Geoffrey West: Networks, Heartbeats & The Pace of Cities

While physics is incomplete there is relatively little we don’t understand when it comes to particle or planetary motions. But physics is incapable of telling us much about life in cities, the beating of our hearts or whether society will implode.

And yet, the techniques of physics have been used to powerful effect in unraveling emergent laws which explain why:

  • Whales live longer than hummingbirds
  • Megacities are more energy efficient than towns …
  • … but the growth of cities fuels unsustainable growth

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 mathematically derive 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 that optimal space-filling networks are fractal-like in nature and scale as if they have an extra dimension. A 3D fractal network scales as if it is 4D. It’s a lot to take in, which is why this conversation felt short for me, even though it was 2 hours.


Geoffrey West: Scale

James Robinson: [00:00:00] All right, Geoffrey West, thank you for joining me.

Geoffrey West: Yes, pleasure, James. Thank you for inviting me. I’m looking forward to our conversation.

James Robinson: You started your career looking at the tiniest of things, at quarks and so forth, and, and, and very far away project, uh, problems like the, 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.

Um, can you tell us how you went about, how did that

Geoffrey West: journey happen? Oh boy, let’s see if I can 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, , wanting to Sort of, I mean, it sounds, sounds arrogant, but understand everything, you know, as a boy, you know, I was always asking questions.

I was interested in everything, as one does when is, you [00:01:00] know, as a young boy and even in high school and so forth. Um, and, I, I always harbored a sort of romantic image. Of what being an academic would be, and I, and that was sort of enhanced by being an undergraduate at Cambridge, just the, the physicality of it, I mean, and, uh, sort of romantic, totally romantic and unrealistic image, and, and, 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.

Um, but I was also very good at mathematics. And, uh, but what I think happened was that, um, that led me naturally to physics because physics seemed to be the only science that actually answered questions. , it was the, they pose them, these, these deep questions and they answer them, but they not only answered, [00:02:00] they answered them.

In a rather precise, quantitative fashion with an analytic, deductive strategy, and that was very appealing. So I ended up doing, as you said, high energy physics, so quarks and gluons and string theory and dark matter and all these wonderful questions. But then, um, but I always sort of was slightly frustrated, um, that I, I was being forced into this box.

even though I had a rather, um, you know, very eclectic group around me, uh, nevertheless, um, uh, so that kept going. And then, um, in the, I guess it must have been the, um, late 80s, 90s when this superconducting supercollider was being proposed and being built, you know, you know, this huge accelerator, um, that, uh, was going to cost at the beginning of the order of [00:03:00] 10 billion and, uh, uh, we were all very excited about it and so on.

And then it was canned in the early 90s. This is

James Robinson: a big facility in the, in the That was going to happen in the USA, right? Yes, in


Geoffrey West: It was much bigger than the Large Hadron Collider, now at CERN. Um, and, uh, it got canned, uh, and, uh, so it was kind of a, obviously a crisis in the field. And I, like many others, uh, were, went into a kind of depressed mode.

But I also went into a mode of, you know, oh, oh, so part of it was It also coincided that, um, cancellation of the superconducting supercollider, the SSC, coincided with one of those waves of, um, anti science that comes to fore every once in a while, and it. It focused [00:04:00] primarily on physics and the comment that was always around was physics was the science of the 19th and 20th century centuries.

The science of the 21st century will be biology. And, uh, well, it’s hard to argue with that in many ways, but it was, but I reacted. You know saying yes, that’s very likely but biology will not be a real science Until it somehow integrates And absorbs the culture and some of the techniques of physics doesn’t have to 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.

Um, but you know, we heard that all the time, but there was also a corollary to that that was either left unsaid, but sometimes said, um, uh, and [00:05:00] 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.

Um, so, uh, sitting around one day, I thought, you know, that, that 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 SSE that I was getting old. I was in my mid fifties at the time, uh, and, uh, I come from a very short lived line of males. Most of us die in our fifties and sixties. And so I [00:06:00] realized that, you know, if, 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 is that? You know, what is it that’s. that is the origin of aging. And, um, I thought that’s an interesting problem to think about, but no doubt there must be tons of work been done in biology on this and in medicine. Um, and, um, so I said, 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, 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.

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, um, you [00:07:00] know, that they teach, uh, elementary biology and that covers all of biology. And you look in the index, nothing about aging and death. Everything else is covered.

So I thought, Ooh, 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, but why do we live a hundred years? So I’d put it in a physicist terms, simplistically, where in 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 and so on. So, um, I started thinking about that, and, um, the, the first thought that I had to start, you know, actually deriving, quote, a theory, [00:08:00] was, look, if the system is going to age, decay, and eventually decay, Disappear, um, obviously you have to understand what it was in the first place that was keeping it alive, you know, because obviously something has gone wrong.

I mean, it’s produced too much entropy or whatever. So, uh, 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. In biology, that is, that, um, 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, the How much energy does the organism need to stay alive?

How much [00:09:00] 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 scaled in an extraordinarily simple mathematical way. There’s a so called power law. Um, uh, and, and the way that’s represented is if you plot, The metabolic rate logarithmically that is going up by factors of 10, um, 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 I was a great subscriber, as we, most of us are, to the idea of evolution by natural selection, and this kind of naive idea. 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 think organisms evolved in.

Not just the organism, but every component of the [00:10:00] 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.

And I thought, my God, you know, there must be an explanation for this. Well, it turned out there wasn’t a satisfactory one, there was no, and by the way, this was true across all of life, wasn’t just sort of mammals and birds or fish, but everything Straight line. Not only that, the slope of this straight line, Max Kleiber had learned, was three quarters, very close to three quarters.

So I thought, and, and so I first thought, that’s great, um, I’ll use this to learn about aging. But I first better understand where this law comes from, myself. Uh, and so I started [00:11:00] biology. And I, I learned, I derived. that law from some fundamental principles. Um, I hooked up with some extremely good biologists and we eventually published.

A paper in science that got a lot of publicity and, uh, you know, I was still running a big high energy group, by the way, I mean, it was sort of weird, it was sort of a hobby 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, this work in biology.

serendipitously led to my sort of adiabatically slowly moving into becoming a kind of pseudobiologist. Yeah, I think,

James Robinson: and in a moment we’ll, I want to go into the details [00:12:00] of where that three, three quarters scaling law comes from and what it means because that’s That’s so fascinating, but I do want to pause here because it’s such an extraordinary story.

This arc going from, you know, being quite a eminent theoretical physicist running a group at Los Alamos in one field, and then, you know, fairly late for most people in their career at least, you, you, you take a completely different track in some ways. We’ll 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, why humans live for a hundred years.

There’s nothing in the literature on this. I’m quite intrigued about that problem. So I’ll, I’ll go and I’ll go and find a solution. Um, And, you know, one wouldn’t expect a lot of [00:13:00] progress, uh, you know, that doesn’t sound like it’s going to be a fruitful start of a research program, but it, it really was. Um, I, I just love these kind of two act books, you know, and, uh, this seems like one

Geoffrey West: of them.

Yeah. So yeah, so of course, by the way, just to repeat what I said earlier, it was a, um, a product of arrogance, ignorance, and naivete. Um, and, 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 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 some, at some semi-conscious level, I had felt constrained or claustrophobic. [00:14:00] Somehow surprising in a way when you think about it, because I was working in string theory, which I think maybe not by then, maybe it had, it had already been dubbed this ridiculous term theory of everything.

Um, and, and here I was feeling claustrophobic to work and one of the things I realized later, by the way, was, um, I had. Also, part of that arrogance was that, um, part of the culture of physics, but particularly high energy physics and theoretical high energy physics, um, 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, um, if it is it. Um, um, that [00:15:00] all you got to do, you have the theory, you have the equation, and then you solve it, and you keep turning the crank, and out come, you know, uh, 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, you know, automobiles, and then there’s iPhones, and it all comes from, you know, just turning the crank, and, uh, because once you have that equation, In a certain sense, it’s all engineering.

So that was sort of, I mean, I’m exaggerating and making a total cartoon version, but that was sort of the mindset. And the, the, the thing that I learned of 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, this is the only place in the universe, as far as we know, some probably are other places, this is it.

This, [00:16:00] this complete mess that we live in on this planet and all these extraordinary processes that take place, um, called life or complex systems, um, are even more challenging, remarkably, than understanding the origins of the universe. Which is weird, you know, 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 will follow is the evolution of the universe, and we’ve done an incredible job. I mean, the progress in cosmology, astrophysics, astrobiology even, has been fantastic in the last 25, 30 years. Um, but It’s, it’s all, you know, what, what some of us call simplicity. That’s not, you know, that because [00:17:00] you can write an equation and try and solve it and continue.

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, that’s not a passion statement, but you know, understanding our brains and consciousness and, you know, What the stock market is going to do and, uh, you know, are we going to solve all the problems of the future of the planet?

Those are a completely different category of problems. That’s right. You can’t write an equation. Yeah.

James Robinson: I think we’re not saying that in principle. There’s some kind of new non physical behavior 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, that is, you know, the underlying dynamics that governs everything.

And in principle, it could be cranked perhaps, but in [00:18:00] practice it can’t. And even if it could, I’m not sure that that cranking would produce understanding. It might produce. You know, the right outcomes, but would it actually explain anything to you in a, in a human sense? Probably

Geoffrey West: not. Um, yes. I mean, we don’t learn anything about life from the fact that, uh, you know, uh, the nuclei of.

of atoms are made of protons and neutrons, or well we do from that, but the protons and neutrons are made of quarks and gluons and so on. 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 in, for life on earth, for the stuff on earth, all the various levels are very closely coupled, and they’re all interrelated.

You can’t do that separation, and that’s what makes, that’s what [00:19:00] allows us to do physics in a way. Is that, uh, especially fundamental physics, because levels tend to get separated from each other. And you can consider them, um, autonomously. Yeah.

James Robinson: Let’s come back to these remarkable scaling laws, which we should say Max Kleiber discovered almost a hundred years ago, I think.

Um, in the 1930s. So it was, you know, it’s incredible that they, they were sort of laid to one side for so long. Um, and. You know, what they say is truly remarkable, that if you double the mass of a, of an organism, uh, so if you go from one animal that weighs half of a, half of another species, that heavier species doesn’t need twice as much food per day.

It needs about 75 percent more. So that’s the three quarters of the, of the exponent that you mentioned. And this is, [00:20:00] this three quarters is remarkably consistent across species. Um, And across kingdoms, it’s not just animals, it’s plants as well. That, that same exponent turns up if you’re looking at, um, like the number of leaves in, in trees, it doesn’t double as you, um, 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 seeing that relationship in the data to then figuring out an explanation for

Geoffrey West: that? So, first of all, I want to just, um, continue with the phenomenology of it. That is, it’s not just metabolic rate, but 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, uh, almost any physiological [00:21:00] quantity trait of any kind of organism Obey 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, you know, how long you live, in fact, um, uh, or how many offspring you have, or how long do you take to mature, you know, all these kinds of, they’re all scary about them. They all have these straight lines. And the, the thing that is so striking is that the slopes of those lines.

Always simple multiples of one quarter. So there’s this extraordinary universality and first discovered by Clymer. But, um, the, the, during the, uh, 30s, 40s and into the 50s even, um, people just added to this so that there’s, you know, huge amounts of data that can be collapsed onto these [00:22:00] scaling curves. And one of the things that helped me in my work was it just so happened to then be.

late 80s, 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. I mean, so, um, uh, but There was interest in these laws, they weren’t sort of put aside then quite, and in fact, you know, many of the most distinguished biologists, Huxley, Hordain, uh, and so forth, um, Darcy Thompson, all were intrigued by these things.

Um, but what killed it, of course, was the molecular revolution. I mean, uh. 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, [00:23:00] etc. And that completely dominated biology 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, I mean, in fact, it was in the Human Genome Project, it was basically said. Once I’ve mapped the human genome, everything follows, you know, we know everything, which was, you know, even I, who knew very little about it, thought that was absurd.

Um, but anyway, that’s, that’s beside the point. Um, so here were these, so they went into sort of, onto a back burner, um, known mostly only to ecologists because for obvious reasons in an ecology, you need to know when you’re talking about interaction of species, um, how their metabolic rates change [00:24:00] with their size and so on.

So many ecologists knew it. And my, my major collaborator, Jim Brown, was a very distinguished ecologist. And he, we came together because he was very. Intrigued as to what the hell the origin of these laws were that he was using, you know, where the hell did they come from? Um, so now let me try to answer your question, uh, indeed, where do they come from?

So the thing that got me, uh, immediately when I realized that, um, uh, that, that these laws were ubiquitous and had this universality to them, was that obviously whatever The underlying principles were had to transcend the, uh, sort of in evolved engineered design of life. That is, you just, you know, if it applies to trees and to mammals, it has to be something that is independent.

Of, uh, [00:25:00] the, the, you know, what makes you a mammal and what makes a tree a tree. And, um, so one of the things that is common, of course, and that’s why the molecular revolution was so powerful, was, of course, genes. Um, and, and you could say, well, it’s encoded in the genes. That doesn’t explain anything, of course.

It just sort of puts it back one step. Um, uh, and so I sort of dismissed that. I didn’t, that was not a very satisfactory answer. And then I thought, well, there is one thing. that is common to all of these, um, first of all, it’s obvious that a lot of these are to do with the use of energy in some form or another, uh, metabolism being the most obvious example.

But, um, you have to distribute energy and maybe all these laws are simply A reflection of the mathematical and physical constraints on the networks that had to [00:26:00] evolve in order to distribute energy. So natural selection, as it evolved multi, 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. Um, let me try and see if it works for mammals.

Just that idea, take that idea for mammals. So, um, 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, um, the [00:27:00] network, say your circulatory system, it’s terminal units, it’s in by the capillaries, 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, I mean, otherwise it doesn’t make any sense. But you have to put that into mathematics. The, the, uh, the second most important one. was that, um, if you look at all mammals, that, um, natural selection, when it evolved different species, uh, uh, uh, than a, than a mammalian, um, did not reinvent all the fundamental components, you don’t start, you know, from the beginning again, it, um, it used the same fundamental units, same, basically the same cells, the same capillaries and so on, so the idea was, That this network ends at a capillary [00:28:00] and then feeds a cell, but the capillary is the same in the mouse as it is in the whale.

That is, and the idea being also that, look, um, if you, um, 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 where, well, 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. The outlets stay the same. And so it is, you know, all the outlets, the faucets, the taps on your, um, 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.[00:29:00]

So that’s another one. But the last one, the last. sort of speculative principle was that, and this is the most important one, was that, um, of all the possible networks that could have evolved, uh, 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, are the, are, um, the ones that have minimized the amount of energy.

That is needed in order to keep, sustain the system. Namely, the idea being, so let’s take the circulatory system again. We all have a circulatory system that is evolved to minimize the amount of energy our hearts have to do. To pump blood through it to supply the cells to keep you alive, um, so that you can [00:30:00] 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. That is more pretty pushing your genes forward, so to speak. Um, that was the translation of that into a physical framework. It comes very

James Robinson: naturally from a physics y way of thinking, I guess, as well. You’ve got to minimize some quantity.

Geoffrey West: And you know something, I, 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 sounds that’s quite profound actually, you know, that, that, that natural select the, the survival of the fittest, so to speak, the continuous feedback, positive feedback in competition in the environment has led to [00:31:00] 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, it’s a sort of a different view of, or a different rephrasing. 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 taught 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 It’s, uh, anyway, but the point about that is that physics operates by optimization.

All the fundamental laws of physics are derived from optimization principles, everything from general relativity to [00:32:00] Newton’s laws. And so, you know, we’re, that’s the way many of us like to think about systems is what is being optimized. And then we have the apparatus. I mean, much of the apparatus of mathematical physics.

Is related to optimization problems and, um, and constraints. Newton’s bead

James Robinson: on a wire was sort

Geoffrey West: of Yeah, that’s right. Exactly. Exactly. That was the

James Robinson: beginning of calculus, um, differential. Exactly.

Geoffrey West: It was very much in that spirit. And so, um I started working out on that, working on that, at first on my, totally on my own, and I made what I thought was progress.

Well, it was progress, I thought I derived, it wasn’t. But I then was hooked up with Jim Brown, a biologist who had been thinking about this as a biologist, as an ecologist. And, uh, He and his student, a man named Brian Enquist, who is now himself a, a [00:33:00] highly established, well known ecologist, uh, we started meeting as, uh, discussing it, and I was telling him what I had done, and they were telling me what I’d done wrong, or what was not right biologically, and getting it straight.

And it took a year for what I had thought I’d derived. And it was basically, I mean, 90 percent was well, maybe 80 percent was basically right, um, to, um, getting it in, in, uh, in shape to write a paper that then was published eventually in science. Um, but it took a year and by the way, it was a real year. I mean, we, we made a commitment at the beginning.

It was kind of an interesting, um, uh, something I’d never done. Um, we met, we were two different institutions and, uh, it turned out. For various reasons, it was very convenient to meet in the middle at the Santa Fe Institute. And that began my association with the Santa Fe Institute. But we [00:34:00] made a commitment that we would meet every Friday morning, beginning about, between 9 and 10, and they would hang around until about 2 or 3, and we would just stay together with a blackboard, and battle things out.

And, you know, I knew no biology. And they were, how should I say, um, challenged, mathematically challenged, I don’t know if that’s a term. Uh, you know, so it took, it took a bit. It was, it was sort of like, often likened it to a marriage, you know, where you, It’s beautiful and wonderful, and then other times you think, Jesus Christ, what am I doing with this, they’re driving me nuts, they don’t understand, you know, this and that, and I’m sure they felt exactly the same.

But it was a wonderful, it was a tremendous collaboration which lasted for about 15 years, actually. But having got that paper, [00:35:00] by the way, the important thing was having done that work, it opened up. Everything. 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, you know, a whole plethora of subjects across biology.


James Robinson: I just want to say, I think I feel like a year doesn’t seem that long, given that you’re just spending your, your Friday mornings on it. So it’s a reminder how much one can accomplish if you, if the time is set aside and the right collaborators are found.

Geoffrey West: You know, I, uh, it’s a good point because I mean, the, the thing was Jim was running a big ecology group.

I mean, if they work in the field, um, and I was running, still running high energy physics up at Los Alamos. So, uh, you know, both of us were working. In our spare time kind of thing on it, but it was became very clear. [00:36:00] 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 had, we’d ever been doing, I mean, I know my love of high energy physics and all the work that I. was quite proud of. Um, this, this was really exciting. I mean, first of all, to go from a totally abstract world of quarks and strings to a world where, you know, you, real thing, you know, vascular systems and metabolic rates and growth rates and cancer and so on was Um, it was very exciting.

James Robinson: Yeah. It’s not, it’s not easy to crank through from the, you know, string theory to figure out why a whale lives so much longer [00:37:00] than a mouse. Um, and I want to, let’s, let’s, let’s go a little bit more into the details on, on this, um, three quarter power. So, so we said that nature is, or evolution is trying to optimize for something and it’s, you know, it’s keeping the energy cost.

Down. So I guess what the networks are trying to do is deliver stuff to the cells, the terminal units as efficiently as possible. Um, and in my mind, at least, it seems like 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 lot of water through a a liter 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. Um. Is that sort of the bones of what needs to be maximized, as it were, kind of a surface area that, that you’re touching all the

Geoffrey West: cells with? If you put it that way, [00:38:00] um, and indeed that’s one way you can look at it, because, um, let me just back off a second to the network and I will come back to that.

Mm hmm. Because you’ve got to examine, it’s right, I mean What you said is correct, but I want to put it in a slightly different form. Um, so, uh, you know, when you grind through the mathematics of, uh, so you have to do the mathematics of a network, as you said, a heartbeat. So the complication here, which is not true for trees, that’s the trees and plants, is you have a beating heart, you know, you don’t have a pump and it’s just pushing like, like a straw, you know, it’s a suck.

You’re going, you’re, you’re beating hard, so it’s pulsatile, um, so, uh, that complicated things, um, but, um, so, uh, but you, nevertheless, it’s the same idea that you’re pushing blood, uh, through the network [00:39:00] down to the cells, and, um, when you do the mathematics of that, what you discover is that, um, um, um, Where that three quarters comes from is that the three, is it 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, in those, is the dimension of space you’re in. So If you were in five dimensions, it would mean five over five plus one. Okay. So, um, and that’s natural that that three would occur somewhere. Um, the dimension of space you have to fill, you have to supply. Um, 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.

That is what you [00:40:00] discover is when you try to, when you optimize this system, the network, um, uh, the network structure that does that is, is a fractal one, namely it’s self similar. Um, that is, it just keeps repeating itself over and over again. So that if you cut 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 it’s, uh, 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 non linearly, but nevertheless, it’s, it’s repetitive. And that minimizes. the, um, energy needed to push through the network. It could also be, it is also, um, if you think of that network as a [00:41:00] surface, I’m sorry, if you think of the capris, all the capris you could lay and they form some weird surface.

Um, what you’re saying is exactly right. It’s the, it’s that, that surface. is effectively maximized with respect to all the changes you can make in the network. So, um, the, the, the trick for mammals with a beating heart that is at first a problem is, you know, you got to push it, you got to, you know, 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, you know, less than a minute, or the blood rushes out. But if you touch a capillary, break a capillary, just scrape your finger, it just oozes out. And so the system [00:42:00] is a part of that fractal nature is extraordinary. That it arranges so that the pressure drop 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’s rushing by, if you’re just like a straight image of a straw, that’s why I’m addressing the question, your image of the straw. If you push, it’s the same velocity at the end as it is at the beginning.

James Robinson: That’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 with a high speed to their end units right they just need to, it’s the very last, you know, centimeter or millimeter they need to travel. So they’ve kind of [00:43:00] like all the all the energy is being used up.

delivering to, um, things further up the chain, I suppose.

Geoffrey West: Absolutely. I must say, um, independent of anything else, uh, when I, um, when, when, when I put it all together and had now this, um, this model, this theory of the cardiovascular system, um, and how it worked. It was quite beautiful. I mean, most, 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, put it, it was this context that was not known and putting it all together. in this form. Much of this has been worked out, um, in various parts, um, much earlier. Even back to, I think, the famous Thomas Young, who was the first to get the speed of blood through, um, you know, through your artery, through your main artery.

Um, but, uh, anyway, that [00:44:00] was the beginning. It turns out Trees, of course, and then you have this is this interesting question. Trees don’t have, um, beating hearts. Plants are quite different. So how does it work there? So you have to do that. In fact, they’re not, it’s not a bunch of pipes joined together. You know, like we are, we’re not the, we’re not like the, the, the plumbing system in your house.

Um, where that’s, that’s who we are, but plants, that plant above you there, um, is a bunch of fibers joined together, 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.

James Robinson: You, you mentioned that it’s 3 plus 1 and, uh, you also talked about the, the fractal nature of these networks. And, and those two points are, [00:45:00] are, are highly related. And I think this comes across beautifully in your book, uh, 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, the piece of paper, uh, 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. There are these, you can draw a very special space filling curve on a piece of like paper, which is when you double a piece of paper, you’re gonna double the ink.

And that’s kind of obvious because if you space filled the paper with ink, you’ve covered the entire area. Um, but that It takes a little bit of, uh, I guess, mathematical imagination, but that trick works all the way up in any dimension. So where we have these, these, um, networks with our bodies filling three dimensional space, um, [00:46:00] the way that they scale up is, is to the fourth power in a, in a certain sense, or at least the, yeah, this, this kind of critical surface area that they can

Geoffrey West: reach.

Yes, so they behave as if we’re in four dimensions, and that’s what’s incredible, the fractal, so you know, I don’t know, 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, you know, the essential part of us, everything from our.

You know, what I just talked about our circulatory system to our brains that we have this kind of self similar property approximately, obviously. Um, and, um, and, and of course, maybe we will talk about that maybe a little bit later that, that permeates nature. And this was the great discovery of, um, Benoit Mandelbrot.

Um, you know, who then showed us some of the mathematics of [00:47:00] fractals. 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. He showed no interest in why would they be like this.

It was very strange. Anyway, that’s beside the point maybe, but, um, but it, 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, uh, was, was fantastic. Because it is, it is extraordinary that, um, we were dominated by Euclidean geometry.

Um, up for almost 2000 years, even though, uh, you know, we got out of Euclidean geometry with, uh, you know, differential geometry and Einstein and general [00:48:00] relativity and so on. But this other kind of geometry and, and the point that Mandelbrot of course kept making is there aren’t right angles and straight lines in nature.

I mean, that’s not how nature works, and I think that’s, you know, it’s a very simplistic cartoon kind of statement, but it’s of course mostly right, and that’s true, and in fact nature is dominated by these self similar fractal quantities, and the curious thing about them is, in terms of their dimensionality, as defined by how they scale.

Um, they can have, uh, 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, um, but these kinds of things, you can double the size, and in fact, uh, all kinds of weird things happen, you know, you get more [00:49:00] or you get less sometimes, so,

James Robinson: uh, The Cox Loaf Lake, I was looking this up, um, which is this, you know, it looks like a kind of classic.

Snowflake. Um, and if you, if you double the size of that, you get, um, not double, but, um, you know, 26 percent extra on top. So it’s factual, a factual dimension is, is 1. 26.

Geoffrey West: Yeah. 1. 26. And that’s true of us. I mean, we’re not 1. 26, but our system, you know, that’s why you have these, the kind of Kleiber’s law and all these quarter powers, um, but it’s all dominated by four.

It’s, it’s the, it’s, 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 or 3. 2, which would have been still fractal. But we actually maximized it and you [00:50:00] can’t go beyond one, it turns out. So three plus one gives you the four.

But the mathematics do that. I mean, you know, I mean, I, I, the way this happened. Historically for me was it’s very typical, you know, I did the calculation and it was, you know, it was a complicated mathematical physics calculation, not, uh, you know, good mathematical physicists would be anyone could be able to do it, but setting up solving it, you get the result.

And you say, wow, that’s great. The degree is fantastic. Now let me try to understand it. You know, where was, you know, what were the essential features through all that hieroglyphics that gave rise to this very simple result? That was because I think that was particularly the startling thing. Um, because when I started that calculation, I said, there’s no way this is three quarters.

I mean, Kleiber fitted it to three [00:51:00] quarters, but it’s probably Point seven three eight And that’s what I’m going to show that it’s point, whatever it is. And I showed him his 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. Yeah.

James Robinson: 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.

Geoffrey West: So wait a minute, what happened here? So that’s why, but it’s very typical in physics. You get a result. Um, especially if it turns out to be, you know, much simpler than you thought.

And then you have to go back and think through what were, what, what was the essential feature? What were the essential features that gave rise to the simplicity that I should have seen a priori?

James Robinson: , So we’ve got to the three quarter law, and it is a genuine three quarters, it’s not an approximation.

Geoffrey West: Well, that’s the thing, yes, I mean, that’s, and the [00:52:00] data does You know, , I mean, that was the original proposal of, of, um, Kleiber and indeed the data certainly, you know, it hovers around that. We’ve done a lot of analysis and of course there’s all kinds of controversies about the data and about this and that, which I find somewhat tedious.


James Robinson: one final comment on the fractal, um, point, uh, we were talking earlier about, um, Sean McMahon, who I interviewed not so long ago, the astrobiologist and his whole thing is looking for bio signatures and it does. I do wonder if, if. You know, if we see some fractal patterns with the right dimension on another planet, would that constitute a biosignature, at least, or a technosignature?

Geoffrey West: So that’s interesting. So, um, I was, funnily enough, the Astrobiology Institute. [00:53:00] Um, they, when it was set up at NASA, I was one of the people they brought in right at the very, very beginning. This is, this has got nothing 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.

And then they invited proposals. And I wrote, this is, this is quite funny in a way. I wrote a proposal with myself, Murray Gell-Mann. And, you know, the famous physicist, right, and someone else who’s now, um, at Harvard, Juan Pérez-Mecader. And we just assumed, you know, that, um, we would get funded, and it got rejected, so I never became, so I got so pissed off, I didn’t, 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 memories of that. Because at that time, I was [00:54:00] thinking exactly about this. I mean, that’s the relevance of this. In fact, part of that proposal was, could you use any of this? This was just one part of the proposal.

Could you use any of this work, this, um, scaling work, the fractal like behavior? It’s nature and so on to, um, say, yes, there must have been life or at least there must have been, uh, this is evidence that there could have been life here. Now, the real problem with that is obvious that fractals, I mean, just as Sean, point Sean was making and his seems to be, uh, his mission is to look for non bio, non, non biological things, abiotic processes that sort of mimic life.

And of course, you know, obviously the most obvious one here is rivers. I mean, you know, if there’s been water and rivers, obviously, you know, so the question then is, [00:55:00] can you have enough data that you can distinguish the fractal dimension of those for a 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, but, um, certainly if you saw, you know, if you saw things that had other potential, uh, biological features, This would be evidence that, um, you should add to that, for sure, that if you did see any kind of, um, 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, um, because it was also part of the astrobiology thing, is that if life exists elsewhere, where?

It will have this kind of structure. It will have to be networked and it will try to [00:56:00] optimize and it will have evolved. Therefore, it will have quarter powers. So that was sort of the, uh, the speculative argument. Maybe this is a

James Robinson: good segue onto. cities, because I think if we, 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, um, the cities here on earth as well.

Um, because as you found cities also behave remarkably similarly in many ways to, to, to organisms. So perhaps take us through, well, You know, how did that next leap in your career come about?

Geoffrey West: Yeah. So that was, um, so it was pretty clear once, you know, 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, [00:57:00] understanding, um, some aspects of cancer.

James Robinson: Perhaps we can talk about that first if, yeah, I’m,

Geoffrey West: well, it might be good to talk about growth actually briefly, because there’s a big contrast with cities there. So growth in this works in a very simple way.

You, you, um, take in food and nutrition, you metabolize, you send the metabolic energy through the networks, networks goes to the cells and it, um, maintains them. Um, and replaces ones that have died, and in a growing phase it adds new cells. So that’s, 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, the network that is controlling as the system is growing, That is the supply. The supply is growing in what we call a [00:58:00] sublinear fashion. The three quarters 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, um, you know, your cells are working, uh, less hard than your dogs, but your horse is working less hard than you. Um, so 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 the sublinear, [00:59:00] 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, and then gradually as the, um, uh, the, the supply Beats out the demand as the, the, uh, the demand beats the supply. Uh, 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 grow following the same curve. And, uh, so that’s great. And that stability, that, that stable configuration that we end in, that most organisms end in, not all, um, plays obviously a hugely important role. In the long term [01:00:00] sustainability of the biosphere, because you’re spending most of your time in a kind of meta stable state, rather than continually changing.

So, um, and I’m gonna, I’m, 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 cities, so cities, so we got into this because I moved to the Sanofi Institute because of this work and the Sanofi 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. Um, so, I was giving a talk on some of this, and, uh, in the audience were two visitors, um, on sabbatical. One was a well known anthropologist, Sander van der Leuuw [01:01:00] 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, I said, and possibly cities, I said, you know, because they’re 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. You know, so we put together a proposal, which was funded. That one was fun. Jen very generously, may I say, and, uh, it got me working on, oh, I was going to work on companies because I thought they were, they were much more interesting than cities. I thought cities were boring, but it turns out I, in my naivete, I hadn’t realized that you couldn’t get.

data on companies without buying it, [01:02:00] you know, that is most of it is, well, it’s almost all proprietary and, uh, um, various, uh, companies have assembled data sets, but you had to pay, I think it was 40, 000 at the time, I should get some large amount of money that we did not have at our disposal. So I said, okay, look.

What we have to do is we have to prove the whole concept of all this by working on this boring problem of cities. Uh, 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. So I put together a different collaboration, a lovely bunch of young people who at that, 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. [01:03:00] Discovered, to my amazement that uh, indeed, well I was sur well, I wasn’t so surprised that they scale. I was surprised. at the exponent, the analog to the three quarters, because the first work that we did, actually the first work. was with a colleague at, uh, the, um, ETH in Zurich, the, uh, it’s like the MIT of Switzerland, um, Dirk Helbing, and he and his student, and, and, uh, we, we put together, he, we put together some data that showed that cities do scale.

in terms of their, um, infrastructure, just like biology. So that was just biology. You know, if you looked at the roads and various things, um, 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.

Um, the only difference being that the [01:04:00] slope It was 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, uh, and the surprise was that not, well, first of all, it confirmed that things scale. Socioeconomic means things like wages, number of patents.

Um, not a crime, uh, not a flu, you know, anything that’s involving interaction of human beings directly. And all those scaled, but they scaled instead of sub linearly, less than one, super linearly, bigger than one. 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, it took me a good 20 [01:05:00] minutes to realize that I was completely wrong. And I completely switched and said, my God, of course, I’m, that’s, it’s, it’s exactly right. That things that are socioeconomic should scale. Bigger than one 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, um, 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 kick myself that I hadn’t thought of that and written it into the proposal, written it somewhere because I can’t claim I predicted it.

That’s for sure. So, um, so the sum total of all this was something that was really, um, very satisfying. We looked at [01:06:00] data across the globe. So that meant North America, Central America. Oh no. Hilarious. Sorry. Central America, 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. That means roads, electrical lines, water lines, scaled with the same exponent, which was about 0. 85, um, across the globe, the same way, roughly speaking, um, but all socioeconomic quantities, whether, as I say, good, bad, or ugly, namely wages.

Crime, [01:07:00] disease, all scaled with the same exponent of about 1. 15. So there was, like biology, a kind of universality, um, even though here now it was bifurcated. It was a, you know, it was a dual universality. The infrastructure behaved differently than the, uh, socioeconomic. But the fact that it’s scaled meant that there were universal principles constraining.

The structure, organization, and growth of cities across the globe. So it was almost as if, it was almost as if, uh, you know, in the industrial revolution came and people realized cities. We’re going to grow, they were growing, and a big international convention was gathered and all the countries came together and said, how are we going to design cities?[01:08:00]

And they said, well, we have to do it according to these scaling laws. So it was almost, you know, and of course, it’s all happened organically. And the question is, how, what, 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, 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 Well, um, uh, I would say that our work and can we derive, of course, A comparable theory 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 [01:09:00] progress. We understand, we’re 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. And the idea there is that maybe it’s to do with You know, cities evolved via, you know, they, what is, 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 that we have evolved in the last, you know, several thousand years. So, um. [01:10:00] But as it evolved, um, and people came together, they need to interact. So maybe one of the optimization principles is you try to, uh, the city evolved 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 even though the streets are all going, you know, especially, you know, 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, maybe it’s the cheapest way. But something is that is an optimization that’s very analogous to the um, kind of optimization that takes place in biology that we talked about earlier. Now, for the socioeconomic, something different, a little bit [01:11:00] 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 number of interactions, and at the same time, and here’s the kicker, and this is totally speculative, Everybody wants more, everybody wants more of everything, including, you know, everything from material well being to even interaction, you know, they want to go to the theater, they want it and so on.

So that’s sort of the idea. And it’s, and, and the hard part of this is not just putting those into mathematical terms, which you can do, but is integrating these two networks. You can’t talk about them truly separately because. You can’t have a network of interaction. So, by the way, the socio economic interaction.

The flow in the network is really information that’s being exchanged [01:12:00] and in the infrastructural network, it’s energy and resources. So in the bigger picture, a city is the interface and integration between on the one hand, it’s physicality. It’s energy, it’s thermodynamics, if you like, with the exchange, with information exchange in social networks, which are tied to that infrastructure.

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, uh, I, I’m, I’m confident of is that, um, 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. That the, you can show that if you do, if you have these [01:13:00] 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 goes into making the city more productive, more exciting, have more interactions, produces more patents, has more crime, is, you know, is more, more opportunities and so on. I mean

James Robinson: intuitively that that feels right like if I can get to the if it’s that much easier to get to a restaurant because it’s that much closer I’m going to go there and you know I’m going to have more interactions um 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 [01:14:00] organisms.

So you double the size of, um, a city and it’s only consuming 75 percent more. Resources. Um, and I’ve heard you say New York is the greener city. 85. Sorry. 85. Yes. 85. The wrong. I was still still on the biological. Yeah, yeah. Uh, yeah. So you, so you, you’re making a 15%

Geoffrey West: saving. Yeah. Which is huge, enormous. I mean, you don’t have many doublings to do your.

Way ahead. So the curious thing about this was that, you know, so much. So during COVID during a pandemic, um, much better 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 [01:15:00] a big city. So that’s the point. You’re going to get it much faster than you are in a small town. You know, if you want to sort of buzzier, sexier life, better be in a big city.

James Robinson: Yeah, and that’s, you know, it’s almost paradoxical that the energy uses is lower, but it is the pace of life is, 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, um, I was thinking of the, uh, there’s that last line of Wordsworth’s, um, poem on, on West, on Westminster Bridge where he says, he’s looking at London from Westminster Bridge and he says, um, You know, all that mighty heart is lying still.

So that’s London at night in, um, 18, the 19th century, uh, 1802, um, so there is this intuition that cities are lively cities, never sleep, you know, all [01:16:00] these kinds of attributions of, uh, animal characteristics to them. And it turns out that in a certain sense, they, they do behave something like. Organisms and, and not following exactly the same scaling laws.

Um, but

Geoffrey West: nonetheless, But there’s this super linearity.

James Robinson: And that’s very

Geoffrey West: different. So that’s the point of departure. Yeah. Where, and that comes about. So how does that, that comes about because the city brings people together. 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 know, 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 [01:17:00] relativity.

It led to Amazon, and it led to, you know, General Motors, and so on. That’s, that’s the process. The city does that. That’s why universities mostly are in big cities.

James Robinson: Yeah, I think, I do find the, the Einstein example interesting because I’m always struck that, that he was, you know, a patent clerk in, in Bern, which I went to once and it seemed like a very sleepy city.

Oh, it’s

Geoffrey West: 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, you know, phase transition, a huge, enormous leap, 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 it.

Urban living, you know, I mean, I mean, places, I mean, Oxford and [01:18:00] Cambridge have this sort of ivory tower image, but they’re actually cities and of themselves, they are cities. I mean, you bring people together and that’s what, and so city, you know, I think you have to extend even the, um, the idea of a city, you know, it’s, um, it’s really the network of people that are connected, uh, it’s, it’s the network of people that are interacting.

James Robinson: Yeah. It’s, it’s, um, Yeah, and it’s curious, I guess, even if Einstein wasn’t actually the greatest physicist, 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

Geoffrey West: discuss with other people, you know, including his wife, of course, who didn’t get credit.

But, uh, so who was a physicist, but anyway, yeah, that’s a, [01:19:00] that’s a deep, those things are urban, you know, come out of Some urban kind of environment. One thing I’m

James Robinson: intrigued about is how much of the additional productivity that can be measured is in some ways, 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 this, the stand, this, 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.

Um, but I, you know, something that is economically measurable results there. And I think there’s like a, there’s a motivating effect of living in cities to do that because everything’s so. Everything is so expensive and perhaps there’s also some social competition going on as well. So what I wonder is [01:20:00] how much of it is to do with us 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.

Geoffrey West: Well, I think it’s both, of course. It is both, but you know, both of them are requiring enormous resources. You know, it’s not like, I mean, there’s this image, you know, when you, when you say thoughts, for example, your first way 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 that’s, but what it does, it costs in your head, you have to be there.

You have to be in that house. 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 [01:21:00] 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.

So it’s quite complex, all of that. I mean, so you’re right. I mean, and that’s what makes trying to really have a. You know, what kind of universal theory of how this all works. I mean, after all, what we’re getting into here is almost socioeconomics. You know, we’re sort of crossing into other boundaries, other fields here, of course, where people try to think of these things.

But, um, it’s, it’s highly non trivial. And, uh, but the scaling laws, to me, are, 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, uh, and, and I see them [01:22:00] as almost obviously, it seems to me, the whole future of the planet depends on what happens in cities.

Um, that’s primarily because, first of all, more than half the globe lives in cities. Um, it’s going to be more like. 75 percent before too long, um, and that’s where almost all the ideas are created, you know, the image, the image of the, you know, the guru going on top of the mountain, or even that image of Einstein, who’s the nearest we have to it, um, is, you know, is very misleading, I think.

The vast majority of ideas and things do occur in an urban kind of environment. And, you know, it wasn’t like, um, you know, as we’ve already, you know, I’m maybe beating a dead horse here. Einstein didn’t come out of nowhere. Yeah, yeah, yeah. There was a whole century of puzzlement, [01:23:00] yeah, yeah. Yeah, he had all that stuff behind him.

But anyway, um, but what I wanted to do was, uh, to now really distinguish. a really important part between cities and organisms. As I said, there’s this positive feedback. So you have the superlinear, you get bigger you are, the more you have per capita, rather than in biology, the bigger you are, the less you need per capita.

Um, so, uh, in terms of growth, because When you go to growth and you have the same idea, you know, you take that same, um, structure that you have in, in biology, it was you have the metabolic rate that gets apportioned 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, the sort [01:24:00] of energy, including the information, and the information translated to energy units, if you’d like the energy. That is coming in to say let’s just 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.

And 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, um, uh, part of it is being a portion 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, the supply. Is now growing with size as distinct from decreasing with size on a per capita basis. Uh, but the, um, the, the demand is still [01:25:00] sort of just adding. So what happens is that the supply completely outruns the demand. 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. Yeah. And that’s because

James Robinson: That’s pretty much what happened. I guess, the reason you’re growing faster than exponential is that for a city of a given, as you double a city, it, it It more than doubles the, um, the, the sort of creativity, the buzz and so on.

Um, and well, that on its own is exponential, but that is then compound that leads to attracting more people into the city. It’s

Geoffrey West: a positive, it’s a. It’s a very fast positive feedback [01:26:00] phenomenon. Yeah. And that’s been the history from, especially since the Industrial Revolution, of course. Um, that has been the history of cities in, in almost across the globe, but certainly in all industrialized nations.

And um, and that’s what we’ve seen. And so actually the theory. As it stands is very satisfying because we say look we have at the basis we have social networks 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 it’s a nice theory it’s got still as I say work in progress to really get to the fundamentals but um It’s a, it’s a very complete picture.

Um, but it has some weird consequences and some very disturbing consequences. And that is that, that, that open [01:27:00] ended growth. Which we love and which is the paradigm, you know, since the, uh, industrial revolution and the, um, 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.

Um, that, um, so 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 going up reaches an infinite number in a finite time.

So, um, what it’s so that, you know, you’ll have the number of, uh, of, of patents or the number of AIDS cases will become infinite. in some finite time. Finite time could be [01:28:00] 10 years, 50 years, 100 years, whatever. We don’t, but in some fine, not infinite time. And that’s obviously crazy. It can’t obviously, 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, um, what happens is that you would then. Um, sort of stagnate and then collapse. So it’s sort of a sophisticated Malthusian argument that you can’t, it’s, you can’t sustain that kind of growth. Now Malthus got it wrong and he got it wrong for good, for good reasons.

I mean, he was attacked and I think for the right reasons, namely that, um, uh, you didn’t take into account that people are going to innovate. You know, and it gets you out of that, you know, he said that agriculture, agriculture could not keep up with the increase in population because population increases [01:29:00] exponentially and agriculture was linear and he was wrong.

Um, but so taking that idea to this theory, and this now is based on, you know, this agrees with data, so it has some, some serious credibility. So as. As this thing goes up and, uh, reaches a singularity, what it, what you realize is that that, what I told you is sort of assuming that, you know, in the big picture, nothing has changed, you know, uh, we’re in some major paradigm that, uh, like the industrial revolution or going way back the bronze age or the stone age, you know, something that dominated somehow The way people structured society and the tools they used and so on.

Uh, in modern times that would be, you know, the computer and most recently the internet. [01:30:00] You know, that’s sort of a, so these big paradigm shifts, these huge innovations, which, um, set the tone and the culture of the way that growth takes place. They sort of fix the parameters in a certain sense. 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 this, 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, 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, [01:31:00] 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, uh, something I haven’t talked about.

And that is that as the system grows, the pace of life increases, things get faster. Yeah. Everything gets faster. The, um, and, um, in fact, we’ve looked at data and the data supports that in agreement with the predictions. Um, so, um, and indeed, one of the things that has to get faster is you have to innovate faster and faster.

So an innovation that might have taken, you know, 50 to 100 years to really develop 1, 000 years ago, make this up, uh, now would only take 10 or 15 years, but you have to do a new one, you know, how long has it been, you know, the internet age is what, 20 years old, [01:32:00] maybe, I don’t know, um, 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, I don’t know.

In fact, you can fill the air, the world, you know, 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 approaching such a point again, a singularity, and we have to make some major shift, maybe in the next, you know, 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 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.

The things change that you’re going to make a [01:33:00] 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 got to do it again, you 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, 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 collapse of the system and the question is how do you get out of that and I’m happy to speculate. But my goodness,

James Robinson: it is a big question.

I wanted to comment just on the, um, I mean, another interesting point of departure between Malthus and. Your ideas is that they were looking at exponential growth, [01:34:00] which is only going to become infinity and infinity and infinity. I mean, that wasn’t the essential problem with their ideas because sure enough, like once you have enough consumption, it doesn’t have to be infinite consumption before it out, it outstrips, um, your production, but as you say, they, they ignored the, yeah, the, the innovation that has happened in cycles and.

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 a hundred million users within weeks, which, um, I have no reason to disbelieve them. In fact, I have more reason to believe them, you know, looking at the history of, of, of product adoption.

Um, 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, [01:35:00] which increases, um, frustratingly at the, you know, uh, not with the 1. 15 exponent, but it gets 10 percent faster every time you double the size of a city, which just one is wonderful.

But clearly, you know, if, if you. I, I did the maths just earlier, and if you put the whole of me, the whole of the U S in, um, New York, I’m just trying to look up my calculation. It was, what was it? I think, 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 into one city, you get, 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 going to happen. Um, and you know, one can get even more fundamental and say, look, well, the density of cities increases with, with, with size, but presumably we’re not going to create black holes [01:36:00] because, you know, before we get to that point, we’re just going to say, this is too cramped.

I don’t like it.

Geoffrey West: But you’ve raised a really important point because, uh, which I’ve pondered. Um, and that is that, um, all this has changed. You know, since, 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, um, it’s, it’s accelerated in a kind of uncontrolled way. 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 with basically the same, the same brain. And yet we’ve adapted extraordinarily to this.

So that’s, first of all, brings up an interesting question of itself, which I find intriguing. [01:37:00] How, you know, how, 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, but then the follow up question, which is the one that I find most intriguing is what is the limit to that?

You can’t have, I mean, it’s, it’s the same thing as, you know, um, in the physical world. As a thing from the neural world, you know, someone could run 100 meters in 9. 8 seconds. Someone may well run it in 9. 7 or 9. 6, and even conceivably in 9, but what about 5 seconds or 2 seconds? Or one second. Well, it’s obviously ridiculous.

You can’t, wouldn’t be a human being, in fact. So there is a limit. We don’t know quite where it is. It’s probably a close city approaching it for running, [01:38:00] but maybe that’s true of our neurological capacity. When is it, and already you can feel that, you can feel that with the extraordinary changes that are taking place with the, you know, 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, you know, 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. Now, it sounds trivial, but you know, these things are, and I’m, you know, I’m reasonably smart. You know, a lot of people Have a struggle with that and they have the equivalent of that um, and they feel disenfranchised almost and uh, and so my conclusion is if you’re like that you vote for trump [01:39:00] because He provides a simple solution, whereas all this other stuff is so complex.

So that is my, that

James Robinson: is a theory of everything, you know,

Geoffrey West: my point there is I’m being totally sarcastic and silly, but my point there is, are we approaching a time? When our brains, our neurology simply cannot adapt to the technology we’re creating. And it may well be that we’ve solved the problem with GPT.

I don’t know, maybe that, that will do it. Or maybe chat GPT is the next major AI. Looks like it may well be the next huge paradigm shift. Just like the internet was may not be it’s too it’s well, I mean despite all the hype. I think it’s way too early to tell It certainly is extraordinary. [01:40:00] I gave you a little problem the other day, very simple problem, and it got it completely wrong, by the way.

You know, as, as it does, I mean, inevitably it’s very human, I have to say. Yeah,

James Robinson: I think, I think it’s extraordinarily good at, um, particular fields of programming and quite broad ones. And, and so I, I, I know I’m convinced that in certain places it is going to. Accelerate production of things and it will be a paradigm shift for the development of software.

Geoffrey West: Absolutely. My fear is mostly that it’s, um, we’re going to give so much, I mean, I already hear it, of course, so much over to it, AI and machine learning. Um, that, um, all kinds of terrible things are going to happen. Um, that, uh, 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 [01:41:00] irresponsible, but you know, that’s the way of the world.

James Robinson: Well, we’re, we’re running up against time. Um, and 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 unless we have interfaced with chat, GVT and so forth.

But, um, But I do, yeah, this throws up so many questions and I just wonder, do you, have you pondered what the answers might be? It seems like we can’t carry on speeding up. Perhaps there’ll be a natural biological break that’s applied, but one has to fear that perhaps that would come too late. Yes.

Geoffrey West: So I don’t know.

I, I, you know, obviously it’s all spec. I mean, by the way, needless to say. A large part of what I, the last, you know, I don’t know, even half hour, 20 minutes, [01:42:00] 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.

Um, but, um, so my, So I got very despondent with some of this, you know, I mean, 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. Um, that, uh, even, you know, and that may be wrong now. I didn’t, I must admit, I was, like many others, taken by surprise.

by how powerful ChatGBT was. I mean, I knew a lot about AI because Center for the Institute has been involved in AI since its beginnings. I mean, AI has been around for 50 years in various forms. Um, but that was a very serious breakthrough. Um, and as you say, will have profound effects in various [01:43:00] parts of, um, you know, productivity, culture and so on.

But, um, so maybe that, That 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, um, 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 policy makers anyway, people, I mean, they make the decisions, they do it. So, you know, I mean. Global warming is a classic example. I mean, only a minority of people really pay serious attention to it. And, uh, you know, we’re not really addressing the problems. Um, so it needs that. So that led me to the crazy idea maybe that, um, well, first of all, a paradigm shift when I, when you [01:44:00] use the word paradigm shift or major innovation, what immediately comes to mind Is a new technology, you know, that’s, 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, um, innovation and paradigm shifts, of course, in no way connotes that has to be technological. Um, it, it could be cultural or political and so forth, who knows. And so, um, it led me to this really, I’m almost embarrassed to bring it up, but the idea that, you know, what we really need is an, is what I call an anti Trump.

You know, you need someone with the charisma and apparent attraction of, uh, of a Donald Trump, namely someone that can change people’s, what we [01:45:00] 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. They can discard science if they wish, and so on.

We need someone that does exactly the opposite. That sort of promotes, sort of a Jesus Christ, or a Martin Luther King, or, I don’t know, Nelson Mandela. That somehow, instead of tapping in to some of the darker sides that we all have, Uh, somehow it, um, 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, but that It’s not. You know, that, that promotes love, love thy neighbor, that, uh, connotes the idea [01:46:00] 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 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 at my age, if I think of life now compared to 20, 40, 60, 80 years ago, the change is absolutely extraordinary.

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. Why could, how can that be? I mean, do you think, I mean, the assumption would be the opposite. We want to reach out to more and be more [01:47:00] giving and less wanting.

So it needs someone that does that, that can somehow articulate that. And, uh, somehow re, re, re center 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 a bit,

James Robinson: it’s all rather flaky. But I think what, what is fascinating to me is that, you know, while you’ve studied these Networks and found what seems to be almost inevitable laws.

They’re clearly not that 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 [01:48:00] convincing the collective to behave differently. But, uh, 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

Geoffrey West: perspective. By the way, I’m glad you said something I should have said much earlier. You know, the nature of these laws. These are not like Newton’s laws, you know, 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. So, um, 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, [01:49:00] 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 that we can’t change them? Or are they quite cultural? And actually with great effort, We can change things in the city. You know, is it, is it like we can stop smoking or wear seatbelts or is it sort of like, you know, this is who we are.

Don’t know if anyone knows the answer to that. Well, I think

James Robinson: 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. The, the way that technology has been developed has been growth focused, but not direction focused, I think.

Um, [01:50:00] and social media has, has been developed to capture our attention, but not direct our attention where it ought to go. I suppose. That’s right.

Geoffrey West: And it goes for, and it tends to go to the odds, whatever the metric is least common denominator. Right. Well, I hope we’ve Yes, I have to go, actually.

James Robinson: I think with this podcast, we’re sort of doing our bit to push back against that.

Geoffrey West: Maybe.

James Robinson: Thank you so much. This has been, yeah, such a, such a tour de force, just like your book. So, um, thanks again. Thank you so

Geoffrey West: much. Appreciate it.