the aesthetic implications of today’s ‘scientific attitude’ … are uncannily similar to those of Ruskin”[3]. You are, it seems, well aware of the aesthetic implications of your own work.


Ball: Yes, very definitely! I have become very much aware of the (obvious) fact that we can respond to beauty only when we can see it. Until one becomes sensitized to the patterns that exist in nature, for instance, one can overlook them entirely, and miss out on the joy of recognizing and admiring them. And an understanding of how those patterns develop can enhance one’s appreciation of them. In this sense, nature really is creative – although what I mean by that is really tied up with issues about why our cognitive system responds so ‘positively’ to these patterns and structures. Perhaps this is an aspect of E. O. Wilson’s notion of ‘biophilia’[4]. Getting to the root of this might have enormous implications for art and architecture …


BH: Brian Goodwin, you have spoken about a “confluence” taking place between the arts and the sciences, which will enable both to participate in “natural creativity” of the kind Phil has touched on. What would you say to those who respond that the arts – architecture in particular – are artificial products, and don’t necessarily need to take their cue from nature?


Brian Goodwin: I believe that we do need to learn from natural process about how to be appropriately creative ourselves, meaning that our activities should be appropriate to whatever is the context within which we are acting. This of course applies to everything we do, not just to art or architecture. The process of bringing something into being is what we and the rest of nature are engaged in all the time, but we have a tendency to assume that what emerges from our looking or feeling or doing was there to begin with and we just became aware of it. However just as quarks and mesons, organisms and galaxies are dynamically generated continuously, from we know not what, to become the natural kinds[5] that we call in the generic language of dynamics, attractors[6], so we and the world we inhabit are generated continuously. The individual properties of these natural kinds reflect the context in which they arise by their particularities. It is this type of process that I believe we need to understand by participating in it, not just by looking at it, with the intention that our activities have the quality of what is called in some traditions ‘right action’.


BH: Ian Stewart, Brian’s position (like that of Stephen Wolfram[7])seems to offer a way of reconciling two apparently opposing views about what the architect should be looking for in nature: its invisible essence or its visible aspects (see note 1). The same could be said about your suggestion that it is the fungibility of patterns – their ability to change in step with the circumstances they face – rather than the operation of eternal, abstract truths, that has enabled the order we see in the world to emerge out of the underlying complexity. This also reminds me of the ideas Christopher Alexander has put forward about pattern, and about “Structure-Preserving Transformations”[8].


Stewart: The process of biological development – growth, in D’Arcy Thompson’s sense of Growth and Form[9] – might be a source of such ideas. But we don’t really [yet] understand the mathematics of growth. Another way to characterise [a Structure- Preserving Transformation] is ‘variation on a theme, with a guarantee that if the original worked, then so will the variation.’ Evolution uses such tricks profitably; I’m sure architecture can do the same. Already has, of course …

            An effective mathematics of evolutionary systems is in its infancy – a big problem being the ‘creativity’ of biology, which repeatedly changes the ‘phase space’[10] of possible behaviours.  Flight, for instance – of insects, initially – changed the evolutionary game completely. I think that the idea of self-evolving systems, be they organisms or buildings or societies, is a very exciting area that will stimulate a lot of new scientific thinking and a lot of new mathematics.



In his new book, The Phenomenon of Life[11], Christopher Alexander argues that “life” is a real property of the organisation of matter, and as such something of which we can come to an objective and measurable knowledge, which can then be applied to – amongst other things – the production of buildings. Did scientists think it was any more than a romantic notion to say that some environments have more “life” than others?


Ball: [P]eople worry rather too much about how to define ‘life’[12]. The fact is that it is a linguistically useful word but not a scientific one. Scientists don’t … themselves draw a sharp boundary between the living and the non-living (how does one classify viruses, for example?) … It was, in fact, one of the central aims of The Self-Made Tapestry[13] to show that structure, order and pattern can evolve in non-biological systems that are every bit as complex as some of those we see in living systems (and which intuitively we therefore often associate with life). One could argue that maybe this shows there is ‘life’ in inorganic systems after all, but it seems to me that this is simply imposing an arbitrary definition of life (= order/pattern) that does not seem to have much in common with the one that is widely accepted at the moment. I’m uncomfortable with redefinitions of such emotive words.


BH: My co-editor, Nikos Salingaros, made the following observation:


[Alexander] talks about life, but at the same time, everything he says can be understood as the distinction between evolved structure and non-evolved, or imposed, structure ...Whether a form is a product of a certain process has nothing to do with psychology. That it leads to our connecting better in a psychological sense says something deep about how our cognitive system is tuned (evolved) to recognize and interpret such structures.


Ball: I agree entirely with the last sentence. And I think that the distinction between evolved and imposed structure is indeed a crucial one. But I don’t see that this need be connected to any notions of ‘life’ …

             Frankly, I don’t think Alexander’s book will get a lot of attention in the scientific community, because there doesn’t seem to be any real science in it. His attempts to broaden the definition of life seem just tautologous: this is what life is because this is how I choose to define what life is.


BH: Brian and Ian – you both think that it is helpful to talk about life as an actual property of matter, and not just something we read into matter – a “Pathetic Fallacy” in other words.


Goodwin: The latest problem to appear clearly on the scientific agenda is how consciousness (and feeling) could emerge[14] in a cosmos that is made up of totally inert, insentient components. Complexity theory always requires that there be some precursor of whatever property is observed to emerge in a system, such as superconductivity or the properties of water or the cooperative behaviour of bees in a hive. The dilemma now is to account for the evolutionary emergence of feeling from a system that has no qualitative precursor of such a property. This would be a scientific miracle, and scientists don’t like miracles. So some other solution needs to be found. My own preference, to save the unity of scientific understanding, is to adopt some position like that of Whitehead or Bergson[15], so that consciousness and feelings are grounded in reality and not some ghostly epiphenomena that are not quite real. However, this will be very firmly resisted by the majority of scientists, and for perfectly good reasons. You do not lightly abandon a position that has been so phenomenally successful at explaining so much of nature. I don’t intend to abandon it either, but I believe that science has to be extended in some way to accommodate the reality of qualities.


Stewart: Life is a process … It’s a collective, emergent property of the bits. In the 60s and 70s biologists thought that life = DNA, but now they’ve realized it’s not that simple. Stu Kauffman[16] has effectively defined life as any “autonomous agent” that can reproduce and carry out at least one thermodynamic work cycle. I’m not sure that’s quite the answer (I want something more abstract) but it’s in the direction that appeals to me.

            What we need, and what Kauffman hopes to provoke, is an effective theory of organization. Life, evolution… but also organizations, and how to make them work. Mathematical politics, even. I don’t think we’re close yet, I don’t think many people understand the issues involved in getting close (maybe only Kauffman and a few others, not me!), but that’s the way the activity is pointing. [Though] it’s worth bearing in mind that on a metaphorical level a lot of these ideas are not news to thoughtful managers …

            Autocatalytic networks[17] are a nice formalization of self-generating order. That’s a step in the right direction.


BH: Do you find acceptable or useful the degree of recursiveness in Alexander’s views on how life as a structure is created?


Stewart: Recursiveness is one of the great secrets. Chicken…egg…chicken…egg… I don’t think we fully understand it (as Wolfram says), but I think Alexander is absolutely right to state its fundamental importance. It is a profound source of creativity. So: yes, it’s very useful indeed.


BH: Ian, can you tell us how the concept of symmetry-breaking explains how pattern and order arise in the world from what, at the level of individual components (molecules, people even), seems undifferentiated or chaotic?


Stewart: If you take some pattern-forming system, and drive it through a series of symmetry-breaking changes, it often goes chaotic. The classic here is Taylor-Couette flow: fluid between concentric rotating cylinders. Fix the inner one, rotate the outer. Bland Couette flow, with full symmetry of a cylinder, gives way to Taylor vortices, stacked on top of each other like a tube of polo mints. Then the vortex boundaries become wavy; then they start to modulate over time. Then the flow goes turbulent – chaotic – and most people thought nothing much changed after that.

            Not so. Recently, my colleague Marty Golubitsky discovered that there’s more going on than that. Chaos has its own patterns, but these are visible only on the statistical level. (An example is spiral chaos, where patches of turbulent fluid move along spiral paths.) The underlying ‘attractor’ can have symmetry. In the Taylor-Couette system, if you continue to speed up the cylinder, the chaotic attractor gains more and more symmetry, until it becomes fully symmetric (and you get fully developed, homogeneous turbulence).

            So, roughly, chaotic systems follow the reverse sequence of symmetries that you see for regular ones. I’m not sure what that means for architecture… well, maybe I do. If you mix everything up too much (as happened in Louvain-la-Neuve in Belgium) you get a town in which every part looks just like every other part. It’s confusing, bland, and doesn’t really work. So in the chaotic regime, you need enough chaos, but not too much …

            Our perceptions like to see symmetry broken in various ways.

            Now: in mathematics there are two kinds of symmetry breaking: spontaneous and forced. In the first, the system itself breaks the symmetry. In the second, the breakage is imposed from outside. I’m mostly interested in spontaneous symmetry-breaking, in my research; Charles [Jencks][18] is mainly talking about forced symmetry-breaking. In that context, his metaphor works better! And it turns out that the two versions are intimately related, so if you work on one, you’d better take account of the other. It’s a question of context, in the end.


Order and Power


Marxist criticism, and Foucault’s philosophy, have prompted us to see order as inevitably an expression of power. The implication is that order cannot exist without strong exercise of top-down power, even if that power is to some extent concealed. This has had serious negative implications for the modern view of classical architecture. Foucault’s acolyte Richard Sennett, for example, blithely and typically remarks of the Pantheon: “The Roman Empire had made visual order and imperial power inseparable: the emperor depended upon making his power seen in monuments and public works.”[19]


BH: Phil, it’s been particularly difficult to discuss the concept of order in architectural circles since the Second World War: if it doesn’t suggest unpleasant political connotations, it seems to bear unwelcome moral ones. However, what seems to be emerging from much of the new sciences of complexity, is a way of discussing order which is free of this baggage.


Ball: I’m wary of portraying ‘complexity’ as too much of a ‘new science’. Many of the tools it uses have been around for decades, even for a century or so. That said, I think you are right: we are now quite happy scientifically with the idea that ‘order’ can emerge spontaneously rather than being imposed – and also that there are types of ‘order’ and ‘structure’ that do not necessarily imply geometrical rigidity. But I suspect that when political and moral philosophers speak of order, they are not at all talking about the same thing as scientists.


BH: Ian, in his interview here, Christopher Alexander defends his approach at length against the common accusation that it is deterministic. Some architects have felt constricted by his catalogue of patterns[20], claiming it inhibits their individuality as artists. Alexander’s defence of patterns – which is that they allow countless possibilities for the creation of order – reminds me a good deal of your own discussion of how, in symmetrical systems, many possible effects can arise from a single cause; many symmetries can follow.


Stewart: Alexander is dead right that pattern and determinism are not the same things. This is the big message from chaos and complexity. Deterministic systems may or may not generate patterns (at least, ones we can recognise as patterns). And many patterns can arise in probabilistic systems (that’s why statistics got going as a worthwhile science).

            What I mean by ‘pattern’ is really some repeatable element of structure. It has to be genuinely significant (I’m sceptical about, say, Elliot waves in economics[21], I think they’re mostly wisdom after the event). Determinism means repeatable rules, and that’s on another level altogether. Patterns can emerge from stochastic or effectively uncomputable systems.


BH: I can see that all this may only become meaningful for architecture if a more vital Building Culture can be encouraged. Traditional building culture seems to have affinities with such things as Stewart Kaufmann’s “autocatalytic networks”, or the “extelligence” of which you have written[22]. Only this would enable the act of building truly to become an exercise in “spontaneous” rather than “forced” symmetry-breaking. Surely it is only in a situation where the whole culture is playing a full part that we can expect greater complexity to coexist with increasing order, so that “antichaos” or “decoherence”, of the kind you and others have described, can come about.


Stewart: I think you’ve put it very well. It’s my earlier ‘context’ point. Specialists are very competent in their own fields, but don’t pay attention to anything outside. This is what went wrong with Biosphere 2: the architects knew that concrete affects the carbon dioxide balance when it cures, but didn’t know this would be a problem. The ecologists knew it would be a problem, but didn’t know that it would happen.

In the 1980s I wrote a series of science fiction stories about ‘Billy the Joat’. JOAT: Jack Of All Trades. He was an expert generalist. We need some of those. (Not too many: see the stories!)


BH: Brian, you have said that “you shouldn’t have too much order. You shouldn’t have too much chaos. Perhaps you should be at the point where you can move backwards and forwards between the two …”. Do you think that a whole culture can exist and flourish on that thin line between order and chaos?


Goodwin: The notion of ‘living on the edge of chaos’ that has arisen in the study of complex systems emphasises the potential of dynamic processes that include deterministic chaos to generate order through symmetry-breaking processes and phase transitions[23]. The emergent  order is immanent in the system as a whole and it manifests when particular conditions are present.


BH: Brian, some of your colleagues at the SFI would decry any attempt to “vindicate Bergson”. Yet, like Alexander’s, your debt to Bergson and Whitehead – and hence some form of animism or vitalism – is undisguised.


Goodwin: Animism is the great taboo of scientific culture, because Western science is founded on its denial. However, nature always has surprises up her sleeve, which is what actually keeps science alive and scientists on their toes …

[A] science of qualities … proposes an extension of ontology and scientific methodology in ways that do not undermine what we have learned, but expands its scope.


BH: You have said that – in, for example, their ability to recognise plants – traditional cultures seemed to understand this science of qualities more readily than we do now. However, those of us who have said similar things in connection with architecture have often been  accused of romanticising tradition; of wanting to go “Back to the Future”.


Goodwin: There is a sense in which we are now going back historically and picking up aspects of knowing that were put aside by Western science so that they can be integrated into a more comprehensive, and more sustainable, manner of living on the planet. The Renaissance recognised qualities and values, and it was love that made the world go round, as we learn from Shakespeare and the Renaissance magi. Then love turned into gravity, an impersonal force that became the expression of a mechanical, clockwork universe. This has now led to contradictions in science (e.g., holistic properties revealed by non-local connectedness in quantum mechanics), the rape of nature and the loss of meaning in human life. We need urgently to heal ourselves and our relationship to reality. There is nothing romantic or utopian about the awakening that is moving us toward a new way of relating to and knowing our world. It is grounded in evidence and the real situation in which we find ourselves. We either move on or perish. It’s a simple as that.


BH: I see a number of parallels between your emphasis on whole organisms – which you sometimes refer to as “generic forms” or “kinds”  – and the interest shown in typology by tradition-orientated architects, including Christopher Alexander with his “Pattern Language”. In all cases, the argument seems to be that there is not an infinite number of legitimate answers to a problem, and that the existence of particular, highly-developed entities (species, building types, a classical canon) tells us something significant about natural creativity: eg. that there are natural limits to it.


Goodwin: I used the dynamic term ‘attractor’, above, to characterise natural kinds which I take to include the elements, biological species, and the myriad forms that we observe in nature, animate and inanimate, including snow-flakes and typhoons and galaxies. Since the world of process is nonlinear, the dynamic entities that emerge tend to be discontinuous and discrete, though we cannot put any bound on their number. Nevertheless, these natural kinds tend to cluster in what I have called ‘generic forms’ that are characterised by the dynamic process that generates them, or the organising principles that underlie their emergence. Typology is then connected with intrinsic dynamic necessity more than historical contingency, which has become the Darwinian reading of species as accidental functional entities with survival properties. [To think of] species as generic forms emphasises their natures and intrinsic values, as well as their dynamic stability in context, and this suggests natural limits to their boundaries which can be related to notions of wholeness such as health, vitality, well-being and beauty …



Quality and Wholeness


Goodwin and Stewart concurred on the need for science to take quality seriously.


BH: Brian and Ian, you have both argued in different ways for the need to take quality seriously, as well as the more holistic view of the world that would follow from this. Could you say a little more about the advantages you see accruing from this?


Goodwin: Since the separation of the arts and the sciences in the Renaissance, we have been systematically separating qualities from quantities, the latter occupying a position of individual peculiarity that has tended to produce highly idiosyncratic art forms that emphasise the individual rather than a collective awareness of relevant creativity. I think that the way out of our Cartesian prison is through a recognition of the primacy of relationships in all process and the secondary position of the individual entity: ‘You exist, therefore I am’, as Satish Kumar puts it in his new book[24].

I take [the science of qualities] to be a major challenge now for addressing many of the pressing issues with which we are faced. This includes the design of buildings and housing, and the way in which we use our land and resources in sustainable ways.


Stewart: Historically, mathematics has mostly been about quantity, and most people still view it that way. I think it was Rutherford who said ‘qualitative is just poor quantitative”. This was fair enough in the sense he intended, but it makes very little sense nowadays. Quantities (numbers) are just one type of ‘quality’. The interesting  qualities are non-numeric, but entirely rigorous and suitable for mathematical analysis. Most modern maths is like that, in fact. So, for example, topologists explore the quality ‘knotted’ and end up with ideas that help with the study of DNA molecules and superstrings.

            Symmetry is a quality. There is no question that in the physical sciences it is a fundamental concept. Superstrings again, for example, are all about alleged hidden symmetries of space and time and new dimensions thereof. I think that subtle variations of symmetry are important in biology – for instance, speciation is a kind of symmetry-breaking: identical organisms cease to be identical. A lot of important questions are best understood by qualitative reasoning.


BH: What do you make of Christopher Alexander’s radical argument, that if we properly address the quality of “wholeness” in a particular situation we also naturally address the more quantitative, functional, issues?


Stewart: I think he has a very good point. A key theme in mathematics, if you look at the history and the interplay of ideas, is that an effective solution to a problem is often also an elegant solution. The thing seems to work on two different levels. So a holistic approach to the large-scale structure may ‘resonate’ with its effectiveness on the human scale, yes.

Having said that: it doesn’t have to. There may be contradictions between the large scale and the small. I suspect that happens when we forget to embed the role of people in the structural principles …

            The paradox of architecture is that a building ought to look good from the outside, but be usable from the inside. Some architectural fashions do well on the first but fall flat on the second. On the other hand, I don’t think that the proliferation of supermarkets with crenellations and little towers, prompted by remarks made by Prince Charles, has actually added much to human existence.


Contradictory uses of the New Sciences


Complexity science is fashionable, so all kinds of claims are currently being made for its relevance to the arts, though not all of them stand up scientifically. Charles Jencks’s New Paradigm in Architecture[25] – a new name for deconstructivism – claims support from the new sciences, as do the arguments in Christopher Alexander’s The Nature of Order[26]. Both authors, for example, cite the work of Ian Stewart and Brian Goodwin in their defence. However, Jencks – Post-Modern to the core – sees science as little more than a “pretext” for making architecture, whereas Alexander – more of a modernist in this – sees it as offering crucial proof of how the world is made, and therefore how we can best intervene in that world. How do we disentangle legitimate from illegitimate applications of these new concepts – or does it matter?


BH: Ian, I thought you sounded very Post-Modern yourself when I read your description of mathematics as a “social construct”. Can you explain what you meant by that?


Stewart: It’s a social construct by a society (of mathematicians) who are very well trained indeed at spotting logical errors. In the end, whether or not a complicated proof is accepted as valid boils down to the collective judgment of that society – there are cases where they got it wrong, too – so the textbook version of a proof as a sequence of statements, each following logically from previous statements, doesn’t capture the social reality. The problem with extremist postmodernism is that it maintains that any opinion is as valid as any other. Science and mathematics do rest on opinions, but those opinions are tightly constrained by experiment and the rules of logic. Even postmodernists enter a room through the doorway and not the wall, although their own stance implies that if enough people decided that the wall was an acceptable entrance, it would be. And if all opinions were equally valid, why is it necessary to argue the postmodernist position against alternatives?

It used to be thought that mathematical truth was shining, perfect, absolute. We now know better, thanks to Kurt Gödel, Alan Turing, Gregory Chaitin and the like. I don’t like the Platonist view that mathematics is ‘out there’ in some ideal universe, not of this world. I think mathematics is being built, day by day, by the combined activities of the world’s mathematicians. It is, in this sense, a social construct.


BH: To what extent do you think that the society of artists should be allowed to misrepresent or relativise scientific concepts for their own ends?


Stewart: I do think that there is a tendency among some people of an artistic bent to try to understand science in the terms that are familiar with them, especially metaphor and verbal arguments. This sometimes works well, but it runs into trouble when the scientific words have a specific technical meaning and the metaphors go wrong. The fiasco with the Sokal article[27] doesn’t mean that all of these metaphors are wrong, but it did make it crystal clear that pretentious language had its own appeal, independently of any meaning. I recall the phrase ‘axiom of choice’ being used very loosely, as if it referred to human free will. Unless you actually understand what that means, you shouldn’t bandy the phrase around.

No reputable science journal would publish an article that tried to spoof science the way Sokal spoofed postmodernism[28].


BH: Phil, you have always been careful, as far as possible, to minimise the use of metaphor in your discussions of the implications of new scientific theories.


Ball: Metaphor is immensely useful – essential really – as a pedagogical tool for scientists and science communicators. But I am constantly dismayed at how, as a culture, we have rather lost sight of what a metaphor is. There is grotesque abuse of what I would call the ‘just as’ argument: just as this happens in this system, so we can conclude that the same thing applies in this other totally unrelated system. One finds that happening a lot to quantum theory, and also to Darwinism. The Uncertainty Principle is one of the most maltreated ideas in science – it is taken as evidence for the assertion that we can never be objective about anything, that we can never avoid perturbing an experiment by looking at it. Few people ask the question ‘by how much?’ [This is an area where I think] we have swept aside the quantitative for the qualitative.


BH: Do you think the “truth” of science risks getting lost in all this?


Ball: The only thing that has come close to appalling me in this sphere recently is the notion that postmodernism might destroy any belief (at least within academia) in real knowledge and understanding of the world. But I don’t think there is much danger of that, at least in the long term – the idea is too patently ridiculous, not to mention pointless. No, I don’t mind at all these other views being raised, even if I remain sceptical of them. I have often found them a valuable spur to clarifying my own views about what science is and where it starts and stops. My only plea is that we should try not to confuse science with philosophy. There are plenty of scientists who are guilty of that.


 BH: Ian, there was an interview with you in Nature some time ago[29] in which you talked about the need to reach beyond metaphors: an example you gave was your description of speciation as a form of symmetry-breaking, which you thought might be more than a metaphor.


Stewart: There seems to be a tendency for science and mathematics to be taking on a more human face in certain respects – focusing on questions about humanity’s place in the universe and on human-level experience. If this development can be continued, and turned into something better than geometric or structural metaphors, then there should be some prospect of applying the same viewpoint to architecture ( which concerns humanity’s place in its human-level environment).


BH: One reason I am asking such questions is that there is clearly more than one way of applying the same new scientific concepts to architecture and urbanism, and not all of them would seem to have the same scientific validity: I am thinking of Charles Jencks compared with Christopher Alexander.


Stewart: I think they both have elements that are worth considering. I know that sounds wishy-washy, but I think that creativity and artistry are so intertwined with accidents of human evolution that it’s expecting too much to get a really neat, tidy formalism that captures them. The best we can hope for is what Jack Cohen and I called the “glass menagerie” in Collapse of Chaos – lots of overlapping paradigms, each working well in its own limited domain …

            I like a lot of what Charles Jencks does, and I’m more familiar with it. I’d characterise his approach as a slightly self-mocking use of visual metaphor with a scientific basis. In some ways he takes it very seriously, but he does enjoy a good joke too. I like that, and I like a lot of his work. But not all of it comes off …

            Alexander writes very well, and I have a lot of sympathy for many things that he says … [He] is more holistic, in attitude if not always in detail, and that appeals to me because I think the biggest mistakes now being made, in everything from science to politics, is to ignore context. It’s in the spirit of complex systems, for instance. But mathematicians always like nice, clever examples, and I get a lot of pleasure from some of Jencks’s instantiations of his principles. Whether the principles hold good, or how widely, are up for grabs; but the best examples are wonderful.

            There does seem to be a common paradigm shift under way in science, art, and society. Maybe that’s an illusion, but I think that ideas shuffle around between human minds and every so often something starts to take root. Our minds are metaphor machines – they can spot connections that are invisible to logic, and be right. The metaphors can drive our thinking …

                        I think that both [Jencks and Alexander] are contributing to the kind of future I’d hope will happen. They are putting forward different paradigms, and at this point I don’t care which, if either, is right. I just think we need effective, new ways to think about our place in the universe, and to express that. All scientific research starts with lots of possible ideas, and modifies them according to what seems to work. That’s what the future will do to their work.


BH: But doesn’t Jencks’s deconstructivist polemic ignore your own insistence that, in the context of chaos it is “symmetry-creation”, not symmetry-breaking, that is the more natural phenomenon; and your argument in The Collapse of Chaos, about symmetry-breaking being more about order than disorder.


Stewart: [His] metaphor is stretched a bit, but I actually discussed this with Charles Jencks [some time ago], and I don’t think it’s stretched to breaking-point. It is, if you wish, one of his jokes, and a rather good one. There is enough of a grain of truth in the metaphor that the reasoning leads to creative ideas. In particular, the tension between the human love of symmetry, and the dislike of too much regularity.


BH: Jencks’s account of The Architecture of the Jumping Universe seems to rely on a similar bit of “stretching” . He speaks of “the creativity and surprise of a universe that evolves in phase changes – sudden jumps in organization” – which, in his view demands an architecture equally unstable. But this seems to be built on a (deliberate?) misconstruction of what is implied by “phase changes” – in which surely the important thing is the stable system which ensues, rather than the “jump” which leads to it.


Stewart: I guess it’s the change that really matters, and the fact that it is sudden. Margaret Boden talks of two types of creativity[30]. One is like writing a new sonnet. The other is like inventing a new art form altogether. The second kind is a phase change, metaphorically. And it’s a much bigger creative jump. That kind of creativity is where the radical new ideas come from. New paradigms, the rebounding of life after mass extinctions… all these look like phase changes. I agree that jumps alone don’t add a lot. But here, I think that the size of the jump can correlate with the degree of creativity, or of novelty. (One of my students, Toby Elmhirst, is trying to formalize innovation as a mathematical model. It seems to need something even more radical than a phase change!)


BH: Phil, does it seem reasonable to you that new scientific concepts are being used to argue for an architecture which eschews stability, and which dwells in a permanent non-equilibrium state?


Ball: This is precisely the point at issue. Why does the one thing (the existence of non-equilibrium states) imply the other (that this is the ‘proper’ mode for architecture)? … I don’t know whether deconstructivist architects understand the science of non-equilibrium or not – although they would certainly be mistaken to imagine that there is anything ‘out-of-equilibrium’ about an asymmetric or strangely shaped building, since it must of course be in mechanical equilibrium to stand up at all. But I do sense a misapplication of the scientific ideas here.


BH: And Jencks’s Jumping Universe? Does the phenomenon of phase transitions really require the architect to think now more about how to break rather than how to make symmetry? This seems a striking  misuse of a new scientific concept.


Ball: You are quite right: phase transitions are unusual points in the ‘phase space’ of possible states, while most of this space is occupied by stable states. If I understand it rightly, Jencks was framing his discussion within the context of chaos theory, so the jumps he is talking about would be out-of-equilibrium dynamical states (that is, where the system isn’t static) – but the same applies. Indeed, raising the notion of a ‘jumping universe’ as a bold new idea in physics is pretty spurious anyway. Phase transitions between equilibrium states have been known since the nineteenth century. One of the points I want to make in [Critical Mass][31] is that much of the framework for understanding stable states and abrupt changes between them was in place at the beginning of the 20th century.

            Moreover, ‘symmetry breaking’ does not necessarily imply transitions to states of low symmetry – that is, asymmetry. Many steady states of non-equilibrium systems have rather high symmetry, such as the hexagons and stripes of convecting fluids. Their symmetry is only ‘broken’ in the sense that it is lower than that of completely uniform (isotropic) states.


BH: To move on to Alexander. At the heart of his method is an idea to which I believe all three of our interviewees subscribe: namely, that wholeness is the starting point; from this, through true (spontaneous) symmetry breaking, the undivided, unstructured, homogeneous, field is progressively differentiated into lesser symmetries possessing stronger structure. Alexander’s design method seems a rare (maybe unique) attempt to participate in this symmetry breaking, this creation of structure out of wholeness.


Ball: This is a nice way of putting it. Intuitively, it seems to make sense. But I’m not sure that it is yet more than a metaphor. It seems to me that the criterion for whether an architectural space ‘works’ or not is still going to be a subjective one. I can see how such an approach can work empirically – for example, if one has a list of possible solutions to specific problems of space or design that people seem to respond to well. But how do you make that scientific? If I have an empty, uniform space, there are countless ways I can break its symmetry. Which is the ‘right’ one?


BH: Brian, do you think the attempt to differentiate between various applications of new scientific concepts to architecture gets us anywhere? Alexander himself sees his work as science, not as some cultural application of science.


Goodwin: I [also] think that we need to move on beyond questions about whether or not post-modern or deconstructivist buildings are consistent with the new ideas that are coming from the new sciences connected with chaos, complexity and the study of emergent order in physics, biology and the social sciences, and to ask what these developments imply with respect to the nature and the practice of science itself. This is because I take these implications to be deeper and more relevant to the practice of architecture than questions about consistency with new scientific ideas. The primary feature of the new science for me is the extension of the domain of reliable scientific knowledge about reality from quantities and their mathematical relationships, to include the qualities of coherent wholes. The distinctive feature of Western Science is the restriction of the objectively real to that which can be measured. This was a good strategy to follow as far as it made sense, and it has gone a very long way. However, the denial of qualities as aspects of reality that are basic to understanding the properties of complex wholes has now ceased to be useful and is causing serious problems in the way we seek to relate to the complex wholes on which the quality of our lives depend (e.g., our bodies, buildings, communities, ecosystems, climate, the biosphere, the earth as a whole). Health is not something that can be measured with an instrument, though specific physiological measurements can be useful in reaching judgements about well-being and disease in bodies.

            … we need to take responsibility for our actions as participants in this creative cosmos and learn to cultivate the awareness of how to engage in right action through attention to feelings and intuitions as well as using our analytical faculties. This is the lesson I take from the new science, that goes beyond the post-modern to a new form of ethical realism, now called (by Roy Bhaskar) critical realism.



Subjectivity and objectivity


Post-Modernists who exploit scientific concepts are able to get by without investing too much in the objectivity of those concepts: they merely sees them as another useful “pretext” for making architecture, in the way that linguistic and philosophical ideas (some now discredited) were in the past. On the other hand, those trying – through participating with “natural creativity” – to fit architecture to the true pattern of the world, do rely on the scientific concepts they apply having objective validity. Can we ever get beyond the idea that the arts – architecture included – have ultimately to be judged subjectively?


BH:  Ian, You have recognised an “innate human appreciation for pattern”. Architects committed to the avant-garde argue that the popular preference for traditional forms is learned, not innate, and that the public could just as easily learn to love marked asymmetry, minimalism, lack of ornament, flat roofs etc. Does the avant garde have a point, or does our “innate … appreciation for pattern” suggest there are limits to what we can learn to love?


Stewart: My own experience is that there are limits to what I can learn to love. Acquired tastes have to be acquired, and sometimes the effort is too much, or the taste simply doesn’t stick. But the avant garde is right to argue that tastes need not be fixed. The human brain has evolved to get bored if things stay the same for too long. It’s a great survival characteristic – if you’re too predictable, predators and parasites may have time to evolve a way to use that predictability against you.

            We are very much creatures of our environment, and we get used to whatever surrounds us when we grow up. But in order for us to grow up, those surroundings have to lie within certain broad limits.

            I don’t see any great point in the kind of art that claims to ‘challenge our conception of what art is’ by producing things like Tracey Emin’s bed[32]. There’s no intellectual gain in that sort of in-your-face ‘challenge’. Anyone can do it. Most people have enough sense not to, and not to be impressed by it.

            The trick is to be open to innovation, without losing your critical sense. The Sokal spoof (and for me, the bed) shows how easy it is to get the balance wrong.


BH: You have predicted that in fifty years time we will have a “rigorous mathematical theory” to help us understand the ways certain patterns emerge from complexity. Do you think by then we may also have come to know why people prefer certain patterns to others?


Stewart: Well… mathematical theories and human psychology are two different things. But it’s a pretty good test of a theory, to see whether it can help us understand how our preferences form. The human brain is a complex system, and consciousness is clearly some sort of emergent property. So if my hope is realised – I could easily be wrong here, it’s such a hard problem – then I’d agree, yes. We would be able to understand how the evolution of the brain, and its perceptual abilities, predisposes us to like particular patterns.

            There are a few examples of this already. Our liking for symmetry in patterns is probably a side effect of the symmetric structure of the early sections of the visual system (layer V1 in the visual cortex has a beautiful symmetry of neural connections, and the panoply of hallucination patterns – revolving spirals, tunnels, spiderwebs – stems from this, for example).


BH: Brian, you seem to agree with Alexander that the qualities we have been discussing are really “out there”, not only in our minds. Indeed, your own science of qualities relies on the possibility of our reaching qualitative consensus. Can we ever hope to answer, to most people’s satisfaction, this knotty question of what is and isn’t subjective in our responses to the world?


Goodwin: The status of qualities is crucial to this whole discussion, and I very much agree with Alexander’s position that they are objective properties of beings as process, whether these are organisms, landscapes, buildings, or organisations. Goethe’s work on colour[33] seems to me a major contribution to our understanding of  qualities as real, inherent in the process we are paying attention to such as a sunset or an apple or a human’s complexion. Colours, and qualities generally, tell us something about the activity that generates it, so that they are not subjective and idiosyncratic but intersubjective and real, though of course observers bring a complex history of experience to any situation. This is why it requires considerable cultivation of the intuition (non-inferential way of knowing) to distinguish between the personal aspects of experience and the objective reality that is revealed.


BH: Phil, do you think it likely that the new sciences could bring about a situation where aesthetics could be taken out of the “subjective” sphere, and made a matter of objective discussion?


Ball: Possibly. But I suspect we’ll agree that there are limits both to how far we can go with this and to how far it is desirable. Most great art (visual, aural, literary, whatever) has an important element of rational planning, but a still greater element of intuition. One can learn pitfalls to be avoided, but one can probably never learn how to make truly great art.


BH: Brian Goodwin has elsewhere[34] made the following observations about the relationship between objective and subjective knowledge in the context of a science of qualities:


… 'objective' knowledge comes from consensus between subjects who agree on particular methods of getting knowledge, as scientists do in acquiring quantitative knowledge about parts of the world by measurement procedures. This gives us a science of quantities, a Galilean science. But we experience more than quantities; we also experience qualities such as color, texture, pain, joy, health, beauty, coherence, and a host of other properties. Science tends to dismiss these as 'subjective', outside the realm of scientific investigation. But people are hankering after a better quality of life — not just the quality of air and water and food, but quality of experience, relationships with people, community values. Subjectivity is getting squeezed out by science, and everything's being turned into this counter-intuitive objective way of looking at the world.


This suggests to me that this whole issue of subjectivity v. objectivity – long familiar in the arts – is now becoming a matter of debate within science also?


Ball: I have a lot of respect for Brian, but I don’t really agree with him on this …

Why insist that science needs to be something it is patently not ‘designed’ to be? Isn’t it like insisting that garage mechanics become poets? It seems to me that the problems only arise (and they do) when we get a small clique of vocal and puritanical scientists insisting that objective knowledge is the only sort worth having. Of course it isn’t. The qualities that Brian lists are absolutely central to human experience, and we dismiss them at our peril. But isn’t there something badly amiss if the only way we can get them taken seriously is to give them a spurious patina of scientific respectability? My view is that we need to make science humbler, not more all-embracing. Mostly science is just a form of doing useful things – of engineering, if you like …

            I’m often baffled by the unease created by what people see as the exclusion of subjectivity from science. (Of course, scientists themselves are always being subjective, but that shouldn’t be news to anyone. The scientific method is all about coping with that and ironing out the biases it might create.) If science ceases to strive for objectivity, it ceases to be science …

            And I have to say that I don’t think there is a great deal of debate about this within science at the moment. It shouldn’t be confused with the debates about the ethical limits or responsibilities of science, essential though those are. Brian has an interesting view, but it’s not really the mainstream view.


BH: Would you say the same about the case Goodwin has made for the continuing validity of “animism”: his inclination, as he expresses it, “to put a tiny bit of feeling or sentience into matter in some form and allow it to get amplified in systems organized in particular ways”[35].


Ball: That’s one solution. Mine is simply to ask ‘What’s the hurry?’ Clearly, the brain and how it creates consciousness are things we still understand very poorly. I can’t help thinking that current attempts to explain things like sentience are going to end up looking like the clumsy attempts of ancient or Renaissance ‘scientists’ to understand complicated things such as conception or comets. They did not have either the requisite tools or the fundamental theoretical framework on which to proceed. So their explanations were more or less qualitative inventions invoking enormous yet untested ideas. Why would we want to repeat that? What’s wrong with saying ‘I haven’t a clue?’

            This is far too grand a way of saying it, but I feel that Brian (and in a different way, Stephen Wolfram – and indeed Alexander, it seems) is like Descartes, trying to explain everything according to one great over-arching scheme. I’d identify myself more as a British empiricist, looking for small-scale and limited explanations that seem to be useful and that ideally conflict with one another as little as possible.


BH: So you think Alexander’s attempts to define “life” constitute a “qualitative invention” rather than real science?


Ball: What I have seen of Alexander’s ideas leads me to suspect that I would find his architecture very pleasing and sympathetic, and much preferable to a lot of buildings today. I applaud his attempts to develop a rational architecture that accords with people’s instincts … [but his] definition [of life] is utterly subjective …

            It seems a shame that he feels it necessary to develop an entirely new and seemingly arbitrary cosmology in order to justify his ideas. The problem is that he speaks of objectivity while apparently wanting to deny such a thing. His prima facie evidence for his theories is his own subjective responses. I think we all probably know what he means when he says he experiences more ‘life’ in certain structures, but to then attribute this as a property of the space or structure, rather than as a psychological construct, seems wholly unjustified. In The Nature of Order he confesses that “I know that it simply is so” – that is, I assert that I am right. I do think that there are times when we must trust the evidence of our senses, in order to avoid the dangers of solipsism – but this is a philosophical standpoint, not a scientific one. Much of this ‘theory of life’ is really about cognitive psychology, projected onto the outside world. It seems to me that it might be more productive to explore why the brain perceives, orders and responds to things this way, not why the world is constructed this way. So in terms of what Alexander has to say about space, life and cosmology, these seem to be [personal] views rather than anything scientists would regard as a theory. In terms of a system for making better architecture, I can well believe that he is on to something useful.


BH: Phil, do you see any connections between the themes being explored in Katarxis 3, and your own concerns with the physics of nature, and – in your new book – of society?


Ball: I see that the potential is there for such links, but I’m not sure it has yet been realised. The general principle – a rational view of how humans use and respond to space – seems to me to be certainly something that could be explored using some of the ideas I outline in my book on the physics of society. In terms of the relation to pattern formation in nature, I still see rather little. It is true that nature often finds good ways to partition space efficiently or to solve the problem of maintaining a structure while it grows, and there may well be lessons in this for us.


BH: In the new book, you deal with people as particles in order to explain certain social phenomena – crowds, traffic flow etc. – in terms of the new scientific principles. How far do you think that these principles can come to embrace, say, collective decision-making about built environment issues? Is it valid to extend them beyond the point where people are making extremely simple decisions about speed, distance from neighbours etc. – not unlike the “boids” in computer simulations of flocking? Do you think it remains valid when the decisions being made are more subtle? Or do particles possessing greater intelligence necessarily weaken the model?


Ball: It’s a good question, and an open one. My suspicion is that the more complex and ‘intelligent’ one makes the ‘agents’ in a model, the further one gets from reality – because once we are in a situation where we have a great deal of choice, simple ‘physical’ models become too psychologically naïve. At present, I think that models of voting behaviour lie close to this boundary: there are several physics-based models of voting, and they suggest some interesting things, but I’m not at all sure how relevant they are to the way people really make up their minds in a political environment that can be so dominated by ephemeral single issues and which is so manipulated by the media. So at present, trying to model situations where too much psychology is involved does, in my opinion, result in a weaker (less realistic, less reliable) model. All the same, one of the messages that emerges from a ‘physics of society’ is that there are robust, collective modes of behaviour even in systems that seem complex (such as negotiation of international alliances). It may well be that such things don’t disappear completely when the choices and psychological complexity broaden.


BH: Do you think it might be possible to try to understand the highly-developed products (buildings, places, cities) of classical civilisations partly in terms of self-organization, given that traditional building culture invested greater freedom of action (within the limits imposed by the various trades) in those diverse individuals actually engaged in building?


Ball: Self-organization is not necessarily about freedom of individual agents. Often, the models that are used to study it place rather severe constraints on the agents themselves: in modelling human behaviour, for example, the agents are often permitted only a few possible courses of action. Termite nests are self-organized, but termites do not exercise a great deal of freedom of choice. The real point is that the collective result of individual actions can be surprising and almost impossible to predict simply by looking at the behaviour of single individuals.

            Of course, classical Greece tended to be at least as geometric and rule-bound as today’s architecture, albeit for different reasons.


BH: What, then, do you think is the right balance between top-down planning, and bottom-up self-organization in a well-balanced social system? Is it ever likely we will achieve such a balance?


Ball: It’s very hard to generalize about this. One of the main messages of Utopia Theory is that it is folly to think that science is going to come up with a single scheme for telling us how best to direct our affairs (or even that science has anything useful to say at all about many social situations.) What a physics of society might do is to help us see which options are realistic and which are not – to see the possible range of choices. Which of them we pick is then a question of making ethical and practical choices about the kind of society we want to live in. But at present there is a danger of trying to ‘plan into being’ an outcome that is simply not a stable state of the system in question. I read a nice quote [some time ago] from the philosopher Michael Oakeshott: “To try and do something which is inherently impossible is always a corrupting enterprise.” Economic markets provide a good example. The loudest voices over the past couple of decades have come from the right, who argue that a totally free, deregulated market is the best solution. They make this assertion without the slightest theoretical basis—there is no evidence that such a market works best for businesses as a whole, nor that it distributes wealth evenly, nor that it makes the best use of available resources. In fact, there is some evidence now that it does none of those things. It was an assertion of personal belief about how they would like to see things done, shored up by the absurd and now discredited (though still much used) notion of market equilibrium. On the other hand, there has been a tendency to try to micro-manage the market, as if to imagine that a little manipulation will iron out all the fluctuations. This too was based on a false belief, a refusal to see that the fluctuations (of almost all sizes) are a fundamental characteristic of the way markets operate. Governments cannot control markets arbitrarily. But with physics-based models, one might be able to start to see the limits of that control. Perhaps we can ‘soften’ the worst convulsions. Perhaps we can level out the wealth inequalities. Perhaps we can avoid imposing some constraints that will have adverse and unintended consequences.

            I think the same [may] sometimes be true for architecture and civic design, for example in the uses of open spaces or in traffic planning.


BH: Can you elaborate on the applications you see for architecture and civic design?


Ball: [It] would be extremely useful for architects to be able to run computer models of people moving about within the spaces they design (including situations such as rapid exits in emergencies) to see how they will function in practice. The results might often be surprising and counterintuitive. The principle, I think, should be to try to mould the environment to the way that people naturally use it, rather than forcing people to try to adapt to a pre-imposed plan. The principles behind the kinds of computer simulation I describe are not too difficult either to grasp or to implement – I think it should be fairly easy to make these tools available. Whether or not people can be persuaded to use them is another matter. Perhaps they will be welcomed! – I don’t know.


BH: I’m reminded by this of some of the earliest applications of computer technology to architecture, in the 1950s and ‘60s – in which Christopher Alexander played an important part[36]. Ian, you also see immediate applications arising from this kind of “functionalist” tradition.


Stewart: I think that some kind of adaptive “cellular automaton” in which cells can move, change shape, divide, or die, according to various rules, may hold the key. You could imagine a self-modifying building, say. Better still, an evolving building, which adapts according to what works and what does not.

            My friend (and former student) Keith Still has thought a bit about such things. His PhD thesis was about mathematical models of crowd flow, and those ideas have since been developed into a commercial system for computer modelling of crowds in buildings. It’s not such a big step to give the computer options, and let it evolve people-friendly buildings by changing bottlenecks or other problem areas. It’s a kind of organic model of the design process …

Keith Still’s approach to crowds is at root combinatorial – to model a crowd of 100,000 people (which is perfectly feasible) the computer holds 100,000 ‘entities’. The programmer provides the rules for movement; the computer works out what they lead to. If linked to a selection procedure for what “works”, this would be an example of an architectural relationship between layout and function. More interesting still would be an understanding of how people-level rules prescribe effective buildings and public spaces. Then we’d get architecture as an emergent process.



Wider implications for architecture and urbanism


I asked all three scientists for their views on the implications for the practice of architecture and urbanism of the new scientific concepts – going beyond mere extensions of functionalism. To begin with, I asked how we might deal with the fact that, fascinating though it is for analysing and appreciating complex phenomena, the concept of “emergence” is not yet refined enough to be a predictive tool, and is still therefore of limited use to the architect and planner.


BH: Ian, you have said that the idea of emergence allows of “no way for humans to trace consequences back to the rules” – a conclusion that is echoed in Wolfram’s principle of “computational equivalence”. Is this conclusion not a pessimistic one for architects believing they can ever uncover, and apply in their own work, the rules that generate living complexity?


Stewart: It may not be that bad. My personal definition of “emergence” is that the logical path from the underlying small scale rules to the overall behaviour is too complex to trace in complete detail. That’s the reductionist programme taken to its logical extreme. But we don’t have to be reductionist. We already understand some emergent systems, in this sense, quite well – crystal structure, let’s say …

Complexity science is necessarily about qualities – these are where progress can be made and where emergence is not necessarily a barrier to understanding. If you bend a stick until it breaks, the details on a molecular level are emergent and horrendously complicated.  (Which fibre goes first affects all the rest.) But qualitatively we all know that if you bend it enough, at some point it will break because it isn’t strong enough to withstand the bending force. That’s a leap across what Jack Cohen and I call the Ant Country of the low-level rules, and a logically valid one too … We can “leap over” the Ant Country, by finding appropriate high-level principles. We don’t have to deduce them in full rigour; we just have to be sure that they’re widely valid.

Symmetry, continuity, statistical properties are simple examples. I hope we can do better than those.

            So architects should continue to follow their noses, and seek out the principles. The reductionist story may not matter that much …

            Many areas of science got through a series of stages: description, classification, prediction, control. Chaos Theory, for instance, began as a descriptive area of mathematics (“This is what the Lorenz attractor looks like”) and has now progressed to the stage where “chaotic control” makes use of chaos to exert control with very little effort (make the ‘butterfly’ flap its wings in the right place and at the right time). Beyond control lies spontaneous evolution of desired or selected characteristics.


BH: Phil, do you share Ian’s optimism on this?


Ball: I think that the techniques of ‘complexity theory’ (a term I dislike, but it will do) can already be used as a predictive tool, because of the possibilities offered by computer simulation. The question of whether an analytical mathematics will emerge is an interesting one, but largely for physicists alone. My suspicion is that Ian may be right; but one of the big obstacles here is that the steady states in non-equilibrium science may depend not just on their own properties but on the history of the system: how it got to be that way. That may not be an insurmountable problem, however. But when scientists can’t handle a problem analytically – with soluble equations – they now typically turn to making simulations on the computer, which don’t necessarily provide a deep and rigorous understanding but do at least allow prediction.


BH: Brian, you have argued that we may only be able to grasp the implications of the new principles science is presenting us with, by learning to participate: not only with nature, but with other people.


Goodwin: In the context of cultural processes, the focus is on participation in which no privileged component or set of components is in control, and appropriate creative activity can arise from an organic process of feeling the way to the order that expresses the lived experience of the whole group. I understand this to be like Alexander’s notion of group or community participation in architectural construction, and the way in which cities with an organic quality have emerged from an ongoing process (in Book 3 of The Nature of Order[37]). It is opposed to any imposed plan from an architect or a developer in which the whole is conceived in advance of the process of creation. Any plan should be held lightly and be allowed to change as the process of construction develops and the participants experience the consequences of particular structures. This process has an element of chaos and unpredictability about it, and resists any rigid planning preconception that has produced such disastrous consequences in city development and housing construction.


BH: I am reminded by this that you refused to prophesy, even in as inherently forward-looking a work as John Brockman’s The Next Fifty Years[38], arguing that we should be “fully tuning in to the present so that the future arrives as an unexpected revelation from engaged action in the now, not from prediction and planning”. This seems to question both the value of history, and the possibility of planning for the future.


Goodwin: To be tuned in to the present implies paying attention to the historical process that brings us to where we are now, but only as an indicator of where we have been and not as a plan to project into the future. I think that planning, to be effective, has to be a kind of facilitation that is prepared to engage with and hold a process of confusion and chaos long enough for something new and relevant to emerge from what has passed as history. This is rather like the alchemical process of dissolution prior to transformation, or the Dionysian aspect of communal action that holds off Appolonian order while new possibilities are explored and experienced. The new order cannot be predicted or planned in advance if it is to be genuinely relevant to context, but as it emerges it can be experienced so that some judgement is exercised through feelings and intuition and observation as the process develops, so that choice and influence can be exercised in the fluid phase of emergence. The right balance between order and chaos in this process can only be gauged through present awareness within the whole community engaged in the activity …

[T]he implications with respect to participation and walking carefully in the present, not making great plans for the future, are clear and connect with Alexander’s approach to planning and living the process of construction … A fundamental aspect of a science of qualities is the process of reaching consensus by communities, whatever their nature and intentions may be … It is not for specialists to judge the quality of the designed space in which people choose to live, but for the people themselves, in discussion with whoever they wish to involve in the process … The age of experts is over, including architects and scientists as decision-makers for others.


BH: The editor of Katarxis, Lucien Steil, was interested to know your reaction to “the idea of a living Tradition in architecture as an organic paradigm, as a natural foundation of the New and as a natural support of an organic collective intelligence.”


Goodwin: My position … recognise[s] the positive potential in human action, as does [Roy] Bhaskar and also Chomsky in his ‘libertarian anarchy’, the belief that human communities can make the best decisions for themselves and are best without any type of elite, privileged subgroup. The aspect of nature that should inform human action is the participatory, ecological, sustainable mode of relationship that we see operating throughout the natural world. The phrase ‘organic collective intelligence’ that Lucien Steil uses is very relevant here.


BH: What you are saying seems to suggest (as the Prince of Wales, for one, has argued[39]) that the fullest community participation is not incompatible with the most sophisticated (one might say classic, or classical) approaches to building and place-making. The new sciences seem to support the idea that greater devolution might go hand in hand with greater sophistication in the end product.


Goodwin: Devolution, going local in all aspects of human activity, does seem to me precisely the way to achieve sophisticated and appropriate artefacts that sit well with the natural world. This is a radically new idea within our whole Western conception of education and planning, which emphasises control and manipulation of nature, but it is the primary mode of acting in many indigenous cultures. By going global, centralised and abstract, we are losing virtually all knowledge of the particularities of place that indigenous cultures have developed, and we are rapidly destroying these cultures and the planet in the process. A homogenised culture is death just as certainly as homogenised energy, maximum entropy, is death to natural creativity.


BH: Do you regard these various indigenous cultures – as some would – as sharing a “perennial philosophy”, expressed through sacred geometry?


Goodwin: My sense of the sacred is [not] something dead and static, such as ‘sacred geometry’ … It is being in touch with the creative process in which we are all engaged, experiencing the continuous coming-into-being that is what we and the rest of nature are, and feeling your way into right action that is the experience of this process in feeling. We need now to engage in this collectively, having experienced what it means to do this individually.


BH: Phil, it seems to me that if complexity science is encouraging all of us – artists as well as scientists – to participate with rather than control natural processes, architects ought to be increasingly interested in more “spontaneous” forms of ordering, and form-making, and less interested in controlling everything by means of “forced” symmetries or asymmetries – more concerned, in other words, with what Salingaros calls “evolved” as against “non-evolved” structure.


Ball: I agree with all of this. It may be, however, that the number of situations in which architects need to consider some form of spontaneous symmetry-breaking is quite small. Pedestrian motion is the obvious example, and Brian [Goodwin] is right that here participation seems very important – what do people want to do, rather than what does the architect want to force people to do. I expect that in urban planning there are other instances – for example, how districts, towns and cities fragment as they grow. Engineers concerned with something like the design of a dam or of river levees need also to think more about how they can collaborate with natural processes instead of trying to control them. But surely a lot of architectural and design choices are aesthetic ones. I was looking [some time ago] at the model for the proposed V&A Spiral. I’m not sure there are any scientific arguments for or against it, but aesthetically it looks to me as though, particularly in that location, it would be abominable …

            Scientific paradigms do influence society in the broadest sense, but I suspect that influence is often rather minor compared with issues about cultural history, political structures, economics and so forth. That said, I would like to think that perhaps the biggest shift in thinking, which would gain support from today’s science, would be away from hubristic and dogmatic ideas about planning and control and towards an empirical approach: “can we predict what will happen if we try to do this?” And then: “is that what we want?” I’m not sure whether there are many signs of that happening yet, however – we live in a political climate in which our leaders feel obliged to tell us what the answers are, rather than confessing that they won’t know until they’ve tested them.


BH: But how could we be sure that if this did happen the balance was maintained, and that subtle, self-organizing processes were not completely overwhelmed by grand plans backed up by political and financial might?


Ball: That is, I think, mostly a political and professional issue. Self-organization challenges the assumption of planners and politicians that they have arbitrary control over a system. They may not take kindly to having this limitation pointed out. It will require the relinquishment of a lot of egotism, and a recognition that in the end plans should not be ‘personal visions’ but ways of assisting and directing what comes naturally.


BH: Stephen Wolfram has said that the reason we don’t see more nature-like complexity in human artefacts is because we narrow our ambitions to addressing certain limited kinds of behaviour, and to dealing only with certain soluble problems. In traditional societies, the Building Culture seemed to be able to generate forms that ensured many different purposes could be served at once – including, of course, the need for Beauty. Even if one could forsee some practicable algorithm being developed that would help us replace some of the qualities lost from the built world, this would probably be incompatible with the way we do things now – namely, architectural profession, building industry, development business. Alexander has always maintained that those things will have to change in some significant ways.


Ball: My impression is that Alexander is right: there would need to be some big changes in working practices. I do not see how these might be easily made, since there is probably a fundamental conflict between doing things the way Alexander would like and doing them in a low-cost and time-limited manner. However, one might imagine that new materials might make a difference to what can be achieved, and at what cost. And I am struck by how, in southern Spain, very attractive and apparently very well thought-out and individualistic houses seem to be made in an apparently economical way from low-cost breeze blocks covered in stucco. Probably a large part of the problem is getting rid of the prevailing one-size-fits-all mentality.


BH: Brian, in yours and Solé’s book, Signs of Life[40], you say that history teaches us that top-down planning and bottom-up self-organization might not have to be in conflict in the same city.


Goodwin: The beauty of many cities is precisely the organic quality of much of their structure, which grew gradually together with the creation of planned spaces and structures as opportunity arose during the development of the city as a collective creation. There are signatures of these organic spaces in the fractal patterns that persist throughout city growth.





[1] in what ways should architecture imitate nature?

There was a distinction in the early-nineteenth century between French and British artists’ attitudes to nature. The first was idealistic (as expounded by Quatremère de Quincy), the second more realist (what was termed by Ruskin a “science of the aspects of things”). The English philosopher Roger Scruton has reintroduced this distinction with his recent insistence that the essence of nature and its appearance are indistinguishable.  Return to text.


[2] discernible structure in music

See Julian Johnson, Who Needs Classical Music?, Oxford, 2002. Return to text.


[3] Ruskin

Peter Fuller, Theoria: Art, and the Absence of Grace, London, 1988. Return to text.


[4] “biophilia”

Edward O. Wilson, The Future of Life, London, 2002. Return to text.


[5] natural kinds

Goodwin explains this idea to Dr. David King in “An interview with professor Brian Goodwin”, GenEthics News, 11, Mar./Apr. 1996, pp. 6-8  Return to text.


[6] attractors

Attractors ( or “Lorenz attractors”) are a phenomenon in the mathematical modeling of non-linear dynamics. They demonstrate that certain systems tend towards a relatively small number of states (two or more), flipping back and forth between them unpredictably, based on very small variations in the predictor variables. (with thanks to Anthony L. Suchman) . Return to text.


[7] Stephen Wolfram,

A New Kind of Science, Champaign, 2002. Return to text.


[8] Structure-Preserving Transformations

These are explained in Part One of Book Two (“The Process of Creating Life”) of Christopher Alexander’s The Nature of Order, Berkeley, c.2003. Return to text.


[9] Growth and Form

D’Arcy Thompson, On Growth and Form, Cambridge, 1917. Philip Ball discusses Thompson’s significance in his Critical Mass, London, 2004. Return to text.


[10] “phase space”

“any abstract space formed [by plotting them on a 2D map] by a position (either linear or angular) and its associated speed”. Such spaces are used to study the behaviour of complex systems. Return to text.


[11] “The Phenomenon of Life”

Alexander, Nature of Order, Book One, c2003. Return to text.


[12] “how to define ‘life’”

See Ball’s article “What is life? Can we make it?” in the August 2004 issue of Prospect magazine.  Return to text.


[13]The Self-Made Tapestry

See Ball’s introductory biography. Return to text.


[14] how consciousness (and feeling) could emerge

The phenomenon of emergence is one where control is exercised by the intrinsic rules of evolution of a system, and not by any external authority. It is discussed in M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, London, 1994; and Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities and Software, London 2001.  Return to text.


[15] Whitehead or Bergson

Henri Bergson (1859-1941) was “the first to elaborate … a process philosophy, which rejected static values in favour of values of motion, change, and evolution” [Enc. Brit.]. He is credited with the notion of “vitalism” or “animism” in relation to organic systems. Alfred North Whitehead (1861-1947), whose 1929 book Process and Reality has been called one of the greatest works of Western metaphysics, developed what he called a “philosophy of organism”, and criticised scientific materialism for having replaced the concrete reality of nature with abstractions. Return to text.


[16] Stu Kauffman

A good starting point for understanding Stuart Kauffman’s ideas is his Origins of Order: Self-Organization and Selection in Evolution, Oxford, 1992. Return to text.


[17] Autocatalytic networks

An “autocatalytic set” is a set of molecules in which the conditions are such that a “coherent, self-reinforcing web of reactions” is set up – the web, in effect, catalyzing its own formation. Described in Waldrop, Complexity, pp. 123-4 et seq. Return to text.


[18] Charles [Jencks]

The Architecture of the Jumping Universe. A Polemic: How Complexity Science is Changing Architecture and Culture, London, 1995; The New Paradigm in Architecture: The Language of Post-Modernism, New Haven and London, 2002. Return to text.


[19] making his power seen

Richard Sennett, Flesh and Stone: The Body and the City in Western Civilization, London 1994, p. 89. Michel Foucault (1926-1984), a friend and colleague of Sennett’s, traced the exercise of power through institutions designed for “exclusion”, such as asylums, hospitals and prisons. Return to text.


[20] catalogue of patterns

Christopher Alexander et al., A Pattern Language, New York, 1977.  Return to text.


[21] Elliot waves in economics

Ralph Nelson Elliot (1871-1948) proposed that the complex cycles of stock prices could be described in relation to five “waves”, the relationship between which can be explained by the Fibonacci series of numbers (a series which also pervades natural forms).  Return to text.


[22] “extelligence”

See Stewart’s contribution to John Brockman (ed.), The Next Fifty Years: Science in the First Half of the Twenty-First Century, New York, 2002.  Return to text.


[23] phase transitions

First-order phase transitions, common in nature, are exemplified by the change from ice to water above a certain temperature. Less common are second-order phase transitions, which are not abrupt, but manage to combine elements of order and chaos in juxtaposition. See Waldrop, Complexity, pp. 228-9. Return to text.


[24] Satish Kumar

Kumar is Programme Director of Schumacher College, and editor of the magazine Resurgence. His new book is You Are Therefore I Am. A Declaration of Dependence, Totnes, 2002. Return to text.


[25] New Paradigm in Architecture

See note 18. Return to text.


[26] The Nature of Order.

See various mentions above. Return to text.


[27] Sokal article

“Transgressing the boundaries: Toward a transformative hermeneutics of quantum gravity”, Social Text, 46/47, 1996, pp. 217-52. Return to text.


[28] Sokal spoofed postmodernism

The so-called “Science Wars”, to which Sokal’s spoof article [above] was a contribution, are further discussed in Jay A. Labinger and Harry Collins (eds.), The One Culture: A Conversation about Science, Chicago and London, 2001. Return to text.


[29] interview in Nature

conducted by John Whitfield.  Return to text.


[30] two types of creativity

Margaret Boden is attached to the Cognitive and Computer Science department of the University of Sussex, and is author of The Creative Mind: Myths and Mechanisms, London, 1990. Return to text.


[31] Critical Mass

See Ball’s introductory biography, and note 9.  Return to text.


[32] Tracey Emin’s bed

Emin’s “My Bed” (aka “The Unmade Bed” – literally that) helped win her the Turner Prize in 1999. It was destroyed in a warehouse fire in 2004. Return to text.


[33] Goethe’s work on colour

Modern physicists have been unkind to Goethe’s Farbenlehre (1805-10), but he himself ranked his scientific work of this kind on a level with, if not higher than, his poetry.  Return to text.


[34] Brian Goodwin … elsewhere

John Brockman, “A new science of qualities: a talk with Brian Goodwin”, Edgewww.edge.org/3rd_culture/goodwin/goodwin_p1.htmlReturn to text.


[35] tiny bit of feeling or sentience

“In the shadow of culture”, in Brockman, Next Fifty Years. Return to text.


[36] earliest applications of computer technology

Alexander’s work on design theory in the 1950s and ‘60s, and in particular his time spent at Harvard – culminating in his hugely influential Notes on the Synthesis of Form, Cambridge, Mass., 1964 – put him at the forefront of computer applications to architecture, and to planning issues such as the optimal design of motorways. Return to text.


[37] Book 3 of The Nature of Order

“A Vision of a Living World”. Return to text.


[38] The Next Fifty Years

See above [“extelligence”]. Return to text.


[39] as the Prince of Wales … has argued

This is discussed in Brian Hanson and Samir Younés, “Reuniting Urban Form and Urban Process: The Prince of Wales’s Urban Design Task Force”, Journal of Urban Design, vol. 6, no. 2, 2001, pp. 185-209. Return to text.


[40] Signs of Life

Brian Goodwin and Ricard Solé, Signs of Life: How Complexity Pervades Biology, New York, 2000. Return to text.