Making Sense - Sam Harris - July 14, 2017


#86 — From Cells to Cities


Episode Stats

Length

50 minutes

Words per Minute

145.34456

Word Count

7,304

Sentence Count

245

Misogynist Sentences

1

Hate Speech Sentences

5


Summary

Jeffrey West 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 is the author of the book, Scale: The Universal Laws of Growth, Innovation, and Sustainability in Organisms, Cities, 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. We don t run ads on the podcast and therefore, therefore, are made possible entirely through the support of our subscribers. If you enjoy what we re doing here, please consider becoming a supporter of what we're doing here by becoming a subscriber. You'll get access to our full-length episodes of the podcast as well as access to all the podcast's premium features, including the most popular podcasting platform, The Making Sense Podcast, wherever you get your podcasts. Subscribe to the podcast today! To find a list of our sponsors and show-related promo codes, go to gimlet.fm/OurAdvertisers. To learn more about our sponsorships and how you can support the podcast, please go to our ad-free membership program, becoming a patron of the Making Sense podcast, becoming one of our platinum sponsor, and receive 10% off the first month's mail discount when you sign up! Subscribe for a year of $99 or more! You get 20% off your first month, plus a 2 months free, plus an additional 3 months free shipping when you become a patron gets the choice of 1 month for two months, and two months get a complimentary membership for the course, and a discount of $50 or two months for VIP access to the second year, plus they get a discount, they also get an ad-only offer, they can choose a complimentary rate of $39/month, and they get full access to make their choice of the making sense of the entire course starting from $99/choice, they get all that they choose, they'll get all of that option, plus all that gets you get, plus two months of the service, they decide, plus she gets a choice of $29/place they get, and she gets all that she gets, and all they also gets, they receive, and you get two months


Transcript

00:00:00.000 Welcome to the Making Sense Podcast.
00:00:08.820 This is Sam Harris.
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00:00:30.520 We don't run ads on the podcast, and therefore it's made possible entirely through the support
00:00:34.640 of our subscribers.
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00:00:46.380 Today I am speaking with Jeffrey West.
00:00:49.720 Jeffrey is a theoretical physicist whose primary interests have been in fundamental questions
00:00:55.080 of physics and biology.
00:00:56.840 He's a senior fellow at Los Alamos National Laboratory and a distinguished professor at
00:01:03.360 the Santa Fe Institute, where he served as president from 2005 to 2009.
00:01:09.560 He's been named to Time Magazine's list of 100 most influential people in the world, and
00:01:15.280 he is the author of the very fine book, Scale, The Universal Laws of Growth, Innovation, Sustainability,
00:01:22.440 and the Pace of Life in Organisms, Cities, Economies, and Companies.
00:01:28.100 And we talk about his book at length here.
00:01:31.400 As you'll hear, Jeffrey is an extremely interesting guy.
00:01:35.120 We ran into a few audio problems at the end, so apologies for that.
00:01:39.760 All I can say is that our robot overlords don't yet have this internet thing fully worked out.
00:01:44.380 But I should say that this conversation is pretty dense.
00:01:48.460 I didn't really appreciate how dense it was until I re-listened to it.
00:01:52.840 There's a lot of information here.
00:01:54.940 Those of you who are students of physics and mathematics will absolutely love it.
00:01:59.940 But some of you will find that you really need to concentrate to follow Jeffrey where he goes.
00:02:06.160 And you might need to rewind from time to time or just listen to the whole thing twice.
00:02:10.720 But this will repay your attention because Jeffrey is doing some very deep and interesting work.
00:02:16.540 And his book is really wonderful.
00:02:19.380 And now, without any further delay, I bring you Jeffrey West.
00:02:30.200 I am here with Jeffrey West.
00:02:32.100 Jeffrey, thanks for coming on the podcast.
00:02:33.940 Yeah, pleasure to be here, Sam.
00:02:35.220 Thank you for inviting me.
00:02:37.320 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.
00:02:52.560 Yes.
00:02:52.980 And it's a fascinating route into basically everything we care about.
00:02:58.100 And the book is filled with disarmingly simple-sounding questions, which turn out not to be simple at all.
00:03:04.980 But they're questions like, why do we live 100 years rather than 1,000?
00:03:09.460 Why do we stop growing?
00:03:10.980 We keep eating all the time, but at some point we stop growing.
00:03:13.640 It's not obvious why that should be the case.
00:03:15.620 Yeah.
00:03:15.820 Why do people die and companies die, but cities don't seem to die?
00:03:20.780 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.
00:03:30.020 And now you're focusing on biological and even socioeconomic questions.
00:03:34.360 And it seems to have been inspired both by the death of the supercollider project in the U.S.
00:03:40.540 and your growing sense of your own mortality.
00:03:42.880 So give us the context of your investigations.
00:03:46.380 Yes.
00:03:46.740 No, thank you.
00:03:47.440 Yes, indeed.
00:03:48.120 You have pinpointed, so to speak, the genesis of this in that I was at some stage happily doing research into quarks and gluons and string theory and fundamental questions of physics, dark matter and so forth.
00:04:08.860 And associated with that, of course, was this marvelous project of the superconductive supercollider to be built in Texas.
00:04:20.040 And, of course, the vision was to open up new vistas at extremely high energies and, therefore, in very short distances and confirm some of our ideas about fundamental forces and the fundamental constituents of nature.
00:04:37.840 But also, you know, just the usual search for, you know, new science, new physics.
00:04:45.180 And sadly, that was canned in the early 90s.
00:04:48.380 And I had been somewhat involved in it.
00:04:52.480 And at the same time, I was into my 50s.
00:04:59.100 And it so happens that I come from a line of short-lived males.
00:05:06.700 Very few live beyond about 60.
00:05:09.260 And many have died in their 50s.
00:05:12.520 I've got a similar problem.
00:05:13.780 I'm just edging into my 50s.
00:05:16.000 And I'm a year shy of the age my father made it to.
00:05:20.300 So, yeah, I follow your mind.
00:05:22.460 Well, very similar.
00:05:23.420 Well, my father did make it to almost 61.
00:05:26.860 But his father, you know, died at 57.
00:05:31.540 And my father's brother died at 54 and so forth.
00:05:34.680 It was that.
00:05:35.080 So it's a similar kind of thing.
00:05:36.220 And so I'd grown up with this idea that, you know, I'd probably die somewhere in my early 60s.
00:05:45.180 That was sort of the lifespan of what was to be expected.
00:05:48.420 And in my 50s, I began to realize that, my gosh, you know, I may only have five to 10 years at most to live.
00:05:57.040 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.
00:06:16.420 That got me to start thinking about some of these big questions in biology originally.
00:06:21.620 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.
00:06:42.780 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.
00:06:54.100 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.
00:07:08.040 And that really got me, you know, because even though, as I said, I agreed with the first part that no doubt biology was going to be significantly important during this century.
00:07:19.740 Nevertheless, I arrogantly and out of ignorance, frankly, sort of came back with the statement that, well, yes, that may be the case, but it won't be a real science unless it starts to...
00:07:35.740 Until it gets a proper case of physics envy.
00:07:38.000 Exactly. Yeah, something like that. Yes, I was hesitating. But to really, you know, start to incorporate the paradigm of physics in terms of it being quantitative, more analytic, based on principles, and therefore more predictive.
00:07:59.920 That kind of paradigm, that kind of paradigm, and also some of the techniques of physics and the question.
00:08:04.720 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.
00:08:20.440 That was where I was coming from before. And I must say, I knew almost no biology at the time.
00:08:27.080 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.
00:08:38.280 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.
00:08:49.620 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.
00:08:59.560 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?
00:09:16.420 You know, what is that related to? We ought to have a theory, you know.
00:09:19.680 So to begin, put it in this kind of arrogant physics way, if biology were a serious science, 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.
00:09:42.100 And by the way, the lifespan of a mouse should be of the order of two or three years, et cetera.
00:09:48.640 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.
00:10:06.320 And in particular, as far as I could tell, no one seems to have asked the question in that form.
00:10:12.560 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.
00:10:25.920 How would you go about trying to show that 100 years is the expected lifespan of an animal our size?
00:10:35.400 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?
00:10:51.060 I mean, apply that to any machine, for example, what is it that, so to speak, wears out or starts to become dysfunctional in terms of its, during its lifespan?
00:11:04.300 And of course, you know, what's keeping you alive is metabolism.
00:11:09.220 That is, you eat and metabolize food to form energy, ATP molecules, currency of energy.
00:11:16.160 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.
00:11:31.500 And in particular, this remarkable scaling law for how metabolic rate, that is the amount of energy any organism needs, you know, per second or per hour to stay alive.
00:11:43.580 How does that, how that scales with the size of an animal?
00:11:48.820 And to my amazement, I learned that it was extremely simple and regular.
00:11:56.820 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.
00:12:07.840 Yes, I was going to come to this, absolutely.
00:12:09.520 Yeah, so let's, let's, the big picture here is that you point out that the phenomenon that we, 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.
00:12:25.180 So can you put that in context first?
00:12:27.420 Yes, sure.
00:12:27.880 So, so first of all, just take organisms.
00:12:33.300 We go from the smallest organism, which is mycoplasma, it's a, you know, tiny sub-bacterial kind of organism, all the way up to the blue whale, that's about 20 orders of magnitude, you know, 20 powers of 10.
00:12:49.640 So it's, it's enormous.
00:12:51.660 If you include, 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.
00:13:01.420 So, you know, I mean, you could even stretch this to 40 orders of magnitude in terms of the structure of life.
00:13:09.800 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.
00:13:23.200 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.
00:13:33.800 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.
00:13:51.820 You know, these, we as life span much more than that, and it's kind of amazing.
00:13:57.560 And so that's the range over which the phenomena I discuss in the book are discussed.
00:14:04.280 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.
00:14:21.580 How do their characteristics scale as you change the size of a mammal?
00:14:26.360 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.
00:14:38.620 And that covers approximately eight orders of magnitude in its mass.
00:14:45.220 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.
00:15:01.520 The aorta is the first tube that comes out of the heart, or even, you know, the size of their hearts, or the length of a limb.
00:15:10.400 But all these various things that you could measure, how long they live, how many offspring they have, and so on.
00:15:16.680 So that's just the concept of scaling.
00:15:20.360 And the remarkable thing is that when you look at any of these quantities, and, you know, one can list maybe 50 to 75 of such characteristics,
00:15:32.200 and ask how do they change with the size of the mammal, they all scale, in that sense, in a very regular fashion.
00:15:41.720 And not only in a very regular fashion, but all in a similar way, mathematically.
00:15:49.300 And that's extremely surprising, naively, at a naive level, because, you know, we believe in natural selection.
00:15:58.280 We believe that all of these organisms have evolved by natural selection, with highly contingent histories.
00:16:05.440 Each subsystem of them, each organ, each cell type, each genome, has its own unique history.
00:16:15.620 So you might have expected that if you plotted any characteristics, such as its metabolic rate versus size,
00:16:25.400 you would get points scattered all over the graph.
00:16:30.600 And quite the contrary, you find that there's a tremendous regularity.
00:16:35.440 It 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,
00:16:47.620 because it's sort of, you know, at its most primitive level, it takes, you know, matter, stuff, and creates life.
00:16:54.880 That's what we're doing, you know, as we eat, and so on.
00:16:57.760 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.
00:17:10.540 And the amazing thing is this even extends to cities that have different cultural histories and different geographies.
00:17:16.840 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, you know,
00:17:27.980 are there other forms of life, such as, you know, more synthetic ones, so to speak, like cities, or even companies,
00:17:35.660 that express similar kinds of regular systematic scaling.
00:17:41.480 And, as I say, later following understanding the biological scaling, when we looked at the data on the scaling of cities,
00:17:53.360 we found a similar kind of scaling, similar in the sense that there was a regular systematic behavior, and the mathematics was the same.
00:18:02.780 The details of it are different, and the details are different in a very important and powerful way.
00:18:11.480 But it was quite similar, and similarly, even with companies, you know, going from a small company of a couple of hundred employees to Walmart or General Motors,
00:18:25.520 there were similar kinds of scaling.
00:18:27.000 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,
00:18:42.220 underlying it seems to be a kind of simplicity, which can be expressed both graphically and mathematically in very powerful and simple terms.
00:18:56.560 So maybe I should say a little bit about what the nature of that scaling is.
00:19:00.460 Yeah, yeah.
00:19:00.860 Would that be helpful?
00:19:02.220 Yeah, that'd be great.
00:19:02.980 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.
00:19:14.000 It's either sublinear or superlinear on your account.
00:19:16.380 So what's the significance of that?
00:19:17.960 Yeah, that's very important because, you know, 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,
00:19:30.560 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.
00:19:39.440 And that's linear scaling.
00:19:41.900 You know, and if it's three times as big, it contains three times as many cells.
00:19:47.580 And that's, roughly speaking, correct.
00:19:49.200 It's a simple linear relationship.
00:19:51.900 However, the scaling of all other characteristics of an organism are nonlinear in the following sense.
00:19:59.860 Take metabolic rate.
00:20:01.420 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,
00:20:09.860 what you discover is you don't need twice as much.
00:20:13.020 You only need 75% as much, even though there are twice as many cells.
00:20:18.240 And this happens systematically.
00:20:20.740 So if you double the size from 4 grams to 8 grams or 4 kilograms to 8 kilograms, it doesn't matter where you start.
00:20:32.460 As long as if you double, you only need, roughly speaking, 75%, three quarters, roughly, the amount of energy.
00:20:39.520 There's a 25% savings on the average every time you double.
00:20:44.240 And that's called an economy of scale.
00:20:46.380 That's a classic economy of scale and means, of course, that the individual cells, since they do scale linearly,
00:20:56.480 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.
00:21:11.160 And so, you know, your cells work less hard in a predictable way than your dogs or cats.
00:21:18.800 But, you know, your horse or your elephant are working even less hard.
00:21:24.900 So this is a pervasive phenomenon throughout biology, this economy of scale, and has far-reaching consequences.
00:21:35.960 So that similar kind of scaling gets repeated across any measurable quantity, whether it's physiological, like the one I mentioned,
00:21:47.460 just something sort of mundane like the length of an aorta, or something quite sophisticated,
00:21:54.020 like the rates at which oxygen diffuses across membranes or how long an organism lives and so on.
00:22:01.140 And these also are governed by an analog to this 25% rule.
00:22:08.640 So time scales increase according to this 25% rule the bigger you are.
00:22:15.040 And generically, the pace of life slows down.
00:22:18.960 So that, in fact, you know, if you took an elephant and you followed these scaling laws for all its physiology and all its rates of life history
00:22:32.680 and scaled it according to that and just kept scaling down, you would end up with a mouse.
00:22:39.020 You know, a mouse is a scaled, you know, at this...
00:22:41.400 A tiny elephant.
00:22:41.920 ...18, 90% level is a scaled-down elephant.
00:22:44.640 And by the way, that brings up something that's very important about the nature of these rules, these laws,
00:22:51.800 and that is that they're not like the laws of physics, which we think of as being precise,
00:23:00.160 like Newton's laws or Maxwell's equations for electricity and magnetism or quantum mechanics,
00:23:04.920 where we have this, you know, roughly speaking, this paradigm that you can...
00:23:11.380 With these principles and laws of physics, you can calculate any physical phenomenon in principle to any degree of accuracy
00:23:19.440 so that, you know, we know the positions of all the planets at any time.
00:23:25.560 We know the positions of satellites at any time.
00:23:29.520 That's why we can, you know, get our...
00:23:32.060 Exchange messages on cell phones and so on.
00:23:35.980 Our cell phones work precisely and so forth.
00:23:38.300 So all this works because the laws of physics are extremely precise
00:23:43.440 and we can calculate things and predict things in a highly precise fashion.
00:23:48.960 That is not true of the kinds of laws that I'm talking about,
00:23:54.520 the kind of scaling laws I'm talking about in biology.
00:23:58.000 These are laws that we technically call coarse-grained,
00:24:02.720 meaning that they're only true to, say, 80%, 90% accuracy
00:24:08.940 so that we can predict or you can predict from these laws the following.
00:24:15.200 So just to give you another example,
00:24:18.320 if you give me the size of a mammal,
00:24:21.380 I can tell you pretty much anything about it,
00:24:24.980 everything from, as I said, its metabolic rate,
00:24:28.160 the complete structure of its circulatory system or its respiratory system.
00:24:33.100 I can tell you about how long it will live,
00:24:38.480 how many offspring it will have, and so on and so forth.
00:24:41.940 You know, all these various measurable characteristics.
00:24:45.020 But I can only do it to 80%, 90% accuracy.
00:24:49.060 And if I ask to make a prediction about a very specific elephant
00:24:52.660 or a very specific mouse,
00:24:55.140 I couldn't do it with anything more than that accuracy.
00:24:59.480 So it's, so to speak, it's for the average animal of that size.
00:25:06.560 But of course, that's extremely powerful,
00:25:10.700 not only because it connects, you know,
00:25:13.160 all these different organisms that seemingly look alike
00:25:17.180 and live in very different environments.
00:25:20.480 It connects them all under sort of one umbrella
00:25:24.820 and shows the kind of unity of life.
00:25:27.860 But also, it provides a baseline for asking about specific cases.
00:25:33.500 You know, you can then look at specific animals
00:25:36.900 or specific individuals of that species
00:25:40.120 and start asking questions using the scaling laws as a baseline.
00:25:45.900 Well, so to talk about one variable here, lifespan.
00:25:50.040 So as you get bigger as an animal,
00:25:53.040 perhaps we should confine this to mammals.
00:25:55.160 As you get bigger, you tend to live longer.
00:25:59.080 And this follows the scaling law that you,
00:26:01.720 this is a consequence of metabolism slowing down
00:26:05.880 and economies of scale?
00:26:07.780 Yeah.
00:26:08.060 So the, so this is, so let me back off now
00:26:12.260 and talk more generally about the origin of these scaling laws.
00:26:16.620 What is, where in the hell do they come from?
00:26:18.740 For example, we just talked mostly here about mammals,
00:26:22.060 but the same scaling laws apply to trees and plants
00:26:25.960 in the following sense.
00:26:27.540 Their metabolic rate scales in the same way as ours does.
00:26:31.540 That is, every time you double the size of a tree
00:26:34.500 in terms of its weight,
00:26:36.480 it uses only 75% more energy, just like we do.
00:26:41.220 But for example, the way it's trunk scales,
00:26:47.200 the trunk of a tree scales,
00:26:49.000 is essentially identical to the way our aorta scales.
00:26:54.040 The tree is its own aorta.
00:26:55.520 It's all aorta.
00:26:56.800 It's all circulatory system.
00:26:57.820 Well, the trunk is the aorta.
00:26:58.960 Yeah, exactly.
00:26:59.680 No, so, so let me, let me take that.
00:27:01.980 Let me, let me go from there.
00:27:03.820 The analog to the tree inside us
00:27:08.780 is our circulatory system.
00:27:11.080 The aorta, the analog to the aorta,
00:27:13.860 which is that first tube, as they say,
00:27:15.700 coming out of the heart,
00:27:17.080 the analog to that is the trunk of the tree,
00:27:20.060 the part that goes up before it branches
00:27:22.320 into two or three other big branches.
00:27:26.160 And indeed, the origin of these scaling laws,
00:27:29.920 because you ask yourself, you know, what is it?
00:27:31.720 What is it that's common among plants, trees, mammals,
00:27:36.260 birds, fish, et cetera,
00:27:38.080 that they all seem to obey these same scaling laws,
00:27:41.980 even though their evolved engineered design
00:27:46.080 is quite different.
00:27:47.640 Obviously, you know, we have beating hearts.
00:27:49.680 Trees certainly don't have beating hearts,
00:27:51.640 just to take a dramatic example.
00:27:54.380 So you ask, what is it that's common among all of them?
00:27:57.060 And what you realize is what's common among all of them
00:27:59.420 is that they have all evolved
00:28:02.260 to be hierarchical branching network systems.
00:28:05.880 And you sort of understand that
00:28:07.740 because, you know, just think of yourself,
00:28:09.540 you're made of 10 to the 14th cells,
00:28:12.280 roughly 100 trillion cells.
00:28:14.580 And each one of those has to be serviced
00:28:17.620 in some, roughly speaking,
00:28:19.660 democratic and efficient fashion.
00:28:21.160 And the way that problem has been solved
00:28:24.120 is by evolving these networks
00:28:27.180 that deliver oxygen and nutrients and so on
00:28:32.280 and information from, if you like,
00:28:35.780 a central reservoir down to the cellular level.
00:28:40.200 And as I say, one, we're very familiar
00:28:42.080 with our circuitry system,
00:28:43.460 our respiratory system,
00:28:45.080 our neural system,
00:28:47.000 our renal system,
00:28:48.000 and so on.
00:28:49.740 And all of these have those characteristics.
00:28:52.460 And the idea is
00:28:53.620 that it is the mathematics and physics,
00:28:59.060 the sort of universal generic mathematics and physics
00:29:02.800 of these network systems
00:29:05.240 at all scales
00:29:06.640 that are being reflected in the scaling laws.
00:29:10.380 And that was the work that I got involved in.
00:29:13.280 And we, you know,
00:29:14.920 it's quite complicated mathematics
00:29:17.880 to work it all out.
00:29:19.660 But out of that pops
00:29:20.960 these remarkable scaling laws.
00:29:24.300 And I want to say a couple of things
00:29:26.060 about the networks
00:29:27.060 because it's not just the networks,
00:29:29.740 but they have special properties
00:29:31.760 which are, roughly speaking, universal.
00:29:35.300 And one of them
00:29:36.660 is that they are
00:29:38.640 what we technically call space filling.
00:29:40.520 It's a very simple concept.
00:29:43.020 And it's simply that
00:29:44.940 whatever the structure of the network,
00:29:48.060 its terminal units,
00:29:49.520 in our case,
00:29:50.360 for example,
00:29:50.900 the circuitry system,
00:29:52.020 the terminal units
00:29:52.880 are capillaries
00:29:53.980 that feed cells.
00:29:55.700 Those capillaries,
00:29:57.180 so to speak,
00:29:57.700 have to go everywhere
00:29:58.640 because every cell in the body
00:30:00.740 has to be fed
00:30:02.160 by oxygen
00:30:04.060 diffusing from blood,
00:30:06.060 from the capillaries
00:30:06.900 to cells.
00:30:07.600 So the endpoints
00:30:10.160 of the network
00:30:11.140 have to end up
00:30:12.380 close by cells.
00:30:15.420 And so the network
00:30:17.080 in that sense
00:30:17.820 has to be space filling
00:30:19.020 and go everywhere.
00:30:20.180 As, for example,
00:30:22.260 in a city,
00:30:23.360 the road networks
00:30:24.920 essentially have to service
00:30:27.460 all buildings
00:30:28.600 and ultimately all people.
00:30:30.520 the street system
00:30:36.340 doesn't leave
00:30:38.280 vast areas of houses
00:30:40.480 without any access to them.
00:30:43.040 So it is with our bodies.
00:30:45.180 So that concept
00:30:45.980 is called space filling
00:30:47.160 and that has to be put
00:30:48.020 into some mathematical terms
00:30:50.300 and that's one of the inputs
00:30:51.940 to the,
00:30:53.100 or one of the constraints,
00:30:54.360 I should say,
00:30:55.560 on the network.
00:30:56.420 I think we could introduce
00:30:57.860 a mathematical concept here
00:30:59.260 that will be familiar
00:31:00.560 to people
00:31:01.220 but it seems relevant
00:31:02.520 that the concept
00:31:03.320 of a fractal,
00:31:05.060 which, you know,
00:31:05.860 I think,
00:31:07.140 it seemed like in the 80s
00:31:08.680 literally everyone
00:31:10.080 knew what fractals were.
00:31:11.520 I mean,
00:31:11.800 like the barber
00:31:12.520 was telling you
00:31:13.260 about the Mandelbrot set.
00:31:15.060 Exactly.
00:31:15.640 So we had reached
00:31:17.700 peak fractal back then
00:31:18.940 but I'm not sure
00:31:20.020 the knowledge has stuck
00:31:21.080 so perhaps you could
00:31:22.160 remind people about
00:31:23.160 what fractals are
00:31:24.200 and their significance.
00:31:24.880 Yes, let me do one last thing
00:31:28.160 before doing that
00:31:29.020 because it relates
00:31:29.760 directly to it
00:31:30.860 and that is another constraint
00:31:33.340 on the network
00:31:34.320 and that is that
00:31:36.640 in some sense
00:31:38.220 the network optimizes the system.
00:31:41.500 I say that loosely
00:31:42.820 but let me give you an example
00:31:44.120 because it leads to fractals
00:31:45.620 and that is that
00:31:47.480 the circulatory system
00:31:50.720 that we have
00:31:52.660 and that has evolved
00:31:54.500 by the process
00:31:55.240 of natural selection
00:31:56.220 and by we have,
00:31:57.840 I mean the we
00:31:58.440 I'm referring to
00:31:59.200 is all mammals.
00:32:00.440 That is all mammals
00:32:01.680 that now exist
00:32:02.600 and all mammals
00:32:03.380 that have ever existed.
00:32:05.700 The one that we have
00:32:07.780 minimizes
00:32:09.340 the amount of energy
00:32:11.220 our hearts have to do
00:32:12.780 to pump blood
00:32:14.060 through our circulatory system
00:32:17.160 to feed cells
00:32:18.380 so that we can maximize
00:32:21.660 the amount of energy
00:32:22.960 we can devote
00:32:24.060 to what is called
00:32:26.980 Darwinian fitness
00:32:27.920 meaning that we can devote
00:32:29.680 to having sex
00:32:31.020 and rearing children.
00:32:33.600 And so
00:32:34.220 that's very important.
00:32:36.940 So that means that
00:32:38.380 whatever the structure
00:32:39.160 of the network is
00:32:40.080 not only does it have
00:32:40.900 to be space filling
00:32:41.720 but
00:32:42.540 its structure
00:32:44.000 has to be
00:32:44.860 that if we changed it
00:32:46.940 in any significant way
00:32:49.180 you know
00:32:49.880 by just say
00:32:50.520 doubling
00:32:51.020 the length
00:32:52.700 of the third branch
00:32:53.960 of your arterial system
00:32:56.000 that would increase
00:32:58.180 the amount of energy
00:32:59.280 your heart has to do
00:33:00.580 and similarly
00:33:01.940 if you halved
00:33:02.900 this eighth branch
00:33:04.300 of your arterial system
00:33:05.640 it would increase
00:33:06.840 the energy.
00:33:07.380 So we sit
00:33:08.200 in a kind of basin
00:33:09.220 of optimization
00:33:11.540 so to speak
00:33:12.340 of minimizing
00:33:13.340 the energy
00:33:13.900 our hearts have to do.
00:33:15.260 It seems to me
00:33:15.680 that that need not be so
00:33:17.800 in evolutionary terms
00:33:19.300 I mean there's a lot
00:33:20.320 obviously
00:33:20.960 there's a lot about us
00:33:22.320 that an engineer
00:33:23.600 would not have put in place
00:33:25.240 and I put
00:33:25.920 I put the prostate gland
00:33:27.360 high on the list
00:33:28.220 of things
00:33:29.040 you would not have engineered.
00:33:30.420 Absolutely.
00:33:31.300 That's just mathematically
00:33:32.160 so at this point
00:33:33.200 we can say
00:33:33.700 that it is optimal.
00:33:34.680 So here was the idea
00:33:35.900 the idea was that
00:33:37.260 you know
00:33:37.840 in order to start
00:33:39.500 to take this idea
00:33:41.060 that networks
00:33:41.800 underlie the scaling laws
00:33:43.060 you have to start
00:33:44.320 putting together
00:33:45.120 the mathematics
00:33:45.720 of the networks
00:33:46.580 and as in all physics
00:33:48.680 you need
00:33:49.420 generic principles
00:33:50.640 that transcend
00:33:51.640 you know
00:33:52.580 the individual system
00:33:53.600 you're looking at
00:33:54.340 and you need
00:33:55.040 you know
00:33:55.680 certain assumptions
00:33:56.500 and one of the
00:33:58.720 simplest assumptions
00:33:59.540 was to assume
00:34:01.000 that there was
00:34:02.100 this kind of optimization
00:34:03.120 that by the
00:34:04.340 continuous process
00:34:05.740 continuous feedback
00:34:07.600 process
00:34:08.400 inherent in natural
00:34:09.680 selection
00:34:10.240 the you know
00:34:11.940 mammals that have
00:34:13.560 survived
00:34:14.500 that we are
00:34:16.100 tend towards
00:34:17.540 minimization
00:34:18.320 of this
00:34:19.580 you know
00:34:20.400 the amount of energy
00:34:21.200 that we use
00:34:21.960 to keep ourselves alive
00:34:23.100 we minimize
00:34:23.820 the amount of energy
00:34:26.180 that is
00:34:27.260 the mundane process
00:34:28.400 of remaining alive
00:34:30.020 so that we can
00:34:32.200 maximize
00:34:33.100 the amount of energy
00:34:34.680 that we put into
00:34:36.220 our genes
00:34:37.500 going forward
00:34:38.360 and
00:34:39.420 you know
00:34:40.860 that of course
00:34:42.020 need not be
00:34:42.900 on the other hand
00:34:44.200 you know
00:34:44.800 if you believe
00:34:45.240 in Darwinian fitness
00:34:46.280 and you had
00:34:48.020 long enough time
00:34:48.860 which we've had
00:34:49.660 you would expect
00:34:50.540 something like that
00:34:51.360 to happen
00:34:51.780 but anyway
00:34:52.120 that was
00:34:52.560 a hypothesis
00:34:53.860 and it was
00:34:55.160 very natural
00:34:55.720 to hook it up
00:34:56.500 to traditional ideas
00:34:58.320 of Darwinian fitness
00:34:59.560 but you're absolutely
00:35:00.960 right
00:35:01.500 there are many
00:35:02.360 aspects of our
00:35:03.440 physiology
00:35:04.100 especially at my age
00:35:06.280 that you begin to realize
00:35:07.600 weren't exactly
00:35:09.240 designed in the way
00:35:10.580 that maybe
00:35:11.360 they were optimal
00:35:12.240 but you know
00:35:13.380 you have to remember
00:35:14.780 that having said that
00:35:17.380 that
00:35:18.320 that's always the case
00:35:20.180 when you look
00:35:20.860 at one individual
00:35:22.120 component
00:35:23.060 you know
00:35:24.560 like you mentioned
00:35:25.340 you know
00:35:25.600 if you look at one
00:35:26.300 specific thing
00:35:27.160 but you have to remember
00:35:28.100 that that is
00:35:29.340 interconnected
00:35:30.280 with everything else
00:35:31.620 it's a systemic problem
00:35:33.240 and the optimization
00:35:34.600 and that's what
00:35:36.040 part of this idea was
00:35:37.700 is not so much
00:35:38.880 that it's taken place
00:35:39.940 at the highly local level
00:35:41.680 and this is extremely important
00:35:43.280 but it's taken place
00:35:44.480 at the systemic level
00:35:45.680 I'm talking about
00:35:46.700 the systemic level
00:35:48.300 of each one
00:35:49.360 of these
00:35:49.800 network systems
00:35:50.980 so it's the entire system
00:35:52.460 going from
00:35:53.620 the heart
00:35:54.680 and the entire
00:35:56.540 structure
00:35:58.000 structure of the
00:35:59.080 circulatory system
00:36:00.340 from your aorta
00:36:01.060 downwards
00:36:01.620 feeding through tissue
00:36:03.480 through capillaries
00:36:05.660 to cells
00:36:06.460 and how that
00:36:07.180 diffusion takes place
00:36:08.360 for example
00:36:08.780 all of this
00:36:09.560 is one huge system
00:36:10.780 and it has to be
00:36:12.040 and the idea
00:36:12.740 is that
00:36:13.240 it is the systemic
00:36:14.380 optimization
00:36:15.220 rather than
00:36:16.760 the local
00:36:17.620 optimization
00:36:19.680 I'll take your point
00:36:20.880 Jeffrey
00:36:21.140 but if you're going
00:36:21.740 to argue
00:36:22.080 that the prostate
00:36:22.940 gland is a masterpiece
00:36:24.040 of nature
00:36:25.060 and it's God
00:36:25.780 you're going to have
00:36:26.860 a tough time
00:36:27.440 on this podcast
00:36:27.860 it is not
00:36:28.160 and I certainly
00:36:32.200 agree with you
00:36:32.880 with that
00:36:33.320 or the way
00:36:34.860 backs are designed
00:36:35.920 for example
00:36:36.580 or the way
00:36:38.320 I mean
00:36:38.680 I still
00:36:39.960 am amazed
00:36:41.680 at the whole
00:36:42.160 process
00:36:42.820 of both
00:36:44.260 reproduction
00:36:45.760 and child
00:36:47.620 delivery of
00:36:49.360 fetuses
00:36:49.940 into the world
00:36:51.620 why does it have
00:36:52.500 to be a medical
00:36:53.080 emergency every time
00:36:54.240 yeah exactly
00:36:55.060 I mean
00:36:55.720 so you know
00:36:56.780 obviously
00:36:57.600 all of this
00:36:58.200 but you know
00:36:58.840 those do not
00:37:00.100 happen
00:37:00.460 my point is
00:37:01.400 they do not
00:37:03.040 happen
00:37:03.520 in a vacuum
00:37:04.680 I mean
00:37:05.200 they're all
00:37:05.720 interconnected
00:37:06.420 you know
00:37:07.180 and no doubt
00:37:08.220 something
00:37:08.780 about that
00:37:10.020 birth delivery
00:37:11.520 has all kinds
00:37:12.780 of other
00:37:13.400 implications
00:37:14.220 not just
00:37:14.980 physiological
00:37:15.600 but social
00:37:16.640 implications
00:37:17.280 of course
00:37:18.080 and so on
00:37:19.500 so I don't
00:37:19.960 want to argue
00:37:20.480 this
00:37:20.840 this is not
00:37:21.500 you know
00:37:22.680 this is a
00:37:23.180 secondary thing
00:37:23.860 really
00:37:24.640 to the main
00:37:25.420 point
00:37:25.840 that
00:37:27.140 you know
00:37:27.720 when you
00:37:28.120 look at
00:37:28.580 these networks
00:37:29.360 and you
00:37:29.880 apply these
00:37:30.880 underlying
00:37:31.840 generic
00:37:32.760 systemic
00:37:33.380 principles
00:37:34.000 to them
00:37:34.740 one of the
00:37:35.920 things that
00:37:36.540 you learn
00:37:37.300 is that
00:37:38.580 the optimal
00:37:39.760 system
00:37:40.320 is fractal
00:37:41.980 like
00:37:42.380 I'll use
00:37:42.820 that word
00:37:43.400 and fractal
00:37:44.240 means
00:37:45.320 another
00:37:45.960 word for
00:37:46.500 it is
00:37:46.760 self-similar
00:37:47.500 and we're
00:37:48.960 all very
00:37:49.480 familiar with
00:37:50.160 it
00:37:50.380 I'm looking
00:37:51.480 out at the
00:37:52.040 moment
00:37:52.380 at a tree
00:37:53.100 and you
00:37:54.980 know it
00:37:55.200 has this
00:37:55.780 hierarchical
00:37:56.540 branching
00:37:57.060 network
00:37:57.540 and the
00:37:58.480 fractality
00:37:59.080 is expressed
00:37:59.740 by the fact
00:38:00.380 that if you
00:38:00.840 cut some
00:38:01.660 branch
00:38:02.240 and remove
00:38:03.260 it
00:38:03.520 it looks
00:38:04.100 like a
00:38:04.420 little
00:38:04.640 tree
00:38:05.060 right
00:38:05.520 and then
00:38:07.420 you can
00:38:07.800 take that
00:38:08.340 little
00:38:08.700 tree
00:38:09.100 and cut
00:38:10.160 a branch
00:38:10.700 of that
00:38:11.200 and take
00:38:12.540 it away
00:38:13.000 and it
00:38:13.340 looks like
00:38:13.800 an even
00:38:14.080 smaller tree
00:38:14.920 and so on
00:38:15.600 and that's
00:38:16.060 the idea
00:38:16.620 that you
00:38:17.340 have this
00:38:17.860 repetitive
00:38:18.660 self-similarity
00:38:19.980 and the
00:38:22.240 theory
00:38:23.020 is one of
00:38:24.760 the things
00:38:25.260 that comes
00:38:26.620 out of it
00:38:27.060 is that
00:38:27.560 there is in
00:38:28.580 fact that
00:38:29.160 the systems
00:38:29.900 should be
00:38:30.620 fractal
00:38:31.220 in order to
00:38:32.280 optimize in
00:38:33.020 the way I
00:38:33.480 said and
00:38:34.060 also
00:38:34.640 critical
00:38:35.760 fill all
00:38:37.600 of space
00:38:38.120 that is
00:38:38.720 that it
00:38:39.260 needs to
00:38:40.260 every part of
00:38:42.180 the system
00:38:42.660 needs to be
00:38:43.220 serviced
00:38:43.660 by the way
00:38:44.720 I use the
00:38:45.360 word fractal
00:38:46.000 like
00:38:46.520 because
00:38:47.240 actually
00:38:48.240 the rules
00:38:49.400 that evolve
00:38:50.060 that come
00:38:50.520 out of the
00:38:51.000 theory
00:38:51.460 actually
00:38:52.760 are
00:38:53.580 variants
00:38:54.460 of a
00:38:54.800 fractal
00:38:55.240 there you
00:38:55.880 know to
00:38:56.120 be a bit
00:38:56.460 more technical
00:38:57.020 about it
00:38:57.620 there it's
00:38:59.340 not a
00:38:59.680 precise
00:39:00.200 self-similar
00:39:01.240 in other
00:39:01.580 words and
00:39:02.480 it's in fact
00:39:03.020 true the
00:39:03.800 data shows
00:39:04.460 this that
00:39:05.020 if you do
00:39:05.560 take a
00:39:05.980 tree and
00:39:06.960 you cut a
00:39:07.540 piece out
00:39:08.020 of it it
00:39:08.740 does look
00:39:09.400 like the
00:39:09.940 tree but
00:39:10.340 if actually
00:39:10.800 if you do
00:39:11.740 measurements
00:39:12.260 the theory
00:39:12.800 predicts
00:39:13.240 this
00:39:13.420 it deviates
00:39:14.540 in a
00:39:15.020 predictable
00:39:15.460 way from
00:39:16.340 the original
00:39:16.840 tree but
00:39:18.140 it's very
00:39:18.500 close to
00:39:19.020 this idea
00:39:19.740 of repetitive
00:39:21.420 self-similarity
00:39:22.500 and one of
00:39:23.860 the wonderful
00:39:24.460 things that
00:39:25.740 you know you
00:39:26.820 discover in
00:39:27.580 all of this
00:39:28.200 and that is
00:39:28.840 related to
00:39:29.420 the scaling
00:39:29.940 laws is
00:39:31.220 that all
00:39:31.980 of these
00:39:32.340 systems have
00:39:33.640 somewhere in
00:39:34.640 them some
00:39:35.980 manifestation of
00:39:38.660 this regularity
00:39:40.620 this fractal
00:39:41.460 regularity
00:39:42.320 that seems
00:39:43.540 that seems
00:39:43.560 to permeate
00:39:44.300 nature
00:39:44.740 and some
00:39:46.540 of that
00:39:46.920 is no
00:39:48.740 doubt
00:39:49.140 related to
00:39:53.540 let's put it
00:39:54.020 that way
00:39:54.420 some of it
00:39:54.980 is related
00:39:55.540 to this
00:39:56.700 idea that
00:39:57.720 something is
00:39:59.160 being optimized
00:40:00.100 yeah so
00:40:00.760 to connect
00:40:01.940 the self-similarity
00:40:03.100 and the
00:40:03.400 seemingly
00:40:03.840 endless
00:40:04.340 divisibility
00:40:05.200 of these
00:40:05.720 branching
00:40:06.200 networks
00:40:06.680 to the
00:40:07.920 space filling
00:40:08.420 problem
00:40:08.860 just in a
00:40:09.420 vivid way
00:40:09.900 this is a
00:40:10.680 fact you
00:40:11.320 describe in
00:40:12.020 the book
00:40:12.360 so if you
00:40:13.060 ask what the
00:40:14.060 size of our
00:40:14.780 lungs are
00:40:16.020 they are about
00:40:17.820 the size of
00:40:18.400 a football
00:40:20.060 but the
00:40:21.260 surface area
00:40:22.500 of the
00:40:23.460 respiratory
00:40:23.880 membranes
00:40:25.120 in there
00:40:25.900 is about the
00:40:27.060 size of a
00:40:27.560 tennis court
00:40:28.060 because of
00:40:28.720 just how
00:40:29.420 how endlessly
00:40:30.220 branching it
00:40:31.020 is down
00:40:31.500 at the
00:40:31.820 smallest
00:40:32.400 scale
00:40:33.220 yeah so
00:40:34.000 it's kind
00:40:34.320 of wonderful
00:40:34.760 feeling that
00:40:35.520 inside you
00:40:36.200 is a
00:40:36.740 tennis court
00:40:37.400 you know
00:40:37.860 I mean
00:40:38.200 actually
00:40:38.620 and indeed
00:40:40.040 if you took
00:40:40.740 your circulatory
00:40:41.440 system
00:40:41.880 and you
00:40:42.200 laid all
00:40:42.680 those
00:40:43.140 vessels
00:40:45.580 end to
00:40:46.220 end
00:40:46.680 I forget
00:40:47.680 the precise
00:40:48.720 answer
00:40:49.020 I think it
00:40:49.380 was a hundred
00:40:50.120 thousand
00:40:50.500 kilometers
00:40:51.820 I believe
00:40:52.280 yes
00:40:52.560 yeah you
00:40:53.780 go around
00:40:54.240 the earth
00:40:54.700 certainly
00:40:55.420 more than
00:40:55.840 once
00:40:56.220 and that's
00:40:57.880 kind of
00:40:58.140 amazing
00:40:58.640 you know
00:40:59.020 it's an
00:40:59.300 amazing
00:40:59.840 image
00:41:01.580 it's almost
00:41:02.480 spiritual
00:41:03.120 that feeling
00:41:03.940 that inside
00:41:04.540 you is this
00:41:05.220 unbelievable
00:41:06.260 length
00:41:07.560 of tubing
00:41:09.700 but that
00:41:11.140 and that
00:41:11.640 it's
00:41:12.060 very systematic
00:41:13.640 you know
00:41:14.120 it's
00:41:14.340 it's
00:41:14.700 it's
00:41:15.300 structure
00:41:15.720 is obeying
00:41:17.100 very simple
00:41:18.280 mathematical rules
00:41:19.700 that are
00:41:20.620 like these
00:41:21.480 kinds of
00:41:21.900 rules
00:41:22.160 that I
00:41:22.380 mentioned
00:41:22.720 earlier
00:41:23.140 these
00:41:23.660 so-called
00:41:24.280 power laws
00:41:25.020 there's
00:41:25.640 something
00:41:25.880 spooky
00:41:26.360 about the
00:41:26.920 power laws
00:41:28.180 themselves
00:41:28.880 I mean
00:41:29.140 there's
00:41:29.500 this one
00:41:29.940 number
00:41:30.380 to which
00:41:30.800 you've
00:41:31.000 alluded
00:41:31.260 that
00:41:31.540 runs
00:41:32.040 through
00:41:32.320 this
00:41:32.600 that
00:41:32.780 almost
00:41:33.160 could
00:41:33.420 put
00:41:33.720 someone
00:41:34.100 in the
00:41:34.380 mind
00:41:34.740 of the
00:41:35.220 pseudoscience
00:41:36.600 of numerology
00:41:37.440 the fourth
00:41:38.040 power
00:41:38.460 the fact
00:41:39.460 that basically
00:41:40.140 all these
00:41:40.540 living systems
00:41:41.300 scale
00:41:41.900 to the
00:41:42.460 one-fourth
00:41:42.940 power
00:41:43.280 well the
00:41:44.280 one-quarter
00:41:44.780 yes
00:41:45.160 the number
00:41:45.560 four
00:41:46.220 is
00:41:47.500 the number
00:41:48.260 that permeates
00:41:48.920 all of
00:41:49.300 these scaling
00:41:49.760 laws
00:41:50.060 I said
00:41:50.420 the three
00:41:50.760 quarters
00:41:51.140 for metabolic
00:41:51.660 rate
00:41:52.160 it's one
00:41:53.180 quarter
00:41:53.620 for time
00:41:55.440 scales
00:41:56.100 for example
00:41:57.520 and so on
00:41:59.620 and for
00:42:00.000 lengths
00:42:00.380 it's very
00:42:00.820 similar
00:42:01.180 it's always
00:42:01.740 one quarter
00:42:02.420 comes in
00:42:03.040 and that's
00:42:03.840 that 25%
00:42:04.860 savings
00:42:05.540 that's not
00:42:06.220 an accident
00:42:06.720 and that's
00:42:07.640 the thing
00:42:08.020 that comes
00:42:08.440 out of
00:42:08.800 the theory
00:42:09.420 based on
00:42:10.540 these
00:42:11.000 mathematical
00:42:11.600 principles
00:42:12.460 of network
00:42:14.640 design
00:42:15.240 and that
00:42:16.520 pops out
00:42:17.240 and that
00:42:18.220 four
00:42:18.700 by the
00:42:19.140 way
00:42:19.520 if you
00:42:20.740 look at
00:42:21.120 the
00:42:21.240 mathematics
00:42:21.680 and ask
00:42:22.140 where it
00:42:22.440 comes
00:42:22.680 from
00:42:22.980 it's
00:42:24.200 the
00:42:24.580 following
00:42:24.840 it turns
00:42:25.180 out the
00:42:25.480 four
00:42:25.920 is actually
00:42:27.200 so to speak
00:42:28.300 not four
00:42:28.960 it's actually
00:42:29.380 three plus
00:42:30.000 one
00:42:30.360 which sounds
00:42:31.020 you know
00:42:31.480 like a
00:42:32.640 paradox
00:42:33.140 it's three
00:42:34.280 plus one
00:42:34.800 meaning
00:42:35.240 the three
00:42:36.640 part of the
00:42:38.160 three plus one
00:42:39.000 comes from
00:42:40.120 the fact
00:42:41.340 that we live
00:42:41.840 in three
00:42:42.160 dimensions
00:42:42.680 the up
00:42:43.800 down
00:42:44.160 and sideways
00:42:44.780 and the
00:42:47.700 one
00:42:48.180 is a
00:42:49.300 reflection
00:42:49.800 of the
00:42:50.600 fractality
00:42:51.340 of these
00:42:52.820 systems
00:42:53.420 that
00:42:55.520 it's well
00:42:57.380 known
00:42:57.800 among those
00:42:58.560 that learn
00:43:00.120 about fractals
00:43:00.940 that they
00:43:02.080 have peculiar
00:43:03.160 sense of
00:43:03.860 dimensions
00:43:04.360 and a
00:43:06.420 fully fractal
00:43:07.180 system
00:43:07.740 is one
00:43:08.720 that effectively
00:43:09.720 adds an
00:43:10.580 extra dimension
00:43:11.380 so there's
00:43:12.040 this kind
00:43:12.400 of weird
00:43:12.980 extra dimension
00:43:13.920 and that's
00:43:16.000 this one
00:43:16.580 so the
00:43:17.420 four is
00:43:17.880 actually
00:43:18.120 three plus
00:43:18.600 one
00:43:18.800 so if we
00:43:19.240 lived in
00:43:19.760 eight
00:43:20.580 dimensions
00:43:21.280 we would
00:43:23.660 be dominated
00:43:24.120 we had
00:43:24.600 life
00:43:25.020 it would
00:43:26.180 be
00:43:26.560 then
00:43:27.320 everything
00:43:27.960 would be
00:43:28.320 dominated
00:43:28.800 by the
00:43:29.300 one-ninth
00:43:29.880 power
00:43:30.320 and we
00:43:32.520 would be
00:43:32.900 instead of
00:43:33.320 saving
00:43:33.940 25%
00:43:35.960 we'd be
00:43:36.980 saving
00:43:37.640 you know
00:43:38.240 one-ninth
00:43:39.020 about 11%
00:43:40.020 I feel the
00:43:41.120 temptation
00:43:41.500 to remind
00:43:42.080 people
00:43:42.380 of just
00:43:42.740 what it
00:43:43.380 means
00:43:43.900 to be
00:43:44.300 adding
00:43:44.660 a dimension
00:43:45.220 here
00:43:45.620 in fractal
00:43:46.420 terms
00:43:46.740 so
00:43:47.480 it's a
00:43:48.480 little hard
00:43:48.760 to do
00:43:49.180 on a
00:43:49.660 podcast
00:43:49.980 but people
00:43:50.540 can look
00:43:51.020 up something
00:43:51.720 a figure
00:43:52.540 I think
00:43:52.940 it's called
00:43:53.200 the
00:43:53.460 is it
00:43:54.140 the Koch
00:43:54.620 curve
00:43:55.220 the K-O-C-H
00:43:56.740 oh yes
00:43:57.660 look this up
00:43:59.500 if you're
00:43:59.880 if you want
00:44:00.400 to follow us
00:44:00.900 down this
00:44:01.220 rabbit hole
00:44:01.620 but there's
00:44:02.420 there's
00:44:02.620 this image
00:44:03.560 or this
00:44:04.860 this curve
00:44:05.500 which is
00:44:05.940 essentially
00:44:06.380 formed by
00:44:07.440 an equilateral
00:44:08.120 triangle
00:44:08.740 being divided
00:44:09.920 on each
00:44:10.480 of its
00:44:10.760 sides
00:44:11.180 by a
00:44:11.620 smaller
00:44:12.040 one-third
00:44:12.920 size
00:44:13.440 equilateral
00:44:13.900 triangle
00:44:14.380 and you
00:44:14.680 keep doing
00:44:15.220 that
00:44:15.400 just adding
00:44:15.940 triangles
00:44:16.480 upon triangles
00:44:17.260 and you
00:44:17.940 develop a
00:44:18.640 kind of
00:44:18.900 snowflake
00:44:19.680 looking image
00:44:20.560 and then
00:44:21.480 when you
00:44:21.720 ask what's
00:44:22.520 the size
00:44:23.620 of that
00:44:24.160 curve
00:44:24.680 of that
00:44:25.080 figure
00:44:25.560 you know
00:44:26.320 given that
00:44:26.920 in the pure
00:44:27.520 mathematical
00:44:28.040 space
00:44:28.440 you keep
00:44:28.900 doing this
00:44:29.300 infinitely
00:44:29.680 well it's
00:44:30.220 a fully
00:44:30.620 self-contained
00:44:31.700 object
00:44:32.400 which actually
00:44:33.360 has an
00:44:34.060 infinite
00:44:34.460 length
00:44:35.720 of its
00:44:36.400 circumference
00:44:37.140 and this
00:44:38.340 has
00:44:38.760 now this
00:44:39.420 doesn't map
00:44:40.260 onto the
00:44:40.660 real world
00:44:41.420 totally
00:44:42.280 because we're
00:44:43.020 not talking
00:44:43.600 about infinite
00:44:44.180 lengths
00:44:44.600 in terms of
00:44:46.100 the world
00:44:46.860 in which we
00:44:47.200 live
00:44:47.380 but it
00:44:47.820 does to a
00:44:48.860 surprising
00:44:49.380 degree
00:44:49.820 and this
00:44:50.520 Jeffrey
00:44:51.080 you could
00:44:51.560 perhaps
00:44:52.020 remind us
00:44:52.580 of how
00:44:53.100 this was
00:44:53.460 first
00:44:53.720 discovered
00:44:54.220 where
00:44:54.720 you try
00:44:55.240 to measure
00:44:55.680 the boundary
00:44:56.400 between
00:44:56.840 two countries
00:44:57.600 and that
00:44:58.240 becomes
00:44:59.080 remarkably
00:45:00.080 dependent
00:45:00.500 on basically
00:45:01.740 how big
00:45:02.340 a measuring
00:45:02.760 stick
00:45:03.040 you use
00:45:03.480 yes
00:45:04.040 indeed
00:45:04.380 yes
00:45:04.820 that's
00:45:05.180 one of
00:45:05.580 those
00:45:05.760 marvelous
00:45:06.180 discoveries
00:45:06.800 that
00:45:07.300 sort of
00:45:08.520 came out
00:45:09.560 of the
00:45:09.760 blue
00:45:10.040 and something
00:45:10.800 that should
00:45:11.780 have been
00:45:11.980 known since
00:45:12.900 the Greeks
00:45:13.400 but wasn't
00:45:14.440 and it was
00:45:15.160 discovered by
00:45:15.720 a man named
00:45:16.380 Richardson
00:45:16.920 who was a
00:45:18.640 kind of a
00:45:19.760 polymath
00:45:20.200 but he was a
00:45:21.080 kind of a
00:45:22.140 geographer
00:45:22.600 and one of the
00:45:24.100 things that he
00:45:24.540 was interested
00:45:25.080 in
00:45:25.480 was
00:45:27.400 the length
00:45:29.860 of boundaries
00:45:30.780 between
00:45:31.800 countries
00:45:32.540 and he
00:45:33.800 was interested
00:45:34.260 in this
00:45:34.660 by the way
00:45:35.300 because he
00:45:35.840 had a
00:45:36.120 theory of
00:45:36.640 war
00:45:37.000 that
00:45:37.760 somehow
00:45:38.360 the
00:45:38.980 incidence
00:45:40.320 of
00:45:40.840 conflicts
00:45:41.440 between
00:45:42.000 nations
00:45:42.600 was
00:45:43.360 proportional
00:45:43.860 to the
00:45:44.520 length
00:45:45.180 of their
00:45:45.460 boundaries
00:45:45.860 and by
00:45:46.180 the way
00:45:46.400 we're
00:45:46.760 talking
00:45:46.980 about
00:45:47.280 he
00:45:49.200 developed
00:45:49.720 that
00:45:50.180 around
00:45:50.760 the time
00:45:51.100 of the
00:45:51.280 first
00:45:51.460 world war
00:45:52.000 but this
00:45:52.800 work on
00:45:53.340 measurement
00:45:53.760 came much
00:45:54.340 later
00:45:54.760 when he
00:45:55.140 was trying
00:45:55.480 to really
00:45:56.540 get a
00:45:56.900 quantitative
00:45:57.320 handle
00:45:57.880 on this
00:45:59.300 and so
00:46:01.280 he got
00:46:02.020 hold of
00:46:02.540 all these
00:46:02.900 maps
00:46:03.420 of
00:46:04.580 various
00:46:05.040 places
00:46:05.620 and he
00:46:06.920 started
00:46:07.160 measuring
00:46:07.600 their
00:46:07.820 boundaries
00:46:08.200 and one
00:46:08.740 of the
00:46:09.000 curious
00:46:09.300 things
00:46:09.600 that he
00:46:09.860 first
00:46:10.100 discovered
00:46:10.580 was that
00:46:12.000 I think
00:46:13.820 the first
00:46:14.240 one was
00:46:14.600 between
00:46:14.880 Spain and
00:46:15.520 Portugal
00:46:15.940 where he
00:46:16.860 found
00:46:17.280 looking at
00:46:18.080 different
00:46:18.480 maps
00:46:18.940 very detailed
00:46:19.660 maps
00:46:20.080 that he
00:46:21.820 got
00:46:22.000 completely
00:46:22.780 different
00:46:23.140 answers
00:46:23.560 I mean
00:46:24.280 I don't
00:46:24.720 remember the
00:46:25.100 numbers
00:46:25.420 I wrote
00:46:25.940 them in
00:46:26.200 the book
00:46:26.540 but
00:46:27.380 you know
00:46:27.880 instead
00:46:28.140 of
00:46:28.320 you know
00:46:28.600 one
00:46:28.820 map
00:46:29.060 might
00:46:29.340 give
00:46:29.740 1100
00:46:31.380 kilometers
00:46:31.960 and then
00:46:33.500 he'd look
00:46:34.500 at another
00:46:34.880 map
00:46:35.240 and you'd
00:46:35.960 get
00:46:36.200 650
00:46:37.040 kilometers
00:46:37.720 and he
00:46:39.000 would look
00:46:39.340 these up
00:46:39.760 in various
00:46:40.180 places
00:46:40.580 and indeed
00:46:41.100 he'd find
00:46:41.520 different
00:46:42.400 books
00:46:44.340 recording
00:46:44.980 these things
00:46:45.600 giving
00:46:45.880 completely
00:46:46.500 different
00:46:46.820 numbers
00:46:47.260 and this
00:46:49.140 was very
00:46:50.040 mysterious
00:46:50.580 and he
00:46:51.860 started
00:46:52.160 looking around
00:46:52.840 and he
00:46:53.160 looked across
00:46:53.820 many
00:46:54.280 countries
00:46:54.720 and he
00:46:55.160 discovered
00:46:55.540 the same
00:46:56.100 phenomenon
00:46:56.600 and he
00:46:58.540 you know
00:46:59.040 he was
00:46:59.300 very puzzled
00:46:59.860 by this
00:47:00.440 and he
00:47:02.580 did realize
00:47:03.280 what was
00:47:03.700 going on
00:47:04.500 but he
00:47:05.640 didn't
00:47:06.180 formalize
00:47:07.680 it
00:47:07.920 it was
00:47:09.140 formalized
00:47:09.660 later by
00:47:10.180 a man
00:47:10.460 named
00:47:10.640 Benoit
00:47:10.960 Mandelbrot
00:47:11.620 who termed
00:47:12.260 the phrase
00:47:12.640 fractal
00:47:13.200 and it's
00:47:14.280 the following
00:47:14.900 it was
00:47:16.060 that
00:47:16.580 when people
00:47:19.140 made these
00:47:19.720 measurements
00:47:20.140 when you
00:47:20.760 make a
00:47:21.180 measurement
00:47:21.580 you have
00:47:23.380 to have
00:47:23.860 a ruler
00:47:24.980 with a
00:47:25.480 certain
00:47:25.680 scale
00:47:26.140 and you
00:47:27.780 have a
00:47:28.040 certain
00:47:28.220 resolution
00:47:28.780 so you
00:47:29.420 might
00:47:29.720 measure
00:47:30.180 someone
00:47:31.000 might
00:47:31.400 measure
00:47:31.780 a
00:47:32.080 boundary
00:47:32.480 using
00:47:33.180 a
00:47:33.760 resolution
00:47:34.200 of only
00:47:34.620 one
00:47:34.860 mile
00:47:35.200 so you're
00:47:35.660 measuring
00:47:35.940 something
00:47:36.320 that's a
00:47:36.680 thousand
00:47:36.940 kilometers
00:47:37.380 long
00:47:37.820 you only
00:47:38.680 care
00:47:39.080 a
00:47:39.400 resolution
00:47:39.840 of a
00:47:40.180 mile
00:47:40.440 but you
00:47:41.040 might
00:47:41.200 have
00:47:41.360 someone
00:47:41.840 that
00:47:42.600 has a
00:47:43.060 resolution
00:47:43.500 of 10
00:47:43.960 miles
00:47:44.380 and someone
00:47:44.900 else
00:47:45.200 might have
00:47:45.560 a resolution
00:47:46.160 of you
00:47:47.600 know
00:47:47.860 I don't
00:47:48.300 know
00:47:48.460 he could
00:47:48.800 even be
00:47:49.180 a meter
00:47:50.660 in principle
00:47:51.520 and you
00:47:53.340 can
00:47:53.540 immediately
00:47:53.960 when you
00:47:54.400 start
00:47:54.620 thinking
00:47:54.940 about it
00:47:55.300 you realize
00:47:55.720 what the
00:47:56.060 problem
00:47:56.360 is
00:47:56.700 that if
00:47:57.600 you
00:47:57.840 measure
00:47:58.420 a boundary
00:47:59.500 which is
00:48:00.000 a squiggly
00:48:00.580 line
00:48:01.120 and you
00:48:02.160 put a
00:48:02.580 ruler on
00:48:03.140 it
00:48:03.340 where
00:48:03.780 the
00:48:05.420 resolution
00:48:06.700 is
00:48:08.020 say
00:48:08.960 10
00:48:09.380 kilometers
00:48:09.880 then anything
00:48:11.180 below 10
00:48:11.980 kilometers
00:48:12.480 you miss
00:48:13.440 but below
00:48:14.580 that 10
00:48:15.040 kilometers
00:48:15.440 the line
00:48:16.260 the boundary
00:48:16.860 may be
00:48:17.360 squiggling
00:48:17.800 around
00:48:18.240 so you
00:48:18.740 miss
00:48:19.100 you measure
00:48:20.000 that as
00:48:20.340 10
00:48:20.580 kilometers
00:48:21.060 but someone
00:48:22.040 else
00:48:22.360 with a
00:48:22.680 resolution
00:48:23.180 of
00:48:23.520 one
00:48:23.740 kilometer
00:48:24.200 would
00:48:24.940 measure
00:48:25.280 it
00:48:25.520 as
00:48:25.940 25
00:48:26.800 kilometers
00:48:27.340 for example
00:48:28.160 so that
00:48:29.780 was the
00:48:30.120 problem
00:48:30.480 he realized
00:48:31.340 and in
00:48:31.840 fact
00:48:32.180 then he
00:48:32.680 discovered
00:48:33.140 that this
00:48:34.380 followed a
00:48:35.100 very regular
00:48:35.780 pattern
00:48:36.260 that if
00:48:37.080 you plotted
00:48:37.620 the length
00:48:38.780 that's measured
00:48:39.580 or reported
00:48:40.280 versus the
00:48:41.420 resolution
00:48:41.980 there was
00:48:43.220 a very
00:48:43.780 simple
00:48:44.340 mathematical
00:48:44.900 relationship
00:48:45.560 and
00:48:46.440 amazingly
00:48:47.260 that relationship
00:48:48.160 is just
00:48:48.780 like the
00:48:49.240 relationships
00:48:49.760 I talked
00:48:50.380 about
00:48:50.660 in terms
00:48:51.260 of things
00:48:51.640 like
00:48:51.940 metabolic
00:48:52.700 rates
00:48:53.300 and all
00:48:53.720 the other
00:48:54.160 characteristics
00:48:54.780 of
00:48:55.120 organisms
00:48:55.620 and
00:48:56.580 that's
00:48:57.360 where the
00:48:57.760 connection
00:48:58.100 was to
00:48:58.680 fractals
00:48:59.320 and it
00:49:00.460 was Benoit
00:49:01.160 Maudenbrot
00:49:01.760 who realized
00:49:03.380 that not
00:49:04.280 just that there
00:49:05.000 was this
00:49:05.360 phenomenon
00:49:05.800 of the
00:49:06.680 problem
00:49:07.080 of making
00:49:08.100 measurements
00:49:08.740 and resolution
00:49:09.660 but that
00:49:11.340 in fact it
00:49:12.180 was self
00:49:12.620 similar
00:49:12.940 boundaries are
00:49:13.860 approximately
00:49:14.580 self
00:49:15.020 similar
00:49:15.360 so if
00:49:16.760 you look
00:49:17.140 at one
00:49:17.520 scale
00:49:18.020 and then
00:49:19.140 scale
00:49:19.560 that up
00:49:20.040 it just
00:49:20.600 looks like
00:49:21.260 what the
00:49:21.940 boundary
00:49:22.240 would look
00:49:22.680 like at
00:49:23.040 the bigger
00:49:23.320 scale
00:49:23.720 and so on
00:49:25.020 and so forth
00:49:25.580 as you said
00:49:26.140 this is a
00:49:27.040 genuine mystery
00:49:27.960 why this
00:49:28.600 wasn't discovered
00:49:29.400 literally thousands
00:49:31.300 of years ago
00:49:32.000 this is one of
00:49:33.160 those things
00:49:33.600 that was just
00:49:34.260 staring everyone
00:49:35.080 in the face
00:49:35.780 and most of
00:49:37.760 science is not
00:49:38.380 like that
00:49:38.820 does anyone
00:49:40.760 understand why
00:49:42.140 this wasn't
00:49:43.400 discovered
00:49:43.860 before
00:49:44.700 if you'd like
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00:49:51.540 listening to
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