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.

Life

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.