Wisconsin Public Television University Place  Geoffrey West Energy, Scaling and Life on Earth  October 1, 2012 UP777    cc >> I'm Jessica Flack and I'm the co-director of the Center for Complexity and Collective Computation in the WID, and before I introduce tonight's topic and speakers, specials guests, I would like to first thank some of the folks in WID who made tonight happen. Maria Peot, Marianne English, Jenny Eagleton, Sarah Shapiro, and Beth Misco, WID's outstanding administrative outreach team. I'd also like to thank Wisconsin Public Television, who's in the back filming the lectures tonight. Everybody at University Communications who's done a great job with help with advertising. Folks at the Isthmus for accommodating changes the last minute. And, of course, the IT team, Alan Ruby in particular here at WID for their support tonight. And, finally, the Center for Complexity and Collective Computation is indebted to John Wiley and to the Templeton Foundation for very much appreciated critical support, financial support of tonight's lecture series. Without this support, we could not have these kinds of events. So, tonight's lecture on the roles of energy and information in the 21st century biology is part of a new public lecture series sponsored by C4, that's the Center for Complexity and Collective Computation, and the series is called John von Neumann Public Lectures in Complexity and Computation. And the lectures are going to be each month at about 7:00 PM the second or third Wednesday over the course of the fall and spring semesters in 2012 and 2013. 

We have a great lineup this fall. The next speaker, the next lecture is on October 17th, and it's by Graham Spencer who you might know as one of the original founders of Excite, and he's currently a partner at Google Ventures. And he's going to be talking about programming the Internet. He's a super smart, broadminded computer scientist. He gives fun, insightful lectures, so I hope to see you guys all there. Energy and information are two of the most fundamental concepts in science, effecting phenomena over a vase range of scales. From quantum mechanics to the origin of life to the evolution of cooperation in human and animals society to, also as you'll hear about tonight, the size and pace of cities. In tonight's lecture, Dr. Geoffrey West and Dr. David Krakauer, who I will introduce momentarily, will explore how information and energy have shaped nature, and they'll discuss the implications and the principles of the future of science, the future of biology, and for society. Some of the questions that we will tackle over the course of the evening tonight include, what really are energy and information? The laws of physics, and specifically the first law of thermodynamics, tells us that energy cannot be created or destroyed. As such, it's said to be a conserved quantity. 

Meaning that the total energy in the universe is a constant. It is this property of energy coupled to the fact that it can be hard to transform into something useful that makes it seem like a finite expendable resource. Now, is the same true for information? Or can information be creative and destroyed? And if so, what does this mean? So, as you'll hear tonight, existing theories of information stress that information increases our understanding of the world around us. In formal terms, we say that information reduces the uncertainty about the environment. But there's nothing in this definition that captures, I think, the fact that most of us, for most of us in this audience, information is really about meaning. It's the knowledge itself, not about reducing uncertainty about the knowledge that we're interested in. So existing formal theories of information have nothing to say about this, what you might call, semantics. Do we need a new theory of information that includes meaning or semantics? That's one of the questions we'll ask tonight. Can we use existing formal theories of information? Or the new ones that we might build to overcome energetic constraints. Or does information only help us find solutions to harness energy more efficiently? These are deep and unanswered questions in physics and biology. 

So, finally, we are going to ask, what would a science of energy and information mean for physics, for computer science, for biology, and for society? So our first speaker is Dr. Geoffrey West. Geoffrey is a theoretical physicist. His primary interests have been in fundamental questions in physics, especially those concerning the elementary particles, their interactions in cosmological implications. Geoffrey received his BA from Cambridge in 1961, his doctorate from Stanford in 1966 where he returned in 1970 as a member of the faculty. He was the leader and founder of the Higher Energy Physics Group at Los Alamos National Lab. And then he moved to the Santa Fe Institute in 2003 where he became a distinguished member of the faculty and eventually became president of SFI for 2005 to 2009. His long-term fascination has been in the origin of universal scaling laws that pervade biology from the molecular genomic scale up through mitochondrian cells to whole organisms and ecosystems. He's currently working to extend the theory of scaling as it was developed in biology to social systems, with the goal of understanding the structure and dynamic of social organizations such as cities and corporations. Tonight, he will talk on energy scaling the future of life on Earth for about 45 minutes. Our second lecturer is David Krakauer. 

David is the director of the Wisconsin Institute for Discovery, co-director of the Center for Complexity and Collective Computation, professor of genetics at UW Madison and external professor at the Santa Fe Institute. A graduate of University of London and Oxford University, he's authored more than a hundred scientific papers, served on several journal editorial boards, and works to bridge the gap between academia and business and also between the physical and biological sciences on the one hand and the social sciences and humanities on the other. His research focuses on the evolutionary history of information processing mechanisms in adaptive systems. But his mind, and I know him well, is perhaps best described as sitting in an intellectual spaces deeply influenced by, I guess, I think, a somewhat idiosyncratic group of some of history's most interesting contributors including John Louis Borges, John von Neumann, Turing, Bill Hamilton, and Sir Thomas Browne. Tonight, he will talk for 30 minutes on the power of information to transfer in the 21st century. Following the lectures of David and Geoffrey, Steve Paulson from Wisconsin Public Radio will lead a panel discussion on the role of energy and information on 21st century biology. Steve is the executive producer and interviewer with To the Best of Our Knowledge, a well known science radio program. Paulson has written for Salon, Slate, the Huffington Post, the Chronicle of Higher Education, The Independent, and many other publications. His radio reports have also been broadcast on NPR's Morning Edition and All Things Considered. His recent book, Atoms and Eden: Conversations on Religion and Science, was published from the University Press. 

So please join me for a bit of a marathon session and welcome Steven, David, and Geoffrey. Thank you. [APPLAUSE]  >> Okay, thank you. Thank you, David, thank you, Jessica, and thank you for inviting me to give this talk and be part of this interesting discussion about energy and information So, this is the title that was given to me, mostly because I was delinquent in giving one myself, and it does sort of cover what I'm going to talk about, but this is kind of a landscape that I'm going to be talking about tonight in terms, primarily, of energy and the ideas surrounding metabolism in biology. And it's a very idiosyncratic view, and as is clear from the introduction, I come to it as a theoretical physicists wondering into areas of biology and the social sciences. And I'm going to begin it, I'm going to take as a point of departure, something that's relevant to this, namely this is supported by the Center for Computation and Complexity, or whatever, complexity was in it. [LAUGHTER] And I wanted to use as a point of departure a statement by Stephen Hawking, who is not someone that works on complexity and not someone that works on biology, but is a highly reductionistic physicist. And here's something he said about 10 years ago: "Some say that while the 20th century was the century of physics, we are now entering the century of biology, what do you think of this?" And many people believe the 21st century is the century of biology and it certainly will be, but more importantly, and this I do believe, is what Hawking says, "I think the next century will be the century of complexity" because many of the problems we're going to face and are facing to do with complex adaptive systems, and I'll be talking a little bit about them, and I want to use this, as I say, as a point of departure because implicit in this is an idea of what complexity is, and that's something I'm not going to discuss except to use it to talk about what is not complex first because it brings in the whole role of energy. And this is a system we're familiar with, the solar system, and this is a system that is often thought of as not complex. It is simple, and by simple, it means that the whole dynamic of that system, the motion of the planets around the sun and, therefore, of the satellites that power our communication systems, are encoded in two very simple looking equations. 

This is a highly non-technical talk. You don't have to understand the equations. Everybody is familiar with the idea F equal MA. But there are two laws proposed by Newton that kind of covers everything to do with the motion of the solar system, the planets around the sun, but much, much else. Much of modern physics is based on these equations or versions of these equations, but critical in this is the flow of energy. The idea that energy is the kind of fundamental thing that's underlying this motion. And one of the crucial aspects of that has already been mentioned by Jessica: the conservation of energy. But if you add to it another set of equations which you don't have to understand but important to understand conceptually, the equations of Maxwell for unifying electricity and magnetism and giving rise to understanding radiation, electromagnetic radiation. That pretty much encompasses much of the kind of world that we live in, and just to take these two equations with these equations is how your cell phone works and allows everybody to communicate and everything else that's pretty much around us. And the word simple applies too because they invoke the idea that you can encode everything in the symbolic fashion, and from that, everything else follows, even down to the quantum level. 

And one of the things I want to emphasize is that, again, these are to do with the flow of energy and because they are simple and they are written in a mathematically precise form, you can calculate things somehow in principled to any degree of accuracy. And one of the great triumphs of 20th century science is this calculation which is calculating the strength of the magnet associated with the electron, and here's the theory to 12 decimal places and here's the experiment agreeing with it to 12 decimal places. It's kind of extraordinary, and this is quite unusual, actually, in the world that we live in because the world that we live in, oh, I forgot about that. I put this slide in just to show you some of the main characters that you're familiar with that I think played an important role in developing ideas of energy. One is Newton. That's a kind of rock star image of Newton. [LAUGHTER] This is Einstein looking like Einstein. And this is Max Planck, the origin of photons. And this is someone-- Oops. This is someone that most people are not familiar with. 

It's another, there was a famous Bill Hamilton here, biologist, very famous ecologist/biologist that Jessica actually mentioned. This is a really deep Bill Hamilton. This is Bill Hamilton. He was an Irishman who sadly drank himself to death, but he encoded something extremely important about energy, and the physicists in the audience will forgive me, but basically he said that all physical systems, in some sense, minimize the amount of energy that needs to be expended. So this kind of a least minimum, least energy principle Hamilton's principle is actually called, technically, the principle of least action, but roughly speaking, this is the framework in which all of physics that encompasses everything from the macroscopic down to string theory operates from is using those principles. And it's has to do based on energy. So, here's a picture of energy. This is energy. We're familiar with it. This is highly complex use of energy because these are highly non-linear effects and you're familiar with them. 

You're also familiar with this. This is the energy that we create on the planet through objects like this, and I'm going to talk a little bit about that shortly. And these are driven, of course, by us, which involve energy. So they're these multiple levels of energy, and they go all the way down to the thing that drives these, us, that drives us to create the light and the energy by which we live, our brains and ourselves. And these, of course, also operate by energy themselves, but they invoke something new that has typically not been considered in physics. And they invoke information, the idea that information necessarily is needed to be put into the system in order to understand the way these systems have evolved and the way they organize and the way they behave. And these systems are typically outside physics, and they form much of the work of biology and the social sciences, and they are complex but, more importantly, they evolve and are therefore adaptive. So these are very different in their nature from the kind of simplistic system that we see in the motions of the planets or even, might I say, in thinking about string theory as the origins of the universe because we can write definitive, precise equations in principle for those. Whereas for these, we have this extraordinarily challenging problem of both integrating information in it and understanding the role of energy. And what I'm going to explore tonight is how far one can take the traditional physics thinking without invoking, explicitly, information to understand some of the organization and dynamics of these systems. 

And then David will talk about information, and maybe in the discussion we'll talk a little bit about the integration. So here's another kind of system which you're familiar with, a forest. And all of these systems obey the second law of thermodynamics, the conservation of energy, and, therefore, the production of entropy which is the kind of random stuff, the dissipative kind of energy that comes from doing work and creating order. It is the resulting disorder that comes from ordering the system. And one of the challenges, and I would even go as far as to say I think the major challenge conceptually in 21st century science is understanding this integration between energy and resources on the one hand, metabolism and biology with information genomics, maybe, and integrate and get a complete understanding of these. These are typically considered separately, roughly speaking, in the kind of academic way in which we think about these things. So, what I'm going to talk about in these systems is, as a physicist, I want a quantitative, predictive, mathematizable in principle, understanding of the dynamics of organization of these systems. And it is clear for the kinds of systems I just referred to, we cannot do what we did for understanding the magnetic moment of the electron. We're not going to get equations that produce precise calculations, but maybe what we can get is what we call coarse-grained descriptions. So, for example, the kinds of questions that we ought to be able to answer quantitatively are questions like this: why is it that I can look across this room and say everybody will be dead in a hundred years? In fact, if I look more closely, I would say that... 

[LAUGHTER] Including myself, might I say. But where does a hundred years come from for a typical life span of a human being? Why isn't it 10 years or a thousand years? And how is that connected to underlying molecular structures of the genome and the complex? Where in the hell does that come from? And why is it that the same stuff, if it were a mouse, only lives two or three years? So those are the kind of coarse-grained questions that one ought to be able to answer in a predictive framework, and I'm not going to talk much about these, but in what role does energy and metabolism play in these? So here's another set of similar kinds of coarse-grained questions. Why do we need eight hours of sleep? Why do we need to sleep? Why is it not two hours or 18 hours like a mouse or four hours like an elephant? Where in the hell do these numbers come from, and why is it that mice get many more tumors during their life span per unit volume than human beings? And, therefore, why in the hell are we doing all these experiments on mice and trying to draw conclusions about human beings? We need to understand those kinds of questions, and the one I really love is, why is it very good to grow babies in your body but not grow cancer which is also part of you? So these are kind of coarse-grained questions, and one that has occupied me in the last few years is, are cities and companies just large organisms that are biological or are cities organisms just, is New York a great big whale and Google a great big elephant, and if that's true, how come organisms die, companies die, but cities don't? And in fact, I would say, roughly speaking, almost no cities die, although you can think of counter-examples. We have done awful experiments to test that. We've dropped two atom bombs on two cities, and 30 year later, they're functioning. Companies, all companies, die. And so one of the questions is, in a coarse-grained way, can we predict when Google or Microsoft are going to go bust? Because they surely will eventually. Okay, so those are the kind of questions, and I want to lead into all of this, this is biology but I want to lead into it via cities because we are facing an extraordinary challenge, and this is addressing the question of how biological our cities and can we understand them that way. We are facing this extraordinary challenge that we live in this exponentially expanding universe of socioeconomic quantities And just to give you an example, we've gone from a few percent being urban to over 80% being urban in just 200 years. The world's crossed the halfway mark. 

We're going to go to somewhere close to 80% by 2050. China's building several hundred new cities in the next 20 to 30 years, and indeed, this statistic ought to freak everybody out that every week from now to 2050, on the average, one and a half million people are being urbanized. Therefore, every two months, there's a New York metropolitan area coming onto this planet. So by the beginning of December, there's another New York metropolitan area. By the beginning of February, there's another one. By the beginning of April, there's another one and so on, inextricably for the next 30-40 years. Now, can I use expletives in this talk? >> Sure. >> Okay, how the [###] are we going to deal with that? [LAUGHTER] This is an extraordinary challenge. So I want to get into that, and it is related to energy. Okay, so, the other aspect to recognize is that all of the tsunami and problems we're facing from global warming to the environment to health problems to crime to resource problems, water, energy, and so on, all are driven by urbanization, by people in cities. 

So that's the problem, but cities are also the solution because they suck all of you into Madison. Cities suck in people, and they are the sources of ideas, innovation, and wealth creation. So, this is what cities are represented by. The good of cities, this is what, in fact, attracts people to cities. All these good things, culture, music, goods and so on, driven and participating in an ever expanding, exponential expanding economy, but if this is the thermodynamic system, which it is, it produces entropy. So it produces socioeconomic entropy. Incidentally, side comment, if you look in any of the standard economics books, you never see the word entropy, but what is more amazing is we've looked in five of the standard texts, only in one did the word energy appear. That's a side comment. Provocative comment. So here's socioeconomic entropy. 

Okay? You're familiar with all this. And the question is, is that what New York and San Francisco looked like 2050? Or that? Or like this? Or this? This is what we want. Or even like that? Beautiful. Or like that in a hundred years. Or that. And most importantly, to maintain that which is a social buzz of a city. The interaction of people. So, here's the question, given this extraordinary role of cities, we need a science of cities. And I'm going to use energy as the major piece of that. So the question is, can we have a science of that, and is that another version of this? Well, if it is, that would be good, actually. 

If this were another version of that because you ask any question that has a quantitative metric associated with it, like how many trees are there of a given size, how many leaves are there on a given branch of a given size, how much energy is flowing through each one, how big is the canopy, what is the mortality rate, what is the growth rate, how far apart the trees of given size, etc, all those can be answered in a quantitative conceptual framework with a bunch of mathematical formulas which, in a coarse-grained way, agrees with data from forests all across the globe. And the question is, can we do the same for this? Sorry, oops. I went backwards. So, well here's some of the commonalities, metaphorically at least, between social organizations and biological organisms which we're all familiar with, and I'm going to show you just very briefly some data that substantiates the idea that we understand a little bit about generically the way forests work. So what this is, is just the plot of the number of trees of a given size. The theory, which I'm going to talk about momentarily, the theory predicts that it goes as the inverse square of the diameter of the tree trunk. So the number of trees of a given size goes to the inverse square of the diameter of the tree trunks which means if you look at trees that are twice the size of any others, there's a quarter of the number, two squared, a quarter of the number. If it were three times, it'd be eighth and so on. So, you get the idea. And there's data and what is important about it, not only does the data fit the theory, but you can see it's just over a period of 30-40 years, this forest, which is a tropical forest, has changed dramatically. 

Lots of trees have died, new ones have grown. Record turnover. But this law has remained robust, and there's data into the '90s and 2000s that continue with that. I'm going to miss this. So here's the kind of framework that I want to invoke. Here's a cartoon of said ecosystem. I could have done the city. And this is the lens that I want to look at it through, and all of these equations actually are really to do with energy flow. Okay. So, another concept I want to talk about very briefly is the concept of scalability that a system needs to be scalable if it is a system that is going to be resilient and evolvable and adaptive to change. 

It needs to be scalable just in the sense that we are scalable. This is us. We have scaled over a range of a hundred million in size and mass. We go down to something that sits on the palm of my hand all the way up to something that's much bigger than this room, and we're all pretty much the same thing. We may look different, but in terms of, in a coarse-grained average way, in terms of our life history and our physiology, we're all pretty much the same thing, and I'm going to show you that in a moment. But even going further in going from the molecular levels, I could have put the genome here, this is what the cartoon of the molecules that produce your energy, all the way through mitochondria to cells to multicellular organisms like this that produce things like this, houses, and produce things like this so that, in fact, what goes on here scales all the way through this to keep this going. All of these have to be scalable because they are highly complex and continuously evolving and continuously adapting. And so there has to be a kind of scalability, and out of that comes the idea that you can't have this being arbitrary. There have to be emergent laws that govern this, and I think the next slide, ah, yes. So, in a similar way to the way we scaled in a much shorter time frame in terms of our growth, and one of the things that I will talk about briefly in a moment is about growth and the fact that the same theory, the same theoretical framework, which I will come to in a moment, which purports to explain the organization, dynamics, growth of forests that I talked about earlier applied to us, to mammals, gives rise to equations like this or pictures like this for the, what is called a growth curve. 

This is the weight as a function of age. This is us. It happens to be a rat version of us. And the line there, the solid line is a prediction from the theory and the points are the data, and you see it's very good. And this can be done for any organism, and if I had time, I would show you lots of other wonderful fits. But the point is that we can understand growth, and I will come to that in a moment, but the important thing I want to stress now, moving to social systems, is if this were taken over to socioeconomic systems, mainly that the organism grows quickly and then stops like we did, I mean one of the amazing things about biology is that we eat, we grow, and then we go on eating but we don't grow, and the theory explains that. I don't have time to go into it. Maybe we can discuss it later. And it's all to do with the input of energy and the distribution of energy and the scaling of the networks that are inside us. But the point is that this would be very bad if it were a socioeconomic system because this is our image of socioeconomic systems, and I showed you a picture before of the economy, always open and expanding. 

And I want to come back to this in a moment. So, here's a picture of the extraordinary scaling in biology. So, let me spend a minute on it. What you see that's plotted here is the most fundamental quantity, certainly from a physicist's view, in biology That is your metabolic rate. How much energy do you need per day to stay alive. The 2,000 food calories a day that you eat to stay alive, and here it is plotted on the vertical axis against the weight, the mass of the organism on the horizontal axis, and it's plotted in a Byzantine way. So I can put mice and elephants on the same graph, and the Byzantine way is that instead of being linear, it goes up by factors of 10. One, 10, 100, 1,000 watts. One, 10, 100, 1,000 kilograms. So we can get everyone on the same graph. 

And what you see is something extraordinary. That there's an extraordinary regularity when we're dealing with maybe one of the most complex and diverse phenomena in the universe. Something unbelievably simple, ridiculously simple has emerged, and this, at some level, astonishing because we believe that each one of these organisms, each subsystem of that organism, each organ, each cell type, each genome has evolved with its own unique history and its own unique environmental niche. So, you might have expected from that natural selection viewpoint that if I plotted anything versus the size of an organism, it'd be all over the map representing, manifesting the historical contingency involved in all of this. No, that's not what you see. You see something ridiculously regular, and that regularity has some extraordinary features. For one, the slope of it is approximately three-quarters, and that three-quarters is less than one. One would be a slope, a line like this. And one is what you might naively expect if you thought everything were pretty much the same at the most naive level. You'd double the size of an organism, double the number of cells, therefore doubling the amount of energy needed to keep it alive. 

That's not what you see. You see something less than one which means, in that language, double the size of an organism, approximately, instead of needing twice the amount of energy, you only need, roughly, 75%. So there's this extraordinary economy of scale as you get bigger, and this is called sub-linear behavior. So it turns out that if you look at any physiological variable that you can measure or any life history event that you can think of, it all has this kind of character. And I'm going to show you a couple of examples. There's heart rate, a very mundane kind of quantity, versus body size. I'm not going to explain it in detail, but what you see is, again, a very simple scaling law. This is your thinking. This is your white matter to gray matter in your brain. Again, a very simple law evolving. 

This is your genomes, and what you see from this is that you have this regular behavior and the other remarkable thing is all the slopes of those, like that three-quarters, are simple multiples of one-quarter. Four plays this amazing role in these scaling laws of extraordinarily complex phenomena. What is underlying them, and this is work I did with colleagues at the Santa Fe Institute, and I'll tell you who they are in a moment, the idea is how in the hell can this be that all of these phenomena have simple scaling laws, and why is it that the scaling laws of the mammals are the same as for birds, fish, crustacea, insects, and so on? How can that be? Well, what could be universal among them? What could be universal is somehow the supply of energy and resources through networks has to be a commonality among them, and the idea here was, is that it is the mathematics, the universal mathematics and geometric topological properties of those networks that transcend design that are constraining natural selection. That's the idea. And I don't have time to go into that other than to say that if you look at these networks, that's your brain, that's your white to gray matter of the brain, that's your lungs, that's a tree, that's a little thing, that's inside an elephant, but they're ubiquitous. And they have these, the postulate is they have these properties, and if you use those properties, put them into fancy mathematics and use Bill Hamilton's principle of energy, least action kind of ideas, out pop all of these marvelous scaling laws, including the number four, the one-quarter, which happens to be, for your information, the dimension that we live in three plus one. And just to add to that, the plus one has to do with the fact that these networks have a fractal-like behavior. That's a kind of tangential remark. So, here's others. This is down at the intracellular level. 

This is the mitochondrial level and so on. So here's that growth again. So, the idea is we have this theory. The claim is we have this wonderful theory based on networks, the mathematics of networks, and that from that we can understand these scaling laws, but also, if you like, we understand the network. We can understand the structure of the network within each of the organisms. And you can use that to go back to this growth and use this kind of idea that if you eat, you metabolize. That energy goes through the network, controls the network which maintains the cells that are there, replaces ones that are dead, and grows new ones. And then, from that, you can mathematize it, and that gives rise to this equation which actually invokes all of the properties of the network and gives rise to these kinds of, what we call, sigmoidal, meaning they stop growing, curves. Okay. So here's kind of a summary of this part. 

We have these amazing non-linear quarter power scaling laws. They represent an economy of scale. The one-quarter is intimately related to flows of energy in networks. One thing I did not emphasize is the pace of life systematically slows with size. So that, for example, heart rates decrease systematically when in to these quarter power scaling laws. The rate of diffusion of oxygen, say, across membranes decreases with size. Organisms live longer systematically. And so on and so forth. Everything to do with time slows down the bigger you are. Growth is sigmoidal. 

It reaches a stable size of maturity. And to emphasize again, the idea is this is all based on mathematics and properties of networks. So, and this is a sustainable system. It's sustainable, phenomenologically, because it's been around a couple billion years or more. Part of that sustainability, I believe, is actually invoked in the fact that things stop growing. They stabilize and most organisms, not all, we can discuss this, most organisms spend most of their mature life in a stable size configuration. Not all and there are exceptions, and we can discuss that. But this leads to a sustainable, resilient system. And the question is, I'm sorry. Yes, so this is the motley crew that I work with. 

Some biologists, some physicists, some chemists. But I then took the work over into social organizations, and there's another motley crew. The top guys did all the work. All the guys at the bottom are famous and did none of the work. [LAUGHTER] And the guys in the middle started off with me and then moved on to other things. Okay, so here's the question, the first question about whether cities and companies are biological. The first thing is, do they scale? So what we said before was that whales live in the ocean and elephants have trunks and giraffes long necks and we stand on two feet and mice scurry around, but in fact, at the kind of 85% level, they're scale versions of one another in this non-linear quarter power fashion. In this mathematical fashion, they're scaled versions of one another. Is that true of cities? And is it the kind of universal scaling as it is in biology? So, are cities scaled versions of one another? Is New York a scaled up San Francisco, which is a scaled up Madison, which is a scaled up Santa Fe? Even though they look completely different. Well, you can only answer that, at first light it's hard to believe, every city feels so unique. 

But of course, you can only answer that by looking at data. But one of the reasons you might think there are scaling phenomena, there are these kind of generic universal similarities, is because cities are, indeed, networks. There's the obvious networks of roads and electrical lines and all the rest of it, like this, and transportation systems, but, more importantly, there's this network which never occurs, essentially, in biology. It is the network of us talking to one another. It's us, social networks, that is unique. It's only been around on this planet for maybe 10,000 years. Maybe in the universe for all we know for 10,000 years. Who in the hell knows. But, certainly, in our solar system. This is it. 

It's new. And it's this. This is just people talking to one another, how they interact with one another. So, oops, I seem to have lost the slide. So, I use this slide. What is the city but the people. Indeed, the city is not the buildings and the roads and all this other stuff. It's us. We are the city, and that stuff is a manifestation of the interactions between us. And that's something that is outside of biology but is integral to biology because it's driven by biology, and it's driven, in large part, by energy, and I'm going to talk about that. 

So, the other part of the network is not just we interact with each other but we prosper. So, I'm going to not say much more about that but go straight to the data and ask the question about scaling. So this is a graph plotted in the same way as those biological graphs were, but this is a mundane one. The number of petrol stations, I was working with European colleagues, the number of gas stations in a city as a function of its size in various countries. And you can see, there's pretty good evidence of scaling again, there's a very simple line on this plot, plotted this way. Very much like biology, and like biology, this would be linear so that you don't, when you double the size of a city, you don't need twice as many gas stations. In fact, what you find from this, you only need about 85% more gas stations. The slope of this line is not three-quarters as it is in biology. It's about .85 it turns out. Most importantly, though, is that they're pretty much the same. 

The slopes of these are the same. The same economy of scale occurs in all these European countries but it occurs in Columbia, it occurs in Chile, it occurs in China. Anywhere you look across the globe, you get the same scaling, and if you look at any infrastructural quantity that you can measure, you get the same scaling as this. There's a consistent, always roughly 15% saving every time you double. Okay? >> Geoffrey? >> Yeah. >> Ten. >> Good, perfect. So this is kind of a mundane quantity, and that's like biology. Looks just like biology except it's .85 instead of .75. But this is something that doesn't exist in biology. 

Wages, super-creative people, and you ask, how do those scale with the size of the city? And here they are. This is wages at the top, and this is super-creatives, so-called super-creatives by a man named Richard Florida. And what you see is there's more fluctuations in the data, but there's pretty good evidence of scaling. But, most importantly, the scaling is different than in biology. The slope of these are bigger than one rather than less than one, and this is critical. Namely, the slope of these you see is roughly about 1.15. So what that says is that if you double the size, instead of needing less per capita, you have more per capita, and I will come back to this in a moment. So here's wages, super-creative. Here's patents. This is some crude measure of the innovation of a city. 

The slope of this is also about 1.15. This is the crime in Japan, a little bit bigger 1.15. This is police, tax receipts, construction, all about 1.15. And there they are, all plotted on one another, just a few of them to show a universality of income, GDP, crime, and patents. Very different things but they all scale in the same way with quite a lot of fluctuations, and the slope of that is roughly 1.15. And we believe that underlying are the universality of social networks. The way we interact with each other is a kind of universal phenomenon whether you're in China, Japan, Columbia, United States, anywhere. The fundamentals of the social interaction is universal, and that is what is being manifested in these scaling laws. These scaling laws are for multiple socioeconomic quantities anywhere in the world. We've looked at data in Europe, United States, China, Japan, Latin America, and so forth. 

What is interesting to substantiate that is this graph which is very recent data which is the number of cell phone, the amount of people you call on your phone, on the average, as a function of city size. So this is a kind of way of tapping in to the network, the social network, and if this theoretical framework of the mathematics of that social network is the right one, the slope of this should be about the same as these other networks. And indeed, we could have plotted this on top of this, and it would fit right on top of it. So this is the number of people you talk to, on the average, as a function of your city size. So, I'm going to miss this. That's what I said a moment ago. And here's kind of a summary of this. The good, the bad, and the ugly. If you double the size of a city or if you look at a city that's twice as big as another city, then systematically across the globe, and you double the size, you can go from 50,000 to 100,000 or 5 million to 10 million, it doesn't matter where you begin to double the size, systematically, income, wealth, patents, colleges, creative people, police, crime, AIDS, flu, all of these things, the good, bad, and the ugly all go up together to the same degree. And, at the same time, you save about 15% on the infrastructure. 

Big cities are good, and the bigger ones are better still both at the collective level. They save on infrastructure per capita. I had a graph which I flipped through. They save on carbon footprint per capita. And at the individual level, everybody is attracted to cities by the first lot of those, income, wealth, number of patents, colleges, and the general buzz of city, and ignore the other bad things. The fact that they're coming along with it, hand in glove, there's more crime, disease, and so forth. Okay. So, the network dynamics is the one that dominates this again, and the networks dynamics has the following interesting phenomenon that if it's sub-linear scaling then we have this pace of life slowing with size, as I mentioned, but if it's super linear, bigger than one like we see in socioeconomic systems in cities and driven by the social networks, then the theory tells you the pace of life systematically increases with size. And so, the pace of life in New York is systematically faster than it is in Madison, which is systematically faster than it is in Espanola, which is a tiny town near Santa Fe in a systematic way. And here's some whimsical data to show you that. 

We've looked at many things. On the left is some data on heart rate versus body size. The one on the right is walking speed. I show you walking speed. People have actually measured walking speed perfect. And you can see it systematically rising, and it's in reasonably good agreement with the data. But why? Because walking, actually, walking in a city is a social phenomenon. Okay, so I'm going to miss this out, I think. Yes. So, this is kind of a summary, and I'm going to finish off in the last few minutes with the last part of this. 

So, unlike biology, super linear scaling, socioeconomic, which has to do with wealth creation and innovation and ideas, dominates, and so you get this kind of 15% rule, which I'm not going to talk about its origins here, that also leads to a systematic increase in the pace of life. And the last thing that I'm going to talk about which is very satisfactory is that if this is true, which it is, and it comes from these networks, then I'm going to talk about growth and the idea of open-ended growth following from this because we're going to use the same kind of growth equation that, again, based on energy equivalent of the flow of energy through these systems leading to maintenance and growth, and that's what we had before for us. The sub-linear scaling leading to boundary growth, and if it's super linear scaling, there's a cartoon on the left, this leads to actually faster than exponential growth. And that's very satisfying. That's great because that's what we see, and that's what we apparently love or have loved for the last couple hundred years. And that's great. However, it has, if you believe the theory, this has a fatal flaw. And the fatal flaw is denoted by this line. And it's called, in the technical language, a finite time singularity. And to put it in very simple language, what it says is that in some finite time, this damn growth curve will go to infinite size, and that's obviously impossible. 

So this is kind of a Malthusian argument. Namely, at some stage, you're going to run out of whatever it is that's keeping the system alive, the resources, the energy, whatever it is, and the theory tells you what happens. It says as you go through this so-called singularity, you stagnate and collapse. That's terrible and we need to avoid that, and we have avoided it. And this is how we avoid it. We avoid it for the very reason that Malthus and Paul Ehrlich were rejected. That is, they did not take into account the fact that we innovate ourselves out of these problems. So I want to finish on this note. So here's the situation. This is, you start at some point and you start growing and you would hit this singularity and collapse. 

So somewhere along here you better change something because this growth was done in the paradigm of whatever the major innovation is. It could be the discovery of iron. It could be the discovery of coal. It could be oil. It could be the invention of computers. The invention of IT, but something major that has a kind of paradigm shift and changes everything. So, this suggests that the way out of this dilemma of collapse is that you innovate somewhere here, and you start over again. You reset the clock, and then you can go on merrily. And, of course, you're going to hit another finite time singularity and collapse unless you innovate again. So you have to keep innovating. 

So there's a kind of theorem if you like. But if you want to continue to have open-ended growth, you have to have cycles of innovation. Well, people have been saying things like that for a long time. Here's the difference, going back to what we said: as you grow and you get bigger, the pace of life increases. So, first of all, the pace of life is increasing. The second thing is, it turns out the theory says yes you can do this, but the time to go from here to here necessarily has to be, and systematically, a lot shorter than the time from here to here. So that you can innovate, you have these cycles of innovation, but they must come quicker and quicker. Okay? So, the image is we're on this treadmill that is going faster and faster, which is difficult to begin with, but at some stage, you've got to jump from that treadmill onto another treadmill that's going even faster. And then very soon, you've got to jump onto another one, and you've got to kind of keep doing this so you have this kind of double acceleration. And the question is, do you suffer a kind of global heart attack from that? [LAUGHTER] So, is this sustainable? Obviously not, ultimately. 

And this is not mine at all. This is someone, I don't know who he is, but he did it and he showed it was great. Oh, this is something I saw in an English newspaper a week ago which I thought illustrated the point a little bit. So here's something, some of you may have heard the idea of singularity from this, what I consider, little bit looney work of Ray Kurzweil. I think it's looney, but he did some wonderful things of collecting data. I don't agree with a lot of this, but what he's plotted here is that here's the paradigm shift. That is, how long it took to create each one of these paradigms versus how long ago it happened. Okay? And what you see is it takes shorter and shorter times to make these shifts, and it's happening faster and faster. And he drew this. All kinds of people have done things like this. 

I'm going to finish up. And, whoops, and interestingly enough, that straight line, if you take this theoretical framework that I just told you about, this continuous innovation and jumping from one treadmill to another, it predicts, almost exactly, that orange line. So that's data kind of supporting it. So I'm going to finish with that, and I'm going to finish with one last image which is this just to give you a sense of things in terms of energy. Our metabolic rate, I didn't point that out on the graph. You remember that graph of metabolic rate? Our metabolic rate in watts is about 90 watts. A little bit less, women versus men. But roughly it's about 90 watts. We're a light bulb. One of these bloody light bulbs is equivalent to one of us. 

So, turning a light bulb off, it's like your mother telling you if you turn it off, you help starving people in Sudan or somewhere. So it's ridiculous having all these lights on, frankly. They're us. We are extraordinarily efficient. That 1,800-2,000 food calories a day is unbelievably efficient. It may seem like a lot of food, but it's just a light bulb. However, and incidentally, that metabolic rate is the metabolic rate we should have for a mammal of our size. That's what we should have. Okay? And if you add in activity, hunting and gathering, which is the way we evolved or versions there of, that number changes from 100 to about 250, the amount of energy we do to hunt and gather and so on. And that also scales the active metabolic rate for mammals. 

So that's what we "should have." Then we started talking to one another. We discovered economies of scale to form communities, and then we started to innovate. And once we innovated, we created all of this [###] around us, all this wonderful quality of life and standard of living that we'd like to have for everybody. And we can ask, what is our real metabolic rate? What is our social metabolic rate of having cars, and lights, and buildings, and all the rest of the stuff? That number goes from about 90 watts to 11,000 watts. And you can turn it around, this has been done on this graph as I did here, and ask, how big is it? What big an animal are we? This is about a dozen elephants. Each one of us in this room and there are seven billion people of us on this planet who all want to be like us, and there's three billion more coming in the next 30-40 years, and they all want to be like us using 11,000 watts. So this is an enormous problem, and I cannot answer the question, what is the future and what does it bring? But I can say that I'm a pessimist. So I'll finish on that. [APPLAUSE]