Making Sense with Sam Harris - #86 — From Cells to Cities

Episode Date: July 14, 2017

Sam Harris speaks with Geoffrey West about how biological and social systems scale, the significance of fractals, the prospects of radically extending human life, the concept of “emergence” in complex systems, the importance of cities, the necessity for continuous innovation, and other topics. If the Making Sense podcast logo in your player is BLACK, you can SUBSCRIBE to gain access to all full-length episodes at samharris.org/subscribe.

Thank you. of the Making Sense podcast, you'll need to subscribe at SamHarris.org. There you'll find our private RSS feed to add to your favorite podcatcher, along with other subscriber-only content. We don't run ads on the podcast, and therefore it's made possible entirely through the support of our subscribers. So if you enjoy what we're doing here, please consider becoming one. Today I am speaking with Jeffrey West. Jeffrey is a theoretical physicist whose primary interests have been in fundamental questions of physics and biology. He's a senior fellow at Los Alamos National Laboratory and a distinguished professor at the Santa Fe Institute, where he served as president

from 2005 to 2009. He's been named to Time Magazine's list of 100 most influential people in the world. And he is the author of the very fine book, Scale, the Universal Laws of Growth, Innovation, Sustainability, and the P of life in organisms, cities, economies, and companies. And we talk about his book at length here. As you'll hear, Jeffrey is an extremely interesting guy. We ran into a few audio problems at the end, so apologies for that. All I can say is that our robot overlords don't yet have this internet thing fully worked out. But I should say that this conversation is pretty dense. I didn't really appreciate how dense it was until I re-listened to it. There's a lot of information here. Those of you who are students of physics and mathematics will absolutely love it, but some of you will find that you really need

to concentrate to follow Jeffrey where he goes. And you might need to rewind from time to time or just listen to the whole thing twice. But this will repay your attention because Jeffrey is doing some very deep and interesting work. And his book is really wonderful. And now, without any further delay, I bring you Jeffrey West. I am here with Jeffrey West. Jeffrey, thanks for coming on the podcast. Jeffrey West Yeah, pleasure to be here, Sam.

Thank you for inviting me. Sam Roberts You have written this fascinating book called Scale, which links the underlying properties of complex systems to both biological and cultural phenomenon, really everything from cells to cities. And it's a fascinating route into basically everything we care about. And the book is filled with disarmingly simple-sounding questions, which turn out not to be simple at all. But they're questions like, why do we live 100 years rather than 1,000? Why do we stop growing? We keep

eating all the time, but at some point we stop growing. It's not obvious why that should be the case. Why do people die and companies die, but cities don't seem to die? And before we get into answering these questions, first tell our listeners how you got into this, because you're a theoretical physicist by training, and now you're focusing on biological and even socioeconomic questions. And it seems to have been inspired both by the death of the supercollider project in the U.S. and your growing sense of your own mortality. So give us the context of your investigations. Yes, no, thank you. Yes, indeed. You have pinpointed, so to speak, the genesis of this in that, you know, I was at some stage happily doing research into quarks and gluons

and string theory and fundamental questions of physics, you know, dark matter and so forth. And associated with that, of course, was this marvelous project of the superconductive supercollider to be built in Texas. And, of course, the vision was to open up new vistas at extremely high energies and therefore at very short distances and confirm some of our ideas about fundamental forces and the fundamental constituents of nature but also you know just the usual search for you know new science, new physics. And sadly, that was canned in the early 90s, and I had been somewhat involved in it. And at the same time, I was into my 50s, and it so happens that I come from a line of short-lived males. Very few live beyond about 60, and

many have died in their 50s. I've got a similar problem. I'm just edging into my 50s, and I'm a year shy of the age my father made it to. So yeah, I follow your line of figure. Very similar. Well, my father did make it to almost 61, but his father, you know, died at 57, and my father's brother died at 54, and so forth. So it's a similar kind of thing. And so I'd grown up with this idea that, you know, I'd probably die somewhere in my early 60s. That was sort of the lifespan of what was to be expected. And in my 50s, I began to realize that, my gosh, I may only have five to 10 years at most to live.

And it was the confluence of that and the death of the super collider and some of the things that were being said in terms of, so to speak, justifying why we shouldn't continue with this huge project that got me to start thinking about some of these big questions in biology originally. And the one thing that really stimulated me and sort of got me emotionally was a statement that many people are familiar with that was being banded around, especially in the early 90s, was, you know, physics was the science of the 19th and 20th centuries, whereas biology is clearly going to be the science of the 21st century. And I must say, is clearly going to be the science of the 21st century.

And I must say, it's sort of hard to argue with that. But there was a corollary to it that was sometimes actually made explicit, oftentimes just implicit. And that was that, you know, we know all the physics we need to know. And, you know, there's no point in, you know, going any further kind of Philistine view of the intellectual enterprise. And that really got me, you know, because even though, as I said, I agreed with the first part that no doubt, sort of came back with a statement that, well, yes, that may be the case, but it won't be a real science unless it starts to... Until it gets a the paradigm of physics in terms of it being quantitative, more analytic, based on principles, and therefore more predictive, that kind of paradigm, and also some of the techniques of physics. And the question, so the big question is, you know, to what extent can biology be

mathematized and put on a kind of principled basis beyond just, in quotes, the principle of natural selection, but to put that into a more solid foundation. That was where I was coming from before I, and I must say, I knew almost no biology at the time. But it was that sort of emotional reaction that got me to start thinking at some stage, well, you know, maybe I should think about that seriously. Maybe I should actually start thinking about how you would, in fact, take this fantastic set of ways of thinking and tools that we've developed in physics, how could you take that to biology? And that's where it coupled up with the question of aging and mortality, that I started thinking a little bit about that. And the way I framed it

in my head was not just what is the mechanism of aging and why do we die, but to make it slightly more quantitative and say, you know, where in the hell does 100 years come from for the lifespan of a human being? You know, what is that related to? We ought to have a then, you know, you should be able to pick up a biology textbook and there would be a chapter about aging and mortality in which there'd be a little calculation that ends up with saying lifespan of a human being should be approximately 100 years. And by the way, the lifespan of a mouse should be of the order of two or three years, etc. And what I discovered as I started to take this more seriously and read not just biology textbooks, but read the literature on aging and mortality, gerontology in general, was that this was not a very well-developed area at that time. And in particular, as far as I could tell, no one seems to have asked the question in that form.

And so I kind of, as a little exercise, so to speak, to, you know, spend my spare time in the evenings or the weekends, I thought, well, maybe I should start thinking about that. How would you go about trying to show that 100 years is the expected lifespan of an animal our size? And what that led me to, first of all, was, you know, if you're going to start thinking about aging mortality, you have to start thinking about what is it that's going wrong in terms of what's keeping you alive. I mean, apply that to any machine, for example. What is it that, so to speak, wears out or starts to become dysfunctional during its

lifespan? And of course, what's keeping you alive is metabolism, that is you, you eat metabolize food to form energy, ATP molecules, currency of energy. And so then I started reading about metabolism. And in so doing discovered, I didn't discover, but I learned about these amazing scaling laws and in particular, this remarkable scaling law for how metabolic rate, that is the amount of energy any organism needs per second or per hour to stay alive, per second or per hour to stay alive, how that scales with the size of an animal. And to my amazement, I learned that it was extremely simple and regular.

Jeffrey, before we jump into biological scaling, let's just answer a couple of higher level questions here, because I don't even think people understand what is implied by the word scaling. Yes, I was going to come to this, absolutely. Yeah. So the big picture here is that you point out that the phenomenon that really concern us, that form the space in which we live, span a range of more than 30 orders of magnitude from molecules to cities. So can you put that in context first? Yes, sure. So first of all, just take organisms. We go from the smallest organism, which is mycoplasma. It's a tiny subbacterial kind of organism. All the way up to the blue whale, that's about 20 orders of magnitude, 20 powers of 10. So it's enormous. If you go down to molecules, you add several more

orders of magnitude. And of course, if you go up to ecosystems and cities, many more. So, you know, I mean, you could even stretch this to 40 orders of magnitude in terms of the structure of life. You know, all of these things are to some extent living. I mean, even at the molecular level, you could talk about living things that are doing things that we would call life, sort of primitive viruses, but all the way up to, as I say, a large ecosystem, and in particular, a city, which you can sort of think of for these purposes as a kind of pseudo-organism. So that's kind of amazing because, you know, as I think I point out in the book, this is much greater scale than the relationship of us to the entire Milky Way, for example,

or an electron to a cat. We as life span much more than that, and it's kind of amazing. And so that's the range over which the phenomena I discuss in the book are discussed. But the phenomenon of scaling that is usually called scaling is how do the characteristics of, you know, let's say, let's just be a little more modest and stick to, say, just all mammals, for example. How do their characteristics scale as you change the size of a mammal? So mammals go from the smallest, which is a shrew, which sits easily on the palm of the hand, all the way up to the blue whale, which is as big as the building I'm sitting in. And that covers approximately eight orders of magnitude in its mass.

And scaling asks the question, well, let's look at characteristics of these mammals, everything from the one I mentioned earlier, metabolic rate, to something a little more mundane, like the length of their aortas. The aorta is the first tube that comes out of the heart, or even the size of their aortas, the aorta is the first tube that comes out of the heart, or even the size of their hearts,

or the length of a limb, but all these various things that you could measure, how long they live, how many offspring they have, and so on. So that's just the concept of scaling. And the remarkable thing is that when you look at any of these quantities, and one can list maybe 50 to 75 of such characteristics and ask how do they change with the size of the mammal, they all scale in that sense in a very regular fashion. And not only in a very regular fashion, but all in a similar way mathematically. And that's extremely surprising naively at a naive level, because, you know,

we believe in natural selection. We believe that all of these organisms have evolved by natural selection with highly contingent histories. Each subsystem of them, each organ, each cell type, each genome has its own unique history. So you might have expected that if you plotted any characteristics such as its metabolic rate versus size, you would get points scattered all over the graph. And quite the contrary, you find that there's a tremendous regularity that gets revealed, suggesting that underlying this extraordinary complexity, because after all, something like metabolism is maybe the most complex process in the universe, for all we know, because it's sort of, you know, at its most primitive level, it takes, you know, matter, stuff, and creates life.

That's what we're doing, you know, as we eat and so on. You know, here's this unbelievably complex process. And yet, if you ask how it scales across this huge range of organisms, it scales in this very simple way. And the amazing thing is this even extends to cities that have different cultural histories and different geographies. Absolutely. So the same thing, after we did this work and explained where these scaling laws come from, it was very natural to ask the question, are there other forms of life, such as more synthetic ones, so to speak, like cities or even companies, that express similar kinds of regular systematic scaling?

systematic scaling. And as I say, later following understanding the biological scaling, when we looked at the data on the scaling of cities, we found a similar kind of scaling, similar in the sense that there was a regular systematic behavior and the mathematics was the same. The details of it are different. And the details are different in a very important and powerful way. But it was quite similar. And similarly, even with companies, going from a small company of a couple of hundred employees to Walmart or General Motors. There were similar kinds of scaling. So, you know, there's this ubiquitous behavior that is quite surprising when you first meet it that says that despite, you know, the daunting complexity and diversity that we see out there underlying it seems to be a kind of simplicity which

can be expressed both graphically and mathematically in very powerful and simple terms. So maybe I should say a little bit about what the nature of that scaling is. Yeah, yeah. Would that be helpful? Yeah, that'd be great. So let's start with the case of biological scaling. And I just want you to go through the significance of the fact that this scaling tends to be nonlinear.

It's either sublinear or superlinear on your account. So what's the significance of that? Yeah, that's very important because if you ask yourself, well, look, if I double the size of an organism or if I look at an organism that's twice the size of another one or in particular, let's take mammals, as I said, a mammal that's twice the size of another, then it contains, roughly speaking, twice as many cells, and that's linear scaling.

And if it's three times as big, it contains three times as many cells. And that's, roughly speaking, correct. It's a simple linear relationship. However, the scaling of all other characteristics of an organism are nonlinear in the following sense. Take metabolic rate. If you double the size of an organism, instead of needing twice as much energy, twice as much food, if you like, to stay alive, what you discover is you don't need twice as much.

You only need 75% as much, even though there are twice as many cells. And this happens systematically. So if you double the size from four grams to eight grams, or four kilograms to eight kilograms, it doesn't matter where you start. If you double, you only need, roughly speaking, 75%, three quarters, roughly, the amount of energy. There's a 25% savings on the average every time you double. And that's called an economy of scale. That's a classic economy of scale and means, of course, that the individual cells, since they do scale linearly, it means that the energy needed to support an individual cell is systematically smaller by this 25% rule, the bigger you are every time you double. And so, you know, your cells work less hard in a predictable way than your dogs or cats,

but, you know, your horse or your elephant are working even less hard. So this is a pervasive phenomenon throughout biology, this economy of scale, and has far-reaching consequences. And that similar kind of scaling gets repeated across any measurable quantity, whether it's physiological, like the one I mentioned, something sort of mundane,

like the length of an aorta, or something quite sophisticated, like the rates at which oxygen diffuses across membranes or how long an organism lives and so on. And these also are governed by an analog to this 25% rule. So timescales increase according to this 25% rule, the bigger you are. And generically, the pace of life slows down. So that in fact, if you took an elephant and you followed the scaling laws for all its physiology and all its rates of life history and scaled it according to that and just kept scaling down,

you would end up with a mouse. A mouse is a scaled, at this 80, 90% level is a scaled down elephant. And by the way, that brings up something that's very important about the nature of these rules, these laws. And that is that they're not like the laws of physics, which we think of as being precise, like Newton's laws or Maxwell's equations for electricity and magnetism or quantum mechanics, like Newton's laws or Maxwell's equations for electricity and magnetism or quantum mechanics, you know, where we have this, you know, roughly speaking, this paradigm that you can count with these principles and laws of physics, you can calculate any physics, physical phenomenon in principle to any degree of accuracy. So that, you know, we know the positions of all the planets at any time.

We know the positions of satellites at any time. That's why we can get our exchange messages on cell phones and so on. Our cell phones work precisely and so forth. So all this works because the laws of physics are extremely precise and we can calculate things and predict things in a highly precise fashion. That is not true of the kinds of laws that I'm talking about, the kind of scaling laws I'm talking about in biology.

These are laws that we technically call coarse-grained, meaning that they're only true to, say, 80-90% accuracy, so that we can predict, or you can predict from these laws the following. So, just to give you another example, if you give me the size of a mammal, I can tell you pretty much anything about it, Everything from, as I said, its metabolic rate, the complete structure of its circulatory system or its respiratory system. I can tell you about how long it will live, how many offspring it will have, and so on and so forth. You know, all these various measurable characteristics. But I can only do it to 80, 90% accuracy. And if I asked to make a prediction about a very specific elephant

or a very specific mouse, I couldn't do it with anything more than that accuracy. So to speak, it's for the average animal of that size. But of course, that's extremely powerful, not only because it connects all these different organisms that seemingly and shows the kind of unity of life. But also it provides a baseline for asking about specific cases. You know, you can then look at specific animals or specific individuals of that species and start asking questions using the scaling laws as a baseline. Well, so to talk about one variable here, lifespan. So as you get bigger as an animal, perhaps we should confine this to mammals, as you get bigger, you tend to live longer. And this follows the scaling law that you,

this is a consequence of metabolism slowing down and economies of scale? Yeah. So let me back off now and talk more generally about the origin of these scaling laws. Where in the hell do they come from? For example, we just talked mostly here about mammals, but the same scaling laws apply to trees and plants in the following sense. Their metabolic rate scales in the same way as ours does. That is, every time you double the size of a tree in terms of its weight, it uses only 75% more energy, just like we do. But for example, the way its trunk scales, the trunk of a tree scales, is essentially identical to the way our aorta scales. The tree is its own aorta. It's all aorta. It's all circulatory system.

Well, the trunk is the aorta. Yeah, exactly. No, so let me take that. Let me go from there. The analog to the tree inside us is our circulatory system. The aorta, the analog to the aorta, which is that first tube, as they say, coming out of the heart, the analog to that is the trunk of the tree, the part that goes up before it branches into two or three other big branches. And indeed, the origin of these scaling laws, because you ask yourself, you know, what is it? What is it that's common among plants, trees, mammals, birds, fish, etc., that they all seem to obey

these same scaling laws, even though their evolved engineered design is quite different. Obviously, you know, we have beating hearts. Trees certainly don't have beating hearts, just to take a dramatic example. So you ask, what is it that's common among all of them? And what you realize is what's common among all of them is that they have all evolved to be hierarchical branching network systems. And you sort of understand that because, you know, just think of yourself, you're made of 10 to the 14th cells, roughly 100 trillion cells. And each one of those has to be serviced in some, roughly speaking, democratic and efficient

fashion. And the way that problem has been solved is by evolving these networks that deliver oxygen and nutrients and so on, and information from, if you like, a central reservoir down to the cellular level. And as I say, we're very familiar with our circuitry system, our respiratory system, our neural system, our renal system, and so on. And all of these have those characteristics. And the idea is that it is the mathematics and physics, the sort of universal generic mathematics and physics of these network systems at all scales that are being reflected in the scaling laws.

And that was the work that I got involved in. And we, you know, it's quite complicated mathematics to work it all out. But out of that pops these remarkable scaling laws. And I want to say a couple of things about the networks, because it's not just the networks, but they have special properties, which are, roughly speaking, universal. And one of them is that they are what we technically call space filling. It's a very simple concept. And it's simply that whatever the structure of the network, it's terminal units. In our case, for example, the circulatory system, the terminal units

are capillaries that feed cells. Those capillaries, so to speak, have to go everywhere because every cell in the body has to be fed by oxygen diffusing from blood from the capillaries to cells. So the endpoints of the network have to end up close by cells. And so the network in that sense has to be space filling and go everywhere. As for example, in a city, the road networks essentially have to service all buildings and ultimately all people. So, you know, the street system doesn't leave vast areas of houses without any access to them. So it is with our bodies. So that concept is called space filling, and that has to be put into some mathematical terms. And that's one of the inputs to the, or one of the constraints, I should say, on the network.

I think we could introduce a mathematical concept here that will be familiar to people, but it seems relevant, the concept of a fractal, which, you know, I think, it seemed like in the 80s, literally everyone knew what fractals were. I mean, like the barber was telling you about the Mandelbrot set. Exactly. So we had reached peak fractal back then, but I'm not sure the knowledge has stuck. So perhaps you could remind people about what fractals are and their significance. Yes. Let me do one last thing before doing that, because it relates directly to it. And that is another constraint on the network. And that is that in some sense, the network optimizes the system. I say that loosely, but let me give you an example because it leads to fractals.

And that is that the circulatory system that we have, and that has evolved by the process of natural selection and by we have, I mean, the we I'm referring to is all mammals, that is, all mammals that now exist and all mammals that have ever existed. The one that we have minimizes the amount of energy our hearts have to do to pump blood through our circulatory system to feed cells, so that we can maximize the amount of energy we can devote to what is called Darwinian fitness, meaning that we can devote to having sex and rearing children. And so that's very important. So that means that whatever the structure of the network is, not only does it have to be space filling, but its structure has to be that if we changed it in any significant way, you know, by just say doubling the length of the third branch of your arterial system, that would increase the amount of energy your heart has to do. And similarly, if you halved this eighth branch of your arterial system, it would increase

the energy. So we sit in a kind of basin of optimization, so to speak, of minimizing the energy our hearts have to do. It seems to me that that need not be so in evolutionary terms. I mean, there's a lot, obviously, there's a lot about us that an engineer would not have put in place. And I put the prostate gland high on the list of things you would not have engineered. That's just mathematically. So at this point, we can say that it is optimal? Yes. So here was the idea. The idea was that, you know, in order to start to take this idea that networks underlie the scaling laws, you have to start putting together the mathematics of the networks. And as in all physics, you need generic principles that transcend,

you know, the individual system you're looking at, and you need, you know, certain assumptions. And one of the simplest assumptions was to assume that there was this kind of optimization, that by the continuous process, continuous feedback process inherent in natural selection, the, you know, mammals that have survived, that we are, tend towards minimization of this, you know, the amount of energy that we use to keep ourselves alive. We minimize the amount of energy that is the mundane process of remaining alive so that we can maximize the amount of energy that we put into our genes going forward. And, you know, that of course need not be. On the other hand, you know, if you believe in Darwinian fitness and you had long enough time, which

we've had, you would expect something like that to happen. But anyway, that was a hypothesis, and it was very natural to hook it up to traditional ideas of Darwinian fitness. But you're absolutely right. There are many aspects of our physiology, especially at my age, that you begin to realize weren't exactly designed in the way that maybe they were optimal. But you know, you have to remember that having said that, that that's always the case when you look at one individual component.

You know, like you mentioned, you know, if you look at one individual component. You know, like you mentioned, you know, if you look at one specific thing, but you have to remember that that is interconnected with everything else. It's a systemic problem. And the optimization, and that's what part of this idea was, is not so much that it's taken place

at the highly local level, and this is extremely important, but it's taken place at the systemic level. I'm talking about the systemic level of each one of these network systems. So it's the entire system going from the heart and the entire structure of the circulatory system from your aorta downwards, feeding through tissue, through capillaries, to cells, and how that diffusion takes place, for example. All of this is one huge system.

And it has to be. And the idea is that it is the systemic optimization rather than the local optimization. Well, I'll take your point, Jeffrey. But if you're going to argue that the prostate gland is a masterpiece of nature and it's God, you're going to have a tough time on this podcast. It is not. And I certainly agree with you with that. amazed at the whole process of both reproduction and child delivery of fetuses into the world. Why does it have to be a medical emergency every time? Yeah, exactly. I mean, so, you know, obviously all of this, but you know,

those do not happen. My point is they do not happen in a vacuum. I mean, they're all interconnected, you know, and no doubt something about that birth delivery has all kinds of other implications, not just physiological, but social implications, of course, and so on. So I don't want to argue this. This is not, you know, this is a secondary thing, really, to the main point that, you know, when you look at these networks and you apply these underlying generic systemic principles to them, one of the things that you learn is that the optimal system is fractal-like, I'll use that word. And fractal means, another word for it is self-similar, and we're all very familiar with it. I'm looking out at the moment at a tree,

and it has this hierarchical branching network. And the fractality is expressed by the fact that if you cut some branch and remove it, it looks like a little tree. And then you can take that little tree and cut a branch of that and take it away, and it looks like an even smaller tree, and so on. And that's the idea that you have this repetitive self-similarity. And the theory is one of the things that comes out of it is that there is, in fact, that the systems should be fractal in order to optimize in the way I said, and also critical, fill all of space. That is that it needs to, every part of the system needs to be serviced. By the way, I use the word fractal-like because actually the rules that come out of the theory actually are variants of a fractal. To be a bit more technical about it, it's not a precise self-similar. In other words, and it's in fact true, the data shows this, that if you do

take a tree and you cut a piece out of it, it does look like the tree. But if actually, if you do measurements, the theory predicts this, it deviates in a predictable way from the original tree. But it's very close to this idea of repetitive self-similarity. And one of the wonderful things that, you know, you discover in all of this, and that is related to the scaling laws, is that all of these systems have somewhere in them some manifestation of this regularity, this fractal regularity that seems to permeate nature. And some of that is no doubt related to, let's put it that way, some of it is related to this idea that something is being optimized. Yeah, so to connect the self-similarity and the seemingly endless divisibility of these branching networks to the space-filling problem, just in a vivid way, this membranes in there is about the size of a

tennis court because of just how endlessly branching it is down at the smallest scale. Yeah. So it's kind of a wonderful feeling that inside you is a tennis court, you know, I mean, actually. And indeed, if you took your circulatory system and you laid all those um vessels end to end i forget that the precise answer i think it was i think it was a hundred thousand kilometers i believe yes yeah yeah you go around the earth certainly more than once and that's kind of amazing you know it's an amazing uh image so it's almost spiritual that feeling that inside you is this unbelievable length of tubing, and that it's very systematic. Its structure is obeying very simple mathematical rules

that are like these kinds of rules that I mentioned earlier, these so-called power laws. There's something spooky about the power laws themselves. I mean, there's this one number, to which you've alluded, that runs through this that almost could put someone in the mind of the pseudoscience of numerology, the fourth power, the fact that basically all these living systems scale to the one-fourth power. Well, the one-quarter, yes. The number four is the number that permeates all of these scaling laws. I said the three-quarters for metabolic rate. It's one-quarter for time scales, for example, and so on.

And for lengths, it's very similar. It's always one-quarter comes in. And that's that 25% savings. It's very similar. It's always one quarter comes in. And that's that 25% savings. It's not an accident. And that's the thing that comes out of the theory based on these mathematical principles of network design. And that pops out. And that four, by the way, if you look at the mathematics and ask where it comes from, it's the following. It turns out the four is actually, so to speak, not four. It's actually three plus one, which sounds like a paradox. It's three plus one, meaning the three part of the three plus one comes from the fact that we live in three dimensions, the up, down, and sideways.

the fact that we live in three dimensions, the up, down, and sideways. And the one is a reflection of the fractality of these systems. It's well known among those that learn about fractals that they have peculiar sense of dimensions and a fully fractal system is one that effectively adds an extra dimension. So there's this kind of weird extra dimension and that's this one. So the four is actually three plus one. So if we lived in eight dimensions, eight dimensions, we would be dominant. We had life. Then everything would be dominated by the one-ninth power. And we would be, instead of saving 25%, we'd be saving one-ninth, about 11%. I feel the temptation to remind people of just what it means to be adding a dimension here in fractal terms. So it's a little hard to do on a podcast, but people can look up something, a figure. I think it's called the, is it the Koch curve?

The K-O-C-H. Oh, yes. Look this up if you want to follow us down this rabbit hole, but there's this image or this curve, which is essentially formed by an equilateral triangle being divided on each of its sides by a smaller one-third size equilateral triangle. And you keep doing that, just adding triangles upon triangles, and you develop a kind of snowflake-looking image.

And then when you ask, what's the size of that curve, of that figure, you know, given that in the pure mathematical space, you keep doing this infinitely, well, it's a fully self-contained object, which actually has an infinite length of its circumference. And this has, now this doesn't map onto the real world totally, because we're not talking about infinite lengths in terms of the world in which we live, but it does to a surprising degree. And this, Jeffrey, you could perhaps remind us of how this was first discovered, where you try to measure the boundary between two countries, and that becomes remarkably dependent on basically how big a measuring stick you use.

Yes, indeed. Yes. That's one of those marvelous discoveries that sort of came out of the blue and something that should have been known since the Greeks, but wasn't. And it was discovered by a man named Richardson, who was a kind of a polymath, but he was a kind of a geographer. And one of the things that he was interested in was the length of boundaries between countries. And he was interested in this, by the way, because he had a theory of war that somehow the incidence of conflicts between nations was proportional to the length of their boundaries. By the way, we're talking about, he developed that around the time of the First World War,

but this work on measurement came much later when he was trying to really get a quantitative handle on this. And so he got hold of all these maps of various places, and he started measuring their boundaries. And one of the curious things that he first discovered was that, I think the first one was between Spain and Portugal, where he found, looking at different maps, very detailed maps, that he got completely different answers. I mean, I don't remember the numbers. I wrote them in the book.

But, you know, instead of, you know, one map might give 1,100 kilometers, and then he'd look at another map, and you'd get 650 kilometers. And he would look these up in various places, and indeed he'd find different books recording these things, giving completely different numbers. And this was very mysterious. And he started looking around and he'd looked across many countries and he discovered the same phenomenon. this. And he did realize what was going on, but he didn't formalize it. It was formalized later by a man named Benoit Mandelbrot, who termed the phrase fractal. And it's the following. It was that

when people made these measurements, when you make a measurement, you have to have a ruler with a certain scale and you have a certain resolution. So you might measure, someone might measure a boundary using a resolution of only one mile. So you're measuring something that's a thousand kilometers long. You only care a resolution of a mile. a mile, but you might have someone that has a resolution of 10 miles and someone else might have a resolution of, you know, I don't know, it could even be a meter in principle. And you can immediately, when you start thinking about it, you realize what the problem is, that if you measure a boundary, which is a squiggly line, and you put a ruler on it where the resolution is, say, 10 kilometers, then anything below 10 kilometers, you miss.

But below that 10 kilometers, the line, the boundary may be squiggling around. And so you miss. You measure that as 10 kilometers, but someone else with a resolution of one kilometer would measure it as 25 kilometers, but someone else with a resolution of one kilometer would measure it as 25 kilometers, for example. So that was the problem he realized. And in fact, then he discovered that this followed a very regular pattern, that if you plotted the length that's measured or reported versus the resolution, there was a very simple mathematical relationship. And amazingly, that relationship is just like the relationships I talked about in terms of things like

metabolic rates and all the other characteristics of organisms. And that's where the connection was to fractals. And it was Benoit Monbrot who realized that not just that there was this phenomenon of the problem of making measurements and resolution, but that in fact, it was self-similar. Boundaries are approximately self-similar. So if you look at one scale and then scale that up, it just looks like what the boundary would look like at the bigger scale and so on and so forth. As you said, this is a genuine mystery why this wasn't discovered literally thousands of years ago. I mean, this is one of those things that was just staring everyone in the face.

And most of science is not like that. I mean, does anyone understand why this wasn't discovered before Mandelbrot was formalized? Well, yes, so I think first of all, I think... If you'd like to continue listening to this conversation, you'll need to subscribe at SamHarris.org. Once you do, you'll get access to all full-length episodes of the Making Sense podcast, along with other subscriber-only content, including bonus episodes and AMAs

and the conversations I've been having on the Waking Up app. The Making Sense podcast is ad-free and relies entirely on listener support. And you can subscribe now at SamHarris.org.