Professor Michael Batty

Caitlin Morrissey

So Michael, what is the DNA of cities in your mind and is it literal, or is it better understood as a metaphor?

Michael Batty

Well, that's a pretty direct and obvious question, really. I mean, to me, it's not literal. It's certainly a metaphor. But in fact, there's even an argument that says that the science of DNA is a kind of a metaphor. It's not literal. But if we really did know how our bodies worked and how our genetics worked, we could well imagine it being differently from the way we represent things. So, for example, the double helix, for example, which is the way DNA is woven into the cell, is a kind of a metaphor to some extent. I mean, a geometrical metaphor. It may or may not be right. It works within the limits of it. So this question about the DNA for cities almost certainly is a metaphor of some sort, or an analogy, even, in that sense. The difference between the analogy and metaphor is not super clear.

But in other words, we're using a branch of science, for example, genetics, et cetera, to think about another branch of knowledge, which is about cities in that sense. And there's a long, time-honoured tradition in doing that. For example, there's an area called Social Physics, for example, which really took basic ideas about Newtonian physics and suggested that we move around cities and locate in cities according to some of those ideas about gravitation and force and things of that sort and potential. So these are these are analogies, really, or metaphors in that sense.

And in some respects, one of the key issues, I think, is that it's not at all clear when people talk about the DNA of cities that they really mean quite what DNA means in genetics, that the DNA is really the instruction set that enables us to create new cells and to create life, the cells being grown, as it were, from a seed. And so the DNA represents the instruction set to grow cells, to perform different functions to some extent. And when you look at where people have thought about DNA in terms of cities, they don't necessarily mean the instruction set, they perhaps even mean the functions that are actually spawned or generated from the instruction set.

In that context, the classic example in terms of the DNA of cities, I think, is that we think of the city as being divided spatially into cells, and the cells themselves have a function, and the instruction set might be the set of ideas that pertain to how the cells actually change and what functions they have. So typically we divide the city up into cells which are all over the city, which define the representation of the city. And inside each of those cells, you have things moving, things changing, et cetera, people moving into the cell. But the actual functions, the actual instructions about how these elements move, are really the nearest we could think of to the DNA instruction set.

Now, a lot of the models don't actually look at the instructions. They look at the individual functions that are moving. So, for example, there's no accident that the DNA of cities came at a time about 15, 20 years ago, people began to think of cities as having cells, and there is a branch of simulation called Cellular Automata Modelling. There is a paper by Elizabete Silva who's at Cambridge in Land Economy. She wrote a paper in Futures a few years ago about the DNA of regions. And when you look at her paper, it appeals to these ideas about cellular growth, cellular automata. Basically, where people have begun to think about the DNA of cities, I think they've looked at the individual elements of the city, which can take place in and out of cells. So different activities, land uses, if you like, or activities with their attributes and so on, which do move around in a place. And the DNA is often thought of as being those bits of the city rather than the instruction set, as in modern genetics, of how the cells do things. That's my interpretation of a little bit of work that's gone on which has talked about the DNA of cities, not really very much.

What is surprising, I think, is that there isn't more work on the DNA of cities, that if you search around for things that are written there's the paper by Elizabete Silva in Futures, there's a paper by Alan Wilson in Environment Planning B, and when you open those papers, Elizabete's paper is really all about cellular automata, cellular growth, which has resonance with DNA, of course, and with cell biology and so on. And Alan's paper is really about dynamics. It's about change and the seeds that need to change and so on. And both papers are not really good analogies or metaphors with DNA, as in genetics in that sense. And then there's a lot of work, some of which I think you know about, for example, on creative cities and so on, that that often appeals to appeals to ideas about genetics and DNA, identifying the components that make successful cities and lead to growth.

And what I was saying was that there isn't that much on a more literal interpretation of DNA when it comes to cities. In other words, people have not looked at the structure of the cell and the relevant genetics, the cell, the DNA instruction set, the way these combine to produce genes and then the cell growth or division which takes all these things into account. That basic model has not been widely applied to cities. It's been more, as you said, in terms of the question, it's more of a metaphor really in that particular context and useful to think about, because obviously cities change, and they become more complex. That's, in my world, a rite of passage, that with time cities are becoming more complex and we're having to run to stand still with respect to the diversification of functions and new technologies in cities, that in some sense the genetics paradigm and the fact that life evolves from very simple things to more complex things is quite an interesting one in that sense and very resonant with cities themselves.

So that's what I think about DNA in terms of cities, that again, to summarise, it's a metaphor rather than a literal issue. And I don't think there'll be many people who would argue otherwise on that particular basis. It depends to some extent, depends how literal, how much a metaphor in some sense. That's what the argument's about. That's not very different from lots of the things that pertain to theories about cities, theories in general, in science, where you might have a physical theory that pertains to biology and vice versa. Now, are you still with me?

Greg Clark

Very much with you. I think maybe it would be helpful, Michael, to hear a little bit about what your own work has illuminated in terms of your curiosity about this, and I think the overview you've just given us is extremely helpful, and you are right that we are in touch with a lot of people in these different spectra. The other one, of course, is people who are kind of urban designers and built environment and architecture types whose interest is in how the shape of the city influences the behaviour of the people within it. But I'm keen to know, in a sense, where your passion is in this discussion.

Michael Batty

Well, many years ago, I was involved as a graduate student, really a long time ago, in the Department of Land Use transportation models, and we still build these things extensively. And through the 70s, into the early 80s, I worked on those sorts of models quite extensively. And one of the issues with respect to the complexity of those models was that in those days that we didn't have very good maps or graphics to represent the outputs of the models. The outputs of the models were great sheets of numbers that had to be interpreted statistically. And we didn't have – I'm recounting here almost the history of computer graphics – we didn't have good graphics, except that in the early 80s when the PC came on stream, the whole PC issue was that that the memory of the computer was partitioned into a graphics area and a non-graphics area. So the screen became the graphics memory, and so we could begin to visualise the graphics quite effectively.

And in some of the early work on land use transportation modelling, I was involved in developing computer graphics for mapping. And the computer graphics didn't look particularly real. It looked rather artificial. So I got involved in looking at techniques for making the graphics on early applications on our workstations much more realistic. And I got into this area called fractals. Now, fractals basically are irregular geometric objects, but they're very simple objects where the irregularity is repeated endlessly across different scales. So imagine you've got a sphere and you want to turn it into something that looks like a planet. Then you can subdivide the sphere into polygons, and keep on subdividing those polygons, which span the sphere, and introducing a little bit of irregularity at various points. And those irregularities produced quite astounding, realistic pictures, and the methods that were used, these iterative methods, really defined a new branch of geometry called fractals. It was associated with a guy called Benoit Mandelbrot, who worked at IBM in Yorktown Heights. And Mandelbrot wrote a wonderful book in '83 called The Fractal Geometry of Nature.

So we got involved in working with fractals, basically, but we got involved in working with fractals because of computer graphics, the ability to render very complex scenes and with more realistic pictures. And in doing that, because me and my colleague Paul Longley were at Cardiff in those days, in the University of Cardiff or the University of Wales Institute of Science Technology then, and Paul was a human geographer from Bristol, he did his PhD Bristol. And I had worked a bit in geography, in geographical analysis, et cetera.

And so we very quickly came across the fact that these ideas of fractals were really deeply embedded in the theory of how the world could be pictured in terms of the geometry. So, for example, typically a fractal is an object where there is a degree of irregularity that repeats endlessly across many scales. The best example is the tree. So if you look at the tree in macrocosm, you see a trunk and then the big branches, on the big branches there are little branches, and on the little branches there are more little branches, and so on ad infinitum. I can't remember the phrase right, but there's lots of clichés about this notion of ad infinitum in geometry, in this particular context. So the idea of fractals is to identify the motif, really to identify the core of how a tree grew. So, for example, the basic element was to basically split a branch into a couple of twigs. If you look at a leaf, for example, on a tree, the leaf has the structure of the tree built within it to some extent. The tree is a brilliant example. So is a coastline. How do you measure a coastline? Once you get down onto the sand and you're measuring around all the rocks and all this sort of thing. There was a famous paper in 67 in Science by Benoit Mandelbrot called How Long Is the Coastline of Britain? The answer is it's infinite, basically, but the answer actually is it depends on your scale of measurement.

So fractals really took off, and fractals basically produced irregularity over many scales. Obviously, there was the computer graphics stuff. But also it looked like the world was fractal from a hierarchical point of view. You know, go back to the 1930s and ideas about the hierarchy of cities with Christaller and so-called central place theory, go back to city size distributions with Zipf and power laws and all of this sort of stuff. All of this kind of social physics very quickly came together in terms of fractals.

So how I got into this stuff, how I got into complexity theory, too, was through notions about fractals. Fractals were these seemingly very simple rules that when replicated, according to a certain order, over different scales, actually generated very complex structures. And of course, the notion that a fractal is organised from the bottom up rather than the top down, that cities grow from the bottom up, they grow from cells that repeat themselves endlessly. If you think of a dwelling unit, for example, it repeats itself endlessly as the city gets bigger, it changes in composition, it transforms itself to some extent through time with technology and also through space, with access to space around it, in other buildings around it.

But you can envisage a theory of the evolution of cities, which starts from very simple cells and begins to move out in that way in fractal-like structure. So the instruction set, if you like, it's not quite the same as the instruction set in DNA, although there are some examples in fractals that think about things in terms of the DNA, Lindenmayer systems, all this sort of stuff, these fractals basically repeat themselves endlessly and you can see how you can think of the city in terms of cells.

So fractal geometry led to cellular development, basically. The idea of a cellular automata is that you have a set of cells and a series of instructions about how they grow. And if you keep on applying those instructions how they grow, then you can build up much bigger pictures where the motif – which might be, say, how the cells split into two like the branches of a tree – that motif is repeated endlessly. And when you actually look at the spatial structure that ultimately emerges, it looks like a big version of the little thing in that sense. So that's basically what a fractal is. The argument, of course, is quite profound in some sense because it says that the world is not really Euclidian at all. It's not a set of straight lines. It's a set of all of these irregularities.

It's not just nature. It's also things like our manufacture. One of the interesting things is the computer chip and its miniaturisation is fractal in some sense, that these things have been scaled down and the same kind of circuitry is reproduced at many different levels. So that's how we got into cellular automata and into fractals. And that led us to thinking about cities and how they grow in this sense.

Now, in this process, we didn't really exploit the analogy of genetics. We didn't particularly think about these elements which led to the development of cities in terms of cellular growth or fractal growth as being the DNA in some sense. Although looking back now, it's quite interesting to think that we could reinterpret a lot of this story through the genetic structure. Indeed, there's lots of suggestive things that have happened along the way in terms of how we actually solve problems of optimisation and so on. There are analogies with genetics, there is something called the genetic algorithms or the genetic code, which basically you have a solution to a problem, and the way you actually improve the solution to a problem with these nonlinear problems, where you can't really ensure there is an optimum, but the way you improve them is to mutate them, basically, and to combine. You get a couple of good solutions; you combine them systematically and get a slightly better solution.

So genetic programming or genetic algorithms emerged in optimisation theory, in analogy, again, to the idea of, you know, a cell mutating and partitioning in some sense. So there's work along those lines which to some extent supported these ideas. All of this stuff really is now classed under the broad concept of complexity theory in that particular context. So that's how we got into the idea of cellular stuff. I should say that about 10 years ago – possibly before Alan and yourself, Greg, had a chat about this, but not that much before because Alan Wilson himself wrote a paper on DNA in his models back roughly then – but we did hold a meeting in UCL, which actually was run by a guy who was then a vice provost at Arizona State University. It was actually called The Genetics of Cities. I must look on my computer to see if I've got anything back from those days 10 years ago. But this guy called John Fink. His name was F-I-N-K. He's something like the vice president at University of Portland in Oregon, I think, at the moment. Or he was. But he was a volcanologist originally. But he was vice-provost of research at ASU in Tempe, in Phoenix. Anyway, he held this meeting in UCL, which was quite a big meeting, actually. I mean, and a number of people, Alan, definitely was there. And a number of people who were involved in modelling and fractals and things of that sort. But also broader than that, in terms of – it wasn't just computer and modelling people and so on. It was also architects and planners to a large extent.

Now, the other thing you asked about, which I do have quite a lot to do with, is the notion about urban design and the whole idea about genetics and urban design. In fact, I was trained as an architect planner originally. So we have quite a strong interest in the visual. That's why we're interested in computer graphics, really, in some sense. But a quite strong interest in the visual. But obviously here in UCL, the Space Syntax Group, for example. Bill Hillier, of course, is departed now. But Bill in particular and Julian Hansen basically worked on a morphological view of cities, which was largely built from what you might call atomic elements, which were what they called axial lines, how far you could see the sort of space syntax that was relevant to buildings originally and corridors and so on in buildings. But then they branched out and began to apply to cities, and the cellular or the atomic element in space syntax was basically the street segment, or more generically, how far you can see in a particular space. And they built quite a strong morphological theory based on the notion that their cells were really streets.

Now, other designers, too – there was a paper in the town planning review years ago on cellular development. It was written by an urban designer. I can't remember his name now, but I know that when we were heavily into the fractal stuff, it's referenced in our book somewhere on fractals. But this guy had written quite an important paper in the 90s, I think, or maybe the 80s, on the idea of cellular growth, basically. And that was actually quite close to the idea of genetics, in some sense. It's the idea that you define the cell and the barrier around the cell and this kind of thing, and how you could reproduce the city with cells, but also, at the same time, he was interested in redevelopment as well. It wasn't just new development. It was redevelopment, regeneration of the cells.

So there's been quite a lot of very graphically, verbally appealing work on this analogy between genetics or the idea of the cell particularly, but also genetics and the notion of the evolution of cities in that particular context that – Salingaros is the guy in Texas, who's a mathematician, who's done some stuff on this sort of thing, also stuff on fractals and so on.

And so that's another dimension to all of this, which is fairly coincident to the fractal stuff, although because they tend to be less mathematically orientated, the connections are not very strong. They're in the literature, but they're not super strong. But we're all looking at the same sort of thing.

Greg Clark

Yes, and Michael, that this is a brilliant explanation and I'm very, very grateful, and I suppose where this takes us to is some of the stuff that I've seen in your published work, which is about the ability either to use the computer-based mathematical modelling or some of these more design-oriented insights to begin to use this idea of the cellular structure of the city, to begin to talk about latent capacity and capability, future shape and form, where and how certain parts or structures might replicate themselves, and ultimately what you would need to do if you wanted to either enlarge the size of a city successfully, reduce the size of the city successfully, or enable a different kind of city to emerge. Is that a fair summary of the application of this, that it starts to help you to think about the future evolution of the city and to understand what are some of the reasonable choices that might be available to you as, for example, larger numbers of people wish to live in cities. Therefore, how can we help cities to evolve to create the capacity?

Michael Batty

Yeah, let me retract one bit, in the sense that when you come to look at what people have done in terms of systematically thinking about cities, for the most part, certainly until thirty years or so ago, people thought of cities as being in equilibrium, right? But in other words, the medieval city, it doesn't change. It doesn't look like the contemporary city or the city of the mid-20th century. But nevertheless, there was a centre, there was a core, there were traffic routes, et cetera, from the edge to the core, people who lived at higher densities and so on. But much of the behaviour, even in the medieval city, was not that different from behaviour in the in the Victorian city and so on. Apart from a technological change, there was technological change, but this was really just being scaled up. So our thinking about cities was that you could model them as if they were in equilibrium.

And much of master planning, although it pertains to the future, is about cities in equilibrium. You look at Atlanta, and it's basically Milton Keynes as complete. If you look at our new town plans, they don't show the stages of evolution or development, the implementation. They show the final product. And so a lot of our thinking, most of our thinking really until comparatively recently has been almost timeless. Of course, this contradicts directly with the message of the granddaddy of urban planning in Britain, Patrick Geddes, who wrote this book, Cities in Evolution. Geddes was a biologist who never got a degree. He sat at the feet of Thomas Huxley at the Royal School of Mines, now Imperial College. He actually was an assistant here at UCL for one year in 1879. And this is where Darwin used to come. Darwin had a house on the site at UCL, not latterly because he was down at the Down House, but Darwin basically – not quite his alma mater, but his home from home, was UCL and the physiology department. And so Geddes was in that tradition, in other words, evolution and evolutionary theory. And of course, this moves on to genetics very quickly from then on. This was really all about the way biology was beginning to think about the world and how Geddes also, who was interested in cities, began to think about how cities should grow. So a lot of Geddes' writings are about how cities evolve, really. In fact, when Geddes also moved off into doing things about cities, he fell into the trap, which was almost inevitable, that when you prepare a plan, it's a master plan and it's static and so on. But throughout his life and his writings, which are pretty chaotic, he was very much involved in the idea that the city actually evolves.

And so this whole issue about equilibrium versus dynamics or time has really been there in planning as a tension since the beginning. And of course, with the development of complexity theory, fractals, all this sort of stuff, dynamics has come back onto the agenda in a big way. So the idea of cities evolving is key, I think, to a lot of complexity theory and the idea of cellular automata models, the idea that the automata contains a set of instructions that suggests how the object will transform itself and grow and decline and change and so on, is central to that kind of thinking about how cities evolve.

The big question, of course, is how can we use this to think about future cities? And of course, in some senses, that assumes that we have really quite good models of how cities function. And to some extent we don't, in the sense that we do have models about how cities grow in bits, but one of the great conundrums is that cities are so complex that at every level of hierarchy you have individuals or groups making decisions. So by and large, if you look at a photograph of London from high up, a couple of miles up or something, you look at a remotely sensed image, the structure of these cities is very clearly nobody planned them. they look like organic organisms that are growing in space. The nightlights photos of the planet are classic in that sense. You see these splodges of light, which decay as the city gets bigger to the edge, showing you the picture of the way cities have exploded in terms of growth. And they are fractal. They have dendritic structures. They look like trees basically, in some senses, filled in. And you can sort of almost see them growing. In one sense, people might think of them as being like cancers or something. But in another sense, cellular growth doesn't necessarily mean bad growth. It can mean good growth. So the whole cellular analogy is quite important in this particular sense.

And when you begin to dig into cities and as you go downscale towards the urban design scale, then you see more and more what we would consider to be conscious planning. In a way, the whole city is planned at every level in terms of rationality, of why people make decisions. But in fact, overall, at any level looking up, the city doesn't look as though it's been planned. There is a hidden hand, I suppose, which is one that we don't quite understand how it all fits together. But there is no top-down decision-making that establishes the plan for the city. Whenever we've had those – the British new towns are not a particularly good example of this, but the big cities like Brasilia are basically – you've got these highly planned structures that as soon as the control goes off, you then begin to get squatter settlements, small neighbourhoods, creating shopping centres, all of that kind of thing. I'm pretty sure in the British new towns that you've got an element of this where new things have developed spontaneously and evolved which have been against the dictates of the plan.

So one of the things I think which the fractal and complexity ideas and genetics ideas are important – one of the things that's very important is the notion that we have to be very aware of what we can plan, and we need to think intelligently about what is possible in terms of planning. So any plan development from the top down is problematic because at some point the planning has to stop. And in other words, you might plan something and implement it, and then when you look at what happens after that, you need quite strong control to keep it in the same structure. If the structures have not been designed by the people who are actually going to live in them, then that's likely to lead to a situation where once others begin to occupy them, then the mechanisms are not in place to maintain them.

I was looking at a – I don't know if you saw it, but there've been these four programs on Manchester, on BBC2, the last four weeks called Manctopia. BBC2 programs on what's been happening in central Manchester. And when I was a student there in the 1960s, when all the slums were coming down and they were building these big mega structures, which 30 years later have come down again, largely because they were built without any sense of how people might occupy them.

And the program in Manchester was very interesting because you had quite modest housing in the centre, built local authority housing, which has simply not been maintained. So it looks terrible, although it's quite solid and actually to good space standards. And they're thinking of dragging this stuff down and building high rise. But of course, when these high rises are built, then there's this whole the question of maintenance. Admittedly, many of these high rises were good, high-quality residential blocks.

But nevertheless, this notion about building so that we can maintain it really is this whole notion about we build from the bottom up. We get good structures where we build from the bottom up. And actually that resonates massively with the great sages of complexity theory, one, Christopher Alexander, right, who believes in building from the bottom up, the other. Jane Jacobs, who argued that that was the way cities should be. They were the great forerunners in our field of complexity theories. Herbert Simon too in his architecture of complexity, sciences of the artificial.

So in some senses, all I'm saying here is that in terms of future planning, then these ideas are very important, not necessarily to tell us how to plan or do things, but to tell us in some sense what are the limits of planning in some senses in that context. I don't think there's much been worked out about how this stuff might be used in some sense. It's one of the great gaps in our literature and our thinking as to how we might begin to use this sort of stuff, because it's genuinely very hard, because we tend to think in terms of large scale structures such as cities.

And then, of course, to think about planning the whole city is very problematic in terms of this notion about cities evolving from the bottom up. Really, in that sense, the notion of one of the things I think in terms of the genetics thing is this notion of the genetic code. It's very intriguing to think we might be able to unravel the code, unravel the instruction set that might pertain to cities. And bits and pieces of even in the articles I mentioned by Alan Wilson and Elizabete Silva and people, Jonathan Fink, bits and pieces on that do get towards how do we unravel the code? Really, that's the sort of $64,000 question, how can we define the code that enables us to know how cities evolve?

Greg Clark

Mike, if I may, I just wanted to come back to you and say, I think you've said some very important things in the last 10 or 15 minutes. And just to reflect back that one of them seems to me that in this whole discussion of the limitations of planning, particularly the limitations of top-down planning, part of the application then of the knowledge that you've been describing in terms of how cities evolve is, if you like, when you have to stop planning and some of the things that you might do instead.

And it seemed to me that you were saying two kinds of things. One is that you might need to plan the foundations, but in a sense, leave the buildings unfinished and allow those to be more organic. And the other thing you were saying, I think, is that there's a co-creation imperative here, that if you like, the thing that will be sustainable is not the thing that is planned top-down, but the thing that is co-created bottom-up.

And there are clearly implications in this for urban regeneration schemes, for major infrastructure projects, for the creation of new cities and new towns, for the development of new districts within established cities. There are lots of, as it were, planning philosophy ideas there, are there not?

Michael Batty

Absolutely. I think this is absolutely central, this notion about organically growing cities. This is not to say that we shouldn't necessarily produce occasionally appropriate megastructures and so on. I think those have their place in some sense, but by and large, to build a sustainable city, it has to develop organically. It has to give opportunities for those who live in it and want to maintain it, those opportunities to actually keep it as it is or make it better in some sense in this particular context. And that probably means that the emphasis on community is all important really, in that sense, that communities have to be built which are resilient enough and in and of themselves do change and evolve.

But the structures that they build, as it were, for living in, et cetera, they too have to evolve in some sense. And so it's a bit like saying, if you put some into a council house and there are rules that say they can't paint the front door, this is a recipe for disaster, basically, because the odds are that the people who own the council housing won't have enough money to be able to paint the front door. So we have rules, and an awful lot of rules in public housing in Britain were based on that notion. Of course, the structures themselves were not really such that you could do a lot with them. If you lived in Parkhill in Sheffield or somewhere like that, or Hume, those flats that only lasted about 20, 30 years, and if you lived in that sort of it was almost impossible as an individual to do anything about the structure. So once things began to decay in terms of the communal areas and the lift shafts and all that sort of thing, it's impossible for the community to do anything, really. So Jane Jacobs says all this in her book, a very perceptive, prescient book, that you've got to adapt the city to what people can actually do.

Greg Clark

Yes. And I suppose by implications, if you create structures that are rigid, you're likely to lead to a situation where they become socially rejected and some kind of social contract or social consensus will break down because the structures are unable to move where the people may wish or want to go. And there's one other question I wanted to ask you, which picks up on some of the stuff I've read that you've co-authored with Geoffrey West.

I think it seems to me there's another application of what you're saying about evolutionary theory and cities and complexity theory, which is that you've begun to observe – and I don't know whether this is part of the fractals analysis or whether it's your other modelling – that, if you like, there are certain repeatable patterns in terms of ratios and geometries between things like transport infrastructure, certain kinds of amenities, certain kinds of feasible densities, certain kinds of services that may be required, and that if you like, you can understand very easily the limitations of sprawl, for example, or that you can understand quite well how do you facilitate high-quality density, as it were. Can you say a little bit about that? Because it seems to me that's a very important application of the sort of the theoretical approach that you've been describing.

Michael Batty

Yeah, I mean, the question about scale – in other words, certain things happen at certain scales – is very much resonant with notions about fractals, basically. The best example, which doesn't really relate, originally at least, to fractals, is the notion of what we call central place theory, that in the 1930s Walter Christaller in Germany basically wrote this book about how you could see the world as being a hierarchy of different city sizes. And the bigger the city, the bigger the hinterland. I mean, these are very obvious ideas. And you would have one big city and two next to the same sort of level cities, down to four cities below that, and eight cities, and so on. There would be a hierarchy of city sizes, meaning that you can only afford in a competitive society to have one big thing. So, if you look at our distribution of cities by city size, you have a very small number of really big cities and a very, very large number of small cities.

And to be a big city, you have to be a small city first. There's the birth and death process of cities. But generally speaking, we have many, many more small cities than we do big cities. And it's the nature of the growth process really to some extent. And so that's very much a fractal idea, really, in some sense, not so much in terms of the geometry, but in terms of the numbers basically of things that you've got and the ability to sustain them in some sense. So you can build a large number of small things and maintain them, but you can't build a very large number of big things in that sense. And in any case, the big thing has to be a small thing.

So essentially these relationships are called power laws. And power laws basically simply suggest that if you draw a frequency distribution, a graph of the numbers of big cities, you have a very small number of big cities and a very large number of little cities. So you have a kind of non-linear sort of relationship between them, if you have size of city on the vertical axis and the number of cities on the horizontal axis or the other way round, effectively.

So in other words, this is the sort of stuff that pertains very much to fractals, thanks very much to social physics to some extent. And of course, it relates a lot to the notion that what happens as the city gets bigger in some sense – so as cities get bigger, they change in terms of the functions. And the argument has been that the bigger the city, the more than proportionate its attraction to important and innovative things and things that generate great wealth. So the implication is that the bigger the city, the more than proportionately it will grow in terms of wealth. So all other things being equal, if I have the choice between living in London or Manchester, I'm likely to get more rewards in a monetary sense, if I live in London than I do in Manchester, say.

Now, because this is quite a contestable argument really to some extent - it's actually a very old argument. It goes back to Marshall, Alfred Marshall, the man who coined the idea of urban agglomerations. So as you get bigger and bigger cities, you get more and more economies of scale, basically in that sense. Of course, the other corollary to that is that you also get more diseconomies of scale. So although you may be able to optimise your outcome if you live in London here, for example, you actually have a lot of costs that people who don't live in London don't have. And this balance between economies and diseconomies is really all-important.

The work that Geoff West has done, and Luis Bettencourt too – Geoff's still at Santa Fe, but Luis is at the University Chicago now – but what they did, they wrote a very influential paper about 13 or 14 years ago about when they looked at American cities, they found that the income per capita increased more than proportionately as the city got bigger. And there were a number of other functions in cities that also increased more than proportionately or less than proportionately. More than proportionately you've got incomes, you've got innovations in terms of the creative city, you've got, let's see, pollution, possibly. You've got crime. Now that's interesting, you get more than proportionate amounts of crime as cities get bigger, which is the downside to this economy. You also got increasingly small amounts of things like infrastructure, like road space, petrol stations and so on as cities got bigger for the simple reason that if you lived out in the country in small places, you had to drive a long way to get to a petrol station.

So in other words, there were some of the infrastructure stuff. You got economies of scale with respect to the development of road systems. You got economies of scale with respect to the development of wealthy people and so on and so forth. But also at the same time, you got an increasing number of poor people. But the poor people were so poor compared to the rich people that when you looked at the aggregate, the rich people win out. The total amount of income increases per capita.

Greg Clark

So you still got more than proportionate per capita income increases.

Michael Batty

Exactly. And in other words, you may have more than proportionate poor people, but the more than proportionate rich people, when you take the average income, it looks as though the city is getting richer in that sense. And of course, if you then factor in a load of these other costs.

Now, the controversy in the Geoff West, Luis Bettencourt's stuff is based on the notion that a lot of people have said it depends where you define the city, how you define it and how you define the boundaries. So, for example, where is the boundary of London, basically? Now, there are many urban geographers – some like Peter Wood at UCL – who have argued for years that Britain is one big city, really, in a sense. It's highly centralised, and arguably, distance-wise, that might be the case. A very controversial issue, generally speaking, in terms of where do you draw the boundary? The issue about if you look at income, you've got to measure what kind of income you mean. But one hell of a lot of income that's generated here in the square mile, for example, really does not originate in the square mile. It originates in the global economy somewhere. So it's a very tricky issue, this question of scale. But nevertheless, it's very important because it's an important point about thinking about how big should the city be in that sense. And it's very relevant at the present time, of course, with the pandemic and so on.

But this is really what Geoff and his colleagues have been saying. And we've done a little bit of work on this. It's not easy to verify his hypothesis about increasingly wealthy cities as they get bigger in the UK. And I think there's a lot of reasons for that which really relate to regional policy to some extent, which has been going on now for 50, 70 years or more, a whole range of different things of that sort on this notion about where does London end and the rest begin and so on. But of course, in North America, you've got very, very distinct – you can't really compare the distribution of cities in North America with the distribution of cities in Britain.

Greg Clark

No. You've got a very large landmass as well.

Michael Batty

Exactly.

Caitlin Morrissey

This has been absolutely fascinating, and I do just have two more questions for you, if that's all right? The first question is, what are the limitations of this idea about the DNA of cities and what does it leave out about the way that cities evolve?

Michael Batty

Limitations. well, the biggest issue is actually defining what we mean by the DNA. I think that at one level, it's quite a straightforward and useful thing to think about the city divided into small units, which we might call cells, which have a degree of similarity. I think that's the first point. The question is whether we can do that. There is still a question mark over how you might divide the city into cells that are sufficiently similar in one sense to be called cells and sufficiently dissimilar to actually show how these cells are actually evolving, basically.

But generally speaking, probably – and there's the scale question here. I mean, what scale do we actually do these things at, what spatial scale? And in some senses that is a major issue. In other words, defining the cell. OK, let's assume we can get over that. And I think in general, people do work at different spatial scales and they have different cellular representations at different scales. Of course, that in and of itself is another thing, that whereas in the human body, we're talking about cells that are similar between many individuals, when we talk about cities and the way we articulate them, different sizes of cities at different scales all can be defined in terms of cells, but the cells will actually differ. So there is a limitation in the sense that in the human body we've got much more coherence and similarity, homogeneity, you might almost say, than in the context of cities. There's much more variability in cities, and that variability means that our applicability of genetics, of genetic ideas is more problematic, really. To search for some standard set of things that might define cells, when it comes to DNA, the actual instruction sets of how the cells change, then how they change, I think again depends on the perspective or articulation of functions in the city that one is interested in.

Having said that, this is really the $64,000 question, right? That everybody has a slightly different perception of what a city is, and generally speaking, how we might apply any theory, not just the idea of DNA, but any theories of the city will depend upon what that perception is. So, for example, I think of the city as urban designers do in terms of small areas in some sense. Let me think about the census geography as output areas, but small areas, the city blocks. Okay, city blocks, that's an easy one. We think about the city as having a sort of fabric at the level of the city block. Then the sort of rules I would have for changing those blocks and what they were would be somewhat different, I think, because at a higher scale, at the scale of wards or output areas and so on, where you might have five thousand people in an area, then the nature of the behaviour of what was actually happening would be different. So at different spatial scales, you get different sets of rules basically. Now it may be possible to develop a fairly robust distinction between spatial scales, but we don't have much experience of doing that. We'd have to have a lot more work going on in thinking about applying these ideas at different spatial scales in different cities, really.

So the limitations are that the nature of the city itself is sufficiently different from the human genome, as it were, to make the idea of the DNA metaphor or analogy problematic. Not necessarily irrelevant, but problematic in the sense that we might find two different groups of people, all with the same feelings about complexity and no worries, no hang ups about how we might mathematise or systematise our thinking. There might be a great of agreement at that level. But the fact that they thought of cities somewhat differently, thinking of them at the metropolitan level, like Greater London in the southeast versus the rest of the country and so on, whereas the same group of people might be interested in in looking at how the cities evolve. It's a very more local level in terms of city blocks and districts and so on. So that's one major issue in terms of the limitation.

The other issue I think I began with to some extent by saying that the elements of DNA, the elements of genetics, if you like, where you have a cell and a nucleus and then you have a set of instructions, the DNA, that gets bound into the cell, and when the cell transforms or changes, you get – or you get genes which spin off from the DNA within the cell, and then you get the transformation of the cell, et cetera, where these instruction sets sort of get transposed to other cells, where your DNA from, the one parent comes to the other and so on – there really isn't anything quite like that in cities. There's plenty of transfer between one place and another, one cell and another in that sense. But there's nothing which is as simple, really, in a way, as the notion about two places combining in some sense to create a parent or a third place in that sense. There may be ways of twisting and thinking about cities in that sense. But generally speaking, I've not really seen anybody. So this, in fact, has limited the DNA analogy.

Most of the writing about it is the notion that it's very suggestive of how we might be able to think about things. And none of this means that it's irrelevant. In fact, it probably means we need to work harder to think about how it might be made more relevant. I think we need to know a lot more about the DNA. I've never really met anybody in our field that is sufficiently good a biologist or geneticist to know how this model might be applied. I think where people have tried to develop it, they've really come up against this problem that they can't conceive of how the city itself would be cast into the same sort of model or same sort of template as the genetic code really in that sense. And so everyone falls back on the idea of being very suggestive. We're looking for the code. We need to find out the code so that we know how the city changes basically in that sense. So that would be my general reaction to that question about limitations, I think.

Caitlin Morrissey

And the final question we have is if we would have asked you the right question, was there anything else that you would have wanted to say about the DNA of cities?

Michael Batty

Well, it would be very useful for somebody to collect together the material where people had referenced DNA of cities. In other words, it would be very interesting for somebody to review the field really in some sense. I don't think it's very big, actually, in terms of numbers of people writing about it. There's quite a lot of suggestive stuff out there on the web, basically, and that's fine, basically.

But taking it a little bit further is the problematic issue. How do we take it further to the point where the analogy becomes useful? And of course, there are all these other areas that impinge on it. So the evolution of cities is very central to this. Regeneration, evolution, transformation, all of this sort of stuff is quite germane, I think, to the development and that sort of stuff could be bound in a bit more with these ideas.