Bobcaygeon / tags / complexity

Tagged with “complexity” (1)

  1. Episode 5: Geoffrey West on Networks, Scaling, and the Pace of Life – Sean Carroll

    If you scale up an animal to twice its height, keeping everything else proportionate, its volume and weight become eight times as much. Such a scaling relation was used by J.B.S. Haldane in his famous essay, “On Being the Right Size,” to help explain certain features of living organisms. But scaling relations go much deeper than that, and they are often much more subtle than the volume going as the cube of the length. Geoffrey West is a particle physicist turned complexity theorist, who studies how features from metabolism to lifespan change as we adjust the size of an organism — or of other complex systems, from cities to computer networks. His insights have important implications for innovation, sustainability, and the best ways to organize life here on Earth.

    Geoffrey West received his Ph.D. in physics from Stanford University. He is currently a Distinguished Professor at the Santa Fe Institute, where he served as President from 2005 to 2009. He has been listed as one of Time magazine’s 100 most influential people in the world. He is the author of Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies.

    Home page

    Wikipedia page

    Amazon page

    TED talk on “The Surprising Math of Cities and Corporations“

    Google Scholar publications

    Download Episode

    Click to Show Episode Transcript

    Click above to close.

    0:00:00 Sean Carroll: Hello everybody, and welcome to the Mindscape Podcast. I’m your host, Sean Carroll, and if you’re familiar with my book “The Big Picture” or any of the various talks I’ve given on that book, you’ll know that one of my favorite factoids is that the average human lifespan is three billion heartbeats. That’s not a very profound fact if you just take the fact that the average human being lives for about 75 years, and do your dimensional analysis to convert from years to heartbeats, the number works out to be about three billion for a typical human being stretching from birth to death.

    0:00:34 SC: But it’s an interesting fact, because it brings home in a slightly more vivid way how short our life is. Three billion is a big number, but it’s not unimaginably big, and unlike years, heartbeats are going by all the time. You’ve squandered several of your heartbeats already listening to me talk right here. And I’ve learned this fact about the three billion heartbeats from today’s guest, Dr. Geoffrey West, who’s a distinguished professor at the Santa Fe Institute. And it’s the context of a much more profound fact about biological organisms here on earth. If you take any particular kind of organism, let’s say, mammals because human beings are mammals, they come in all shapes and sizes. There’s tiny little mice, there’s big old blue whales or elephants, but there are relationships between the size of an animal in mass, for example, the number of kilograms the thing has, and other biological facts such as how long it lives. Bigger animals, whales and elephants, live for much longer than tinier things like mice or squirrels.

    0:01:38 SC: Meanwhile, there’s another relationship between your size and your heart rate. Big animals like whales and elephants have very slow heartbeats. Tiny animals have very rapid heartbeats, and you can see where this is going. These two facts exactly cancel out. The average number of heartbeats for mammals, is approximately the same for tiny little mice, or big old blue whales, or elephants. It’s not an exact relationship. In fact, the number for a typical mammal works out not to be three billion but one and a half billion which maybe you could argue is roughly what we had, we human beings, back in the state of nature before we had pasteurized milk and Obamacare and things like that. But the point is that something is going on that goes beyond mere biology, there’s some reason why there’s a relationship between how fast your heart beats, how massive you are, and how long you live.

    0:02:34 SC: That’s what got today’s guest, Geoffrey West, interested in biology, networks, and complex systems. He started his academic life as a particle physicist, but he read about these scaling relations, and he realized from his physics point of view, no one understood them. No one knew why things were like that. So he and his collaborators developed a theory that explains why you get this relationship. As an animal gets bigger, it lives longer, but its heart slows down; the pace of life is slower for larger animals. These days he’s extending that analysis not just to individual animals, but to cities or cultures, or other kinds of networks that fill our daily lives today. This kind of analysis is absolutely crucial for sustainability, for thinking about how we live in the world, for choosing how to manage our life here on earth. Geoffrey West is the former president of the Santa Fe Institute, and he’s the author of a wonderful recent book called “Scale: The Universal Laws of Growth, Innovation, Sustainability and the Pace of Life in Organisms, Cites, Economies and Companies.” It’s not the most elegant title, I’ll give you that, but it’s an extremely important and hopefully influential book that helps us understand the world we live in. So, let’s go.


    0:04:10 SC: Geoffrey West, welcome to the podcast.

    0:04:12 Geoffrey West: Hey, nice to be here, Sean. Thank you for inviting me.

    0:04:14 SC: So I have to ask, when you’re on an airplane going to a conference, traveling around the world, and you find yourself sitting next to an inquisitive type and they say, “So, what do you do for a living?” [laughter] What is your answer to that kind of question?

    0:04:30 GW: Oh goodness me, that’s a tough one. And it always stops me in my tracks. But because I’m slightly misanthropic and, but what do I say? I think I always lead off pretty much by saying, “I’m a physicist.” And then I quickly say, “I’m a physicist, but I work now a lot, and questions, challenges that are considered outside of usual physics and I’ve done quite a lot of work in, what I would consider fundamental questions in biology, and now about cities, companies, and I’m particularly interested in the whole question of global sustainability.”

    0:05:19 SC: Right.

    0:05:19 GW: So I sort of do it in that, I mean maybe not quite as linearly, as that, but effectively.

    0:05:25 SC: But now, in your youth, you were more or less mainstream. Theoretically…

    0:05:29 GW: Absolutely.

    0:05:30 SC: So what kinds of things did you work on then, and what happened?

    0:05:33 GW: So yeah, so most of my career, meaning the first 30-odd-years, I did definitely what you would call mainstream particle physics. Even entering it when I would say, the kinds of things you work on and you’ve made your name on were considered way out there… [laughter] They weren’t questions a real physicist should be answering or asking.

    0:06:00 SC: Right. Cosmology’s dark era.

    0:06:01 GW: Yeah yeah it was like come on, you know. And I think one of the, by the way just tangentially, one of the great things that has happened in physics is that we do ask those questions and we address them seriously and it’s now developed into its own thing, and it’s a profound influence. But back then, I was the mainstream physicist working on… Well I entered it very fortunately, at a really opportune moment because these famous experiments which got the Nobel prize at Stanford, on which eventually we interpreted as discovering quarks, were taking place, the results were just coming out, and I had been sort of…

    0:06:52 SC: This is the early ’70s.

    0:06:54 GW: Well they were the late ’60s actually, late ’60s. I got my PhD in ’66, and those, the accelerator at Stanford was just being completed and the first experiments were being performed and the results that changed everything, which were results on an experiment that at the time was thought of as mundane and uninteresting appeared, and they were quite surprising, and as I say eventually they were interpreted as the evidence for quarks and that was a very exciting period, as one tried to interpret those experiments, try to formulate models and then theories and, ultimately, the evolution towards something called Quantum Chromodynamics.

    0:07:46 SC: QCD.

    0:07:46 GW: QCD. The theory of the strong interactions and that was very exciting.

    0:07:52 SC: And did you feel that this is what life was going to be like? Every few years, you would discover a new layer of structure, of matter, new fundamental laws?

    0:08:00 GW: Absolutely. No, in fact I would say, during that period, from probably ’68-’70 onwards, through the ’70s into the early ’80s, we were kind of spoiled because every year there was a new fantastic discovery that either… Or confirmation of something, and it was just a marvelous period, and it culminated in the development of the so-called Standard Model where we see some part of Grand Unification, or at least we saw that you could contemplate Grand Unification of the electromagnetism with the strong forces and so on. And that was just immensely exciting and then that led to this naivety that it would only be a few more years when we could get gravity into the picture.

    0:09:01 GW: As I say, it really was a period of immense excitement, but a period of being spoiled as one does. It reminds me a bit, it actually is sort of interesting when I look back on it, because it also had some of the flavor of the ’60s and ’70s in society. You know, the emergence from the ’50s and early ’60s, and kind of the image of suburban America with your 2.4 children. The image of that we all had, to suddenly the psychedelic revolution, the Vietnam War, and what the demonstrations and anti-war movement brought, the Civil Rights movement.

    0:09:47 SC: But then we hit the Reagan era.

    0:09:48 GW: And then we hit, exactly, and so it is that in physics, we hit not because of a Ronald Reagan or because there was a vote, but because it turns out that nature was not quite as forthcoming as we thought or we weren’t smart enough despite what I do think was, even though I’ve been quite critical of it, I think an extraordinary development and that is of String theory.

    0:10:13 SC: Right.

    0:10:15 GW: It was a marvelous leap.

    0:10:18 SC: But you did mention discoveries and/or confirmations, and there was a shift. So after the mid to late ’70s, there weren’t a lot of more surprises coming our way. We were confirming things that we had models that explained, and indeed it’s sort of the dirty little secret of particle physics, there haven’t been any surprising…

    0:10:37 GW: No! Exactly! Exactly. There’s been nothing that is, sort of… In fact the big things, as you know better than I, of gravitational waves, of the Higgs particle and so on, are confirmations of things that in one case were predicted. I know, whatever, 70 years ago or whatever or longer actually, and then the other 30, 40 years ago or whatever it’s been. But a long time. But I mean very exciting that we have confirmed those, but also, especially in the case of the Higgs, it really in some ways, it’s like the end of something.

    0:11:24 SC: That’s right.

    0:11:24 GW: Rather than, I mean gravitational waves I think you could see it is the end of something in a certain way. But it’s also the beginning of something.

    0:11:32 SC: For astronomy it’s certainly the beginning of something.

    0:11:33 GW: It is, exactly. And that’s the thing, it’s now even so that we can use it as a tool again. Whereas the Higgs is sort of putting a full stop, a period at the end of something. It’s now done. And the big questions that have been there since the mid-to-late ’70s remain. A: How does gravity fit? But even within Grand Unified, we’re left with all these parameters and where do they come… We’re unified in a certain sense, but in the sense that a physicist would like, ultimately we’re still a long way away.

    0:12:11 SC: No one thinks it’s the right final theory of everything, what we have right now, but it’s compatible with all the data. This presumably played a role in your choice to become a less mainstream physicist.

    0:12:22 GW: Yes. Well, it did in the following sense, that it was frustrating as time went on, but also, we suddenly developed this idea putting all our eggs into the Superconducting Super Collider basket. And with the idea that with this longer reach of energy, it would reveal something exciting, new. It would, in fact, confirm the Higgs, of course but…

    0:12:52 SC: And this was to be sort of the United States’ version of the Large Hadron Collider…

    0:12:56 GW: Exactly.

    0:12:57 SC: But bigger and better, and maybe even sooner, had it all come to be.

    0:13:01 GW: Absolutely. And in fact, one of the great ironies again, maybe you’d use the word, “dirty little secret” this is also a sort of dirty little secret, I think, is that in the days in which people were promoting the SSC, you know, to get the money for it and just to drum up the general interest. Of course, CERN, the Europeans had responded by saying “We’re gonna make this Large Hadron Collider” which would be almost an order of magnitude less in energy. And the “dirty little secret” was that the US physics community continually bad mouthed the LHC. It was like, “Oh it’s useless. There is no reason to believe whatsoever they can discover anything.” “The reach just isn’t far enough. You’ve certainly gotta go to, whatever it was, 12, 15 or even… Ultimately 20 TeV.” And the “dirty little secret” is in the context of, now that the LHC is the only game in town, and we are involved in it, and it discovered the Higgs, all we could do is talk how fantastic it is, and what a great idea. [laughter] So, physicists are also prone to emotions and politics and all the rest.

    0:14:22 SC: They’re human beings.

    0:14:22 GW: They’re human beings. So I’m not blaming anyone, but it is, but we sometimes, certainly in those days, I would say, I think the high energy physics community was, of course, very arrogant because it felt it was doing the most fundamental, and therefore the most important science on the planet, but also, that we were immune from the human foibles such as this. And I think, both of those things have been damaged and destroyed… Rightfully, I think. I think we were overly arrogant, overly self-involved, self-centered, it ended with calling String theory, the theory of everything. Which already connotes a certain attitude towards everything else, right?


    0:15:13 GW: So, and I think that’s been, in a certain sense, that’s been healthy for the field actually, to be honest.

    0:15:21 SC: Sorry, the ‘that’, does it mean…

    0:15:22 GW: No, ‘that’ meaning this extraordinary intellectual narcissism, coupled with arrogance. Which, I think, might have served us well for quite a long while. Not saying that was necessary but…

    0:15:41 SC: But not questioning yourself, does motivate you to…

    0:15:43 GW: Yes, it does. And especially when you think you’re doing the most exciting fundamental physics that has universal applicability and is the meaning of life, kind of thing.

    0:15:55 SC: Yeah, that’s right.

    0:15:56 GW: And that’s very exciting. And that was mostly unsaid part of the culture.

    0:16:03 SC: But when the Superconducting Super Collider was cancelled by Congress in the 1990s, so that affected your…

    0:16:08 GW: That certainly affected me, yes it did. Yeah, it affected me for obvious reasons, but it also, because I was at Los Alamos at the time, and we had some significant involvement in building one of the detectors with, in fact, led by Barry Barish from Caltech…

    0:16:31 SC: My Caltech colleague.

    0:16:31 GW: Your Caltech colleague who, of course, got the Nobel Prize for the LIGO experiment. But we were heavily involved in that. And I was the theorist, I wasn’t directly heavily involved, but that was part of our program. But also, I’ve gone off on a slight tangent here, there was another phenomenon. So, I was in my 50s at the time and I come from a line of short-lived males.

    0:17:01 SC: Ah. [laughter]

    0:17:05 GW: My father died at 61, my grandfather at 57, and so on back. We’re all… None of us, the male line doesn’t live very long, it turns out. And for different reasons, by the way, which is interesting of itself. But, the reason I say that is because I grew up with the idea that it was exceedingly unlikely, or rather, you expect to die at about age 60.

    0:17:36 SC: Wow.

    0:17:36 GW: And here I was, you know, I don’t know what it was, 53, 54 or maybe… And I realized, my God, we’ve had the death of the SSC, I’m 54, 55, whatever it was at the time, and “My God,” I probably only have five years…

    0:17:52 SC: Lots of stretching.

    0:17:52 GW: Maybe stretch it 10 years, and wow, that’s… When I should start thinking about what I’m gonna do when I grow up kind of thing. And, now the SSC is gone, this has a big psychological effect… But another thing was happening. The death of the SSC was driven by, to some extent, by a big anti-science movement in the US, which comes up every once in a while. But in particular, it was an anti-physics one, and even more particular, it was an anti-high energy physics one. So that it was a very peculiar situation that even our colleagues in other parts of physics were not supportive. And, in fact, they had this mistaken idea that if they killed the SSC, they would all be rich kind of image, which turned out to be completely untrue.

    0:18:50 SC: To be fair, the SSC would have been very expensive…

    0:18:52 GW: Of course.

    0:18:52 SC: And had all that money going to the rest of physics, they would have been rich but that never… This never would happen.

    0:18:58 GW: No, it was a humongous amount of money on the scale of a science experiment, no question, and there were, obviously, questions about its viability, what it would actually do it and so on… All kinds of good questions. But nevertheless, okay, there was this anti… Particular anti-high energy physics. But one of the things I used to hear both at Los Alamos, which, after all, is a national lab with huge numbers of activities going from the weapons program, all the way through to the multiple areas, particularly, the physical sciences. But I also heard it in the holes of the of Department Energy, which were the funding agency for the SSC, was this famous statement, “Physics was the science of the 19th and 20th centuries. Biology is the science of the 21st century.” And the corollary, which was usually not said, but I did hear it said, was, “Therefore, no need to do any more fundamental physics. We know all the physics we need to know.” That was…

    0:20:09 SC: That was said very explicitly.

    0:20:12 GW: Very explicitly. And that really threw me. And so, I reacted emotionally to the idea that… Well, first of all, on reflection, it was obvious. Biology was gonna be a major science of the 21st Century. No one could doubt that. It was clear. It was poised for that.

    0:20:31 SC: And if your question had been, “Do we know all the fundamental particle physics we need to do biology and chemistry?” Then the answer is, “Yes.”

    0:20:39 GW: Yes.

    0:20:40 SC: There are other kinds of physics.

    0:20:41 GW: Absolutely. I understood that.

    0:20:42 SC: String Theory or Grand Unification will have no impact on biology.

    0:20:46 GW: No impact. So this is one of the… We should discuss that, because I think that’s… It remains an issue. Why are we doing things that have in any way that we could immediately conceive anyway, any foreseeable influence on betterment of human life on the planet, making America great again or whatever. In fact, well, I’d like… Very much like to come back to that.

    0:21:10 SC: Okay.

    0:21:11 GW: But along more personal lines, I was… I reacted, A, to the idea that that’s nonsense. You know, that’s really crazy that you gotta support all the physics and you gotta have people think about fundamental questions. If we are to address fundamental questions in biology. That’s sort of part of the culture. And more specifically, I reacted by saying that, if biology were a real science [laughter] It would be… You know, you’d have equations and principles and you’d be able to mathematize things. I mean, all very well. We all know the Principle of Natural Selection. Darwin’s contribution was fantastic, but except in a limited way, it doesn’t predict the kinds of things we in physics would think you would need to predict, if it were a complete theory.

    0:22:14 SC: You would want a curve that you could fit get data to and see how beautiful your prediction is.

    0:22:18 GW: Exactly. And in fact, I used to say, very, very sarcastically, “If you had a real theory, then you could predict that they should be human beings.” I mean, which is taking it to an extreme. But… So I would push back with that at various meetings and discussions. And then I started to think, “My God, maybe I should take that seriously.” Biology really does need… What I would say is biology needs not just the techniques that physics uses, the mathematical techniques, but equally and possibly even more important, it needs to integrate in a way of thinking, a certain culture, which I… And I must tell you this was out of this arrogance of the high energy physicists, and also out of ignorance of biology. So it was really emotional. You know, I mean…

    0:23:15 SC: A perfect storm, really.

    0:23:16 GW: Perfect storm for disaster. But then I started thinking about it, and I combined these two things. The fact that maybe I was gonna die soon, the SSC is dead. And they’re telling us that physics should be dead. The kind of physics I’m excited about. And we should all be doing biology. And I thought about that. I thought, “You know, I wonder if biology were a science, like physics, there ought to be, in a biology book, a calculation of why it is that my life span… ” Even though I’m only gonna live to 60, or 65, I thought at that time, “Even conceivably I wouldn’t live to a 100.” Where does the 100 years come from? So I started reading biology books.

    0:24:08 SC: So you’re worried not about why 60, but why not a second or a millennium?

    0:24:13 GW: Yeah. So, where does the scale… Where does the overall scale… That’s the physicist way of thinking. Not just the mechanism, what is the mechanism that’s leading through aging to mortality, but what sets the scale of aging, of lifespan, of the 100 years? So I started reading, and I went to the libraries and I had a great time studying the literature, because it was easy to read, because it turned out to my amazement, that the question of mortality and even aging is, it was then a complete back water really relative to most of the other things that you think about. And you can… And a metric of that is the following.

    0:25:03 GW: I started looking at these big fat biology textbooks, that they use in undergraduate biology classes. They cover all of biology and they were very useful by the way, in my own education, just obviously learning things that I had not been educated about. But I’d look in those, and I quickly discovered that I must have read at least half a dozen, maybe more. And I discovered sure, there’s a chapter on metabolism, a chapter on growth, there’s a chapter on reproduction, on genes, and even ecology and so on. Nothing on mortality or aging. You could look in the index. Most of them wouldn’t even mention it. And I thought, “This is extraordinary.” When you think about it, it’s the second most important event in an organism’s life.

    0:25:54 SC: Yeah.

    0:25:55 GW: It’s birth and death, and there’s nothing about death, and I was absolutely shocked at that. And then I discovered as I say reading that, and it was fairly easy to read the literature, because there was not much technical stuff having been done. It was stuff that you only had to know, sort of freshman biology to be able to follow it, and there was nothing quantitative, almost nothing. There were survival curves and so on, but…

    0:26:28 SC: I remember, I invited biologist Bonnie Bassler to give a colloquium in the Caltech Physics Department, and she talked about bacteria and quorum sensing and the students were blown away, because they were pounding the… Our graduate students in physics were pounding their heads against these problems, that they really needed to work hard just to ask a question that we didn’t know the answer to. And in biology like, I don’t know the answer to half a dozen questions that you think up over the afternoon. Right?

    0:26:57 GW: Sure, sure. Exactly. So it was quite different. So anyway, I started in the evenings sort of speak, or when I was stuck on the physics I was doing, which was very easy to be stuck on, because I was still doing string theory, or being slightly depressed about the SSC, I would work on this problem. I’d think about it, I’ve read, as I said, I’ve a lot of the literature and I started thinking about it, and that caught me… And one of the things I quickly discovered in the literature, were these remarkable scaling laws. And because, in looking at the literature for longevity, I learned that there was an approximate scaling law for longevity as a function of size, function of the mass of an organism, and it was relatively simple one, even though there was a lot of variation in the… A lot of fluct… Noise in the data. But…

    0:27:56 SC: Sure. Of course. How should we think about what a scaling law is?

    0:27:58 GW: Yeah. So let’s talk about that, because I wanna… That’s a good point of departure. So a scaling law in its most simple form is, you take any system and you ask what happens if I increase all of its lengths by a certain parameter. Double its size, triple its size, what happens? So the simplest obviously is, if you take a rectangle and you double the size of each side, the area doesn’t double, it goes up by a factor of two times two, which is four. So that’s very trivial and the volume of a similar object goes by a factor of eight, two times, two times, two. That’s the simplest form of of scaling, a scaling law. It’s one case a square and the other case a cube.

    0:28:43 GW: So generalizing that, one can then ask about… Let’s just go immediately to biology. If I measure some characteristic of an organism, and it could be something as fundamental, which is what I wanna get into, as metabolic rate. How much energy, how much food, if you like does it need each day to stay alive, how did the 2000 food calories, roughly speaking, that we need, how does that scale from the smallest mammal… Let’s just stay with mammals, the smallest mammal, to the blue whale? Is there some regularity? That was the thing that I also learned about, that these scaling laws and in particular, the scaling of metabolic rate had already been discovered. People had collected data… Well, a man named Max Kleiber originally had collected this in the ’30s, and discovered an extraordinary regularity, that it was incredibly simple scaling law, which we call a power law, which… I’ll say it in English and then I’ll say, and I’ll translate it.

    0:29:55 GW: So the scaling law is as a function of mass, it goes to the three-quarters power of its mass which means…

    0:30:04 SC: What goes as the three-quarter…

    0:30:06 GW: I’m sorry, the metabolic rate.

    0:30:07 SC: The metabolic rate. So the… Your heart rate…

    0:30:10 GW: No, just how much food you need each day. Let’s stay with that first. That scales with the three-quarters power of mass, that’s the way you say it mathematically. Three-quarters power of mass means that you cube the mass that’s the three, and the quarter means you take the square root twice. So it’s a very bizarre law from that viewpoint.

    0:30:37 SC: Well, at least it’s saying that bigger things need more food but less per gram.

    0:30:42 GW: Less per gram and systematically, so the thing that surprised me was that it was so simple, mathematically simple, and also that there was a law anyway, that any law should exist because we have this notion that natural selection invokes the idea of random processes within an environment. And that any characteristic of an organism, whatever it is including the organism itself, but also it’s the nature of its cells, the nature of its genes have a unique historical history and they’re historically contingent. It depends on what’s happened in the past and…

    0:31:28 SC: I mean, biologists love to show us the diversity of life with all these different things.

    0:31:32 GW: Absolutely, that’s their big thing, that’s Darwin, that’s their big thing and that’s why they often argue physics and mathematics has actually nothing to do with biology because there aren’t any simple things like that. And here was this… A law about maybe the most fundamental quantity in biology, how much food do you need to stay alive? And it was showing extreme regularity. And whereas as I say, from a naive natural selection viewpoint, you would have expected if you plotted on a graph, metabolic rate on the vertical axis versus size on the horizontal axis, the points would be sort of all over the graph reflecting the historical contingency of an evolutionary history of each organism.

    0:32:23 SC: Yeah, why shouldn’t two mammals of the same body mass have very different metabolisms because they had different mechanisms that evolution gave them.

    0:32:30 GW: Exactly, so this was pretty amazing to me, but what was even more amazing was that, if you looked at any physiological characteristic that could be measured or any life history events such as how long you live, how long you take to mature, the rate at which you grow, with all these kinds of things, they also had a very similar, very simple regular behavior. And as I say, just to emphasize again, in marked contrast to the naivety that we have about natural selection. Furthermore, and this was critical from a physicist viewpoint, the… What we call the exponent, the three-quarters in metabolic rate was repeated across all of these different characteristics. So…

    0:33:22 SC: For totally different quantities.

    0:33:24 GW: For different quantities like…

    0:33:24 SC: They are asking questions about it.

    0:33:25 GW: Some as mundane if you like, is heart rate, some as profound really as life span that we talked about earlier, but things like the length of your aorta, something like that, or the number of leaves on a tree as a function. But so I learnt, and I was very fortunate at the time, that a few years earlier, four books had come out at pretty much the same time summarizing all of this. So there must be anywhere from 50 to 100 of self-scaling laws, depending on what you wanna call them. And it had been before the Second World War, it had been an area, because they were discovered in the ’30s, it was an area of significant concerns. So many famous biologists had spent time thinking about it, Huxley and D’Arcy Thompson and JBS Haldane and some of the big names in mid-century biology. But with the late ’40s and ’50s came the molecular revolution and the discovery of DNA and the double helix, and that completely changed everything. And these questions, which are to do with multi-cellular organism… Actually they’re not just to do with multi-cellular organisms but to do with sort of more macroscopic behavior…

    0:35:10 SC: Everyday life scale kind of behavior.

    0:35:10 GW: Yes. Was sort of swept under the rug and forgotten and everything turned to molecules and genes, in particular genes, so that that was the paradigm we should be thinking about biology. And in retrospect, it sort of parallels a little bit physics that in my years as a high energy physicist, I think that part of that culture was that, “Look, all we need to know is the fundamental laws and that’s why the theory of everything was so important because once you got the fundamental laws, we can calculate anything and everything including biology.” All it is in some weird way, is turning the crank for these equations and that will pop all these marvelous things.

    0:35:58 SC: And I don’t think that very many people said that explicitly nor would they even have defended it if you asked but there was some sort of…

    0:36:05 GW: Yes.

    0:36:06 SC: Attitudes…

    0:36:07 GW: Exactly.

    0:36:08 SC: That underlay what was important versus what was sort of a waste of time.

    0:36:12 GW: Exactly, so I don’t think anybody ever said it and you’re exactly right, if anyone had said that people would have said, “Well, yes, of course it’s very important.” Those fundamental laws are crucial, important and they will lead to all this, but it’s true, you will need to develop other techniques. There would’ve been a very soft version, but it was still there and it was in the culture, and also in the culture was in a certain sense, again, I did actually hear it stated that it was not very common was, all the rest of those things, those things were engineering…

    0:36:53 SC: Engineering, yes.

    0:36:53 GW: You know, as if that was pejorative…

    0:36:55 SC: Not in a complimentary way.

    0:36:57 GW: Yes, as it was pejorative. And it was very much echoed goes back a long way, of course to the famous statement of Lord Rutherford, the discoverer of the atom, the famous one, “All science can be divided into two; physics and stamp collecting.”

    0:37:13 SC: Stamp collecting, yes. I was always slightly embarrassed by that, and then one of my CalTech colleague has a poster with that quote on his wall, he was very proud, right.

    0:37:21 GW: This was part of it, so we know it’s there, and… But anyway, so going back to the medical revolution and the genomics, what had evolved was a similar kind of arrogance, I think has evolved that that is everything. So that we ended up not so long ago with this idea that it was fantastic. We should map the human genome, which is phenomenal and it’s a fantastic achievement, but the hype about it was, once we’ve done that…

    0:37:56 SC: It’s engineering.

    0:37:57 GW: It sort of solved everything.

    0:38:00 SC: It’s engineering after that.

    0:38:00 GW: It’s engineering after that. We’ll have personalized medicine and all diseases, and all syndromes are gonna be understood and solved, and so on. We are at the Santa Fe Institute and one of my first visits to the Santa Fe Institute was by Leroy Hood. He was one of the initiators of the genome project and he was here talking about it. And I listened to it. It was a very, very good talk but he said this, very explicitly, and I was amazed that he was giving that talk because he wanted to get computer scientists and people thinking about computer involved in doing the engineering part. [laughter] Anyway, and I thought at the time, “My God, this is really extreme.” But we had that.

    0:38:47 GW: So this area had migrated, this area to do with organisms in particular, and the more macroscopic thinking had migrated into ecology. So ecology and evolutionary and what’s called evolutionary biology that became the home for some of this stuff. And I got involved because I had started working on this, as I said, on my own and as I thought about it, I had learnt about and discovered, I discovered by reading, I learned about all these marvelous scaling laws and I said, “This is unbelievable.” I can’t believe that there isn’t a theory out there that the biologists said that it’s all been solved, and this is now whole end. I discovered that there wasn’t any, it had just stopped, literally stopped in its tracks. So, I thought, this is a marvelous problem to work on now, in the context of, “Does physics have any relevance for biology?” Kind of thing.

    0:39:52 SC: Can we have a theory that would help explain this observed phenomenon that has a curve and you fit the data?

    0:39:58 GW: Yes, can we derive can we construct a principled theory from which these laws can be derived and we can also make further predictions?

    0:40:08 SC: And just so we, the people in audience have the direction in which these things go… You’ve mentioned that larger animals live life at a slower pace.

    0:40:18 GW: Yes.

    0:40:18 SC: Their hearts beat more slowly.

    0:40:19 GW: Yes, let me elaborate because I just said the scaling laws. So let me give you some other examples. So heart rates, for example, decrease with size, but they decrease in a very regular fashion so that it is that… I said in the metabolic rate is you take the… You cube it and then take the square root twice. For heart rates, they decrease according to taking the square root twice, that’s it.

    0:40:49 SC: The minus one-fourth power.

    0:40:49 GW: The minus one-fourth in mathematical language and so it is with many other things. The radius of your aorta scales with one that is… The three-eighths is the analogue to the one quarter… But you see, the eighth has a four in there.

    0:41:11 SC: You don’t get five-sevenths.

    0:41:12 GW: You don’t, exactly. So this number four, permeated all of these scaling laws. So I thought this is fantastic, for physicist, there’s a true universality. And that’s what physicists concern themselves about at the deepest level. Are there systematic kinds of phenomena and do they have kind of what we call universal behavior and are there universal characteristics? And here was one saying something astonishing that this unbelievably complex and diverse phenomena called life around us, is constrained by the number four.

    0:41:56 SC: Yeah. [laughter]

    0:41:57 GW: I mean, I thought…

    0:42:00 SC: Magic.

    0:42:00 GW: This is like magic. Where in the hell does this number come from? So that was the state of mind I was in when I started thinking about it, and I did… And the first thing you think about is what is common. You realize that whatever the underlying mechanism is, it must transcend the evolve design because it’s true for plants, trees, it’s true for mammals, it’s true for birds, insects, and so forth.

    0:42:27 SC: In other words, there’s some happy place for an organism to live and evolution gets you there. You can take different paths…

    0:42:34 GW: Many…

    0:42:34 SC: But this is where you will end up.

    0:42:35 GW: Exactly, exactly, exactly, it can take many different paths and it gets manifested in different ways, in the sense that we have a beating heart and a respiratory system, a tree doesn’t. In fact, we are a bunch of tubes, we’re like plumbing, but a tree is a bunch of fiber bundles joined together and sprays out like electrical cable sprays out. So these are quite different engineered designs, but they satisfy the same scaling laws. So you ask yourself, something has to transcend that. And then it doesn’t take very long to think it through and realize that look, the huge problem that an organism has is that it’s made up of an enormous number of components, particularly cells. It’s got some enormous… We have 10 trillion, 10 to the 14th, and they have to be sustained and serviced in a roughly speaking democratic and efficient fashion. And it’s obvious what has happened, we’ve developed networks, these… And if you think in those terms, you realize that you are a bunch of networks. Everything from your, as I said, circulatory-respiratory systems, your renal system, even your bones are a big network…

    0:43:55 SC: Nervous system.

    0:43:56 GW: Your nervous system, your neuro system, the very thing that you think of as you, the white and grey matter in your brain. Those are also just branching systems. The synapses and neurons and axons are all networks.

    0:44:13 SC: So, sorry… A network, of course, is not a particular TV station, or like in TV station, [laughter] we’re thinking of…

    0:44:18 GW: Very good, that’s so true. Thank you.

    0:44:19 SC: So I could draw a piece… Some dots on a white board or a piece of paper and connect them with lines…

    0:44:26 GW: Yes.

    0:44:26 SC: And that would be a network.

    0:44:27 GW: That would be a network.

    0:44:28 SC: You’re thinking of a particular kind of hierarchical…

    0:44:30 GW: Yes.

    0:44:30 SC: Branching network.

    0:44:31 GW: Most of these networks that you… It’s not absolute, but most of these networks are high hierarchical like your circulatory system, there’s a beating heart, there’s an aorta that comes down out and then it branches and continues to branch all the way down, serving your organs, all the way down to the capillaries that feed cells. So it’s this branching network and most of the dominant networks in our bodies have that kind of characteristic. So, I sort of had this idea that it must be some universal features of networks, there must be… Well, in the language of physics, is a universality class of networks that have this feature, that have somewhere in them this one quarter, this four.

    0:45:22 SC: They know about the number.

    0:45:23 GW: They know somehow.

    0:45:25 SC: What could that be?

    0:45:26 GW: So what could that be indeed? So what I did first was simply try to solve the question of, “How does that circuitry system work?” Just to take that as a physics problem.

    0:45:40 SC: A simple warm-up problem. Good.

    0:45:40 GW: A warm up. It turned out to be quite complicated.

    0:45:43 SC: Who would have guessed?

    0:45:44 GW: Who would have guessed? And it was a wonderful challenge, mathematical-physics challenge, which I… Was quite frustrating at times, but I enjoyed immensely. I could use all of the classical mathematical methods that I’d been taught as a graduate student and I used throughout…

    0:46:06 SC: Yes.

    0:46:06 GW: My career and they all came to bear on this and I eventually solved it and… But I then in solving it, I had to think, “What is the principle? What are the principles that are constraining this network?” And…

    0:46:25 SC: Sorry… Just by solving it you mean constructing a mathematical model that matched…

    0:46:30 GW: That matched… I’m sorry, that matched. Yes, the real…

    0:46:30 SC: What we know about the circulatory system.

    0:46:34 GW: What we know about our circulatory system.

    0:46:35 SC: It’s what a physicist means by solving this system right?

    0:46:36 GW: That’s right, I’m sorry. So I’ve mathematical equations…

    0:46:39 SC: Yeah.

    0:46:40 GW: So you have to write the mathematical equation for the blood flow through your vessels and that’s complicated because it’s a pulsatile flow, it’s being beaten by the heart. It’s being boom-boom-boom. And not only that, it goes through a vessel and then that vessel branches…

    0:46:57 SC: Yeah.

    0:46:58 GW: So some goes down, one tube… One down the other and so you got to deal with that and then it bifurcates again or trifurcates even, so you had to deal with all that. And so I did all that mathematics and there’s all kinds of formula you derive for that, but you have to constrain it. It’s not some arbitrary network, and that’s what I realized quite early on. And it turned out I put together three generic principles but only in the context of circulatory systems to begin with, and then I realized later these were generalizable to all these networks and they were the following. The first is the network has to be what we call space-filling. It has to go everywhere, every cell in the body has to be supplied by blood, has to be supplied by oxygen.

    0:47:46 SC: Blood, oxygen, energy.

    0:47:49 GW: So therefore the terminal unit, the capillary has to end near the cell so it can be fed, so that’s called space-filling.

    0:47:56 SC: And we know how many cells there are, they fill the body.

    0:47:58 GW: Sure-sure. Second was, which was something to do with natural selection, as I thought about the scaling laws and our relationship to other animals, other mammals. And that is that, yes, we look quite different, but we obviously have a lot in common, but in particular as different mammals evolved, natural selection kept certain things in variant, it had certain building blocks. It did not reinvent cells in order to make a dog as distinct from an elephant. It kept those same building blocks. So, in terms of the network, the cells were essentially the same. But also with things like capillaries, the end of the network, that’s the thing that feeds the cells. So, I…

    0:48:48 SC: Well, natural selection is naturally very lazy, right? It takes what you already have…

    0:48:52 GW: Absolutely.

    0:48:52 SC: And says, “How can I improve things a little bit?”

    0:48:55 GW: Exactly.

    0:48:55 SC: Just by tweaking what we already started. It doesn’t start and then initiate.

    0:48:56 GW: So, you don’t reinvent things a priori every time, and you’re very parsimonious in that. So that was the second idea, the kind of invariance of terminal units. And the last was taking a real physicist’s viewpoint, and that is that something is being optimized. Physics operates almost entirely in almost all levels, particularly the fundamental level, from optimization principles. All our fundamental equations in motion are derivable from optimizing things we call the action, or whatever.

    0:49:41 SC: If a beam of light goes from one one point he to another, it takes the shortest time.

    0:49:44 GW: The shortest path, yes. So this is fundamental to physics. And so I postulated, hypothesized, that our circulatory system in particular, has evolved so as to minimize the amount of energy our hearts have to do to pump blood through it. That is… And I didn’t have it quite formulated at that time, but I’ll jump ahead. It was only later when I started a very intense collaboration with biologists, and natural selection is what they think about all the time. And it was really this idea that the real reason for that, from a natural selection viewpoint, is that you minimize the amount of energy that is needed for the organism to stay alive, to live, so that you can maximize the amount of energy you devote to reproduction and to raising of offspring. So, to your Darwinian fitness, you maximize Darwinian fitness by minimizing the amount of energy that you need to support and sustain the system. So this was one very specific case, going back now to the circulatory system that you minimize the amount of energy our hearts have to do to pump blood through it, and so we have all these equations.

    0:51:16 SC: So that’s it. You have three principles…

    0:51:18 GW: Three principles and you know the dynamics, and then it’s a matter of solving…

    0:51:24 SC: Equations…

    0:51:25 GW: Those equations with those constraints. And it’s very similar to what we were doing in field theory in high energy physics, it’s the same conceptual framework that is. Anyway, out of that popped to my absolute delight and amazement, this one-quarter power. Now, I have to interrupt that make it… It sounds very straightforward, but it wasn’t. I struggled a great deal, first of all, trying to solve them, and understand the biology and so on. And a serendipitous event occurred, and that was that I got a call from the Vice President of the Santa Fe Institute who called me up to say, “Jeff, there’s a biologist, very well-known biologist that is involved with the Santa Fe Institute, and he is very interested in getting a physicist involved in trying to understand scaling laws in biology.” And I said…

    0:52:34 SC: “Do you know anyone?”

    0:52:35 GW: And I said, “I can’t believe this.” I said, “I can’t believe… ” I’ve actually… The last almost year, as a kind of hobby, I’d been working on that, and I think I’m close to solving it. But it’s fantastic, I need a biologist… He may need a physicist, I need a biologist. So that, to cut a very long story short, that began an extraordinary collaboration, with a man named Jim Brown, who had moved recently to the University of New Mexico and was involved with the Santa Fe Institute. And he had a marvelous student named Brian Lindquist, who is himself now well known ecologist. And a fantastic collaboration developed, where we got all this straight. And it took us almost a year from then to get everything straight, and it was a huge commitment, by the way, because I was running high energy physics at Los Alamos.

    0:53:32 SC: Oh, right. Still you had the day job, yes.

    0:53:34 GW: I still had a day job I was running the… I was involved with the theory group, and we were running… We were still involved with many high energy experiments, and I was the spokesperson or the connection with the DOE anyway. And Jim ran a big ecology lab out in the field and so on, and we both agreed to devote Fridays to this at the Santa Fe Institute. And it was huge, it was an enormous commitment. That came after a few meetings and we did and it was… And it required that actually. So we would meet, we would meet here at the institute, between 9:00 AM and 10:00 AM, on a Friday morning and they would leave here about 2:00 or 3:00 in the afternoon. And we would, the three of us at the beginning, we just… We had the blackboard. A lot of it was blackboard and a lot of it was just bullshit, going back and forth because I didn’t know the biology and, how shall I put it? They were mathematically challenged. [laughter]

    0:54:41 GW: So I had to take… You know really things that we take so much for granted and really work hard at explaining them and they were fantastic at explaining in very simple terms, biological mechanisms, and also very importantly, what is important. Because that in ones education, that is something we don’t often recognize, is having a mentor who really guides you. It’s not actually teaching you but what is important, and this is the way you should be thinking about this.

    0:55:14 SC: And to those out there who are not professional scientists, we should point out this idea of standing at the blackboard and discussing things and learning things and having a feeling you’re making real progress. It doesn’t get better than that.

    0:55:25 GW: No absolutely, thank you Sean, I can’t… Honestly it was fantastic and it doesn’t get better than in a very curious way. Your ideas are going back and forth and you’re writing equations and then you realize they are completely wrong, the idea is wrong, you were completely… And you get depressed so many times you’re depressed so you sit there and certainly with this I would sit down and think, “Why am I involved with these guys? They can’t… They’re not able to write an equation.” And I’m sure they felt the same way about me. So there’s all of that, but that’s part of it and I’ve often said it’s sort of like a marriage, a good marriage.

    0:56:04 GW: ‘Cause that all comes with it. And so it was a phenomenal period for me, and that collaboration lasted for about 15 years and of course it evolved, we got new… Post-docs and other people joined us and other senior people joined us. We had a chemist had joined us, another ecologist, we had students from Physics, students from Biology. It was marvelous actually we created this body of work.

    0:56:38 SC: Right, but then I don’t wanna switch topics too abruptly but it wasn’t too long before you went from explaining all of the scaling laws in biology to saying, “Well, once I have my networks… ” Oh, actually, I’m sorry, we didn’t say where the four came from, did we?

    0:56:51 GW: No, so I should tell you that.

    0:56:52 SC: Gotta get that in there, yes, sorry.

    0:56:53 GW: So it is from the networks, but let’s put it in sort of simple layman’s. You have to do all the calculations and you have to do all… But it is roughly… What the four turns out to be is three… The three of the four is a reflection of the fact that we live in three-dimensional space, the space-filling that I talked about.

    0:57:15 SC: Space-filling networks.

    0:57:15 GW: If we were six-dimensional… If we lived in six dimensions, it would be… That three would have been six and then there’s a plus one. And so four is actually three plus one and the plus one…

    0:57:30 SC: I knew that.


    0:57:33 GW: Very loosely speaking comes from the following, those principles and in particular the optimization lead to these networks being fractal-like, self-similar, that is they repeat themselves as one goes down through the network.

    0:57:50 SC: The bird’s-eye view looks very similar to the zoomed in view.

    0:57:52 GW: Exactly, or if you cut a big branch of a tree, and you take it away, it looks like a little tree. And that self so-called self-similarity, you can derive and that is fed by the optimization. This optimization kind of a constraint leads to that and it turns out one of the curious properties of fractal geometry is it increases what we think of as dimensionality of the system, and you can increase it and it increases it maximally and that maximality happens to be one, you can’t go more than one. And so biological organism, natural selection has taken advantage of fractal geometry to increase the dimensionality and increase its efficiency and its way of interfacing with whatever the external environment it is.

    0:58:56 SC: Otherwise large mammals would eat enormously more caloric input everyday to get through the day.

    0:59:02 GW: Absolutely.

    0:59:02 SC: But these networks solve the problem of… With maximum efficiency, getting the oxygen through themselves.

    0:59:07 GW: On the average, exactly, exactly. So we are all manifestations of that.

    0:59:12 SC: And there’s networks all over the place.

    0:59:15 GW: There’s networks all over the place and indeed somewhere along the line, it started to occur to me that this is a paradigm for other problems and in particular social organizations and even more particular, to cities, cities… And of course, there’s been a long history of thinking of cities as kind of super organisms and we often use metaphors from biology, metabolism of city, DNA of a company and so on. And so I was… I started at least thinking about it and I thought, “Well, why not?” But again a serendipitous event came along.


    0:59:56 SC: Okay.

    0:59:56 GW: And that is… I was here at the Santa Fe Institute, I was not part of the Santa Fe Institute. But I was here on this once a week basis and I gave a colloquium one time on my biology work, and in the audience were a couple of very good social scientists who came to me afterwards and said, “You know, we’re so intrigued by this, I’m sure we can use this to start understanding things about cities and other social organizations.” And to cut a very long story short, we formed a new collaboration.

    1:00:33 SC: You’re giving us the impression that all great science happens by accident because it just happened in your talks.

    1:00:36 GW: Well, mine does in a way. Mine does and I don’t know I feel… It happens… I don’t know if it’s accidents, but I often think that any new idea that I’ve had, I often feel it’s not to do with… I know this sounds weird, but it’s not much to do with me.

    1:01:00 SC: But I don’t think it does sound weird because one of your discoveries about cities is that they sort of provide the environment for these things to happen by letting the interactions happen.

    1:01:09 GW: Exactly Sean, I think that is what is happening to all of us, and it’s sort of the unconscious part of the city.

    1:01:19 SC: Yeah.

    1:01:19 GW: And it is. So I often say that… I even said and others I think have probably said it, in many ways the city is our greatest invention because it’s a machine that brings us together and facilitates and enhances social interaction and provides positive feedback mechanisms for enhancing that to create ideas, to innovate and to create wealth and it’s certainly true that most of those ideas, most of those conversations and interactions that take place don’t lead anywhere, or there’re to do with personal… but amazingly that phenomenon occasionally leads to the theory of relativity or to Google or to Microsoft or to…

    1:02:14 SC: The Santa Fe Institute?

    1:02:17 GW: The Santa Fe… Whatever, but that’s what the city is, it is that machine for doing that.

    1:02:21 SC: A friend of mine, a theoretical physicist was… We were having a late night conversation and he says the following, he said, “If you divide human history into the most recent 10,000 years and all the years before that, there were a lot more people in prehistory, there were a lot more people older, longer than 10,000 years ago, but all the good ideas seem to be in the recent 10,000 years,” and we were wondering why that was and there are hypothesis like, “Well they were too busy hunting and gathering” and in fact the data are that hunter-gatherers… They have lot of leisure time.

    1:02:55 GW: Lot’s of time, yes.

    1:02:57 SC: So in fact things like the city density.

    1:03:01 GW: No, the city is the mechanism by which we do this. So anyway we formed a collaboration and unlike the biology where I was extremely fortunate that the scaling laws had already been put together, developed, the phenomenology so to speak had been organized in these four books that I mentioned earlier that had been published and by the way I didn’t say it because these people who were quite senior people had worked on it earlier, this was the end of their careers, molecular revolution, genetics had taken over and they were kind of summarizing.

    1:03:46 SC: Right.

    1:03:46 GW: And the amazing thing about those was when I discovered that there was no theory, they just showed all the stuff. Anyway, the cities weren’t… Not in that position. What I learnt was that surprisingly no one had looked at the scaling of cities.

    1:04:04 SC: So you wanna know about how things like presumably energy use or roads or something like that change as the city gets bigger and bigger.

    1:04:11 GW: Exactly. So you could ask… I think the very first question we asked when this was still an incipient collaboration. It was with a man that’s now very well known, social physicist. I don’t know what you call them these days, works in social organizations came out of physics and ended up helping at the ETH in Zurich, and a student but we worked together first was, “How does the number of gas stations scale with city size?” Very mundane kind of question.

    1:04:54 SC: But one would guess, the number of people is proportional to the number of gas stations ’cause they all need gas.

    1:04:57 GW: That’s what you would have thought naively. Yes they all need gas. So when we looked at the data we discovered amazingly that it looked just like biology. It was that, it scaled in a very systematic way following this same mathematical power-law scaling, but the exponent, the analog to the three quarters, the quarter powers I mentioned earlier, that was not a quarter power, it was 0.85 meaning to put it in English that if you doubled the size of a city instead of needing twice as many gas stations, very roughly speaking you only need 85%. So there’s this marvelous economy of scale the bigger the city, and the original paper only looked at four European countries and they all expressed the same scaling law and somewhat later when the collaboration was more formed, more formalized and in particular two people brought onboard, one was a physicist, a very good physicist named Luis Bettencourt, who had been working… Came out again, came out of nuclear physics actually. And a man named Jose Lobo, who was… Had been associated with the Santa Fe Institute, was an urban economist.

    1:06:18 GW: He was at Cornell at the time, but they were very good data analysts, and they… One of the things they did was they looked at data from around the globe, just first gas stations. And discovered the same scaling law everywhere, but even more amazing was that if you looked at any infrastructure, at least the ones we could get data for like length of all the roads, length of electrical lines, water lines, blah blah blah. They all had the same scaling with this 15%, this 0.85, and that was sort of amazing, and it was just like biology, except 0.85 instead of 0.75 kinda thing.

    1:06:58 SC: Is that because cities are not truly three-dimensional space filling organisms?

    1:07:01 GW: Well, we wondered, but yes. And in fact I think that… Yes, from that viewpoint the answer is yes. The dimensionality plays a crucial role and ultimately does. But I should say right up front now I would say… Oh so, let me back off a second. So the obvious thing is, again, even though New York doesn’t look like Los Angeles, which doesn’t look like Chicago, which doesn’t look like Santa Fe, they’re all network systems, they’re all doing the same thing.

    1:07:36 SC: Yeah.

    1:07:36 GW: So just as the whale doesn’t look much like an elephant, which doesn’t look much like a human being, they’re actually doing all the same things biologically and so in that sense, not surprising, they are scaled versions of each other. So it is that cities within a given urban system are indeed scaled versions of one another, but following in terms of the infrastructure, a similar laws as biology, but with a exponent of 0.85, as you say, to do somewhat with their dimensionality. They are more two-dimensional, obviously, but also their network systems, that was the other point, and it’s clear, is that like biology, their networks, their road networks, electrical networks…

    1:08:20 SC: Are they optimizing some equivalent of the heart rate?

    1:08:22 GW: That’s the question, what are they optimizing? And how much have they optimized? So in terms of those networks, I believe that in many ways, those networks are optimizing things like time to get from A-B.

    1:08:37 SC: Okay.

    1:08:37 GW: And distances you want to supply things as directly as possible, but you still gotta do it in a network way because you got to supply, it’s a…

    1:08:46 SC: But, is it safe to say, we don’t yet have the development of theory for cities that we have for organisms?


    —Huffduffed by Bobcaygeon