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26| Networks, Heartbeats & the Pace of Cities — Geoffrey West
166 Plays9 months ago
Why do whales live longer than hummingbirds? What makes megacities more energy efficient than towns? Is the rate of technological innovation sustainable?
Though apparently disparate the answer to these questions can be found in the work of theoretical physicist Geoffrey West. Geoffrey is Shannan Distinguished Professor at the Santa Fe Institute where he was formerly the president.
By looking at the network structure of organisms, cities, and companies Geoffrey was able to explain mathematically the peculiar ways in which many features scale. For example, the California Sea Lion weighs twice as much as an Emperor Penguin, but it only consumes 75% more energy. This sub-linear scaling is incredibly regular, following the same pattern across many species and an epic range of sizes. This is an example of a scaling law.
The heart of the explanation is this: optimal space-filling networks are fractal-like in nature and scale as if they acquire an extra dimension. A 3D fractal network scales as if it is 4D.
Chapters
(00:00) Introduction
(02:56) Start of conversation: Geoffrey's Career Journey
(03:25) Transition from High Energy Physics to Biology
(09:05) Exploring the Origin of Aging and Death
(11:20) Discovering Scaling Laws in Biology
(12:30) Understanding the Metabolic Rate and its Scaling
(25:40) The Impact of the Molecular Revolution on Biology
(28:39) The Role of Networks in Biological Systems
(49:07) The Connection between Fractals and Biological Systems
(01:00:29) Understanding the Growth and Supply of Cells
(01:01:07) The Impact of Size on Energy Consumption
(01:01:46) The Role of Networks in Growth and Supply
(01:02:30) The Universality of Growth in Organisms
(01:03:13) Exploring the Dynamics of Cities
(01:06:12) The Scaling of Infrastructure and Socioeconomic Factors in Cities
(01:07:36) The Implications of Superlinear Scaling in Cities
(01:11:50) The Future of Cities and the Need for Innovation
Recommended
Transcript
Introduction of Geoffrey West and the Influence of Spatial Dimensions
00:00:00
Speaker
I'm James Robinson. This is Multiverses. The shape of our world affects the shape of our lives. The fact that we live in three stretched out spatial dimensions has surprising implications. It underpins, for example, a set of laws which determine not only how heart rate varies from species to species, but how the pace of life increases in cities as they grow in population.
00:00:22
Speaker
guest this week is Geoffrey West, a theoretical physicist. He started studying out particles and ended up leading group at Los Alamos, but he became interested in problems from biology, in particular the problem of lifespan, why some species live longer than others.
West's Transition from Physics to Biology
00:00:38
Speaker
And as he set out studying biology, he came across a century-old conundrum, Kleiber's Law.
00:00:43
Speaker
Kleiber's law describes how the metabolic rate of species changes with their mass, depends on their mass. So, for example, a species that weighs twice as much as another one doesn't require twice as much food. It only requires 75% more. So there's an economy of scale here. And this relationship is incredibly regular. It's an example of the scaling law.
00:01:06
Speaker
And to cut a long story short, Jeffrey solved this conundrum, and he solved the conundrum of lifespan too. And the kernel of the solution is this. Organisms are networks. They're networks of cells connected by a vascular system. And these networks don't scale in the same way as the mass. They have a peculiar scheme because of their fractal nature, or fractal nature, sorry.
00:01:30
Speaker
Jeffrey got interested in what other systems that are networks and how they scale. Do we also see interesting behavior for companies and cities, for example? Indeed we do. So if you take a city and you double its in size,
00:01:47
Speaker
its energy usage doesn't double. It only goes up by 85%, so there's a similar economy of scale here. But the productivity of that city, which you can measure, for example, by the number of patents per head or the number of restaurants, the productivity doesn't double as you double its population. It goes up by 115%, it more than doubles.
00:02:08
Speaker
And this makes cities these huge engines of growth, because as cities grow, they become yet more productive and yet more attractive to people, so they grow even more. And this leads in fact to super exponential scaling, faster than exponential scaling in the production that comes from cities. And that is not sustainable. So I don't know what the answer is there, but that's a serious problem.
00:02:34
Speaker
This is a marvellous conversation for me. Jeffrey is as wonderful a storyteller as he is a brilliant scientist. I thoroughly recommend his book, Scale, but without further ado, this is Jeffrey West. Jeffrey West, thank you for joining me. Yes, pleasure, James. Thank you for inviting me. I'm looking forward to our conversation.
Journey from Physics to Biology
00:03:05
Speaker
You started your career looking at the tiniest of things, at quarks and so forth, and very far away problems like the origin of the universe. But you've ended up in a very different place looking at enormously large systems composed of lots of little things and speaking to the issues that concern us every day. Can you tell us how you went about, how did that journey happen?
00:03:32
Speaker
Oh boy, let's see if I could keep it brief. Well, first of all, of course, I don't suppose any of it would have happened had I not had a sort of natural predilection to wanting to sort of, I mean, that sounds, sounds arrogant, but understand everything, you know, as a, you know, I was always asking questions, I was interested in everything as one does when is, you know,
00:03:58
Speaker
as a young boy and even in high school and so forth. And I always harbored a sort of romantic image of what being an academic would be. And that was sort of enhanced by being an undergraduate at Cambridge, just the
00:04:16
Speaker
the physicality of it, I mean, and so romantic, totally romantic and unrealistic image. And I sort of had this image that I'd always be around people asking questions across the entire spectrum of life, so to speak. But I was also very good at mathematics.
00:04:39
Speaker
And what I think happened was that led me naturally to physics, because physics seemed to be the only science that actually answered questions. They posed them, these deep questions, and they answered them. But they not only answered them,
00:04:58
Speaker
in a rather precise, quantitative fashion with an analytic, deductive strategy. And that was very appealing. So I ended up doing, as you say, Heinji physics, corks and gluons and string theory and dark matter and all these wonderful questions. But then, but I always sort of was slightly frustrated
00:05:22
Speaker
that I was being forced into this box, even though I had a rather, you know, very eclectic group around me. Nevertheless, so that kept going. And then in the
00:05:40
Speaker
I guess it must have been the late 80s, 90s when this superconducting supercollider was being proposed and being built, this huge accelerator that was going to cost the beginning of the order of $10 billion.
Major Project Cancellation and Shift to Biology
00:05:59
Speaker
And we were all very excited about it and so on. And then it was canned in the early 90s.
00:06:05
Speaker
This is a big facility that was going to happen in the USA, right? Yes, in Texas. It was much bigger than the Large Hadron Collider, now it's certain. And it got canned. And so it was obviously a crisis in the field. And I, like many others, went into a kind of depressed mode. But I also went into a mode of
00:06:36
Speaker
You know, oh, so part of it was it also coincided that cancellation of the superconducting supercollider, the SSC, coincided with one of those waves of anti-science that comes to fore every once in a while. And it focused primarily on physics. And the comment that was always around was,
00:07:04
Speaker
Physics was the science of the 19th and 20th centuries. The science of the 21st century will be biology. Well, it's hard to argue with that in many ways, but I reacted saying, yes, that's very likely, but biology will not be a real science.
00:07:24
Speaker
until it somehow integrates and absorbs the culture and some of the techniques of physics. It doesn't have physicists necessary, but it needs to think more like physics. Now, by the way, this was total arrogance and total ignorance because I knew no biology and it was coming out of pure defensiveness and reaction to this SSC thing.
00:07:47
Speaker
But we heard that all the time, but there was also a corollary to that that was either left unsaid, but sometimes said. And that was, there's no need to do any more fundamental physics. We know all the fundamental physics we need to know. Let's devote our resources to other things. And I felt that was completely mistaken. So sitting around one day,
00:08:17
Speaker
I thought, you know, I keep saying this statement that biology won't become a real science that does physics. You know, it's sort of stupid, but maybe I should try to put money where my mouth is and try to think of doing some biology of my own. Well, that happened to coincide also with some concerns obviously initiated to some extent by the collapse of the SSC that was getting old. I was in my mid fifties at the time.
00:08:48
Speaker
And I come from a very short-lived line of males. Most of us die in our 50s and 60s. And so I realized that if genetics play a role, I probably don't have more than about 10 more years. And I started thinking about it. I thought, why
Discovery of Kleiber's Law
00:09:07
Speaker
is that? What is it that is the origin of aging? And I thought, that's an interesting problem to think about. But no doubt, there must be
00:09:18
Speaker
tons of work been done in biology on this and in medicine. And so I, but I started thinking about it. And then I started thinking a little more seriously by going to the library and actually reading about it. And one of the things I discovered was that in fact, it was a total backwater that despite the fact that at least the way I think about it, it's the second most death is the second most important event in the life of an organism.
00:09:47
Speaker
birth being the most important, but death is, you know, that's it. And yet here you found, you know, here it was a backwater. I looked in these big fat books, you know, that they teach elementary biology and the covers all of biology, and you look in the index, nothing about aging and death. Everything else is covered.
00:10:08
Speaker
So I thought, oh, that's good, because that means that maybe this is something I can think about. But then another thing I realized was that I had set myself not just the question, why do we age and why do we die?
00:10:23
Speaker
But why do we live a hundred years? So I'd put it in a physicist terms, simplistically. When the hell does the scale of life come from? You know, why a hundred years? Why not a thousand years? You know, what are the knobs that you can turn to make us live a thousand years or what knobs have been turned by natural selection?
00:10:44
Speaker
and so on. So I started thinking about that. And the first thought that I had to start actually deriving, quote, a theory was, look, if the system is going to age, decay, and eventually disappear, obviously you have to understand what it was in the first place that was keeping it alive.
00:11:11
Speaker
You know, because obviously something has gone wrong. I mean, it's produced too much entropy or whatever. So, and that's called metabolism in biology. So I didn't know much about that. So I started reading about metabolism and I learned about these extraordinary scaling laws.
00:11:28
Speaker
in biology, that is that, and we will hopefully talk a little bit about that later on, but I discovered, I discovered, I learned reading that there was this famous law discovered in the 1930s by a man named Max Kleiber that said that metabolic rate, from a physicist's viewpoint certainly, but maybe also a biologist, the most fundamental quantity of life. How much energy does the organism need
00:11:56
Speaker
to stay alive. How much food does it need to eat per day to stay alive? If you asked, how did that scale with the size of an organism? That's scaled in an extraordinarily simple mathematical way. There's a so-called power law. And the way that's represented is if you plot
00:12:15
Speaker
the metabolic rate logarithmically that is going up by factors of 10 on the vertical axis against weight plotted logarithmically on the horizontal axis, all the points fitted on a straight line. And that blew my mind because
00:12:35
Speaker
I was a great subscriber, as most of us are, to the idea of evolution by natural selection and this kind of naive idea that it's all historically contingent. Everything depends on what's happened before and the frozen accidents that have happened and the kind of environmental niches thing organisms evolved in.
00:12:55
Speaker
not just the organism, but every component of the organism. Therefore, you would have expected if you plotted anything as complex as metabolic rate versus size, there would be, you know, there might be some correlation, but the points would be all over the graph, reflecting historical contingency. This was quite the contrary.
00:13:17
Speaker
And I thought, my God, you know, there must be an explanation for this. Well, it turned out that there wasn't a satisfactory one. There was no you. And by the way, this was true across all of life. Wasn't just sort of mammals and birds or fish, but everything followed this straight line. Not only that, the slope of this straight line, Max Clyber had learned, was three quarters, very close to three quarters. So I thought,
00:13:45
Speaker
And so I first thought, that's great. I'll use this to learn about aging. But I first better understand where this law comes from, myself. And so I started biology.
00:14:01
Speaker
I learned, I derived that law from some fundamental principles. I hooked up with some extremely good biologists, and we eventually published a paper in Science. They got a lot of publicity. And I was still running a big high-end group, by the way. I mean, it was sort of weird. It was sort of a hobby.
00:14:22
Speaker
still, but it became very clear that this was much more exciting than the Epsilon progress I was making in string theory that anyway, no one was paying much attention to anyway, whereas here I was getting accolades for doing this work in biology. So that serendipitously led to my sort of adiabatically slowly moving into becoming a kind of pseudo biologist.
00:14:52
Speaker
Yeah, I think in a moment, I want to go into the details of where that three-quarters scaling law comes from and what it means, because that's so fascinating. But I do want to pause here, because it's such an extraordinary story. This arc going from being quite an evident theoretical physicist running a group at Los Alamos
00:15:20
Speaker
in one field, and then, you know, fairly late for most people in their career, at least, you take a completely different track in some ways, it will find out that you actually use the tools of a theoretical physicist. But you know, it's an extraordinary, it's, it's an incredibly ambitious program to say, Oh, no one's no one's figured out why animals, why, why humans live for 100 years.
00:15:46
Speaker
There's nothing in the literature on this. I'm quite intrigued about that problem, so I'll go and find the solution. And one wouldn't expect a lot of progress. That doesn't sound like it's going to be a fruitful start of a research program, but it really was. I just love these kind of two-act books, and this seems like one of them.
00:16:10
Speaker
So, of course, by the way, just to repeat what I said earlier, it was a product of arrogance, ignorance and naivete. And it's true, I did not expect that this would have, you know, that I better solve the problem, frankly. And I didn't expect that, you know, that this would lead to a change in direction of my career. But I was very open to it. That's why I told the SSC, I was very open to it, because
00:16:39
Speaker
it was for two reasons. One was because the field I was in was going through a crisis and stagnation. And also I realized that at some semi-conscious level I had felt constrained or claustrophobic somehow. Surprising in a way when you think about it because I was working in string theory which I think
00:17:05
Speaker
Maybe by then, maybe it had already been dubbed this ridiculous term, theory of everything. And here I was feeling claustrophobic about the theory of everything to work. And one of the things I realized later, by the way, was I had also part of that arrogance
00:17:28
Speaker
was that part of the culture of physics, but particularly high-energy physics and theoretical high-energy physics
00:17:38
Speaker
was and is still to some degree that all you need to know is the fundamental equations. You know, if you knew, you know, if string theory is it, and it is beautiful, by the way, I'm not putting any of that down, quite the contrary. If it is it, that all you got to do, you have the theory of the equation, and then you solve it and you keep turning the crank,
00:18:04
Speaker
and out come the origins of the universe and the Big Bang, and then come galaxies, and then planets, and then you have the Earth, and then there's life, and then there's automobiles, and then there's iPhones, and it all comes from just turning the crank. Because once you have that equation, in a certain sense, it's all engineering.
00:18:27
Speaker
I'm exaggerating and making a total cartoon version. But that was sort of the mindset. And the thing that I learned was the obvious, that equally challenging and even more exciting in some ways is the messy stuff that exists on this planet. As far as we know,
00:18:50
Speaker
This is the only place in the universe, as far as we know, some probably are other places. This is it. This this complete mess that we live in on this planet and all these extraordinary processes that take place called life or complex systems are even more challenging, remarkably than understanding the origins of the universe, which is weird.
00:19:22
Speaker
Because physics has built into it. The culture is that there is an equation, a fundamental equation, and from that follows everything. Well, one thing we'll follow is the evolution of the universe. And we've done an incredible job.
00:19:38
Speaker
progress in cosmology, astrophysics, astrobiology even has been fantastic in the last 25, 30 years. But it's all what some of us call simplicity. Because you can write an equation and try and solve it.
00:20:02
Speaker
and continuum, I mean, it's a linear, almost linear process. Whereas trying to understand what's going inside your head at the moment, you know, we're probably never under, I mean, that's not a personal statement. But you know, understanding our brains and consciousness, and you know, what the stock market is gonna do, and you know, are we gonna solve all the problems of the future of the planet? Those are a completely different category of problems. It's not like an equation.
00:20:32
Speaker
Yeah, I think we're not saying that in principle, there's some kind of new non-physical behaviour that emerges, right? In principle, if you could crank that equation, it would produce, or it does indeed, if we had the equation, a theory of everything,
00:20:51
Speaker
that is the underlying dynamics that governs everything. In principle, it could be cranked, perhaps, but in practice, it can't. And even if it could, I'm not sure that that cranking would produce understanding. It might produce
00:21:06
Speaker
you know, the right outcomes, but would it actually explain anything to you in a human sense? Probably not. Yes, we don't learn anything about life from the fact that, you know, the nuclei of atoms are made of protons and neutrons or where we do from that, but the protons and neutrons are made of quarks and gluons and so on.
00:21:32
Speaker
It doesn't, you know, so there is this, which physicists recognize, there's this level structure, and those levels are to varying degrees uncoupled. In some cases, they're highly coupled. And the trouble for life on Earth, for the stuff on Earth, all the various levels are very closely coupled, and they're all interrelated.
00:21:53
Speaker
You can't do that separation and that's what makes that that's what allows us to do physics in a way is that especially fundamental physics because levels tend to get Separated from each other and you can consider them autonomously. Yeah.
Biological Scaling Laws and Energy Constraints
00:22:12
Speaker
Yeah let's come back to these remarkable scaling laws, which we should say max climber discovered and
00:22:19
Speaker
almost 100 years ago, I think, in the 1930s. So it's incredible that they were sort of laid to one side for so long. And what they say is truly remarkable, that if you double the mass of an organism, so if you go from one animal that weighs half of another species,
00:22:47
Speaker
That heavier species doesn't need twice as much food per day. It needs about 75% more. So that's the three quarters of the exponent that you mentioned.
00:22:59
Speaker
This three-quarters are remarkably consistent across species and across kingdoms. It's not just animals, it's plants as well. That same exponent turns up if you're looking at the number of leaves in trees. It doesn't double as you double the mass of the tree. It again only goes up by three-quarters. That's an incredibly striking thing. How does one go from
00:23:28
Speaker
seeing that relationship in the data to then figuring out an explanation for that.
00:23:34
Speaker
So first of all, I want to just continue with the phenomenology of it. That is, it's not just metabolic rate where you already said it, number of leaves. It's almost anything. You can make what is extraordinary. And the thing that really got me wasn't, I mean, the metabolic rate got me. But then when I learned very quickly that almost any physiological quantity trait of any kind of organism
00:24:04
Speaker
obeys similar laws as does any life history event. So a physiological trait would be like number of leaves or the length of your aorta and so on. And life history would be how long you live, in fact.
00:24:18
Speaker
or how many offspring you have or how long do you take to mature, you know, all these kinds of, they're all scared about them. They all have these straight lines and the thing that is so striking is that the slopes of those lines are always simple multiples of one quarter.
00:24:37
Speaker
So there's this extraordinary universality and first discovered by Kleiber. But during the 30s, 40s, and into the 50s even, people just added to this so that there's huge amounts of data that can be collapsed onto these scaling curves. And one of the things that helped me in my work was it just so happened that in the
00:25:05
Speaker
In the early 80s, two or three books had been written summarizing all of this data, basically. And so it was already there, ready to be explained, if you like.
00:25:23
Speaker
There was interest in these laws. They weren't put aside then quite. And in fact, many of the most distinguished biologists, Huxley, Hordain, and so forth, Darcy Thompson, all were intrigued by these things. But what killed it, of course, was the molecular revolution.
00:25:43
Speaker
I mean, the realization that we can really understand very important, powerful aspects of life from a molecular viewpoint and with the discovery of the structure of DNA, et cetera. And that completely dominated biology.
00:26:03
Speaker
And to varying degrees still does. I mean, that viewpoint, much like high energy physics has the viewpoint that everything can be, you know, if you know the fundamental laws of quarks and gluons, you get everything. There's sort of this naive view in biology. If I, oh, I mean, in fact, it was in the human genome project.
00:26:24
Speaker
was basically said, once I've mapped the human genome, everything follows. We know everything, which was even I who knew very little about it thought that was absurd. But anyway, that's beside the point. So here were these, so they went into sort of onto a back burner, known mostly only to ecologists because
00:26:48
Speaker
for obvious reasons, in an ecology you need to know when you're talking about interaction of species, how their metabolic rates change with their size, and so on. So many ecologists knew it. And my major collaborator, Jim Brown, was a very distinguished ecologist. And we came together because he was very intrigued as to how the origin of these laws were that he was using. Where the hell did they come from?
00:27:18
Speaker
So now let me try to answer your question. Indeed, where do they come from? So the thing that got me immediately when I realized that these laws were ubiquitous and had this universality to them was that obviously whatever the underlying principles were had to transcend the
00:27:45
Speaker
sort of involved engineered design of life. That is, if it applies to trees and to mammals, it has to be something that is independent of what makes you a mammal and what makes a tree a tree. And so one of the things that is common, of course, and that's why the molecular revolution was so powerful, was genes. And you could say, well, it's
00:28:14
Speaker
encode in the genes. That doesn't explain anything, of course, that just sort of puts it back one step. So I sort of dismissed that. That was not a very satisfactory answer. And then I thought, well, there is one thing that is common to all of these. First of all, it's obvious that a lot of these are to do with the use of energy.
00:28:37
Speaker
in some form or another, metabolism being the most obvious example, but you have to distribute energy. And maybe all these laws are simply a reflection of the mathematical and physical constraints of the networks that had to evolve in order to distribute energy. So natural selection,
00:29:03
Speaker
as it evolved, especially multicellular organisms, but even, you know, unicellular ones with huge numbers of components, it had to evolve networks that distributed energy and information to all the various components in a roughly, let's say, democratic efficient way. You know, just thinking in a very coarse-grained way of thinking about it. So I thought, well, maybe that's the origin of it,
00:29:32
Speaker
Let me try and see if it works for mammals. Just that idea, take that idea from mammals. So I started to look at the structure of networks and I wrote down the mathematics of these networks and wrote down some generic universal principles that I thought might apply to them. Like for example, one is obvious. One is that the network, say your circulatory system,
00:30:02
Speaker
It's terminal units, it's M by the caprese, have to end up feeding all the cells. So the network has to be what's mathematically called space filling. It has to go everywhere. Otherwise it doesn't make any sense. But you have to put that into mathematics. The second most important one was that if you look at all mammals,
00:30:28
Speaker
that natural selection, when it evolved different species that are mammalian, did not reinvent all the fundamental components. You don't start from the beginning again.
00:30:45
Speaker
It used the same fundamental units, basically the same cells, the same capillaries, and so on. So the idea was that this network ends at a capillary and then feeds a cell. But the capillary is the same in the mouse as it is in the whale. And the idea being also that, look,
00:31:11
Speaker
If you, in your house, the end of a terminal unit is your, is an electrical outlet plug in the wall. Now you live in a, I don't know why, let's say you live in a modest size building, but I don't know in Edinburgh, but in London and certainly in New York, there are skyscrapers. When they scale up to a skyscraper from your house, they don't scale up the electrical outlets.
00:31:40
Speaker
the outlets stayed the same. And so it is all the outlets, the faucets, the taps on your sinks and so forth, all these outlets. So I said, okay, that's almost certainly true of the sorts of systems that have evolved biologically. So that's another one. But the last one, the last
00:32:02
Speaker
sort of speculative principle was that, and this is the most important one, was that of all the possible networks that could have evolved, that even if they're space filling and have these invariant terminal units, the ones that actually have evolved by the process of natural selection, and this is where natural selection really comes in,
00:32:28
Speaker
are the ones that have minimized the amount of energy that is needed in order to sustain the system. Namely, the idea being, let's take the circulatory system again, that we all have a circulatory system that has evolved to minimize the amount of energy our hearts have to do
00:32:51
Speaker
to pump blood through it to supply the cells to keep you alive so that you can maximize the amount of energy you can devote to sex and reproduction and the rearing of offspring. So that was my, in the end, our translation of Darwinian fitness
00:33:12
Speaker
That is more pushing your genes forward, so to speak.
Optimization in Natural Selection
00:33:18
Speaker
That was the translation of that into a physical framework.
00:33:24
Speaker
It comes very naturally from a physics-y way of thinking, I guess, as well. You've got to minimize some quantity. And you know something, I did that and I just sort of did, you know, we did it and so on. And it was only much later, I realized, shit, you know, that's really, I mean, I hate to say this, that's quite profound, actually. You know, that natural, the survival of the fittest, so to speak, the continuous
00:33:52
Speaker
feedback, positive feedback in competition in the environment has led to those that can maximize their Darwinian fitness by minimizing the amount of energy they need to devote to keeping themselves alive, that mundane part. So it's a whole different, sort of a different view of, or a different rephrasing
00:34:17
Speaker
of natural selection. And it's sort of interesting, because it's only in the last couple of years, I thought, it's so weird, we never emphasize that in our work. I mean, we talk, we say it, but it deserves, I've often thought it deserves a little essay or something that sometimes I should write, trying to promote that as a just, you know, a different way of thinking about it. It's, from my viewpoint, it's equivalent. It's not a, anyway, but the point about that is that
00:34:48
Speaker
Physics operates by optimization. All the fundamental laws of physics are derived from optimization principles, everything from general relativity to Newton's laws. And so that's the way many of us like to think about systems, is what is being optimized?
00:35:09
Speaker
And then we have the apparatus. I mean, much of the apparatus of mathematical physics is related to optimization problems and constraints. Yeah. Newton's bead on a wire was sort of... Yeah, that's right. Exactly. Exactly. That was the beginning of calculus, differential. Exactly. It was very much in that spirit. And so I started working out on that, working on that. I first, totally on my own, and I made
00:35:38
Speaker
what I thought was progress. It was progress, I thought I'd write, it wasn't. But I then was hooked up with
00:35:46
Speaker
Jim Brown, a biologist who had been thinking about this as an ecologist. And he and his student, a man named Brian Encrest, who is now himself a highly established, well-known ecologist, we started meeting as discussing it. And I was telling him what I had done. And they were telling me what I had done wrong or what was not right biologically and getting it straight. And it took a year.
00:36:16
Speaker
for what I had thought I'd derived. And it was basically, I mean, 90% was, well, maybe 80% was basically right, to getting it in shape to write a paper that then was published eventually in science. But it took a year, and by the way, it was a real year. I mean, we made a commitment at the beginning. It was kind of an interesting
00:36:43
Speaker
It's something I'd never done. We met, we were two different institutions, and it turned out for various reasons it was very convenient to meet in the middle of the Centre for the Institute. And that began my association with the Centre for the Institute. But we made a commitment that we would meet every Friday morning, beginning about between 9 and 10, and they would hang around for about two or three, and we would just stay together.
00:37:12
Speaker
with a blackboard and battle things out. And, you know, I knew no biology and they were, how shall I say, challenge, mathematically challenged.
00:37:28
Speaker
You know, so it took a bit. It was sort of like, often liken it to a marriage, you know, where you get, it's beautiful and wonderful. And then other times you think, Jesus Christ, what am I doing with this? They're trying to be nuts. They don't understand that, you know, this and that. And I've felt exactly the same.
00:37:49
Speaker
But it was a wonderful, it was a tremendous collaboration, which lasted for about 15 years, actually. And having got that paper, by the way, the important thing was having done that work, it opened up everything.
00:38:06
Speaker
because metabolism underlies so many things. And so the network theory underlies so many things, you could just sort of apply the same kinds of ideas to a whole plethora of subjects across biology. Firstly, I just want to say, I feel like a year doesn't seem that long, given that you're just spending your Friday mornings on it. So it's a reminder,
00:38:31
Speaker
how much one can accomplish if the time is set aside and the right collaborators are found? That's a good point because I mean, the thing was Jim was running a big ecology group, I mean, doing work in the field. And I was running still running high energy physics up at Los Alamos. So, you know, both of us were working in our spare time kind of thing on it. But it was became very clear
00:38:59
Speaker
Maybe it was more than, it was probably a year and a half as I think about it. But anyway, it became very clear to all of us that this was one of the most exciting things not only we were doing then, but we'd ever been doing. I mean, despite all my love of high-energy physics and all the work that I was quite proud of, this was really exciting. I mean, first of all, to go from a totally abstract world
00:39:30
Speaker
of quarks and strings to a world where, you know, real things, you know, vascular systems and metabolic rates and growth rates and cancer and so on was very exciting. Yeah. It's not easy to crank through from the
00:39:56
Speaker
know, string theory to figure out why a whale lives so much longer than a mouse. Let's go a little bit more into the details on this three-quarter power.
Scaling in Biological and Urban Networks
00:40:09
Speaker
So we said that nature is or evolution is trying to optimise for something and it's
00:40:17
Speaker
you know, it's keeping the energy costs down. So I guess what the networks are trying to do is deliver stuff to the cells, the terminal units, as efficiently as possible. And in my mind, at least, it seems like
00:40:34
Speaker
What they need is as large a surface to do that as possible. It's sort of like if you're trying to push a litre of water through a straw, you're going to have to work pretty hard. But if you want to push it through a big fat pipe, it's very easy. Is that sort of the bones of what needs to be maximised, as it were, kind of a surface area that you're touching all the cells with?
00:40:58
Speaker
You can't put it that way and indeed that's one way you can look at it because let me just back off a second to the network and I will come back to that.
00:41:09
Speaker
Because you've got it exactly right. I mean, what you said is correct. But I want to put in a slightly different form. So, you know, when you grind through the mathematics of so you have to do the mathematics of a network, as you say, a heartbeat. So the complication here, which is not true for trees, that's trees and plants, is you have a beating heart.
00:41:35
Speaker
You don't have a pump that's just pushing like a straw. It's a suck. You're going, you're beating hard. So it's pulsatile.
00:41:47
Speaker
So that complicated things. But nevertheless, it's the same idea that you're pushing blood through the network down to the cells. And when you do the mathematics of that, what you discover is that where that three quarters comes from,
00:42:11
Speaker
is that the three, actually it's not three quarters, what the result is is three divided by three plus one, which is of course three quarters, but the three in that is the dimension of space you're in. So if you were in five dimensions, it would have been five over five plus one.
00:42:33
Speaker
Okay, so that's natural that that three would occur somewhere. The dimension of space you have to fill if the supply. The plus one is subtle, but it's to do with your statement about maximizing surface area effectively, because what it is, it reflects the fractality of the network.
00:42:58
Speaker
That is, what you discover is when you optimize this system, the network structure that does that is a fractal one, namely, it's self-similar. I don't know. That is, it just keeps repeating itself over and over again so that if you cut
00:43:17
Speaker
One, you go down the network and you cut a little piece out, and you removed it from the network, and then you blew it up. It would look just like the old network. So you have to blow it up in a nonlinear fashion given by the equations, but there is a operation that just reproduces the old network. So it just sort of repeats itself nonlinearly, but nevertheless, it's repetitive.
00:43:45
Speaker
And that minimizes the energy needed to push through the network. It could also be, it is also, if you think of that network as a surface, I'm sorry, if you think of the caperas, all the caperas you could lay and they form some weird surface,
00:44:09
Speaker
What you're saying is exactly right. That surface is effectively maximized with respect to all the changes you can make in the network. So the trick for mammals with a beating heart
00:44:26
Speaker
that is at first a problem is you gotta push it, your blood comes out of your heart at a very, I've forgotten the numbers and it's been too long since I've looked at this, but it comes out very fast. You know that, if you cut an artery, you don't live very long, less than a minute, or the blood rushes out. But if you touch a capillary, break a capillary, you just scrape your finger, it just oozes out.
00:44:55
Speaker
And so the system is a part of that fractal nature is extraordinary that it arranges so that the pressure drop
00:45:09
Speaker
from the very high pressure of the heart comes to almost nothing at the bottom, so that when the capillary reaches the cell, blood can efficiently diffuse across the cellular membranes to feed the cell. Otherwise, if it was rushing by, if you're just like a straight image of a straw, that's why I'm addressing the question, you're an image of the straw. If you push, it's the same velocity at the end as it is at the beginning.
00:45:38
Speaker
There's a beautiful explanation of why blood comes out so slowly because clearly it makes sense. It would be a waste of energy if your blood was delivered at high speed to their end units, right? They just need to, it's the very last centimetre or millimetre that they need to travel. So they've kind of like, all the energy has been used up delivering to, you know, things further up the chain, I suppose.
00:46:08
Speaker
I must say, independent of anything else, when I put it all together and had now this model, this theory of the cardiovascular system,
00:46:25
Speaker
and how it worked. It was quite beautiful. I mean, by the way, one of the things, of course, I discovered a lot of this, needless to say, was known, I mean, in one form or another. It was this context that was not known and putting it all together in this form. Much of this had been worked out.
00:46:43
Speaker
in various parts much earlier, even back to I think the famous Thomas Young, who was the first to get the speed of blood through your artery, through your main artery. But anyway, that was the beginning. It turns out trees, of course, and then you have this interesting question. Trees don't have beating hearts. Plants are quite different.
00:47:11
Speaker
So how does it work there? So you have to do that. And in fact, it's not a bunch of pipes joined together like we are. We're not like the plumbing system in your house. That's who we are. But that plant above you there is a bunch of fibers joined together.
00:47:31
Speaker
you know, like an electrical cable and it sprays out those branches are just the spraying out of the fibers into different branches. And so you have to do that, you know, that that's a whole different calculation. You mentioned that it's three plus one. And you also talked about the. The fractal nature of these networks and those two points are
00:48:01
Speaker
highly related and I think this comes across beautifully in your book scale that when you have the way that something scales can add an extra dimension to its behavior as it were so if you if you just draw a line on a piece of paper and you double the
00:48:21
Speaker
piece of paper. If you've drawn a straight line, well, you've used, you know, that would require twice as much ink. You've drawn a line which is twice as long. But there are these, you can draw a very special space-filling curve on a piece of paper, which is
00:48:36
Speaker
when you double a piece of paper, you're going to double the ink. And that's kind of obvious, because if you space-filled the paper with ink, you've covered the entire area. But it takes a little bit of, I guess, mathematical imagination. But that metric works all the way up in any dimension. So where we have these networks with our bodies filling three-dimensional space,
00:49:01
Speaker
The way that they scale up is to the fourth power in a certain sense, or at least this kind of critical surface area that they can reach. Yes, so they behave as if.
00:49:14
Speaker
We're in four dimensions. And that's what's incredible, the fractal. So I don't know if we want to have a little tangential conversation about fractals and the wonders of fractals, but we are fractals. I mean, that is the essential part of us.
00:49:33
Speaker
everything from what I just talked about, our circulatory system to our brains, that we have this kind of self-similar property, approximately, obviously. And of course, we will talk about that maybe a little bit later, that permeates nature. And this was the great discovery of Benoit Mandelbrot, who then showed us some of the mathematics of fractals.
00:50:00
Speaker
I mean, the curious thing about Mandelbrot, if he was a mathematician, and he showed no interest in why it was like that, that was most peculiar, actually. I knew Mandelbrot, and I used to, in fact, I once had a big argument with him about that. But he showed no interest in why Mandelbrot
00:50:20
Speaker
would they be like this? It was very strange. Anyway, that's beside the point maybe. But his discovery was fantastic. I mean, his promotion of it and discovery and looking across the breadth of science to show examples of it, I think was fantastic. Because it is extraordinary that we were dominated by Euclidean geometry.
00:50:48
Speaker
for almost 2000 years, even though we got out of Euclidean geometry with differential geometry and Einstein and general relativity and so on. But this other kind of geometry
00:51:04
Speaker
And the point that Mandelbrot, of course, kept making is there aren't right angles and straight lines in nature. That's not how nature works. And I think that's, you know, it's very simplistic cartoon kind of statement, but of course, mostly right. That's true. And in fact, nature is dominated by these self-similar fractal quantities. And the curious thing about them is
00:51:32
Speaker
In terms of their dimensionality, as defined by how they scale, they can have dimensions that are not integers. As you said, you have a line and you double its size, it's twice the length. I mean, almost by definition, you think.
00:51:51
Speaker
But these kinds of things you can double the size and in fact all kinds of weird things happen. You know you get more or you get less sometimes. I think that the cox snowflake I was looking this up which is this you know it looks like a kind of classic snowflake. Yeah that's right.
00:52:12
Speaker
And if you double the size of that, you get not double, but 26% extra on top. So it's factual. A factual dimension is 1.26. Yeah, 1.26. And that's true of us. I mean, we're not 1.26, but our system, that's why you have these kind of Clybers law and all these quarter powers. But it's all dominated by
00:52:36
Speaker
It's that it's as if we're in four dimensions because the fractal dimension we have evolved to essentially maximize. I mean, we could have had a fractal dimension of 3.7.
00:52:54
Speaker
or 3.2, which would have been still fractal, but we actually maximized it. And you can't go beyond one, it turns out. So 3 plus 1, that was either 4. But the mathematics did it. The way this happened historically for me was it's very typical. I did the calculation.
00:53:17
Speaker
And it was a complicated mathematical physics calculation, not a good mathematical physicist would anyone be able to do it. But setting up, solving it, you get the result. And you say, wow, that's great. It agrees. Fantastic. Now let me try to understand it. What were the essential features through all that hieroglyphics that gave
00:53:45
Speaker
rise to this very simple result. Because I think that was particularly the startling thing. Because when I started that calculation,
00:53:54
Speaker
I said, there's no way this is three quarters. I mean, Kleiber fitted it to three quarters, but it's probably 0.738. And that's what I'm going to show that it's point whatever it is. And I showed it was three quarters. So I spent a lot of time trying to figure out what the hell was going on here that it's such a simple result.
00:54:16
Speaker
Yeah, it's not like any of the numbers you tend to get in physics, which is just like, you know, the gravitational constant is some very long, complicated number. So wait a minute, what happened? So that's why but it's very typical in physics, you get a result, especially if it turns out to be, you know, much simpler than you thought.
00:54:37
Speaker
And then you have to go back and think through what was the essential feature, what were the essential features that gave rise to the simplicity that I should have seen a priori. So we've got to the three-quarter law and it is a genuine three-quarters, it's not an approximation. That's the thing, yes. And the data does, you know,
00:55:03
Speaker
I mean, that was the original proposal of Kleiber. And indeed, the data certainly hovers around that. We've done a lot of analyses. And of course, there's all kinds of controversies about the data and about this and that, which I find somewhat tedious.
00:55:24
Speaker
Just one final comment on the fractal point. We were talking earlier about Sean McMahan, who I interviewed not so long ago, the astrobiologist. And his whole thing is looking for biosignatures. And I do wonder if we see some fractal patterns with a wide dimension on another planet, would that constitute a biosignature, or at least a techno signature?
00:55:53
Speaker
So that's interesting. So I was, funnily enough, the Astrobiology Institute. When it was set up at NASA, I was one of the people they brought in right at the very, very beginning. This has got to do with anything. But in fact, I wrote a, and so they, you know, we were involved in the early discussions of what it should be doing and so forth and so on.
00:56:19
Speaker
And then they invited proposals. And I wrote, this is quite funny in a way, I wrote a proposal with myself, Murray Gell-Mann, a famous physicist, and someone else who's now at Harvard, Juan Perez-Maccadero.
00:56:38
Speaker
And we just assumed, you know, that we would get funded and it got rejected as I never became. So I got so pissed off, I sort of withdrew from the Astrobiology Institute whole thing. Juan is a major member of it now. But anyway, that's got nothing to do with anything other than my own members of that. Because at that time, I was thinking exactly about this. I mean, that's the relevance of this. In fact, part of that proposal was
00:57:07
Speaker
Could you use any of this? This is just one part of the proposal. Could you use any of this work, this scaling work, the fractal light behavior, its nature and so on, to say, yes, there must have been life here, or at least there must have been. This is evidence that there could have been life here. Now,
00:57:30
Speaker
The real problem with that is obvious that fractals, I mean, just as Sean, point Sean was making and his seems to be his mission is to look for non-biological things, abiotic processes that sort of
Scaling Laws in Cities vs. Biology
00:57:49
Speaker
mimic life. And of course, you know, obviously the most obvious one here
00:57:53
Speaker
is rivers I mean you know if there's been water and rivers obviously but you know so the question then is can you have enough data that you can distinguish the fractal dimension of those for biological one and is that meaningful and so on so we you know I played around with that for a bit it was a you know it's a long shot
00:58:14
Speaker
But certainly, if you saw things that had other potential biological features, this would be evidence that you should add to that, for sure.
00:58:30
Speaker
that if you did see any kind of either remnant or if the thing was actually still supposedly still alive, that it had this kind of structure. Because I did, oh, so one of the things I did believe in all that was that, because it was also part of the astrobiology thing, is that if life exists elsewhere, it will have this kind of structure. It will have to be networked
00:58:59
Speaker
and it will try to optimize and it will have evolved, therefore it will have quarter powers. So that was sort of the speculative argument.
00:59:11
Speaker
Maybe this is a good segue on to cities, because I think if we were to look up through a telescope and look at a city on, you know, discover an alien city, it would probably have some very similar properties to the cities here on Earth as well. Because as you found, cities also behave remarkably similarly in many ways to organisms. So perhaps take us through, well, you know, how did that next leap in your career come about?
00:59:41
Speaker
Yeah, so that was...
00:59:45
Speaker
So it was pretty clear. One of the things we didn't talk about yet, and we may or may not come back to, is that this work, I did say it applied to many things. We took it into many different areas of biology, understanding growth, understanding some aspects of cancer, the Asian problem. Perhaps we can talk about that first. Yeah. Well, it might be good to talk about growth, actually briefly, because there's a big contrast.
01:00:15
Speaker
with cities there. So growth in this works in a very simple way. You take in food and nutrition, you metabolize, you send the metabolic energy through the networks, networks goes to the cells and it maintains them and replaces ones that have died. And in a growing phase, it adds new cells.
01:00:40
Speaker
So you can write that down as an equation. It's controlled by the network and so on. But here's the point. The network that is controlling as the system is growing, that is the supply. The supply is growing in what we call a sublinear fashion. The three quarters
01:01:03
Speaker
is less than one. And one of the things also didn't say that that implies that the energy needed to support a cell is less the bigger you are. It decreases systematically the bigger you are according to this quarter power law. So your cells are working less hard than your dogs, but your horse is working less hard than you.
01:01:32
Speaker
going back to the growth, that's supplying the cells, but the supply is decreasing as the system gets bigger because it's only decreasing per cell as it's getting bigger because you're adding in a linear fashion, you just keep adding cells. So you're adding the demand is growing faster than the supply because the supply is growing in this sublinear
01:02:01
Speaker
The demand is growing approximately linear. Linear always beats sublinear. Therefore you stop. So you can derive the equation. It says, and the solution says you grow quickly at the beginning.
01:02:14
Speaker
And then gradually, as the supply beats out the demand, as the demand beats the supply, you stop. That's why you stop and derive. And it's quite beautiful, actually. And you can see that if you rescale accordingly, all organisms can be, and you look through the right lens, all organisms are following the same curve.
01:02:43
Speaker
And so that's great. And that stability, that stable configuration that we end in, that most organisms end in, not all, plays obviously a hugely important role in the long-term sustainability of the biosphere because you're spending most of your time in a kind of metastable state rather than continually changing.
01:03:10
Speaker
So and I'm going to I'm so we needed to go through that because when we come to cities, you'll see it's not like that. So here's what so cities. So we got into this because I moved to the Center for Institute because of this work.
01:03:28
Speaker
And the Center for Institute is this extraordinary place where people from all disciplines, all backgrounds, all stages of their career are all together in one place and all kinds of interesting collaborations, interactions, integrations take place. So I was giving a talk on some of this.
01:03:52
Speaker
and in the audience were two visitors on sabbatical. One was a well-known anthropologist, Sander van der Luhe from Paris, and the other was a well-known economist statistician, David Lane. And they said what I'd already thought about, I brought it up in the talk, actually, I said, you know, it would be really interesting to take this paradigm, as a physicist, it would be really interesting to take this paradigm and apply it to other systems like companies
01:04:22
Speaker
I said, and possibly cities. I said, you know, because their networks, they're sort of organismic in some way. And these guys went sort of bonkers and said, fantastic. That's what we should be doing. So we put together a proposal which was funded. That one was fun. Gen very generously, may I say. And it got me working on. Oh, I was going to work on companies because I thought they were they were much more interesting. I thought cities were boring.
01:04:52
Speaker
But it turns out, in my naivety, I hadn't realized that you couldn't get data on companies without buying it. That is, most of it is, well, it's almost all proprietary, and various companies have assembled data sets. But you had to pay, I think it was $40,000 at the time, I forget, some large amount of money that we did not have at our disposal. So I said, OK, look.
01:05:23
Speaker
What we have to do is we have to prove the whole concept of all this by working on this boring problem of cities. We'll look at cities and then we'll motivate that to get funding so we can buy data and do the real problem of companies.
01:05:41
Speaker
So I put together a different collaboration, a lovely bunch of young people. So as the thing from biology where the scaling laws were known, here they basically were not known. So these guys had to go out, scrape around for the data,
01:06:00
Speaker
and discovered my amazement that indeed, well, I wasn't so surprised that they scale. I was surprised at the exponent, the analog to the three quarters.
01:06:14
Speaker
Because the first work that we did, actually the first work was with a colleague at the ETH in Zurich, it's like the MIT of Switzerland, Dirk Helbing, and he and his student.
01:06:30
Speaker
We put together some data that showed that cities do scale in terms of their infrastructure, just like biology. If you looked at the roads and various things, which are very similar to your cardiovascular system, and you plot various things, they scale in the same way when you plot logarithm against logarithm, they're nice straight lines.
01:06:58
Speaker
The only difference being that the slope was 0.85 instead of 0.75. Okay, so we need to understand that. But then the collaboration grew and it expanded into socioeconomic quantities. And there was the big surprise. And the surprise was that not
01:07:23
Speaker
Well, first of all, it confirmed that things scale. Socio-economic means things like wages, number of patents, amount of crime, amount of flu, anything that's involving interaction of human beings directly. And all those scaled, but they scaled, instead of sublinearly, less than one, superlinearly, bigger than one.
01:07:50
Speaker
So, and I'm embarrassed to say I was surprised when I first saw that. In fact, I said, something must be wrong. It took me a good 20 minutes to realize that I was completely wrong. And I completely switched and said, my God, of course it's exactly right that things that are socioeconomic should scale bigger than one.
01:08:17
Speaker
because the bigger you are, what bigger than one means, the bigger you are, the more you have per capita. So the bigger the city, the higher the wages, the more restaurants per capita, the more inventions, the more patents per capita, and so on. So I said, it's obvious, that's right, we should have guessed that a priori. And I was really, I still kicked myself that I hadn't
01:08:45
Speaker
thought of that and written it into the proposal or written it somewhere because I can't claim I predicted it. That's for sure. So so the sum total of all this was something that was really very satisfying. We looked at data across the globe. So that meant North America, Central America. Oh, no. I'm sorry. Central America.
01:09:15
Speaker
North America, South America, Europe, Asia, that means China, Japan, let's see where else, I don't know, wherever we could find data. And what we found was the same scaling everywhere for the same thing. And that was kind of mind blowing, that was great. But we discovered that all infrastructure, roughly,
01:09:38
Speaker
That means roads, electrical lines, water lines, scaled with the same exponent, which was about 0.85, across the globe the same way, roughly speaking. But all socioeconomic quantities, whether, as I say, good, bad, or ugly, namely wages, crime, disease, all scaled with the same exponent of about 1.15.
01:10:05
Speaker
So there was, like biology, a kind of universality, even though here now it was bifurcated. It was a dual universality. The infrastructure behaved differently than the socioeconomic. But the fact that it's scaled meant that there were universal principles constraining
01:10:31
Speaker
the structure, organization and growth of cities across the globe. So it was almost as if it was almost as if, you know, the Industrial Revolution came and people realized cities were going to grow. They were growing. And a big international convention was gathered
01:10:56
Speaker
And all the countries came together and said, how are we going to design cities? And they said, well, we have to do it according to the scaling laws. So that was almost, you know. And of course, it's all happened organically. And the question is, what is the organic principles? What are the organic constraints that have led cities despite the fact that they're different geographies, different cultures, different histories that
01:11:24
Speaker
the time and energy that went into the politics and the planning individually of each of these places, they all end up sort of lying close to these scaling curves. So these huge constraints obviously are at work and what are they? Well, I would say that our work, and can we derive, of course, a comparable theory
01:11:49
Speaker
that we did, as was done in biology, to derive the 0.85 and 1.15 and so on. Well, the answer is that we've made progress, but it's still a work in progress. We understand we're
01:12:05
Speaker
very sure of the underlying dynamics, but it's extremely hard to derive a really fundamental theory that unambiguously gives these answers. So the idea is the following. The infrastructure is like biology, and it's to do with, again, an optimization.
01:12:26
Speaker
And the idea there is that maybe it's to do with cities evolved via, what is the point of a city? The whole point of a city is to bring people together in order for them to interact, to facilitate interaction, to increase wealth, to have more ideas, to innovate, to increase quality and standard of life. It's this incredible machine
01:12:54
Speaker
that we have evolved in the last several thousand years. But as it evolved and people came together, they need to interact. So maybe one of the optimization principles is you try to, the city evolved
01:13:14
Speaker
for people to try to get from point A to point B in the quickest way you can get to various centers in the quickest way so that was that even though the streets are all going you know especially
01:13:26
Speaker
You're in Europe. I mean, the streets don't, it's not a grid. But nevertheless, when people try to go, even now, when you try to go to pick up your kid at school, that's what you're doing. You try to go, roughly speaking, the quickest way or maybe it's the cheapest way. But something is that is an optimization that's very analogous.
01:13:50
Speaker
to the kind of optimization that takes place in biology that we talked about earlier. Now, for the socioeconomic, something different, a little bit different, and that is that you want to optimize, and that's part of that infrastructure thing, the number of interactions, the rate of interactions. You want to optimize the number of interactions. And at the same time, and here's the kicker, and this is totally speculative, everybody wants more.
01:14:21
Speaker
Everybody wants more of everything, everything from material well-being to even interaction. They want theater, they want it and so on. So that's sort of the idea. And the hard part of this is not just putting those into mathematical terms, which you can do, but is integrating these two networks.
01:14:44
Speaker
You can't talk about them truly separately because you can't have a network of interaction. By the way, the socioeconomic interaction, the flow in the network is really information that's being exchanged. In the infrastructure network, it's energy and resources.
01:15:05
Speaker
So, in the bigger picture, a city is the interface and integration between, on the one hand, its physicality, its energy, its thermodynamics, if you like, with information exchange in social networks, which are tied to that infrastructure.
01:15:28
Speaker
And it's hard to put that into mathematics and it's still ongoing. But we're pretty sure. You can show, for example, one of the things that I'm confident of is that
01:15:44
Speaker
you notice the superlinear is 1.15, which is 0.15 above linear, and the 0.85 is 0.15 below linear. And that is no accident. But you can show that if you have these networks integrated, one sort of compensates the other. And it's almost as if the saving that you're making as the city grows, or as you make a bigger city,
01:16:14
Speaker
goes into making the city more productive, more exciting, have more interactions, produces more patents, has more crime, has more opportunities, and so on. I mean, intuitively, that feels right. If it's that much easier to get to a restaurant because it's that much closer, I'm going to go there.
01:16:42
Speaker
I'm going to have more interactions. Yeah, it's again, it's it's worth just pausing for a minute to cash out some of the implications of this, just crunching the numbers that firstly, as cities get bigger, in a way they get more efficient, just like organisms. So you double the size of
01:17:06
Speaker
a city and it's only consuming 75% more resources. And I've heard you say New York is the greenest city. 85. Sorry, 85. Yes, 85. Still still on the biological. Yeah, so you're making a 15% saving. Yeah, which is huge, enormous. I mean, you have many doublings to do your
01:17:31
Speaker
way ahead. So the curious thing about this was that, you know, so much. So during COVID, during a pandemic,
01:17:40
Speaker
much better to be in a small town because the interactions are much less. And you're much less likely to have catch COVID in a small town than you are in a big city. So that's obvious in a certain way, but you can put numbers to that actually. It's much faster in a big city. So that's the point. You're going to get it much faster.
01:18:05
Speaker
than you are in a small town. But if you want a sort of buzzier, sexier life, better be in a big city.
01:18:13
Speaker
And it's almost paradoxical that the energy use is lower, but the pace of life is faster. And I do want to comment here as well that it's so intriguing that for the longest time people have talked about cities in this anthropomorphic or maybe biomorphic way. I was thinking of the, there's that last line of Wordsworth's poem on Westminster Bridge where he says, he's looking at London from Westminster Bridge and he says,
01:18:42
Speaker
you know, all that mighty heart is lying still. So that's London at night in the 19th century, 1802. So there is this intuition that
01:18:59
Speaker
Cities are lively, cities never sleep, you know, all these kind of attributions of animal characteristics to them. And it turns out that in a certain sense, they do behave something like organisms and not following exactly the same skating laws, but nonetheless. But there's super linearity. Yeah, and that's very different. Yeah.
01:19:24
Speaker
So that's the point of departure. And that comes about, so how does that, that comes about because the city brings people together.
01:19:34
Speaker
And so you have a situation that A talks to B, B talks to C, C talks back to A, and you build on each other. You're continually having positive feedback in those interactions. And you're creating ideas all the time. Now, all those ideas are useless and pointless to anybody else, mostly, and they die very quickly. But the whole point is that the spirit of that dynamic has led to the theory of relativity.
01:20:03
Speaker
It led to Amazon and it led to, you know, General Motors and so on. That's the process. The city does that. That's why universities mostly are in big cities. Yeah, I think I do find the Einstein example interesting because I'm always struck that he was, you know, a patent clerk in
01:20:23
Speaker
in Bern, which I went to once and it seemed like a very sleepy city. Oh, it's still a city. It's still a city. And, you know, it's it's, it's that the ideas around that now Einstein, of course, made a
01:20:39
Speaker
you know, phase transition are huge enormously. But you know, it's like, it's sort of like the Newtonian, if I've seen further, it's because I stood on the shoulders of giants. It's not like Einstein did it totally in a vacuum. He had all that stuff behind him, which came out of urban living. I mean, places, I mean, Oxford and Cambridge have this sort of ivory tower image, but they're actually cities. Yeah.
01:21:07
Speaker
And of themselves, they are cities. I mean, you bring people together. And so city, I think you have to extend even the idea of a city. It's really the network of people that are connected. It's the network of people that are interacting. Yeah.
01:21:35
Speaker
Yeah, and it's because I guess even if Einstein wasn't actually the greatest physicists, he had access to all the resources. It made me think of you going to the library to get those books on biology. You know, that's one of the complicated things that the city does with other people, you know.
01:21:54
Speaker
including his wife, of course, who didn't get credit. But so who was a physicist? But anyway, yeah, that's, that's a detail about things are urban, you know, come out of some urban kind of environment. One thing I'm intrigued about is how much of the additional productivity that can be measured is in some ways,
01:22:20
Speaker
firstly, possibly an accounting trick in that, you know, I can tell you a joke now, and if you find it funny, you might laugh, but you're not going to pay me for it. But if I go across the road, and I go to the stand, this famous comedy club, and I tell a joke that I might just get paid, I mean, it's unlikely, but you know, I'm not consuming any more resources or doing anything different, really. But I
01:22:45
Speaker
something that is economically measurable results there. And I think there's a motivating effect of living in cities to do that because everything is so expensive. And perhaps there's also some social competition going on as well. So what I wonder is how much of it is to do with us
01:23:05
Speaker
you know, producing more ideas through interactions, and how much of it is the capture, commercialization and dissemination of ideas and products based on ideas that is motivated by this kind of boiler room of a city? Well, I think it's both, of course, it is both, but you know, both of them are requiring enormous resources.
01:23:30
Speaker
You know, it's not like, I mean, there's this image, you know, when you, when you say thoughts, for example, you first of all, you think, well, thought doesn't cost anything. Of course it does. I mean, first of all, it costs a little bit of metabolic energy. But what it does, it costs in your head, you have to be there, you have to be in that house.
01:23:49
Speaker
you have to heat the house, you have transportation, you have entertainment, you have all of Edinburgh there, and that all goes into producing that thought. I mean, that thought costs actually a lot of money, and it's much more expensive, that thought, than a thought that took place 200 years ago, actually, because the infrastructure needed to keep you here and doing that is much higher.
01:24:18
Speaker
So it's quite complex, all of that. So you're right. And that's what makes trying to really have a kind of universal theory of how this all works. I mean, after all, what we're getting into here is almost social economics. We're sort of crossing into other boundaries of other fields here, of course, where people try to think of these things. But it's highly non-trivial.
01:24:45
Speaker
But the scaling laws, to me, were a window onto opening up some of this territory to try to understand what that dynamic is and why cities are so important. And I see them as, almost obviously it seems to me, the whole future of the planet depends on what happens in cities.
01:25:10
Speaker
That's primarily because, first of all, more than half the globe lives in cities. It's going to be more like 75% before too long. And that's where almost all the ideas are created.
01:25:26
Speaker
the image of the guru going on top of the mountain, or even that image of Einstein, who's the nearest we have to it, is very misleading, I think. The vast majority of ideas and things do occur in an urban kind of environment. And it wasn't like, you know,
01:25:51
Speaker
As we've already, you know, I'm maybe beating a dead horse here. Einstein didn't come out of nowhere. Yeah. Yeah. Yeah. Yeah. So I'm ready. I had all that stuff behind it. But anyway, but what I wanted to do was to now really distinguish a really important part between cities and organisms.
01:26:20
Speaker
Hey, as I said, there's this positive feedback. So you have the superlinear you get. The more you have per capita rather than in biology, the bigger you are, the less.
01:26:31
Speaker
you need per capita. So in terms of growth, because when you go to growth and you have the same idea, you know, you take that same structure that you have in biology, it was your metabolic rate that gets a portion between maintenance on the one hand and growth on the other. Here you have to invoke something called social metabolic rate. So you could imagine, we've sort of implicitly been talking about it.
01:27:02
Speaker
the sort of energy, including the information, the information translated into energy units, if you like, but the energy that is coming in to say, let's just take a city for the moment, coming into the city that's driving everything. And what it's doing on the one hand is maintaining the city as it is, that it's repairing the roads and the buildings and repairing the people with doctors and hospitals and so on. So it's doing all that maintenance work. But then, of course,
01:27:32
Speaker
Part of it is being apportioned to growing new stuff, growing new buildings, roads, developing different areas, adding new people, and so forth. Well, the difference here now is that the driving force
01:27:47
Speaker
the supply is now growing with size as distinct from decreasing with size on a per capita basis. But the demand is still sort of just adding. So what happens is that the supply completely outruns the demand.
01:28:10
Speaker
So instead of growing and then stopping, you just continually grow. Not only do you grow faster and faster and faster, which is what we see. In fact, you end up growing faster than exponential.
Implications of Super-Exponential Urban Growth
01:28:25
Speaker
Yeah. And that's because I guess the reason you're growing faster than exponential is that for a city of a given, as you double a city, it
01:28:37
Speaker
It more than doubles the sort of creativity, the buzz, and so on. And, well, that on its own is exponential, but that leads to
01:28:53
Speaker
attracting more people into the city. It's a very fast, positive feedback phenomenon. And that's been the history, especially since the Industrial Revolution, of course. That has been the history of cities almost across the globe, certainly in all industrialized nations. And that's what we've seen. So actually the theory
01:29:23
Speaker
as it stands is very satisfying because we say, look, we have at the basis, we have social networks.
01:29:30
Speaker
where we have this positive feedback, which gives rise to super linear scaling. And the super linear scaling then gives rise to super exponential growth. And that's what we see. So it's actually, it's a nice theory. It's got still, as I say, work in progress to really get to the fundamentals, but it's a very complete picture. But it has some weird consequences and some very disturbing consequences.
01:29:59
Speaker
And that is that open-ended growth which we love and which is the paradigm since the Industrial Revolution and the discovery of fossil fuels and their exploitation and capitalism and entrepreneurship and all these marvelous things that allow us to do what we're doing now.
01:30:25
Speaker
That's the result of all that. But unfortunately, the mathematics of it has built into it something that's called a finite time singularity. This word singularity now comes in. And what that means in English is simply that that growth curve
01:30:41
Speaker
going up, reaches an infinite number in a finite time. So what it's so that you would have the number of patents or the number of AIDS cases would become infinite in some finite time. Finite time could be 10 years, 50 years, 100 years, whatever. But in some not infinite time,
01:31:09
Speaker
And that's obviously crazy. It doesn't make any sense. But the theory tells you what happens. It says that as you go up and you approach the singularity, what happens is that you would then sort of stagnate and then collapse.
01:31:30
Speaker
So, it's sort of a sophisticated Malthusian argument that you can't sustain that kind of growth. Now, Malthus got it wrong, and he got it wrong for good reasons. I mean, he was attacked, I think, for the right reasons, namely that you didn't take into account that people were going to innovate.
01:31:53
Speaker
and it gets you out of that. He said that agriculture could not keep up with the increase in population because population increases exponentially and agriculture was linear. He was wrong. But so taking that idea to this theory, and this now is based on, this agrees with data. So it has some serious credibility.
01:32:21
Speaker
So as this thing goes up and reaches a singularity, what you realize is that what I told you is sort of assuming that in the big picture, nothing has changed. We're in some major paradigm like the Industrial Revolution or going way back the Bronze Age.
01:32:48
Speaker
or the Stone Age, something that dominated somehow the way people structured society and the tools they used and so on. In modern times, that would be the computer and most recently the internet. So these big,
01:33:05
Speaker
Paradigm shifts, these huge innovations which set the tone and the culture of the way that growth takes place. They sort of fix the parameters in a certain sense.
01:33:20
Speaker
So that gives you a hint as to how you get out of this. What it says is, you do what we've done. Namely, as you grow in this very fast, super exponential way, before you reach the singularity, you better make a major innovation, a major paradigm shift. You better reinvent yourself. You better reset the boundary conditions. Start over again.
01:33:45
Speaker
which is effectively what we've done. So we go along these curves, you're approaching a singularity, you discover, I don't know, coal. Boom. Then you discover, well, more recently you invent computers, as I say,
01:34:05
Speaker
Then you invent the Internet and so on. And so that's great. That's what we've done. The hitch to this is that something I haven't talked about, and that is that as the system grows, the pace of life increases, things get faster. Yeah.
01:34:25
Speaker
Everything gets faster. And in fact, we've looked at data, and the data supports that in agreement with the predictions. And indeed, one of the things that has to get faster is you have to innovate faster and faster.
01:34:43
Speaker
So an innovation that might have taken, you know, 50 to 100 years to really develop a thousand years ago, make this up. Now would only take 10 or 15 years. But you have to do a new one, you know, how long has it been?
01:35:00
Speaker
You know, the internet age is what, 20 years old, maybe? I don't know. We're going to have to do another one like it, maybe in 15 years, or we're going to have to do one soon. In fact, you can fill the air. So the pace of life is increasing. We have to do things faster and faster. You have to innovate faster and faster. If you don't, you'll collapse. And we're now
01:35:23
Speaker
approaching such a point again, a singularity, and we have to make some major shift, maybe in the next 10 to 20 years. And we don't know, of course, can't predict what that is. We can guess, we can speculate as to what that is. But the point is that a major
01:35:45
Speaker
People were right in criticizing Malthus and people like the Club of Rome and people like Paul Ehrlich, who all predicted collapse because none of them seriously took into account innovation.
01:36:01
Speaker
The things change that you're going to make a major innovation. This does take that into account. And it says, yes, you can postpone the collapse, but you can't stop it because you're just putting off to the next time and you've got to do it again. You've got to make another innovation, but you have to do it quicker than you did the last one and so on and so forth. So if you took a sort of reductio ad absurdum view of this,
01:36:28
Speaker
Um, you'd have to end up making a major innovation, you know, sort of every month, which is ridiculous. So, um, so this has built into it. It's the, the collapse of the system. And the question is how do you get out of that? And I'm happy to speculate, but my goodness, it is a big question. I wanted to comment just on the, um, I mean,
01:36:54
Speaker
Another interesting point of departure between Malthus and your ideas is that they were looking at exponential growth, which is only going to become infinity at infinity. That wasn't the essential problem with their ideas, because sure enough, once you have enough
01:37:13
Speaker
consumption. It doesn't have to be infinite consumption before it out strips your production.
Innovation, Urban Growth, and Political Shifts
01:37:22
Speaker
But as you say, they ignored the innovation that has happened in cycles and it seems is happening in quicker and quicker cycles. What comes to my mind is chat GPT claiming to be the most quickly adopted tool in history and getting to 100 million users within weeks, which
01:37:44
Speaker
I have no reason to disbelieve them. In fact, I have more reason to believe them, you know, looking at the history of product adoption.
01:37:51
Speaker
But it does seem that at some point, just biological limits are going to call a halt to this. I mean, several things come to mind. In your book, you have this wonderful example of walking pace, which increases frustratingly at the, you know, not with the 1.15 exponent, but it gets 10% faster every time you double the size of a city, which just is wonderful. But clearly, you know, if you
01:38:17
Speaker
I did the maths just earlier, and if you put the whole of the US in New York, I'm just trying to look up my calculation. What was it? I think then that came out to maybe 12 miles an hour, which wasn't too bad. It's like jogging. But then if you put the whole of China,
01:38:38
Speaker
into one city you get like 350 miles an hour and maybe that'll happen maybe we'll sort of turn ourselves into cyborgs or we'll be going around with roller skates or something but i don't i don't think that's gonna happen um and you know
01:38:53
Speaker
one can get even more fundamental and say, look, well, the density of cities increases with size, but presumably we're not gonna create black holes because, you know, before we get to that point, we're just gonna say, this is too cramped, I don't like it. But you've read a really important point because, which I've pondered, and that is that all this has changed
01:39:21
Speaker
You know, since we formed cities, this whole dynamic has been in place. It was very slow until the Industrial Revolution, and now it's gone bonkers, you know, in the last 200 years. And it's accelerated in a kind of uncontrolled way.
01:39:39
Speaker
Yet we are the same biology. We're the same, not only as we were when we were hunter-gatherers and started becoming sedentary 10,000 years ago, but 100,000 years ago or longer. We're basically the same brain. And yet we've adapted extraordinarily to this. So that first of all brings up an interesting question of itself.
01:40:01
Speaker
which I find intriguing. How has our brain been able to adapt so extraordinarily quickly to this fast changing environment that we're in? I mean, that of itself.
01:40:15
Speaker
But then the follow-up question, which is the one that I find most intriguing, is what is the limit to that? I mean, it's the same thing as in the physical world as the thing from the neural world. Someone could run the 100 meters in 9.8 seconds. Someone may well run it in 9.7 or 9.6 and even conceivably in 9.
01:40:45
Speaker
But what about five seconds? Or two seconds? Or one second? Well, it's obviously ridiculous. It wouldn't be a human being, in fact. So there is a limit. We don't know quite where it is. We're probably closely approaching it for running. But maybe that's true of our neurological capacity. And already you can feel that.
01:41:12
Speaker
You can feel that with the extraordinary changes that are taking place with the new gadgets and new inventions. And every year, there's another bloody new iPhone that you have to adapt to or whatever. And I'm 83, and I have to adapt to it. Suddenly, my colleagues decide, we've got to use Overleaf. So I have to learn Overleaf. Oh no, now we're going to do a Google Docs.
01:41:37
Speaker
Now, it sounds trivial, but you know, these things are, and I'm, you know, I'm reasonably smart, but you know, a lot of people have a struggle with that. And they have the equivalent of that. And they feel disenfranchised almost. And, and so my conclusion is, if you're like that you vote for Trump.
01:42:05
Speaker
because he provides a simple solution. Whereas all this other stuff is so complex.
AI Advancement and Human Neurology
01:42:13
Speaker
So that is my, not my point there is I'm being totally sarcastic and silly, but my point there is
01:42:27
Speaker
Are we approaching a time when our brains, our neurology, simply cannot adapt to the technology we're creating?
01:42:38
Speaker
And it may well be that we've solved the problem with AI and chat GBT. I don't know. Maybe that, that will do it. Or maybe chat GBT is the next major AI looks like it may well be the next huge paradigm shift. That's like the internet was may not be it's too, it's, I mean, despite all the hype, I think it's way too early to tell. It certainly is extraordinary.
01:43:03
Speaker
I gave it a little problem the other day, a very simple problem, and it got it completely wrong, by the way, you know, as it does. I mean, it's very human, I have to say. Yeah, I think it's extraordinarily good at particular fields of programming and quite broad ones. And so I'm convinced that in certain places it is going to accelerate
01:43:28
Speaker
production of things and it will be a paradigm shift for development of software.
Concerns Over AI's Impact
01:43:34
Speaker
My fear is mostly that we're going to give so much, I mean I already hear it of course, so much over to it, to AI and machine learning that all kinds of terrible things are going to happen.
01:43:50
Speaker
that you know because people are so naive because most of the people that do this that make these decisions have absolutely no idea how this thing works and what it is and what its consequences might be I mean it's quite irresponsible but you know that's the way of the world well we're we're running up against time um that's another constraint that that seems very human we're probably not going to be speaking at a million words per minute in the year 2100
01:44:20
Speaker
unless we have interfaced with chat GPT and so forth. But, but I do. Yeah, this throws up so many questions. And I just wonder, do, have you pondered what the
01:44:35
Speaker
answers might be. It seems like we can't carry on speeding up. Perhaps there'll be a natural biological break that supplies, but one has to fear that perhaps that would come too late.
01:44:53
Speaker
So I don't know, obviously it's all, I mean, by the way, needless to say, a large part of what I, the last, I don't know, even half hour, 20 minutes is speculative, clearly. It's a different character than the first part of the discussion. But a part that's very extremely interesting and enjoyable and should be, one should participate in, I think. But so my,
01:45:22
Speaker
So I got very despondent with some of this. That is that I couldn't see how we're going to get out of this. It looks like the system's doomed to collapse eventually. And that may be wrong now. I must admit I was, like many others, taken by surprise by how powerful
01:45:43
Speaker
chat GBT was. I mean, I knew a lot about AI because Santa Fe Institute has been involved in AI since its beginnings. I mean, AI has been around for 50 years in various forms. But that was a very serious breakthrough.
The Role of Policymakers in Future Developments
01:46:00
Speaker
And as you say, we'll have profound effects in various parts of, you know, productivity, culture and so on. But so maybe that
01:46:12
Speaker
qualitatively also will change things, I don't know. I sort of think not, that we'll still run into the same kinds of problems. Because one of the things that you realize in all this, so it doesn't matter how much science one does, the future of the planet lies with politicians. You know, that is policymakers anyway, people, I mean, they make the decisions, they do it. So, you know, I mean,
01:46:40
Speaker
Global warming is a classic example. I mean, only a minority of people really pay serious attention to it. And we're not really addressing the problems. So it needs that. So that led me to the crazy idea maybe that, well, first of all, that a paradigm shift, when you use the word paradigm shift or major innovation,
01:47:07
Speaker
What immediately comes to mind is a new technology. That's the way we've talked about it in the past, especially in more recent years. That's been the way we talk about it. And we just talked about another one, AI. But innovation and paradigm shift, of course, in no way connotes that it has to be technological. It could be cultural or political and so forth.
01:47:35
Speaker
Who knows?
Need for Charismatic Leadership with Positive Values
01:47:36
Speaker
And so I'd love me to this really, I'm almost embarrassed to bring it up, but the idea that what we really need is what I call an anti-Trump. You need someone with the charisma and apparent attraction.
01:47:56
Speaker
of a Donald Trump, mainly someone that can change people's, what we presume to be, fundamental views in one year. That is, you know, they don't have to believe in truth. They don't need evidence.
01:48:14
Speaker
discard science if they wish, and so on. We need someone who does exactly the opposite, that sort of promotes a sort of a Jesus Christ or a Martin Luther King or Nelson Mandela, that somehow, instead of tapping in to some of the darker sides that we all have,
01:48:36
Speaker
somehow taps into is the spark that sets off a coherent collective effect of the good in people. I know this sounds all very naive and 1960s, maybe that's what I'm influenced by.
01:48:55
Speaker
But that, you know, that promotes love, love thy neighbor, that connotes the idea of collective behavior, that we don't have to continually want everything and have everything. That, you know, that, I mean, it is weird. I mean, roughly speaking, the quality and standard of life
01:49:19
Speaker
probably has monotonically increased, maybe at a slower rate. For the last, I don't know how many years, you know, I mean, when you think of the things around you, I mean, I don't know how old you are, but certainly my age, if I think of life now, compared to 20, 40, 60, 80 years ago, the change is absolutely extraordinary.
01:49:41
Speaker
and it has been going on. But so why is it that with that happening, people are so unhappy and so disgruntled and want to have authoritarian rule? How can that be? I mean, the assumption will be the opposite. We want to reach out to more and be more giving and
01:50:05
Speaker
less wanting. So it needs someone that does that, that can somehow articulate that and somehow re-centre the direction and focus of human beings because it's fairly universal. What a wonderful note to end on. It's all flaky. You better not show any of that. It's all flaky.
Societal Networks and Potential Dynamics Change
01:50:32
Speaker
But I think what is fascinating to me is that
01:50:36
Speaker
You know, while you've studied these networks and found what seems to be almost inevitable laws, they're clearly not. We have a means of pushing back against these dynamics and deciding the networks that we have around us and how we interact with them. And, you know, it does come down to individuals and maybe one person
01:51:04
Speaker
convincing the collective to behave differently. But yeah, one can't, it doesn't seem, it doesn't seem clear that we can engineer our way out of this solution with a new technology. But as you say, maybe the paradigm shift is not a technological one, but a shift of perspective. By the way, I'm glad you said something I should have said much earlier. You know, the nature of these laws
01:51:32
Speaker
These are not like Newton's laws or Maxwell's equations or theory of relativity or quantum mechanics. First of all, these laws are stochastic, meaning there's lots of variance. That's one of the big questions, how much variance in all these laws, in the biology or the social ones.
01:51:53
Speaker
So there's that. And then there's the other that to what extent can you, you know, if you believe everything I've talked about, then the problems we're facing and it's sort of obvious and we are rooted in our social networks. And the question is, are they a given? Have they, you know, are they so ingrained in our DNA
01:52:20
Speaker
that we can't change them? Or are they quite cultural and actually with great effort, we can change things? Is it like we can stop smoking? Or wear seatbelts? Or is it sort of like this is who we are?
01:52:39
Speaker
I don't know if anyone knows the answer to that. I think anyone can stop smoking if they, you know, if the cigarettes go away. And it might be similar to, you know, if we perhaps that technology does have something to answer for here.
Critique on Technology and Media Metrics
01:52:55
Speaker
The way that technology has been developed has been
01:52:59
Speaker
growth focused, but not direction focused, I think. And social media has been developed to capture our attention, but not direct our attention where it ought to go, I suppose. And it goes for, and it tends to go towards whatever the metric is, least common denominator. Right. Yeah.
01:53:24
Speaker
Yes, I have to go actually. I think with this podcast, we're sort of doing our bit to push back against that. Thank you so much. This has been such a tour de force, just like a book. So thanks again. Thank you so much.
01:53:58
Speaker
you