21. Chaos and Reductionism
Transcription for the video titled "21. Chaos and Reductionism".
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Stanford University. We are not going to work our way through the behavior on the right and march to the left. And instead we'll be trying to come up with some ideas that are going to apply to everything we hear about and hear. And overall these are probably the most difficult lectures of the course, the most difficult material. In part because I'm not sure if I completely understand what I'm talking about, but also because this is intrinsically some really different ways of thinking about things in the realm of science. And that's one of the reasons why I forced you guys to read this chaos book. And again as I think I mentioned in the first lecture, this insights a subset of people to passionate enthusiasm about the book. It insights another small subset into just the most greatest level of irritation that this was assigned and everybody else is just vaguely puzzled and kind of sort of sees the point, but how come? This book when I first read it and so my first introduction to the whole field, this was like the first book I had read where I finished it and immediately started over again. First one since like where the wild things are in terms of influence. This was incredibly challenging book in terms of questioning all the ways in which I think about sort of reductive science.
Fundamentals Of Science And Activity Discussions
One homework (01:43)
And hopefully it will do the same for you. And as part of it posted, there is your one and only homework assignment of the entire course, which just to make things easier will not be collected or looked at. But what you should do is there's a whole exercise up there in generating something that are called cellular automata. Do not panic yet. There's plenty of time to panic where you will be making some of those on your own. And all I ask from you guys in terms of making sense of these exercises is do not sleep between now and Friday.
Start of science (02:17)
Spend all of your time working on them. Do nothing else. Take occasional breaks to eat or the bathroom, but other than that do nothing but this between now and Friday. And let's see how everybody feels about it on Friday. Okay. So picking up where we need to start off with is trying to get a framework for the standard Western approach to understanding complicated systems with scientific bases. 400 or so AD, Rome falls, collapse of the Roman Empire entering an unbelievably dark period in terms of ignorance, in terms of the dark ages throughout Europe, the level at which people did not understand how the world worked, the level at which people had lost knowledge from previous times, books were gone, philosophers were gone. The level of just isolation, intellectual isolation was phenomenal. It was during that period, it was as if 500 years before people had known the cure for cancer and for AIDS and for being able to fly on your own and all of that, and somehow in the aftermath of the empire falling apart, all of that knowledge was lost. Literacy went down the tubes and this was a period that gave rise to words like having an audit, having an audit about your finances, making an oral argument before the judges, having hearings about something or other before the court, because all of these were about speaking about auditory transmission of information, because nobody could read anymore. This was a period where there was no Western European language that had the word progress or ambition in it, these were non-existent concepts at the time. Utter intellectual isolation, utter social isolation, during that time vast majority of people lived in small villages where you would go 50 miles away and people spoke a dialect that you could not understand. That degree of isolation estimates are the average person never went more than 12 to 15 miles away from where they were born in their entire life, incredible isolation, and incredible ignorance ultimately about how you explain causality in the world, because all of the information was gone. Then something dramatic changed in the year 1085, which is the first European Christian conquest of a major Islamic city, a major Moorish one, in this case Toledo in Spain, Spain at the time, which was Moorish, known as Al-Hombra at the time. This was the first city to fall through Christian troops, since Islam swept in there, and this was basically sort of a second rate kind of city, this was not a major center. Toledo, but simply by European forces having captured that city, something extraordinary happened, which was within that city was a library with more books than existed in all of Christian Europe put together. The simple library and the sort of out of the way, Podonk sort of city there, out in the boondocks, one run at the mill library there had more cumulative information than was available to all of Europe at the time. And suddenly Europe got to rediscover philosophers, Aristotle, Plato, all of that. They got to rediscover logic, they got to rediscover all the great works, suddenly all of those flooded back into Europe, and the first beginnings of sort of a modern mindset about complexity started to emerge. People suddenly began to do things like be able to think transitively with transitivity in a transitive manner, where you would see A is bigger than B, B is bigger than C, and you had this startling revolutionary notion, which is you now can know something about the relationship between A and C without having to directly compare them with each other. This was an astonishing sort of logical breakthrough. Syllages and syllages and suddenly appeared in Europe for the first time in centuries, the ability of people to do things like say if all things that glow have fire, then stars glow and the stars have fire, syllogistic thinking, that had been utterly gone. And suddenly people began to think about where is, where that had been lost for centuries, and all of that culminated in a certain sort of emergence of what we would now call science, Thomas Aquinas coming up with an amazing and amazing quote that summarizes all of what was happening at the time. He listed three things that God could not do. The first two were just sort of theological stuff. God cannot sin. God cannot make a copy of himself. It's the third one that was just earth shaking. Third, even God cannot make a triangle with more than 180 degrees. And in that one concept Aquinas had just said if it comes up against sort of the old knowledge and science, science wins. And that was an absolute landmark moment. God could do anything but still can't make a triangle with more than 180 degrees. This was the beginning of a transformation of the world. And this immediately had impact all sorts of domains, not just this very pedestrian one, which is if something broke, you could fix it. That was a concept that was very, very rare around then. But the ability to construct events by looking at overlapping fragments. A crime has occurred. And there's no individual who has watched the entire crime happen, but one person saw what happened from points A to C. And suddenly there was this realization that you can figure out what went on by putting these various overlapping bits of data together, completely revolutionary idea and completely transformed the notion that how do you figure out if somebody did a crime prior to this period, what you would do is throw them in a river, for example. And if they sank and drowned, obviously they had done the crime. Good luck there in terms of having figured that out. Good detective work. That's how you figured out if somebody had done something wrong or not. You set fire to them. And if they burn, oh, they were obviously guilty. And suddenly this concept instead, not only using facts, not only using observational data, but that you could derive what occurred without any one individual having seen the whole thing. You can reconstruct things with overlapping. This was just landmark. This just transformed everything.
And somewhere around this time began to emerge what we would recognize to be sort of the proto-baby steps of what would be model science. And in the aftermath of this period came what is basically the single most important concept in all of science in the last 500 years, which is the idea of reductionism. To find very simply if you want to understand a complex system, you break it down into its component parts. And when you understand the individual parts, you will be able to understand the complex system. And when you understand the complex system, you will be able to understand the complex system. And what's intrinsic in that is the concept of linearity of additivity. You got something complex and you break it down to its component parts. And once you figure out how those component parts work, all you need to do is add them together and they will increase in their complexity in a linear manner and you will produce the whole complex system. This is westernized reductionism. And it came with a bunch of corollaries that we take for granted by now. The first one being in a reductive system where the component parts and how they work just add them together and in a straightforward way that will produce your complex system. One sort of consequence of that is if you know the starting state of a system, as defined here, if you know what the little component parts all are, if you know the starting state, you will have 100% predictability of what the full complex mature system will look like. So starting state allows you to predict what comes later. And related to that, if you know the complex system, you can figure out what was the starting state. That there is point for point relationship between the simple building blocks and the complex systems that come out the other end. And this gave rise to an extraordinary thing which was the ability to extrapolate, to be able to see the answer to something in different iterations and to use the same rules and apply them over and over. Okay, what do I mean by this? Suddenly this amazing notion that okay, if x plus y equals z, you will then know that x plus 1 plus y is going to equal z plus 1 and x plus 2, all of that. And the same exact principle would hold for some like bizarre idiot equation or whatever like that. It doesn't really matter what all of this is. You know absolutely beforehand simply by this business of additivity of component parts that whatever this is, it's going to equal z plus 1. You could come up with an answer to something without having to go through the calculations all over again. You could go through x plus whatever and you know it's going to be z plus whatever without having to sit there and measure it. You could extrapolate. You can use reductive knowledge, the linearity going from this to this. You're still using the same rules that allows you to go from this to this. Applications of it, a purely reductive linear set of systems and this was revolutionary. So that's great. You don't need to go through all the calculations at every step of the way to be able to note the starting state and thus note with the mature state is about. Look at the mature state. You know what the starting state was point for point to relatedness. That's great. Finally, another feature of reductive systems like these is the really fancy ones require blueprints. What do I mean by blueprints in this case that requires already a notion of what the mature state is supposed to look like. Which is intrinsic in what I just said. If you know the starting state, you will know the mature state. But the belief that in terms of quality control, you have to have some representation of what the mature state is supposed to look like. A blueprint in order to know if you're doing the right thing, feedback along those lines, you feel really going to do something hard and fancy. In this reductive world, you've got to have a road map at the beginning. You have to have a blueprint. You have to have something that already shows you what the outcome is going to be when you apply these linear additive rules.
And the way you go about doing it is shaped by the blueprint, the instructions that are intrinsic in this. This is everything about westernized reductions. One important additional component to it. Which is you go measure something or other and what's the normal temperature in humans 98.6. There's no way you take a whole bunch of perfectly healthy humans and they're all going to have 98.6. There's going to be 98.6 and there'll be variability around it. And you could express that sort of you wind up having an average of 98.6. And some sort of term that denotes variability. There's variability. There's different values for something that winds up averaging out to something like this. And thus this critical question in a reductive world of thinking about science and the way fancy things work, what do you make of variability? What is variability about? An intrinsic in this whole world of no the starting stake, you know the mature state. You know how the starting state was. The rules allow you to extrapolate. It takes a blueprint. Intrinsic in there was an absolute clear opinion as to what variability is. Which is to say it's noise, it's junk in the system, it's a pain in the rear and it's stuff you want to get rid of. What is intrinsic in this whole reductive view is noise represents instrument error. Instrument error, instrument in the largest metaphorical sense. Instrument, somebody's observation to machinery. Variability represents noise, represents the system you use to measure stuff, to observe stuff, not working perfectly. It represents something you want to avoid.
Golden Arm Activity continued (16:46)
And what was also intrinsic in that reductive view is the surest way to avoid that is to become more reductive. The notion that the closer you look to a phenomenon, the more detail you see it with, the more you are looking at a more reduced level closer to the component part, the closer you will be to seeing what's actually going on. And as you look closer and closer, variability should disappear. Because the variability is just noise in the system. And if you're trying to measure people's body temperature by being up in a Zeppelin and looking at people with your sort of binoculars and trying to see if they're sweating or not and come up with an estimate then, that's going to be a lot more variable than if you now do something more reductive like put your hand on their forehead. Oh, do they feel hot or not? And thus there will be less variability. And even less if you now invent yourself a thermometer, this whole notion that as you get fancier techniques for examining a phenomenon, as you get techniques that allow you to be more and more reductive and look closer and closer, there will be less variability. Because sitting way down at the bottom of all this reductive processes, there is an iconic and absolute and idealized norm as to what the answer is. If you see anybody not having 98.6, it's because there's noise in your measurement systems, variability is noise, variability is something to get rid of, and the way to get rid of variability is to become more reductive. Variability is discrepancy from seeing what the actual true measure is. And that has been a driving force essentially on all of science in terms of the notion of inventing new ways to look at things more powerful microscopes, more powerful ways of measuring the levels of something rather than a blood stream, all of them built around the notion that the closer we look to the component parts, the closer we will be to seeing how the system really truly works and be able to finally see what truly is going on without the noise, because all noise is discrepancy from what is truly going on. So in that view, what you of course wind up having is an extension of that in beginning to think about how bodies work and biology and all that as you begin to look at that as an example of the very complicated system. And of course what you then have in a reductionist view is if you want to understand how the body works, you need to understand how the organs work. And if you want to understand how organs work, you need to understand how cells work and cells all the way down to molecules all the way down there and the notion that the closer you get to all the way down there, and once you understand things down at that level, the more accurate your answers will be, and all you do then is add the pieces together and out comes your whole body. So where does that begin to cause problems? The fact that the body simply can't work that way. A whole bunch of realms in which reductionism has to fail when you're looking at biological systems. One example of this, first one, and this is immediately jumping into neurobiology, this was classic work worked on by these two neurobiologists, anyone who was in bio-core, sort of went through me haranguing about how great these guys were. And what they found was a phenomenally clean, reductive world of how you extracted information from the visual world around you. I will spare you the details because it's not important, but what they basically showed was you could find individual cells in the retina that corresponded to individual neurons in the simplest part of the visual cortex. And between them, you had simple point-for-point reductive relationships. If you stimulated this one retinal cell, it's associated neuron in this part of the cortex would get excited and have an action potential. If you shift your electrode over a smidgen and stimulate the one right next to it, the neuron right next to this one is going to get stimulated. In other words, if you know the starting state, which receptors in the eye have been stimulated, you have 100% predictability of which neurons appear are going to fire and the converse know which ones fired here, and you have complete information about the starting state. And what they did was begin to build on that. They showed that insofar as that first layer of the cortex had this one-to-one correspondence with one cell here to one cell there, what did individual neurons know about in this simple part of the visual cortex, these neurons knew how to recognize dots. Each neuron could recognize a dot and one dot only, and was the only neuron that recognized it. This was a point-for-point reductive system and take all those individual little neuron component parts, each of which then knows something about one dot and put them together and you could begin to get some information about what just hit the eye. What they then showed was the next layer of the cortex, and again to simplify things as much as possible, what they began to see was you would now stimulate one of those retinal cells and one neuron in the first layer of cortex would get excited, nothing would happen in the second layer. Shift over, stimulate the next one over, next one over, nothing in the next part of the cortex, over, over, over, over, over, over, and then suddenly one of the neurons in the second cortex gets excited. If and only if you first stimulate this photoreceptor, followed by this, followed by this, followed by this, followed by this, what does that neuron know about, light moving in a straight line in this direction? That part of the cortex could extract the information from that first layer and put them together and get different sorts of information, and thus you would have another neuron there that would code for an angle, that was slightly different than the other one there, and then ones for different parts of the cortex, different parts of the visual system, and very long lines or very slow moving lights or things like that.
Reductive System (23:44)
What do neurons in that second layer know about? They know how to recognize straight lines. And you could see again this is a reductive system because you know the wiring that goes from one layer, from the eye to this layer to this layer, and thus if you know what's going on here, you can work backwards and know what's happening there and what's happening in the eye and same with the other direction, a point-for-point system where now you're beginning to extract a higher level, a hierarchy of analysis with the same exact reductionism. And just to then begin to show what they then went on to, again, this is very simplified, now you begin to get neurons here, one of them will respond to this line. Another will respond to this line, another will respond to this line if and only if these three neurons are firing simultaneously one neuron in the next layer of the visual cortex would fire. What do neurons there know about? Each one knows about a curve and one curve only. Same exact thing again, which is point-for-point reductionism. If you want to understand the system, you need to understand how every single neuron is wired to every next one in line, and once you've got that, all you need to know is what information, what activity is happening at any level, and you've got 100% knowledge of what will be going on here and here and here, a purely reductive system. Everybody loved this. This was the greatest stuff that happened in neurobiology. This was arguably the most important work in neurobiology between, like, 1950, 1975, the two of them got their Nobel Prize. People would have given them a dozen if they could have, because what had they just solved? They just showed how the brain processes sensory information, how it extracts information from the world around and turns it into complex bits of sensory information. Because it was completely obvious at this point what was going to happen, which was above this, there would be a layer that had neurons that could respond to a certain number of curves simultaneously. It can start seeing three dimensions, and then above that is one where the three dimensions are changing over time.
Grandmother Neuron (26:06)
It can detect movement of a three-dimensional object, and the notion was you would be able to just go up layer after layer of reductive point to list wiring, and way up on top you would have this super duper, a super duper layer of visual cortical processing, and all the way up on top, somewhere up there you would now have a neuron that knew one thing and one thing only, knew how to recognize your grandmother's face at this angle. And the notion would be that right next to it was another neuron that recognized your grandmother's face at this angle, and then one like this, and right behind were the rows of neurons recognizing her grandfather, and everybody decided this is it. Just take this world of human and visual stepwise extraction of information and keep going, and that's how the brain winds up recognizing faces. And meanwhile, people subsequently showed in the auditory cortex that the correspondence between one cochlear cell and hair cell there, recognizing a single note up to chords, up to okay. So now you go up enough layers there, and you will find a layer that were single neurons that will know your grandmother's favorite symphony. And that's it all the way up. You would eventually find neurons that were specialized in really complex sensory information, and all you had to do was just keep going like this in this purely reductive way, and you've got it up there on top. And people at the time actually did refer to these as grandmother neurons. The notion that enough layers up here, you would get neurons that responded to a really complex thing, and only to that, and it was the only neuron that responded to that point for point, one thing and one thing only, and that all you needed to do was just keep doing this, and you would eventually get neurons that recognized your grandmother. So right around the time that Hubel and Diesel got their third layer here, and this took them about 15 years, they decided to go study something else in the visual system, and that turned out to be at least as interesting as this stuff. But everybody else leapt in at that point to try to find the next layer, next layer, and next layer. And Hubel and Diesel had shown a remarkable bit of wisdom or intuition by bailing on the field at that point, because to this day hardly anybody has ever shown the existence of a grandmother neuron. They're all the way down there. They simply don't exist. Okay, that's a lie. They do exist, but there's very few of them. There's sparse coding. Occasionally you find neurons that show grandmother neuron-like processes, neurons a single neuron that will respond to a face, and only one type of face, way up there in many layers of visual cortical processing. There are some of those. And there was a paper in Nature some years ago, which was one of the weirdest papers I have ever seen. Really interesting in terms of what it showed, but weird from the standpoint of what were these folks thinking to actually test this? And they were recording from the very upper layers of visual cortex in monkey brains, and they found some neurons that responded. One neuron would respond only to a certain human face, encoding a grandmother type neuron. Here's the bizarre thing in that paper. What they discovered were neurons in the brains of these rhesus monkeys, where there would be a single grandmother-esque neuron, and what they found was a neuron that would respond to a picture of Jennifer Aniston. You think I'm being sarcastic. They found a Jennifer Aniston neuron, which would respond to a photograph of her at all sorts of different angles, a caricature, all of that. They went and showed the grandmother specificity of this by showing that, and this is in the paper, it did not respond to Julia Roberts. It did not respond to Brad Pitt. Perhaps very meaningfully with that, it did not respond to Jennifer Aniston and Brad Pitt in the same picture. And God knows what was going on with Angelina Jolie with that. The one other, okay, this shows how bizarre it is. The one other thing they discovered, this neuron would respond to, was a picture of the Sydney Opera House. What's up with that? So this is a two-knowledge, almost a perfect reductive gram over neuron, bizarre thing being, "What made these guys figure?" I know, let's go get a picture of Jennifer Aniston and show it to the recent monkey and see what happens. Where'd that come from? I recall there was not a whole lot of illuminating information in the methods section as to where those sort of pictures came from, but so there are some of these. Some of them do exist cases of what people in the field call sparse coding, where you only need a few neurons to recognize some really fancy things like Jennifer Aniston. Nonetheless, the vast, vast majority of the attempts to find grandmother neurons fail dismally for a very simple reason. Okay, how many neurons do you need where each one knows one dot and one dot only? You need the exact same number of neurons as the number of photoreceptors in your retina. How many neurons do you need in this layer that turns these into lines? Well, you need one that's good to respond to a line of this length and then one that will respond to this length and one of this length and one of that length and then one that's a slightly different angle.
You need like 10 times more neurons in this layer than this to be able to pull off that processing. How many neurons do you need in this layer, like 10-fold, 100-fold more than here, and how come you don't even have the next layer let alone grandmother neurons and a certain numbers because you run out of neurons. There's not enough neurons in the brain, let alone the visual cortex, to process stuff that way. You can't have a layer above that because you run out of neurons. In other words, there's not enough neurons in the brain to do face recognition and a point-for-point reductive manner. The system breaks down because of lack of enough numbers of things. And what people have been doing ever since then, what's become the dominant sort of approach in that field is an explicitly non-reductive approach, which is now looking at something called neural networks. Information, the really fancy complex information, like what everybody else from friends look like except for the anise de neuron, really complex information is not coded for in a single protein, a single synapse, a single neuron. It's coded for in patterns and patterns of activation across hundreds, thousands of neurons, networks that are interacting. So you have a complete crashing and burning of what up to here seem like the greatest demonstration of point-for-point reductive processing of sensory information, which just led you all the way up to grandmother neurons, and they basically don't exist because you run out of neurons at this point. You can't solve the problem of recognizing faces by using reductive component part neurobiology. Next domain where it falls apart as well. Okay, what do we have here? Either we've got a canal on Mars, or we've got a frost pattern on a window, or we've got a tree, or we've got a pattern of like lung branching, or some sort of... What do we have? We have a bifurcating system. And the characteristic of a bifurcating system is it is scale-free. On a certain level, if this is what a drainage line looks, you know, the Nile emptying out into sort of the Mediterranean, as seen by a satellite, and if you're looking at the dendrites on one single neuron with an appropriate microscope, if you look at it formally in terms of the branching pattern, you can't tell which one you are looking at. The complexity of the branching is scale-free. So it turns out some of the most important things we have in our bodies are bifurcating systems. All the branch points on neurons are bifurcating, and maybe what we'll post is some amazing pictures of bifurcating dendritic trees on neurons, and they're called dendritic trees, because they look just like trees, and when they get more complex for some reason, you are said to have increased their arborization, using terms straight out of triology. So neuronal complexity in terms of its branch points. Look at the circulatory system, and it's the same thing as a bifurcating system. You've got your descending aorta, which is ascending here, and then it splits into two and splits into two and splits into two, and it is a tree bifurcating into a whole bunch of little capillaries at the end. You look at the pulmonary system, and it is the exact same bifurcation coming down your trachea, which splits into two bronchos and splits into bronchioles, whatever, and it's the same exact thing. So you've got this theme of bifurcating systems throughout living systems in the body, and notice the difference in scale. If this is blood vessels, we are talking about millions of cells making up the blood vessel walls, but here we are seeing potentially the exact same complexity of branching in a neuron that's a single cell, independent of scale. You can adjust this complex branching, coming off of a single neuron, as the branching you're getting in a gazillion different capillaries in the tree of projections that comes from the same exact degree of complexity. So now we come to the problem here, which is, so how does the body code for that? How does the body give out the instructions as to how to make a bifurcating system? And this is where you immediately run into trouble. What's the world we're sort of oriented to? In a purely reductive world, there is some sort of set of rules telling an aorta that's growing like this, that there is some gene or genes which specify the point where this bifurcates, and this bifurcates, and it's two inches in diameter or something. Meanwhile, at a later point where it's about an ancient diameter, it bifurcates, it's a different gene or set of genes that specifies this bifurcation. And another type of gene that specifies the next one, and those are obviously going to be totally different sorts of genes than specifying the same branching patterns in the neuron. This is one cell. Here you're having to specify thousands of cells, and at what point do they stop adhering in a certain way? So you can make a split there, and you look at this, and suddenly you've got the same problem, which is there's not enough neurons that exist.
You Cant Code for the Extraneous Factors (37:28)
There's not enough genes in the genome that exist to be able to code this way. You can't code for bifurcating systems in a living organism that covers completely different scales from one cell up to zillions of cells. You can't code for it in a point-for-point reductive way where the points down at the bottom, the component parts, are individual genes. You can't code for recognizing your grandmother with simple reductive component parts of neurons. You can't code for the bifurcating systems in the body because these will bifurcate out to millions of capillaries, and there's only 20,000 genes. The reductive approach breaks down here as well. Reductive point-for-point approaches break down when you get to the cortex trying to do something fancy, like recognizing faces instead of dots. And it breaks down when you look at bifurcating systems that have to have a plan to split and then split and then split a million times to get all the capillaries out there. You can't code for it with a reductive approach. If there's not enough neurons, there's not enough genes. Next way in which reductionism fails. And the notion that if you know the starting state, you'll know the complex version and the other way around all of that. And we've already gotten this. We got this backwind in the molecular genetics lectures, which is the role of chance in these systems. All of that stuff we heard about, about sort of molecules vibrating brownie in motion and what that winds up doing is when cells split, it's going to be unequal distributions of mitochondria. It's going to be things that sheer chance is going to throw off your ability to deal with a reductive point-for-point system. You take identical twins and they're each at the like fertilized egg stage. And what you know in a reductive world is when it splits them to in this twin and splits it to in this twin, these are going to be, this cell is going to be identical with this one. This one identical with this all the way down to single molecules because this is a reductive world in terms of how they split. And what we know is by the time a cell splits for the first time, this split is going to distribute the mitochondria between these two differently than distributed between these two. Even at the first cell division, chance is throwing off this ability to know the starting state and know what the complex system is going to be. So reductionism breaks down there as well. The fact that chance plays a role in any of these systems. But mitochondria wind up dividing unequally the transcription factors. You remember all that stuff from there. Same exact thing with transposons, with genes jumping around. You throw in that randomizing chance element into there as well. You can't take the starting states and wind up building on it. An example in behavior, a guy named Ivan Chase, who does really interesting research with dominance behaviors, the emergence of dominance and different species. Okay, so you are going to have a colony of like ten fish. And what you do initially is each one of them is in a tank of their own. And you set up a round rob and tournament. You get every possible pairing of fish. You put them against each other. And you see which one is dominant of that pair. So you've done all of that. And you were able to derive a dominance hierarchy. Where the number one fish is the one that dominated all the other nine in those dyadic interactions. Number two dominated eight of them so on. It is simply a process, a syllogistic expansion to be able to then generate a dominance hierarchy. Pure, I know the starting state, every single dyad and what the outcome was, I can now predict what the dominance hierarchy is going to be when you put all the fish together. And what he sees of course is once you actually get the fish together in a social group, there is no resemblance whatsoever. The dyadic pairing dominance outcomes has zero predictability over what the actual dominance hierarchy is going to be like. Why should that be? Because chance plays a role as well. You are a fish and you've learned this transitivity stuff as fish are able to do, at least in Professor Fimmall's lab. And they are able to do if he defeats him and he defeats me, I better give that guy a subordinating gesture. We've now just fit together two of those pieces establishing the dyad beforehand. But what if the guy happens to be facing the other way and doesn't see him dominating him? And you've just lost the chance. Chance interactions, wind up driving the system, random movement of the animals and such. Wind up meaning knowing the starting states of the dominance relations of every single dyad gives you zero predictability of what the complex system is going to look like.
The Westernized Focus on Reductionism (42:43)
So what we have over and over here is amid this wonderful westernized focus on reductionism and this is going to tell us exactly how complex systems work. And now the starting state and the full one, we're seeing here over and over in biological systems ranging from behavior of entire organisms down to genes reductive systems break down. Because there's simply not enough pieces in there to explain complex function in a point for point reductive component part broken down, add them up together afterward way. And there's no way to deal with the fact that chance plays a role in biological systems. So what have we just gotten to here? 500 years or so into this reductive program. What we're seeing is if you kind of are interested in behavior or the brain or any of that stuff, what you've just discovered is the most interesting domains of brain function of genetic regulation. The most interesting stuff can't be regulated in a classical reductive way. It breaks down there, it can't be that way, it's got to be something else.
Chaotic Systems (43:53)
So what this will do now is transition us into this whole issue of chaotic systems. What happens when you have a system that is not reductive, where there is nonlinear non-additivity, where you suddenly have a very different picture. If a clock is broken, you take the pieces apart and you find the one tooth or one gear there that's missing and you fix that and you now are able to put the pieces back together in an additive way and you will affix the clock. A clock can be fixed using reductive point for point knowledge. Now you have a problem with something else. You have a cloud that doesn't rain enough during a drought. How are you going to figure out what's wrong? I know let's divide the cloud in half and then get better tools so we can divide each half into half and each half into half and eventually we'll get like one molecule worth of cloud and a gazillion of them. We understand how each one of them works and put it together and then we'll understand why there's a drought. It doesn't work that way. Reductive approaches can be used to fix clocks. Reductive approaches can't be used to understand why clouds don't rain and the whole point of all of chaos in these lectures here is when you look at the interesting complex biological systems, they're clouds. They're not clocks. You need a whole different explanatory system. Let's take a five minute break and we will transition to beginning to look at what chaoticism is about. Doctor of Science showing that westernized reductionism is really good for fairly uncomplicated systems breaking down at component parts. The whole world of the stuff we find interesting, it can't work because there's not enough component parts. There's not a blueprint that has enough elements in it and because of the role of chance. What this transitions us into are nonlinear systems, non additive systems where you break something down to its component parts and you study almost pieces and you put it back together again and it's going to be different. They've added up differently. You understand the starting point in a system and you are going to have no predictability about what the complex form is about because the pieces don't add up in a straight linear manner. Okay, what do I mean by this? As we begin to approach this, what is chaoticism about? Here we have a distinctive thing. We have a difference between two different ways in which things can be deterministic. Here's a -- no, you're just coming up with a number series. And there's a rule. There's a rule which determines what the next number is going to be in this sequence, which is just that one. This is a deterministic system. It is a periodic one in that knowing what the rule is and knowing which point you're at, someone could say, what's it going to be in 15 steps down the line there and you don't need to say, well, number one is going to be five, number two is going to be six, number, you don't need to do that, you recognize a periodicity that allows you to predict pieces way down the line simply by applying the same deterministic rule over and over.
Deterministic and Aperiodic (47:21)
This would be a system that's both deterministic and periodic. Now, in contrast, you can get a system which is deterministic but aperiodic, which is where we're heading very quickly. You have some system where there's a sequence of numbers, there's a sequence of places on a three-dimensional matrix, there's a sequence, and there are rules for how you go from each step to the next one. But the thing is, you can't just apply the same rule over and over. You cannot sit here and say, if we start at number five and give them what the rule is, I know what it's going to look like, ten of these down. The only way to know is to see what five produces as the first step, what that produces is the second step. You cannot see periodicity, you could not see patterns that repeat. The only way to know the complex form is to go stepwise and apply the rule over and over again, because the relationship between any one step here is going to be different from any other one.
Applied Science And Predictability
Straightforward Additive (48:34)
Here, it's always the same, each one is one higher. Straight forward additive, you just keep doing it over and over again. In an aperiodic system, you have rules, it's determinist, but the rules are such that the spaces, the difference with each step is not constant. The only way you could know what the number is going to be like, x number of rounds down is you got to do this. And then this and then this and then this, this is an aperiodic system. At any given one of these points, the rules exist for you to know what the next one is going to be. But the rules don't exist for you to know what the one to down is going to be unless you figure out what this one is. You've got to march through in that sort of way, it's aperiodic, there are no patterns that can be used over and over again. Third version is one that's like the people mistake for what I'm talking about here, which is a system which is non-determinist because there's randomness in there. And in that one, going from this one to the next one, there's no rule. It's totally random what the next number is going to be. And the one after that is totally random. In that one, you have no predictability, you're going to have to go every single step down the line, but it's not a determinist system. There's no set of rules that are being applied over and over again. The nature of this one does not specify the nature of that. It's not determinist in that way. That's not where we're going to be interested in here where randomness comes in. What all of these non-linear systems are about, these chaotic systems are ones where they are determinist. There's rules for how you go every step along the way, but the relationship given any given step is non-linear.
The Chaos Book (50:33)
They're not identical and thus the only way to know what's happening to down from here is to know what's happening one down. The only way to do that and thus by definition, this cannot be a system where knowing the starting state allows you to know the mature system without having to go through every single calculation. Knowing the mature state doesn't tell you what the starting state was unless you're willing to do all the back calculations because it's not reductive in that sense. Where would this begin to manifest itself? Into the Chaos book, and I think it was page 27 or so that you get the water wheel coming up for the first time, and go and look at this picture, obsess over it, understand what that page is about. Because it begins to show how these properties of non-linear a periodicity wind up producing chaotic systems. Okay, so you've got this water wheel and it's got these buckets here and they've got holes in the bottom and you can have a very simple steady state. You just put in a little bit of water such that the water is basically as soon as it gets here, it's running out, it's coming out to the same state. This never fills, the water wheel doesn't turn. Now you begin to fill up at a higher rate, and what that does is it's a little bit asymmetrical.
This is heavy enough that it now begins to push the wheel down, and as it's going down, this next one is getting filled, and this next one, and all the while it's emptying out. So constant input of water, a rate of things emptying, the wheel turns. It's possible to get a rate at which you're pouring water into the system where it will do precisely that for the rest of time. It will turn at a set speed, it is a steady state, it's an equilibrium state, it is stable, such that if you sit here right now and somebody tells you, under in this circumstance like this, the wheel is turning this fast in this direction with this force, you can sit there and you can tell them thus exactly what it will be doing, four thousand, seventy years from now on Tuesday afternoon. It is a periodic system, you don't have to sit there and go through every second between now and four thousand years from now, it is steady state, and you can apply a periodic, there's periodicity, there's a reductive quality to it. Now what you do is you put in the water with a little more force, and what begins to happen is the wheel turns faster, because it's filling up with water faster, so it's moving this way faster, that's great, that's totally logical, but at some point if you're doing that, there's going to be too little time for these buckets to empty out, they're going to start having more water when they're coming up on this side, because it's moving fast enough that they're not emptying, and at some point there's going to be enough water left here that it will suddenly change direction. Okay, it's possible if you get the water pressure just right that you can get a steady state pattern there, it will go around three times when you're putting in water with a speed, it will go around three times at this speed and with this force, and when it's gone around three point seven three times, it will change direction from one point seven turns, and then it will go three point seven times around, and once again it's a periodicity, it's simply a periodicity with two components to it, two changes of directions. First time you're going this way, and oops this fills up, so you have your first change of direction, and then at some point the balance is such that you get your second change of direction, and you start the process all over again. There's a pattern, a periodic pattern to it that just happens to have two components. You've doubled the number of components in it by putting more force in the system, but once you understand that rule, okay, at this speed, at this rate, with this force of water, it's going to change direction at this point, for this length of time, then it's going to change direction again. Knowing that, you can now sit here and be told exactly how full, how fast with what force, and you can now tell exactly what this water wheel is going to be doing 4,700 years from now. It is still a reductive periodic system. Now you put in the water with even more force, and what you begin to see is, as the wheel is moving fast enough, it will have sort of this first spin in this direction, and then it will change direction, and because the buckets are now emptying out that much slower compared to the rate at which the water is coming in, it will change direction once more, and once more back this way. And you're back to your starting point. In other words, now we have a completely periodic reductive system that has four components in it, four changes of directions, before you get back to exactly the starting point and do it all over again. You've simply gotten a more complex version of a totally predictable periodic system. And what you see is, as you put in more and more water force in there, you keep getting doubleings of your periods. You will now get spinning where it goes through eight changes of directions before it starts the exact thing over again, and doing that, and you can still predict 4,000 years from now, 1632, all of that, and throughout you can be graphing in a sort of way of representing it. This is the simple system here. That's the single rotation. Here's when you get a first doubling, and it does something like that. Here's when you get the point. You can represent it that way, and you see it is still, you let it keep running like this, and there will be the same periodicity, the same pattern that will go over and over for the rest of time.
Nonlinear Chaotic System (56:39)
It's still a reductive periodic system. It's just gotten more complicated. And then, somewhere in the doubling process, something happens. And the something that happens is, it becomes a non-linear chaotic system. As you increase the force on the system, the force here being, the force of water coming in there, at some point with the force of water increasing, it's going to stop this perfect periodic doubling of the components, and it's going to shift over to a chaotic pattern now. How do you define that as a chaotic pattern? It will shift over to a pattern of spinning this way in the back for a while, and it will generate a pattern which never repeats.
There's no periodicity anymore. It generates a pattern that is going to be infinitely different along the way, because you're putting that much force in the system. It has become chaotic. And what is obvious here is an implication, is knowing here gives you no predictive values, the ability of what's happening 4,000 years from now. The only way to know what's happening 4,000 years from now is to study what the wheel does for 4,000 years. You can't sit there and recognize a periodicity and just do it over again and again. And what the discovery of chaos was about was that in structured, reductive linear systems, when you increase the amount of force on it, there's a doubling and quadrupling in all of that. It just gets more complicated and reductive that there is a transition point where it suddenly becomes chaotic and the pattern never ever repeats, and there's no predictability. And sort of the founding generation of chaoticists, this is what they were showing with things like water wheels, where you can see the exact same thing. You have a cylinder, and what you're applying in here, and it's filled with water, and you're applying heat to the system. And what you begin to get after a while is convections or whatever it's going to. Stuff moves, and as you put in the heat of even more changes, direction, it's the same thing, and at some point when the heat gets high enough, it breaks into boiling. It breaks into turbulence, it breaks into a chaotic system where there is no periodicity, there is no repeating of these patterns. And an amazing insight by one of the first people in the field, this guy York, was that any time you see periodicity of an odd number, you've just guaranteed that you've entered chaotic terrain. That, as you call it, period three, as soon as you're going instead of a single period, double for whatever, as soon as you see the first evidence, as soon as any system like this begins to have three components before you go. So, this is what a chaotic system is about, which is you have a starting state, and as you increase the force on the system, the periodicity of the predictability breaks down, and eventually you get, as the critical thing, a pattern which never repeats. And thus, the only way to know what that pattern will be doing, x amount of time down the line, is to run the system from now until time x.
Applied Science (01:00:17)
There is no predictability from here as to what's happening at x. You've got to sit there and march through it, because it's an aperiodic system rather than one like this. So, what the entire sort of starting point for chaoticist was, that you get these non-linear systems, and people are noting them, mathematicians, physicists, whatever, in systems like that for a long time, and what would they do, right around the point that things would become chaotic, they would say, well, this is just getting perturbed by now, it's not functioning properly anymore, because it's not working in a linear, periodic manner. Something's wrong with the system, something along the lines of noise and variability, we will stop studying it up to that point. And if you say, we're going to stop studying it until it gets to that point, the last bit of periodicity, what do you come away with, a very distorted view that all the interesting things in the world work in reductive periodic systems? Because what you've just done is say, I'm totally disturbed by these non-linear chaotic things that happen at an extreme, so I'm going to decide they're just anomalies, and we're only going to study in this domain and reach the conclusion that the entire world works in this domain. Kinda like behavior geneticists who say, I want to understand the heritability of the trait, and I want to understand it very cleanly, so we're going to study it in only one environment.
Scientific Concepts And Examples
Forced Impact (01:01:54)
Because if you study in a bunch of environments, it gets noisy and variable and messy data, no it doesn't, it is showing you that the heritability is zilch, it's showing you that you've just artificially excluded your ability to see what's happening. And the founding generation, the chaoticist, took the stance that what you've got is all the interesting stuff about complex systems out there are all functioning out in the chaotic realm, and what science has been spending forever doing is looking the other way and pretending it's not there and restricting the studying of complex systems to just these first baby step domains of the periodic doubling most of the world is doing this, and most of science has worked very, very hard to ignore this. So once you get this, you begin to get some really interesting implications. So now you find a way, you get one of these chaotic systems, and you first study it when it is still in a nice straightforward periodic way. A little bit of water is coming in, and it's turning like this at a set speed and come back 4000 years from now on and still be doing the exact thing. It's a great periodic system, and you can come up with a graph of which direction it's turning, would be here or here and how fast, with what force, whatever, and you will come up with a single dot, which represents this rotating in this direction at this set speed and this is this point of stability, this point of complete predictability. A feature of a periodic system like this, when it's in this boring linear reductive way, is you can mess with it, and after a little bit of time, it will settle back into the same system. You briefly hold the water wheel, and that throws things off, and then you let it go, and it goes back to what it was doing, and it will take a little bit of time for it to go back to where it started. And the way of viewing this graphically is it's doing this forever, and now you go mess with it, you hold it, you turn off the water for a second, whatever, and for a while it does this, and it does this, and does this, and does this, and eventually it gets pulled back to this spot, it goes back to this point of stability of predictability, it is attracted to this point. And thus linear systems like this have attractors, something where when you mess with it, the system will equilibrate and go back to where it was attracted to the real solution to the problem. And if you're looking at it at any point here, and it's not here, because here instead, and here instead, and here instead, all that is is noise in the system, and you're in the process of getting rid of the noise back to the pure perfect state, the pure perfect description of how the system works. So now you look at what's going on when instead you've got it to the point of chaos, a chaotic system, and what you see is, okay let's assume that was where the attractor was, and what you see is when you're mapping the speed, the direction that it's turning, the force, all of that, it's doing this, and it will do this for a while, and we'll do this, and we'll reach that critical point where suddenly it changes direction, and we'll do this for a while, and then it will change direction again, and then this and this, and what you have is this butterfly wing pattern that became one of the iconic images in early chaos. What do you have here? You've got a description of how the system is working now once it's hit this chaoticism, it's not settling down into a repeating pattern. The fact that it is never here and staying there, that's the business that you could never predict, it is constantly oscillating, it is constantly chaotic. So now you ask, and you say, well that's pretty strange, because it's not actually touching this spot, but it just keeps going around it, it's clearly pulled to it, but in a very different sort of way than when you get a perturbation, and quickly it does this. This is being attracted back to this pure starting point, and here it never actually quite gets there, but it's sort of being pulled by it, what do we have here? We have a strange attractor, and that was the terminology that came into the field. A regular old attractor is one that would pull down to a single stable point, this is the predictable, utterly predictable state of the system right now. A strange attractor is one that has to do with the fact that it's going to oscillate like this, but it's never going to settle down into a single point. And suddenly there's a very different implication there, because here when you're not yet at this spot, what's this spot, its noise, its variability, and hang on, and it's going to go away because it will eventually reach the real answer. And systems with strange attractors, what do you make of the variability, it's not noise, it is the phenomenon.
Butterfly effect (01:07:21)
There is no absolute pure answer in there, there is not some idealized, the real correct answer, and you're just futzing around here, and if only you had better control in the system, you would eventually get it to look like this. This is a myth, this is imaginary. In complex systems there is no answer as to what you are supposed to be observing, and everything else is variable noise, this is the system itself. Critical expansion on that. So you're looking at this and you're saying, "Okay, what is this, this is measuring, you know, in whatever units of time, where the wheel is, what direction, what speed, all of that kind of stuff." It's a whole bunch of data points, and the data points will just keep doing this forever and ever, unpredictably. Wait a second, you say, at some point it's got to cross that, you know, here, this spot here, and at some point it's circling around, and will circle and come through exactly that point. And right now at that point, if you apply the same equations, the same determinist rules, right at that point, the next point should be this, and the next point should be this, and what have you just done? You're beginning to repeat yourself. You've just had periodicity, wait this really isn't chaotic, as soon as one, it hits the same point that was there previously, it suddenly should repeat the pattern a little bit again. It's periodic, it stopped being a chaotic system. How can this be? Because they've got to touch the same points, look at all that. And this was the next critical concept in the field, which is, you look at this point and maybe it's coordinates, you know, 6'3" in a standard graph or whatever, and that's what the coordinate was, the first time it was there. And now spinning around, it's just come there a second time, it's back in the same spot. Oh no, it's repeating, it isn't chaotic and unpredictable and going on for infinity, and it just fell apart, it doesn't really work this way, until you look a little bit closer. And you look a little bit closer, and it turns out, this is not 6'3", this coordinate was actually 3.7. And you look closer here, and this one was 3.8. In other words, it's not really in the exact same spot, it never gets to the same exact spot again. Wait a second, well we really measured it now, and in fact both of them are 3.7's, the exact same end look a little bit closer, in order of magnitude closer, and they'll be it, and take it out a million decimal places, and they still get it out. And they still look like they're in the exact same point, a million decimal places out, in terms of accuracy, and a million in one is where they will differ a little bit, and thus they're not in the same spot. Critical next concept with this, which is, if that's the case, and they're, you know, a million decimal places out there, they are differing by one decimal place way out there. What that means is the fact that one of them 4,000 digits out there is 8.2, and, no, this, and 8.3 and gazillion zeros before that, it means at some point this is going to function differently than this. This will produce a different spot than that. They won't go to the same next place because they're actually different numbers. And if a million digits out that tiny difference will change the functioning of that a million minus one digits out there, that will then potentially change the functioning of a million minus two digits out there, all the way up.
Scale free (01:11:19)
In other words, the consequences of this tiny little difference gets amplified. And this is what's called the butterfly effect. In the standard sort of jargon in the field, the butterfly effect is the fact that the way a butterfly flaps its wings in, you know, Korea will change the weather system in Indiana. And this is absolutely the case because of these butterfly effects, the very local consequences of something like a butterfly flapped its wings versus if it hadn't flapped its wings, what have you just done to air movement on the planet? You were a million digits out there and you've just changed that this very last digit went from three to four because the butterfly flapped its wings and that's going to cause a difference. One digit before that and one digit and these are already beginning to differ. And by the time it gets up to any level higher, it's differing enough that the next spot will differ as well. What are you doing? This is why the pattern could never repeat and why it's going to do this instead. Because on some level of magnification in a chaotic system like this, you never have the exact same location. The exact same coordinates occur a second time. Somewhere, however number of digits out there you need to go, the two of them will differ and that difference can potentially amplify upward in a butterfly effect. If you do it that way, you suddenly have a very different view which is all the way out of gazillion decimal places out there and they differ like this. This isn't noise in the system, this isn't variability, this is intrinsic to the system and the fact that this will now expand and amplify the consequences is why the whole system is unpredictable because of these butterfly effects. Okay, let me just think about, so the critical point here is in this strange attractor realm, not only is there no predictability, that's an important point. And the closer you look, you will still see the same degree of noise, variability, noise is not something that goes away, but almost philosophically this critical point in a system, a linear boring system with an attractor, this is the answer. In chaotic systems, there's no real answer and if you're out here, it doesn't mean that you're not correct, you're not quite there, there is no there there.
The notion that there is a solution at the center is a fabrication of the data oscillating around there, there is no correct idealized answer in there, this is the idealized answer which is a completely unpredictable system. Okay, what's intrinsic in this now is this fact that even though you now look in order of magnitude closer, there's still this variability stuff which can amplify as a butterfly effect up and make a huge difference, and you look in order of magnitude closer and there's still a butterfly effect potentially, and it doesn't matter how many digits you go down, how closely you look, how good your reductive tools are. The variability is still going to exist down there, and the way to describe this here is, thus this is a scale-free system. The nature of variability is exactly the same if you're looking at a whole number or if you're looking at a number taken out to three decimal places or three Google Flex places, and that sort of thing, that it's independent of how many steps down there you're examining the system, the fact that there will still be the difference and it can still butterfly its way up to make a difference there means that all of this stuff is scale-free, it doesn't matter how closely you are looking at it. In other words, the whole reductive philosophy of the closer you look, the better your measurement tools, the more variability is going to go away in a scale-free chaotic system regardless of what degree of reduction, of what degree of detail, you are looking at the system with the amount of noise is going to proportionally remain the same because it's not noise, it is the system. So you don't have this reductive notion that all we need to do is get better tools and look closer and closer and noise will go away because it is noise, this is the phenomenon at any scale you look at. And this introduces the notion, thus, of what a fractal is because a fractal is a complex pattern, a visual pattern, an equation that produces a pattern, things of that sort, where it is scale-free. The appearance of it is the same no matter what scale you look at, the complexity of it is the same no matter how close you look at it, the degree of variability is the same because it's not variability, it's intrinsic to the system. Okay, ways to define a fractal because this has become sort of a very trendy sort of subject and there's a number of different ways to think about it. Most formally, what a fractal is, is information that codes for a pattern where, for example, it can code for a pattern that is a line, and thus is a one-dimensional object, but where the line is moving around with such complexity with such an infinite amount of complexity because even if you look closer, it's going to be just as complex proportional to the closer and closer. In other words, this is going to be an infinitely long line in a finite space, which begins to make it sound kind of more eventually, this is more beginning to resemble a two-dimensional object. What a fractal is, is some object, some property that's a fraction of a dimension. If this goes on infinitely, it's a line, but it's really much more than a line, but it's not quite two-dimensional, it's 1.3 dimensions. It's a fractal, a fractal is a system that has fractional dimensions to it, where just the infinite amount of complexity, the closer you look, it's still going to be like this, means that this is a line like no other line, it's one that's infinitely long, packed in a finite space, it's more than a line, but it's not quite a two-dimensional, it's a fraction, it's a fraction of a dimension. That's the formal mathematical definition of a fractal. For our purposes, it's instead as well, no matter how close or how far away you look at it, the amount of variability is the same. Thus, we have absolutely a classic fractal system, if these are canals on Mars, or if these are the dendrites of a single neuron, no matter what dimension, what resolution you're looking at it with, the degree of complexity, the degree of variability remains proportionally constant, it's a fractal. Bifurcating systems are classic fractals, and the variability within the system is constant regardless of what scale you were looking at. And thus, it's telling you the variability isn't noise variability, it's instead what the system is actually about. So, so I'll look here. Okay, so, so you see these fractal properties, the circulatory system is a fractal with roughly the same degree of complexity as is the pulmonary system in its branch points, as in the dendrites of a single neuron, as are the branches of the tree, they're all fractals, they're complexity, their variability is independent of scale, this is what you begin to see.
Indicative issues (01:19:55)
In all these physiological systems, these fractals that have equivalent scales of complexity, that infinitely different, vastly different, scales of magnification. And as a hint of where we're heading on Friday, what that begins to tell you is, you can solve this problem of coding for these vastly bifurcating systems, where this is made of a billion cells, and this is a single cell, you can use some very similar cells, and all the rule has to be is scale free. We will see exactly what I mean by that on Friday, but this begins to solve the problem of, there's not enough genes in there. And what this introduces is the notion of there being fractal genes, genes that give instructions that are independent of scale. And we'll see lots more about that on Friday. So you've got these fractal systems all over the place, where the point over and over and over again is, the variability isn't variability noise, it is what the system is all about, there is no absolute state where the closer you get, the more it suddenly is going to seem clean and non-variable. An example of this, an example of this in the biological literature, and this was actually a study I did about 15 years ago with probably the most obsessive undergrads. I've met in all my years here at Stanford, which was great because the study was only doable because he was at his mind obsessive. Okay, here's what the study was about. I was thinking about, well, this chaos fractal stuff, amid all of us functioning with a standard model that, God, if only we could measure this down to the single cell level, then we'd really know what's happening because that's going to be so much better than blood values because that's noisy, working with that model of the more reductive you get, the cleaner the data are going to be. And then here's this whole other world of these nonlinear fractal systems saying it shouldn't work that way. So it struck me to do a study. And what I wanted to do was study the data generated in the scientific literature at different scales of reductionism and see what happens to the variability. And the point here was to make it as well controlled as possible, thought for some subject that was sort of bio 150 related and came up with an ocean that won't be interesting to look at what are the effects of testosterone on behavior. Just taking any sort of question out of this course, what are the effects, and you can answer that on the level of societies. Okay, people who are agriculturalists tend to have different testosterone levels than hunters, all of that. How does that affect things like behavior? You can ask that on the level of a single individual. What does a person's testosterone levels tell you about behavior? You can ask on an Oregon system level what's happening to blood pressure throughout the body and cerebral oxygen delivery as a function system down to a single Oregon. What's happening to the brain down to a single cell molecule all the way down, you see the logic of it. So what we did, and I used we in the most parasitic way possible, what we did was to go to the literature, the scientific literature, and for a reason we picked a literature not a contemporary one at the time, but one that was ten years old. And we looked at every journal out there that we could come up with that ever had papers in the realm of that could be interpreted as the effects of testosterone on behavior. Up from anthropology journals comparisons between different groups down to people doing x-ray crystallography on testosterone receptors. And what this madman I had hanging out with me at that point did was go through every single one of those papers. And first classify it, is this an organismal one? Is this a multi-organism one? Is this a cellular or is this a subcellular all of that? And then measure how variable were the data in that study. This was a drag. Because what he had to do was, okay, so there would be some figure in one of these papers looking like this. And what this tells you is for this group, here's the average, and this is a measure of how much variability there was. And this tells you there was a lot more variability in this measure than this one all of that. You could come up with something to do not worry about the details here. Something called a coefficient of variation. Which is you ask how much variability is there relative to the total size of this. And thus what you will get is, say a circumstance, if this is 100 units high, and in this case this is 10 units high, and in this case this is 50 units high. In this case your coefficient of variation would be 50%. Your variance is half the size of the thing you're studying.
Coefficient of VariationExample (01:25:05)
In this case coefficient of variation would only be 10%. It's much less noisy data. So what he did was his little ruler there, and the next three and a half years with nothing else to do, he went through these hundreds of papers. And for every single figure he measured what was the mean, and what was the error bar in every single finger. And thus what was the coefficient of variation for that piece of info of data, for that figure, for that entire paper that would have 11D different bars of data in there. And he's measuring the way and going mad from this. And eventually what he could then do was stick in the average coefficient of variation in all of the papers in the organismal category. And all the papers in the cellular category and all the way down. Reductive science, what's the prediction? As we go from the big organismal papers all the way down to the subcellular submolecular ones, the noise, the variability, the coefficient of variation should be decreasing as you get more reductive. That would be the traditional interpretation. The chaotic fractal interpretation would be, it's not noise, it's not noise that you want to get rid of with better tools. It is intrinsic, I'm going to leave there, oscillatory stuff, which is the system rather than the discrepancy from the system. It would predict that the relative amount of noise, the variability, the coefficient of variation shouldn't be trending towards decreasing. There shouldn't really be a relationship between what level you were examining, the phenomenon and the amount of variability. So an insane amount of work later, this was his, like what he spent the early 1990s on, producing this one figure here. This was it, this was if he wept with pride and happiness when we finally saw this going from, this is the coefficient of variation on all the data and all the papers that year that were at the organismal level. About an 18% coefficient of variation. Organ system, single organ, multicellular, single cell, subcellular, is there a trend towards variability decreasing? Absolutely not. It's not going anywhere. It's remaining fairly constant. Looking over scales of magnification, ranging from societies down to crystallography on single molecules, the data don't get cleaner, they don't get less variable because it's a fraction. One additional possibility there was that part of what was going in was you're looking at the entire literature in that year and we all know some of those papers are going to be kind of garbage and not very good science. Maybe that's the noise in the system and there's enough noise that it swamps at every single one of these levels. Here was the advantage that we had been looking at papers published 10 years before. You could now see how many times that paper was cited in the subsequent 10 years. In other words, you could find the papers that were considered by people in that field to be the really good ones versus the ones that were junk. Now they did the whole analysis only on the papers that were in the top 10 percentile of influence the best papers in the field and it wants it looking exactly like this. It's a fractal system as you get closer and closer to measuring what's really happening while down the level of single molecules, you don't get any cleaner data because it's a fractal system. It's a chaotic fractal system. So that was really interesting. What was even more interesting was after that when we tried to publish the paper. So we got it together and we wrote up this paper and we sent it off to one of my favorite neuroscience journals and after a couple of weeks the editor wrote back saying this is totally cool stuff. This is really interesting. This has really made me rethink some stuff. This is very stimulating stuff. I don't see what it has to do with our journal though so we really can't publish it. So then I sent it off to my favorite end of chronology journal and two weeks later back comes a letter from the editor saying whoa totally cool stuff. Come home for dinner and bring that piece of paper with you but I don't quite see what it has to do with our field and marching our way up and down all the different relevant journals and those different disciplines and each time they come back saying, whoa, isn't that interesting. I can't wait to tell my friend who is the social anthropologist or the Atre Christlor isn't it? But I don't see what it has to do with our particular field here and we couldn't get it published in a journal that specialized in any single one of these levels. So ultimately we published in this journal a sort of philosophical proceedings of medicine and biology as far as I can tell I was the first person under age 80 to ever publish a paper in that journal. It's the journal of somewhat demented senile elderly emeritus professors who are now writing their philosophical pieces because they're not generating data anymore. Like I broke the age barrier on that journal and they published in there and in the year since it has had like zero impact on the literature in terms of anybody quoting it in terms of anybody citing it. Actually that's not true. There's this mathematician in Moscow. This guy started writing to me about three months after the paper came out and he basically said this was the most wonderful thing he had ever read and I had transformed his life and he loved me and he's been writing about once every three weeks since. His English is not very good. Either he wants to adopt me or he wants me to adopt him. I'm not quite sure of that.
Challenges To Reductionism And Normativity
Fractals blow trashed science apart (01:30:52)
But as far as I get that's like the only person who noticed it there showing this point that this is but what does it have to do with our discipline. So what we see here is a pro-utifride. What fractals do is blow apart the notion that get even more reductive than they were back in the 1500s and will get better data. It doesn't get better because it's the same degree of variability because the variability is the, whoa where could go. The variability is the system rather than discrepancy from the system. Fractals show that as well. What we'll begin to see on Friday is how you can now use fractal systems to solve some of those problems of not enough neurons, not enough genes.
Hooray for us... (01:31:53)
Okay, so in first pass what did today seem to be about this endless trashing of reductive science and you know that's how you fix a broken clock but the world of really interesting things are like broken clouds and are non-linear aperiodic systems that are just as interesting and just as complex no matter what scale you look at them at. Hooray most of science makes no sense whatsoever. Hooray for us. We are the Vanguard. Okay, that's a drag because that really doesn't accomplish a whole lot because what there has to be is a substitution. So where is the actual predictability? Where is the actual insight coming from? And that's what Friday is about which is this whole field of complexity emergence. What we'll look out for there. But the last point here winds up being okay, okay, terrific. You've convinced me you've trashed linear additive periodic systems and 500 years worth of books of science need to be burned at the stake.
Is Reductionism Useful? (01:32:45)
Is classical reductionism good for anything? Yes, we already know it is. It's good for when clocks are broken. No, no, no, I mean is it good for anything in the realm of stuff that we're interested in and how like biology works and how behavior works. Any of that and what you get is it's very useful and very effective if you're not very picky, if you're not very precise. In example, there's some miserable disease out there that's wiping out people left and right and it's this viral disease and you're trying to figure out how to come up with a vaccine for it. And you finally come up with a vaccine and you start distributing it to people and what you see is exactly what Jonah saw was that it did wonders for preventing polio, but one in 560 kids instead would get a worst case of polio. So you could now ask a very reductive question which is, is this vaccine what happened in that one kid? And what we'll see at that level is if you're trying to ask that, that's not going to be if we understand what happened in that one kid, we're going to have to understand their individual cells all the way down and get better and better numbers because it's okay, we've just entered the world where it's actually a nonlinear chaotic system, where's the reduction is useful on the average, it's a whole lot better that kids got this vaccine than they didn't get the vaccine. You want reductive classical dead white male reductive predictable science, it's if you have a community of kids who get injected with this versus a community that doesn't, they're going to be healthier.
There Is Never a Penistrin (01:34:30)
Don't ask me about one particular individual, let around one particular individual's immune system, the reductionism breaks down there, but if fancy satisfying science for you counts as do they tend to be healthier than them, reduction is great, that is sufficient. Suppose your question is, well, is there a certain time of the year, what's the weather likely to be in January versus in June, you are never going to have reductive tools that can tell you on any particular day what the temperature is going to be three years from now, but if all you want to know is in general it's warmer in June than in January reductive tools that exist now are sufficient. And when you look at what people do in their research in the labs and places like this in my lab, all of that when you sit there and you say, whoa, we just learned when they're trying to like figure out the cure of some disease by finding the mutation. Whoa, that's really a reductive approach and we just learned that's gibberish. Whoa, everybody toss out what they do. It's actually quite useful because you're not very picky about what you want out of it. My lab, for example, studies, what happens in brains after there's a stroke and trying to figure out gene therapy stuff that you can do, and we can't tell you why one rat out of eight is not going to be helped by this procedure, whereas three rats are wonderfully so and oh, I know, let's look at their single molecules, that's not going to do it. And what we're going to do to humans somewhere down the line. Most of what the science research is about and when you look at the labs around here and you look at the labs you work in, if those of you, lots of you, do research, it's reductionism is a perfectly good thing to use because you're not being too picky. You do not want to come up with an explanation for how every neuron and every developing grasshopper on Earth bifurcates at this point, you want to know in general somewhere around hours three to four after the egg starts or the grasshopper parents meet and fall in love or whatever it is that in general, that's when you begin to get differentiation here.
No Norm to Deviate From (01:36:39)
Your science is great. So as long as most of what we're asking is this sort of science where you just kind of need to have a general predictive sense reductionism is just fine.
Product Upfront (01:36:55)
But nonetheless, underneath all of it, when you really want to understand the systems, it's anything but reductionism and probably the most important philosophical point is when you look at these interesting complex systems, there is not a the answer. There is not a the solution to what is this water wheel is going to be doing. And thus, all of us who are out there, not quite matching the perfect one. It is not that we are being deviating from what the real answer, what the real norm is supposed to be. The variation is what it's supposed to be. All of the things that are interesting when you measure them and they look like this, it's not because they are failing to be what they're supposed to be and match the norm.