21. Chaos and Reductionism

At Stanford University, we're not going to work through right-wing behavior and marching left and instead we're going to try to come up with some ideas that will apply to everything we hear here and generally um. They are probably the most difficult lectures of the course, the most difficult material, partly because I'm not sure I fully understand what I'm talking about, but also because they are intrinsically about really different ways of thinking about things in the domain. of Science and that's one of the reasons I forced you to read this book of

chaos

and again, as I think I mentioned in the first lecture, this incites a subset of people to become passionate, you know, enthusiastic about the book, um, it incites another small subset to just the highest level of irritation that this was a sign and everyone else is vaguely baffled and somehow sees the point, but how come this book when I first read it and in my first introduction to the whole field was like this? the first book I read I finished and immediately started the first one again, because, like Where the Wild Things Are, in terms of influence, this was an incredibly challenging book in terms of questioning all the ways I think about a kind of science reductionist and Hopefully, it will do the same for you and as part of this, published, is your only assignment in the entire course, which just to make things easier will not be collected or examined, but what you need to do is that there is a set . exercise to generate something called cellular automata, uh, don't panic, but there's plenty of time to panic since you're going to be doing some of those on your own and everything I'm asking of you in terms of making sense of these exercises is to do not sleep between now and Friday spend all the time working on them do nothing else take occasional breaks to eat or go to the bathroom but other than that do nothing more than this between now and Friday and let's see how it goes everyone feels about it Friday is fine, so choose What we need to start with is trying to get a framework for the standard Western approach to understanding scientifically based systems about 400 after the falls of Rome, the collapse of the Roman Empire, entering an incredibly dark period in terms of ignorance in terms of the Middle Ages throughout Europe the level at which people did not understand how the world works the level at which people had lost the knowledge of previous times books disappeared philosophers disappeared the level of isolation just the intellectual isolation was phenomenal it was during that period it was as if 500 years before people had known the cure for cancer and AIDS and to be able to fly on their own and all that and somehow after From the fall of the Empire all that knowledge was lost, literacy went to the graves and this was a period that gave rise to words like have an audit have an audit on your finances make an oral argument before judges have hearings about something u something else before the court because this was all about talking about auditory transmission of information because no one could read anymore this was a period when there was no Western European language that had the word progress or ambition, these were not non-existent concepts in that time, total intellectual isolation, total social isolation during that time, the vast majority of people lived in small villages where you would go 50m away and people spoke a dialect that you couldn't understand, that degree of isolation is estimated that the average person would never moved more than 12 to 15 miles from where he was born in his entire life, incredible isolation and incredible ignorance, ultimately, about How do you explain quality in the world because all the information disappeared?

Then something changed dramatically in the year 1085, which is the first European Christian conquest of a major Islamic city, one of the main Mish, in this case Toledo in Spain Spain at the time it was Mish and known as Alhamra at that time, This was the first city to falter with Christian troops since Islam invaded there and this was basically a kind of second rate city. It was not an important center of Toledo, but simply because European forces had captured it. In that city something extraordinary happened that was within that city, there was a library with more books than existed in all of Christian Europe.

I put together this simple library and this kind of secluded Podunk town in the Boondock, a stream of... The mill library had more cumulative information than was available to all of Europe at the time and suddenly Europe was able to rediscover the philosophers Aristotle Plato all of that they came to rediscover logic they came to rediscover all the great works suddenly all of those flooded In Europe and the first beginnings of a kind of modern mentality about complexity began to emerge, people suddenly began to do things like be able to think in transitivity, transitivity with transitivity in a transitive way, um, where you would see that a is larger than b b is larger than C. and you had this amazing revolutionary notion that now you can know something about the relationship between a and C without having to compare them directly to each other.

It was kind of an amazing logical breakthrough. The syllogism suddenly appeared in Europe for the first time in centuries. ability of people to do things like say: If all things that shine have fire, then the stars shine and therefore the stars have fire. The syllogistic thinking that had completely disappeared and suddenly people started thinking in ways that had been lost for centuries and all of that came to an end. In a certain kind of emergence of what we would now call science, Thomas Aquinas came up with an amazing quote that summarized everything that was happening at the time and listed three things that God could not do; the first two were simply a kind of theology. things that God cannot sin God cannot make a copy of himself is the third that was simply shocking third even God cannot make a triangle with more than 180° and in that concept that Aquinas had just said if he encounters knowledge old and science wins and that was an absolute historic moment.

God could do anything but he still can't make a triangle with more than 180°. This was the beginning of a transformation of the world and this immediately had an impact on all kinds of domains, not just this one. a very vulgar one, that is, if something broke, you could fix it, that was a concept that was very, very rare back then, but the ability to construct events by observing overlapping fragments a crime has occurred and there is no individual who has observed all the crime happened, but one person saw what happened from points a to c one saw from B to d another from C to and suddenly realized that you can discover what happened by putting together these various bits of overlapping data, a completely revolutionary idea and completely transform the notion that how can you know if someone committed a crime before this period, what you would do is throw them into a river, for example, and if they sank and drowned, obviously, they had committed the crime. crime, good luck in terms of having discovered it. that was some good detective work, that's how you found out if someone had done something wrong or not, you set it on fire and if it burned, oh, they were obviously guilty and suddenly this concept doesn't just use facts, it doesn't just use observational data. , but you can derive what happened without any individual having seen everything, you can reconstruct the things superimposed on this was just a milestone, this just transformed everything and somewhere around this time what we would recognize as a species began to emerge of Proto bab steps of what to be modern science and after this period emerged what is basically the most important concept in all of science in the last 500 years, which is the idea of ​​

reductionism

defined 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 can understand the complex system

reductionism

that is at the center of everything we do in science and modern science. Centuries worth of the idea that complicated things can be explained by looking at their components. parts the smaller pieces that compose them and what is intrinsic to that is the concept of linearity of additivity. You have something complex and you break it down into its component parts and once you figure out how those component parts work, all you need to do is add them together and their complexity will increase linearly and you will produce the whole complex system.

This is Westernized reductionism and it came with a lot of corollaries that we now take for granted. The first is a reductive system where the component parts and how they work, just add them up and in a simple way that will produce your complex system. A sort of consequence of this is if you know the initial state of a system as defined here, if you know what the small component part is. If you know the initial state you will have 100% predictability of what the entire complex mature system will look like, so the initial state will allow you to predict what is coming next and related to that, if you know the complex system you will be able to discover What was the initial state?

The initial state that there is a fundamental relationship between simple building blocks and complex systems that come out the other end and this gave rise to something extraordinary which was the ability to extrapolate to be able to see the answer to Something in different iterations and use the same rules and applying them over and over again, what do I mean by this, all of a sudden, this amazing notion that okay, if X plus y = z, then you know that x + 1 + y is going to equal Z + 1 and x +? 2 all of that and the same exact principle would apply to some weird idiotic equation or something, it doesn't really matter what all this is, you know absolutely in advance simply from this matter of additivity of components that, whatever it is, it is Yes is going to be equal to Z + 1, you could get an answer to something without having to do the calculations again.

You could go through X plus whatever and you'll know it's going to be Z plus whatever without having to sit there and measure. If you can extrapolate, you can use reductive knowledge, the linearity that goes from this to this, you are still using the same rules that allow you to go from this to this, its applications are a purely reductive linear set of systems and this was revolutionary, so it's great. You don't have to do all the calculations every step of the way to be able to observe the initial state and therefore not know what the mature state is all about.

Look at the mature state. You know what the initial state was point by point. the relationship is great, finally, another characteristic of reductive systems like these is that the really sophisticated ones require blueprints, what do I mean by blueprints in this case? That already requires a notion of what the mature state is supposed to look like, which is intrinsic to what I just said. if you know the initial state, you will know the mature state, but the belief that in terms of quality control you must have some representation of what the mature state is supposed to be, a model for whether you are doing the right thing.

If you're really going to do something difficult and sophisticated in this reductive world, you have to have a roadmap at the beginning, you have to have a blueprint, you have to have something that already shows you what the result is. be when you apply these linear additive rules and the way you do it is determined by the model the instructions that are intrinsic in this this is all about Westernized reductionism an important additional component which is that you are going to measure something or another and you know, what is the normal temperature in humans 98.6, there is no way that you take a bunch of perfectly healthy humans and they are all 98.6, there will be 98.6 and there will be variability around them and you could express that kind of you end up having an average of 98.6 and some kind of term that denotes variability, there is variability, there are different values ​​for something that ends up averaging something like this and therefore this critical question in a reductionist world of thinking about science and form in which elegant things work, what do you do a variability, what is the variability and intrinsic in this whole world of know the initial state, do you know the mature state, do you know the mature state, did you know what the initial state was like, the rules allow you Extrapolate it, do you need a model, everything intrinsic?

There was an absolutely clear opinion about what variability is, that is, it's noise, it's junk in the system, it's a pain in the ass, and it's stuff you want to get rid of. What is intrinsic to this entire reductive view is that noise represents an instrument. instrument of error instrument of error in the broadest metaphorical sense instrument the observation of someone a The variability of machinery represents noise represents the system you use to measure things to observe things that do not work perfectly represents something you want to avoid and what also One way to avoid this is to become more reductionist is the notion that the closer you look at a phenomenon, the more details you will see, the more you look at a more reduced level, the closer to the parts that make it up. , the closer you will be to seeing what really happens. is happening and asAs you look closer and closer, the variability should go away because the variability is just noise in the system and if you're trying to measure people's body temperatures by being on a Zeppelin and looking at people with your binoculars and trying to see if are they sweating or not and make an estimate, then that will be much more variable than if you now did something more reductive like put your hand on their forehead, oh, do they feel hot or not?

So there will be less variability and even less if you now invent a thermometer, this whole notion that as you get more sophisticated techniques for examining a phenomenon, you get techniques that allow you to be more and more reductive and look at more and more of nearby, there will be less variability because, sitting at the bottom of all these reductive processes, there is an iconic, absolute, idealized norm as to what the answer is, if you see someone who is not 98.6 it is because there is 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 the discrepancy in seeing what the true true measurement is and that has been a strength essentially driving force of all science. in terms of the notion of inventing new ways of looking at things, more powerful microscopes, more powerful ways of measuring the levels of one thing or another in the bloodstream, all based on the notion that the closer we look at the component parts , the closer we will be. be seeing how the system actually works and being able to finally see what's really happening without the noise because all the noise is a discrepancy of what's actually happening, so from that point of view, what of course you end up having is an extension of that and start thinking about how similar bodies work and biology and all that as you start to look at that as an example of a very complicated system and of course what you have then in a reductionist view It's if you want to understand how the body works, you need to understand how the organs work and if you want to understand how the organs work you need to understand how the cells work and the cells down to the molecules and the notion that the closer you get to all the very down and once you understand things at that level, the purer, the more precise your answers will be and all you do then is add the pieces together and your whole body comes out, so where does that start to cause problems?

The fact that the body just can't function, it works that way, a lot of realms where reductionism has to fail when analyzing biological systems, an example of this first and this is an immediate jump to neurobiology, this It was a classic work carried out by these two neurobiologists. anyone who was in the bionucleus told me how cool these PA guys from the skillful and visel neuroscientists were. Absolute giants in the field from the 1950s to the 1960s, everyone thought they had figured out exactly how the cortex worked and what they found which was a phenomenally clean reductive world of how you extracted information from the visual world around you.

I'll spare you the details because it's not important, but what they basically showed was that you could find single cells in the retina that corresponded to single neurons in the simplest part of the visual cortex and between them you had simple points for reductive relations if you stimulated this retinal cell, its associated neuron in this part of the cortex would become excited and have an action potential if you moved your electrode over a bit and stimulated. the one that is right next to it, the neuron that is right next to it, will be stimulated; In other words, if you know the initial state, which receptors in the eye have been stimulated, you have 100% predictability of which neurons up here will fire and conversely, know which one fired here and you will have complete information about the initial state and What they did was they started to build on that, they showed that to the extent that that first layer of the cortex had this Ono, a correspondence with a cell here to a cell there, what did the individual neurons in this simple part of the cortex know? visual cortex?

These neurons knew how to recognize points. Each neuron could recognize a DOT and a single dot and was the only neuron that recognized it. This was a point for the reductive system and. take all those little component parts of individual neurons, each of which knows something about one point, and put them together and you can start to get information about what just came to the eye, which they then showed was the next layer of the cortex and again for simplicity. To the extent possible, what they began to see was that now you would stimulate one of those retinal cells and a neuron in the first layer of the cortex would be excited, nothing would happen in the second layer, you would change the stimulation of the next one. about the next about nothing. in the next part of the cortex again and again and then suddenly one of the neurons in the second cortex becomes excited if and only if you first stimulate this photoreceptor followed by this followed by this followed by this followed by this what Do you know that neuron that light moves in a straight line in this direction?

Which part of the cortex could extract the information from that first layer and put them together and get different types of information and so you would have another neuron there that would encode a The angle was slightly different, another one from time to time, for different parts of the CeX, different parts of the visual system and very long lines or lights that move very slowly or things like that. What do the neurons in that second second layer know? Do you 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 so if you know what's happening here, you can work backwards and know what's happening there. and what is happening in the eye and in the same way in the other direction, a forum point system where now you are starting to extract a higher level, a hierarchy of analysis, but exactly the same reductionism and then start to show what They continued again.

This is very simplified now you start to have 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 simultaneously activating a neuron in the next layer of the visual. the cortex would fire what the neurons there know, each one knows about one curve and only one curve, exactly the same thing again, which is the starting point of reductionism. If you want to understand the system, you need to understand how each neuron is connected to each next one. line and once you have that, all you need to know is what information, what activity is happening at any level and you have 100% knowledge of what is going to happen here and here and here.

A purely reductive system. Everyone loved it. This was the best thing that happened in neurobiology. This was possibly the most important work in neurobiology between 1950 and 1975. They both earned their Nobel Prize. People would have given them a dozen if they could, because what they had just solved simply showed how the brain works. processes information from sensors, how it extracts information from the world around it and turns it into complex chunks of sensory information because at this point it was completely obvious what was going to happen, and on top of this there would be a layer that had neurons that could respond to a certain number of curves simultaneously, you can start to see three dimensions and then, above there is one where the three dimensions change over time, you can detect the movement of a three-dimensional object and the idea was that you could go up layer after layer of reductive.

Dot list wiring and up, you would have this super duper layer of visual cortical processing and all the way up, somewhere up there, you would now have a neuron that knew one thing and only one thing knew how to recognize your grandmother's face. at this angle and the idea would be that right next to it there was another neuron that recognized your grandmother's face at this angle and then one like this and right behind it with the rows of neurons that recognized your grandfather and everyone decided that this was it, just take this world. from huil and visel gradual extraction of information and moving forward and that's how the brain ends up recognizing faces and meanwhile people later showed in the auditory cortex that correspondence between a clear cell, a hair cell, recognizing a single note, even strings, See you then. now go up enough layers there and you'll find the layer where the individual neurons will know your grandmother's favorite symphony and that's it, eventually you'll find neurons that were specialized for really complex sensory information and all you had to do was just keep going like this. this purely reductive way and you'll have it up there and people at the time actually referred to these as grandmother neurons, the notion that in enough layers up here you would get neurons that responded to a really complex process. thing and only that and it was the only neuron that responded to that point by point one thing and only one thing and that all you had to do was keep doing this and eventually you would get neurons that recognized your grandmother all over the place.

When Tubil and Visel got their third layer here and this took them about 15 years, they decided to go study something else in the visual system and it turned out to be at least as interesting as this, but everyone else jumped in at that point to try to find the next layer and the next layer and the next layer and puble and visel had shown a remarkable amount of wisdom or intuition in abandoning the field at that point because to this day almost no one has demonstrated the existence of a grandmother neuron throughout time. Down there they simply don't exist, okay, that's a lie, they do exist, but there are very few, there is scarce coding, from time to time you find neurons that show processes similar to grandmother's neurons, neurons, a single neuron that will respond to one face and only one type of face.

Up there, in many layers of visual cortical processing, there are some of those and a few years ago there was a nature article that was one of the strangest articles I've ever seen, really interesting in terms of what it showed, but strange since the point of view of What were these people thinking to try this? They were recording from the upper layers of the monkeys' visual cortex and brain and found some neurons that responded. A neuron would respond only to a certain human face and would encode a grandmother-type neuron. Here is the Something strange in that article what they discovered were neurons in the brains of these reesus monkeys where there would be a single grandmother xes neuron and what they found was a neuron that will respond to an image of Jennifer Aniston.

Do you think I'm being sarcastic? they found a Jennifer Aniston neuron that would respond to a photograph of her at all kinds of different angles, a caricature of it all. They went and showed Grandma the specificity of this by showing her that and this is in the document, she did not respond to Julia Roberts. he didn't respond to Brad Pit perhaps in a very significant way with that he didn't respond to Jennifer Aniston and Brad Pitt in the same photo and God knows what was happening with Angelina Jolie with that the other one is fine, this shows how strange the other one is What They discovered that this neuron would respond was an image of the Sydney Opera House.

What's up with that? So this is almost perfect reducing grandmother two-neuron knowledge. The strange thing was what made these guys think. I know, let's take a photo of Jennifer Aniston. and show it to Reese's monkey and see what happens, where she comes from. I remember there wasn't much insightful information in the method section about where those kinds of images came from, but there are some of these. There are cases of what people in the field call sparse coating where it only takes a few neurons to recognize some really sophisticated things like Jennifer Aniston; However, the vast majority of attempts to find granny neurons failed miserably for one very simple reason, okay?

Do you need neurons where each one knows one point and only one point? You need exactly the same number of neurons as the number of photoreceptors in your retina. How many neurons do you need in this layer that converts them into lines? Well, you need one that is you're going to respond to a line of this length and then one that's going to respond to this length and one of this length and one of that length and then one that has a slightly different angle and all you need is like 10 times more neurons in this layer than in this one to be able to carry out that processing, how many neurons do you need in this layer about 100 times more than here and why don't you even have the next layer and much less grandmother neurons and acerin numbers because you run out neurons?

There aren't enough neurons in the brain, let alone the visual cortex, to process things that way. You can't have a layer on top because you run out of neurons. In other words, there are not enough neurons in the brain to do facial recognition at one point. In a reductionist way, the system collapses due to the lack of a sufficient number of things and what thepeople have been doing since then, what has become the dominant kind of approach in that field is an explicitly non-reductive approach that now looks at something called neural network information. Really sophisticated and complex information, like everyone else on Friends, except the anista neuron.

Really complex information is not encoded in a single protein, a single synapse, a single neuron, it is encoded in patterns and patterns of firing across hundreds of thousands of neural networks that are interacting, so you have a complete crash and burn. of what until now seemed like the greatest demonstration of the reductive processing of sensory information from Point Foro that simply took you to grandma's neurons and basically they do not exist because you run out of neurons at this point the problem of recognizing faces cannot be solved using the reductive component neurobiology next domain where it also falls apart, okay, what do we have here?

We have a canal on Mars or we have a frost pattern on a window or we have a tree or we have a lung branching pattern or some kind of what we have, we have a bifurcation system and the characteristic of a b-division system is that it is scaleless. at a certain level if this is what a drainage line looks like, you know that the Nile flows into a kind of Mediterranean as seen by satellite and if you are looking at the dendrites of a single neuron with an appropriate microscope if you look at it formally in terms from the branching pattern, you can't tell which one you're looking at.

The complexity of branching is scaleless, so it turns out that some of the most important things we have in our bodies are branching systems. All neuron branch points are bifurcating. and maybe what we will post is some amazing images of dendritic trees branching into neurons and they are called dendritic trees because they look like trees and when they become more complex for some reason they are said to have increased their arborization using direct terms. Outside of the triology, the neural complexity in terms of its branching points looks at the circulatory system and it's the same as a bifurcated system, you have the descending aorta that ascends here and then it splits in two and it splits in two and it splits it. and it's a tree divided into a bunch of little capillaries at the end you look at the pulmonary system and it's exactly the same baton going down your trachea that divides into two Broncos and then it divides into bronchioles and it's exactly the same So you have this systems thing bifurcated into the living systems of the body and you notice the difference in scale, if it's blood vessels, we're talking about cell ions that make up the walls of the blood vessels, but here we're potentially looking at exactly the same thing. complexity of branching in a neuron that is a single scale-independent cell, you can have branches just as complex coming out of a single neuron as the branching you're getting in a zillion different capillaries in the projection tree comes from exactly the same degree. of complexity, so now we come to the problem here, which is how does the body code for that, how does the body give the instructions on how to make a branching system and this is where you immediately run into problems: what is a world?

In some ways we are oriented to a purely reductive world, there is some kind of set of rules that tells an aorta that it is growing so there is some gene or genes that specify the point where it bifurcates and this bifurcates and it is 2 inches long. diameter. or something like that, meanwhile, at a later point where it's about an inch in diameter it branches, it's a different gene or set of genes that specifies this branch and another type of gene that specifies the next one and obviously they will be totally different types of genes . Instead of specifying the same branching patterns in a neuron, it is a cell.

Here you have to specify thousands of cells and at what point they stop adhering in a certain way so you can do a division there and you look at this and all of a sudden. You have the same problem: there are not enough neurons, there are not enough genes in the genome to be able to code this way. Bifurcated systems cannot be encoded in a living organism that covers completely different scales than a cell. to billions of cells that you can't code in a reductive way where the dots at the bottom of the component parts are individual genes that you can't code to recognize your grandmother with simple reductive component parts of neurons that you can.

It does not code for the branching systems in the body because these will branch into millions of capillaries and there are only 20,000 genes. The reductive approach breaks down here as well. Point Forum's reductive approaches break down when you get down to the crust trying to do something sophisticated like recognize. faces instead of points and it breaks when you look at bifurcated systems that have to have a plan to split and then split and then split a million times to get all the capillaries out, you can't code it with a reductive approach. there are not enough neurons, there are not enough genes, the next way M reduction fails and the notion that if you know the initial state you will know the complex version and vice versa, all of that and we have already obtained this, we recover it when in the molecular genetics lectures what the role of chance is in these systems, all those things we hear about molecules vibrating in motion and what that ends up doing is that when cells divide, there will be unequal distributions of mitochondria.

For things like that, chance is going to ruin your ability to deal with a point-by-point reductive system. You take identical twins and each one is at the fertilized egg stage and what you know in a reductive world is when it divides. in two in this twin and divides it two in this twin these are going to be this cell is going to be identical to this one this one identifies with this one down to individual molecules because this is a reductive world in terms of how it divides and what we know is that when a cell divides for the first time, this division will distribute the mitochondria between these two differently than between these two, even in the first cell division, the possibility of losing this ability to know the initial state. and I know what the complex system will be, so the reduction is M and it breaks down there, and the fact that chance plays a role in any of these systems, the mitochondria end up dividing unequally, the transcription factors, remember all that there, exactly the same. thing with transposons with genes jumping around, add that element of random chance there too, you can't take the initial states and end up building on them an example and the behavior of a guy called Ivan Chase who does some really interesting research with dominance behaviors. emergence of dominance in different species, so you were going to have a colony of like 10 fish and what you do initially is each of them is in their own tank and you organize a free-for-all tournament in which you get all the possible pairs of fish, you put them against each other and see which one is dominant in that pair, so you did all that and you were able to derive a dominance hierarchy where fish number one is the one that dominated the other nine in those dietary interactions number two They dominated eight of them, so it is simply a process, a syllogistic expansion to then generate a hierarchy of pure dominance.

I know the initial state of each diet and what the result was. Now I can predict what the dominance hierarchy is. It's going to be when you put all the fish together and what he sees, of course, is that once you actually put the fish together in a social group, there's no resemblance, the dominance results from dietary pairing have no predictability about what it's going to be. the royal dominance hierarchy. like why should it be because Chance also plays a role, you're a fish and you've learned this transitivity thing since fish can do it at least in Professor Final's lab and they can do it if he defeats him and defeats him.

You better give that guy a nod of subordination. Now we just fit two of those pieces together by establishing the dyad beforehand, but what if the guy is looking the other way and doesn't see you dominating him and you just lost? the possibility that chance interactions end up driving the random movement of the animals' system and that ends up meaning that knowing the initial states of each diet's dominance relationships gives you zero predictability of what the complex system will look like, so what have? and here it is in the middle of this wonderful Westernized focus on reductionism and this will tell us exactly how complex systems work and we will know the initial state and we will know the complete state that we are seeing here over and over again in biological systems ranging from the behavior of entire organisms Down to genes, reductive systems break down because there simply aren't enough pieces there to explain a complex function. systems, so what have we arrived at here after 500 years or so in this reductive program?

What we're seeing is that if you're interested in behavior or the brain, any of those things, what you've just discovered are the most interesting domains of brain function of genetic regulation. The most interesting things can't be regulated in a classically reductive way. , it breaks down there, it can't be like that, it has to be something else, so what this will do now is transition into this whole topic of chaotic systems what happens when you have a system that is non-reductive where there is non-additivity not linear where suddenly you have a very different image if a watch breaks, you separate the pieces and find the missing tooth and gear? and you fix that and now you can put the pieces back together additively and you will have fixed the clock. a clock can be fixed using reductive knowledge of Points 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 find out what's wrong?

I know let's divide the cloud in half and then get better tools so we can divide each half in half and each half in half and eventually we will get like one. Cloud molecular verses and millions of them, we understand how each one of them works and we put them together and then we will understand why there is a drought. It doesn't work that way. Reductive approaches can be used to fix clocks. Reductive approaches can , so let's take a 5 minute break and move on to start looking at what chaotic is in productive science, showing that Westernized reductionism is really good for fairly simple systems that break down into parts, the whole world of things we encounter interesting.

It doesn't work because there aren't enough components, there isn't a plane that has enough elements and because of the role of chance and what this makes us are non-linear systems, non-additive systems where you break something down into its components and study it all. those pieces and you put them back together again and it will be different, they have added up differently, you understand the starting point in a system and you were not going to have predictability about what the complex shape is about because the pieces do not add up in one way. linear way okay? What do I mean by this as we start to get closer to this?

What is Chaotic ISM all about? Here we have a distinctive thing. We have a difference between two different ways things can be determined. CI. Here's a no. You are simply creating a series of numbers and there is a rule that determines what the next number in the sequence will be, which is simply adding one. This is a deterministic system, it is periodic in the sense of knowing what the number is. The rule is to know where you are, someone could say what it will be 15 steps down the line and you don't need to say well, number one will be five, number two will be six, number you. you don't need to do that, you recognize a periodicity that allows you to predict pieces in the future simply by applying the same deterministic rule over and over again, this would be a system that is both deterministic and periodic, now instead you can get a system which is deterministic but periodic AP, which is where we are heading very quickly.

You have a system where there is a sequence of numbers, there is a sequence of places in a three-dimensional Matrix, there is a sequence and there are rules about how to go from each step to the next, but the thing is that you can't just apply the same rule over and over again. again, you can't sit here and say if we start at number five and given what the rule is, I know what 10 of these are going to look like in the future. The only way to know is to see what produces five as a first step.

What it produces as a second step. You can't see the periodicity. You can't see repeating patterns. The only way to know the complex form is to go step by step and apply the rule over and over again. Again, because the relationship between any step here will be different from anyanother here, it is always the same, each one is one. More direct and superior additive, just keep doing it over and over again and a periodic system has rules, it is deterministic. but the rules are such that the spaces, the difference with each step is not constant. The only way to know what the number will be like X number of rounds down is to do this and then this and then this and then this.

This is an AP periodic system at any of these points, the rules exist for you to know what will be next, but the rules do not exist for you to know what will be one two down unless you find out what this is so you have that going that way is periodic AP there are no patterns that can be used over and over again the third version is one that people confuse with what I am talking about here which is a system that is not deterministic because there is randomness there and in that It goes from this to the next, there is no rule, it is totally random what the next number will be and the next is totally random and you have no predictability, you will have to take each step forward, but it is not a deterministic system, there is no set of rules that they are applied over and over again the nature of this does not specify the nature of that it is not deterministic in that way that is not what we will be interested in here where randomness comes into what all these non-linear systems are about these chaotic systems, they are those where they are deterministic, there are rules for how you progress each step of the way, but the relationship given at any given step is not linear, here they are not identical and therefore it is the only way to know what it is. what happens two down from here is knowing what is happening one down the only way to do it and therefore by definition this cannot be a system.

Knowing the initial state allows you to know the mature system without having to go through all the calculations and knowing the The mature state does not tell you what the initial state was unless you are willing to do all the back calculations because it is not reductive in that sense. Where would this begin to manifest? Well in the book of

chaos

and I think it was the page. 27 around the time the water wheel first appears and you go and look at this image, you become obsessed with it, you understand what that page is about because it starts to show how these properties of a non-linear periodicity end up producing chaotic systems, okay? ? you have this water wheel and these buckets here and they have holes in the bottom and you can have a very simple stable state: you just put some water in so that the water basically comes out as soon as it gets here it's running out it's coming out to the same state this it never fills the water wheel it doesn't spin now you start to fill at a higher rate and what that does is it's a little bit asymmetrical this is heavy enough that now it starts to push the wheel down and as it goes down the next is filled and the next and all the time it is emptied, so that a constant input of water at a rate of things that are emptied, the wheel rotates it is possible to obtain a speed at which you pour water back into the system where it will do just that for the rest of the time it will spin at a certain speed it is a stable state it is in the equilibrium state it is stable so that if you sit here right now and someone tells you the following Under these circumstances, the wheel spins so fast in This Direction with this Force, you can sit there and you can tell them exactly what it will be doing in 4,070 years, on Tuesday afternoon, it is a periodic system that you do not have.

Sitting there and going over every second from now until 4,000 years from now is a stationary state and you can apply a periodicity, there is a periodicity, there is a reductive quality, now what you do is you put in the water with a little more force and What starts to happen is the wheel spins faster because even though it's filling with water faster, it's moving this way faster and that's great, it's totally logical, but at some point, if you're doing that, There will be very little time for these buckets to empty. We found out that they're going to start getting more water when they come up this side because it's moving fast enough that it won't empty out and at some point there will be enough water here that it will suddenly change direction, okay?

It's possible that if you get the water pressure right, you can get a steady state pattern, it will go three times when you're putting water in with one speed, it will go three times at this speed with this force and when it's gone. about 3.73 times it will change direction for 1.7 turns and then it will make 3.7 turns and once again it is a periodicity, it is simply a periodicity with two components, two changes of direction the first time you go in this direction and Wow, this is filling up! Then you get your first change of direction and then at some point the balance is such that you get your second change of direction and start the process again.

There is a pattern, a periodic pattern, which turns out to have two components. We have doubled the number of components by putting more force into the system, but once you understand that rule, okay, at this speed at this rate with this force of water, it will change direction at this point for this period of time and then change of steering again knowing that now you can sit here and be told exactly how full, how fast, and how hard, and now you could tell exactly what this waterwheel is going to do in 4,700 years. It is still a reductive periodic system. into the water with even more force and what you start to see is that as the wheel moves fast enough it will have a sort of first turn in this direction and then it will change direction and because the wheel the hubs now they are emptying so much slower compared to the speed at which the water enters, it will change direction once again and once again it will return this way and return to its starting point.

In other words, we now have a completely periodic reductive system that has four components. changing directions before returning exactly to the starting point and doing it all over again, you have simply obtained a more complex version of a totally predictable periodic system and what you see is that as you apply more and more water force, you continue to get Al double its periods, it will now start to spin where it goes through eight changes of direction before exactly starting again and doing that and it can still predict 4000 years from now 16 32 all of that and throughout the process it can be graphing in a sort of way to represent it this is the simple system here is the single rotation here is when you get a first duplication and it does something like this here is when you get the point you can represent it that way and you see that it is still, you let it continue working like this and there will be the same periodicity, the same pattern that will repeat itself over and over again for the rest of time, is still a reductive periodic system, it has simply become more complicated and then somewhere in the duplication process something happens and What happens is that it becomes a non-linear chaotic system as the force on the system increases, the force here is the force of the water that enters there at some point and the force of the water increases, it will stop this perfect periodic doubling of the components. and now it's going to change into a chaotic pattern, how is that defined?

As a chaotic pattern it will change to a pattern spinning this way and then back again for a while and as it continues it will generate a pattern that never repeats, there is no periodicity. It just generates a pattern that will be infinitely different along the way because you are putting so much force into the system that it has become chaotic and what is obvious here as an implication is that knowing here does not give you the ability to predict values ​​of what what's going on. What will happen in 4,000 years, the only way to know what will happen in 4,000 years 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 and over again and what that means is the discovery of chaos. What it was about was that in structured reductive linear systems, when you increase the amount of force on them, it doubles and quadruples and all of that becomes more complicated and reductive, that there is a transition point where it suddenly becomes chaotic and the boss never ever. it repeats itself and there's no predictability and kind of a chaotic founding generation, 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 here and it's full of water and you're applying heat to the system and what you start to get after a while is convection or whatever it is that moves and as you put heat it changes direction even more, it's the same thing and at some point when the heat increases enough, it breaks into a boil, it breaks in turbulence, it breaks into a chaotic system where there is no periodicity, there is no repetition of these patterns and a surprising insight from one of the first people in the field, this York guy, was that every time you see the periodicity of an odd number, you have just guaranteed that you have entered a chaotic terrain that, as he called it, period 3 as soon as you go instead of a single period, double four, whatever, as soon as you see the first evidence, as soon as any system as this starts to have three components before the pattern repeats it is about to disappear in a chaotic ISM so this is what a chaotic system is all about i.e. you have an initial state and as you increase the strength about the system, the periodicity, the predictability is broken and eventually you get as a critical element a pattern that never repeats itself and therefore the only way to know what that pattern will do x amount of time in the future is to run the system from now until time x there is no predictability from here as to what it is. happening at , mathematicians, physicists, whatever in systems like that for a long time and what would they do right at the point where things would get chaotic, they would say well, this is already being disrupted, it's no longer working correctly because it's not working in a linear periodic manner. , something is wrong with the system something like noise and variability we will stop studying it until that point and if you say we are going to stop studying it until it reaches that point, the last part of the periodicity, what do you get with a very insightful answer distorted belief that all the interesting things in the world work on reductive periodic systems because what you just did is say that I'm totally disturbed by these nonlinear chaotic things that happen on one end, so I'm going to decide that they're just anomalies and they're just We're going to study in this domain and come to the conclusion that the whole world works in this domain, kind of like behavioral geneticists saying ooh, I want to understand the heritability of a trait and I want to understand it very clearly. so we are going to study it in a single environment because if you study in several environments you get noisy, variable and confusing data no, it is not like that, it is showing you that the heritability is zero, it is showing you that you just studied it. artificially excluded their ability to see what is really happening and the founding generation, the chaotic, took the position that what they have are all the interesting things about complex systems that exist, they all function eight in the chaotic realm and what science has been spending forever.

To do is to look the other way and pretend it's not there and restrict the study of complex systems to just these early domains of periodic duplication. Most of the world is doing this and most of science has worked very, very hard to ignore this, so once you understand this, it starts to have some really interesting implications, so now you find a way to get one of these chaotic systems and you study it first when it's still in a nice, direct, periodic form, a little bit of water goes in and it spins. so at a certain speed and come back in 4,000 years we will continue doing exactly the same: it is a large periodic system and you can generate a graph of which direction it would be rotating here or here and with what speed and with what force. and you will get a single point that represents this rotation in this direction at this set speed and this is this point of stability, this point of complete predictability, a characteristic of a periodic system like this when it is in this boring linear reductive form, are you ?

You can alter it and after a little time it will return to the same system. You hold the waterwheel briefly and that messes things up and then you let go and it goes back to what it was doing and it will take a while. A little bit of time for it to get back to where it started and one way to look at this graphically is that it's doing this forever and now you screw it up, hold it, turn off the water for a second and for a while it does it. this and does this and does this and does this and finally is attracted back to this point returns to this point stability of predictability is attracted to this point and so linear systems like this have attractors something that when you mess with With that the systemit will balance and return to where it was drawn by the real solution to the problem and if you look at it at any point here and it is not here because instead it is here and it is here in its place and here in its place all that is there is noise in the system and you are in the process of getting rid of the noise back to the perfect pure P state, the purely perfect description of how the system works, so now you look at what is happening when you have to do it instead.

The point of chaos is a chaotic system and what you see is okay, let's say it was where the tractor was and what you see is when you're mapping the speed, the direction it's turning, the force, all of that, it's doing this and we. We'll do this for a while and we'll do this and we'll get to that critical point where it suddenly changes direction and we'll do this for a while and then it changes direction again and then this and this and what you have is this butterfly wing pattern that becomes became one of the iconic images in the initial chaos.

What do you have here? You get an idea of ​​how the system is working now, once it gets to this chaotic ISM, it's not settling into a repeating pattern. that is never here and stays there that is the business that you could never predict is constantly oscillating constantly chaotic, so now you ask and say, well, that's quite strange because it's not actually touching the place, it just keeps going around, it's Of course it is attracted to it, but in a very different way than when you receive a disturbance and quickly. This is drawn back to this pure starting point and here it never actually gets there, but it's like it's drawn to it?

What do we have here? We have a strange attractor and that was the terminology that entered the field on a regular basis. The old attractor is one that would go down to a single stable point. This is the predictable and completely predictable state of the system at the moment. A strange attractor is one that has to do with the fact that it is going to oscillate like this but it is never going to stabilize. at a single point and suddenly there is a very different implication there because here, when you are not yet in this place, what is this place, its noise, its variability and hold on and it will go away because eventually you will get to the real answer and systems with strange attractors, what do you think about variability?

It is not noise, it is the phenomenon. There is no absolute and pure answer. There is no idealized answer, the true and correct one. And you're just hanging 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 about what you are supposed to be observing and everything else is variable noise this is the system itself critical expansion in that then you are looking at this and you say, okay, what is this? This is measuring, you know in any unit of time where the wheel is, what direction, what speed, all of that, it's a bunch of data points and the data points just keep doing this forever and ever unpredictably wait a second you say that at some point it has to cross you know here this place here and at some point it is going around and it will go around and it will pass exactly through that point and right now with that point if you apply the same equations the same deterministic rules right at that point the next point it should be this and the next point should be this and what did you just do are you starting to repeat yourself you just had periodicity wait this is really not like that chaotic as soon as one reaches the same point that was there previously suddenly it should repeat the pattern again it is periodic stops being a chaotic system, how can this be? because they have to touch the same points look at all that and This was the next critical concept in the field, which is if you look at this point and maybe it's the coordinates that you know, 63 on a standard graph or whatever, and that's the coordinate that was the first time it was there and now, turning, it has just arrived there. the second time it goes back to the same place oh no it's repeating it's not chaotic or unpredictable and it goes on ad infinitum and it just fell apart it doesn't really work that way until you look a little closer and you look a little closer and it turns out that this is not 6 and three, this coordinate was actually 3.7 and you look closer here and this one was 3.8 in other words, it's actually not in exactly the same place, it never gets to exactly the same place again, wait a second, Well.

We actually measure it now and in fact, they're both 3.7 exactly the same and we look a little bit closer, an order of magnitude closer, and they'll take it out a million decimal places and they still look like they're at the exact same point, a million to one decimal place in terms of precision and a million to one is where they will differ a bit and therefore are not in the same place. The next critical concept with this is if that's the case and there you are. Know a million decimals, they differ by one decimal, what that means is the fact that one of those 4,000 digits is 8.2 and no, this and 8, three and a gazillion zeros before that, it means at some point this . is going to work differently than this, this will produce a different place than that, they won't go to the same next place because they are actually different numbers and if you remove a million digits, that small difference will change how that million less works. one digit out there that will potentially change the functioning of a million minus two digits up there, in other words, the consequences of this small difference are amplified and this is what is called the butterfly effect and the kind of standard jargon in the field the butterfly effect is the fact that the way a butterfly flaps its wings in Korea will change the climate system in Indiana and this is absolutely the case because of these butterfly effects, the very local consequences of something like how a butterfly flapped its wings. versus if it hadn't flapped its wings, what did you just do with the movement of air on the planet?

You have a million digits out there and you just changed that this last digit went from 3 to four because the butterfly flapped its wings and that will cause a difference one digit before that and one digit and these are already starting to differ and when it gets to one level higher, it will be different enough that the next point will also differ. What are you doing? This is why the pattern could never repeat itself and why it will do this because at some level of increase in a chaotic system like this you never have exactly the same location, exactly the same coordinates occur a second time somewhere, no matter how many digits you need. the two will be different and that difference can potentially be amplified upwards in a butterfly effect.

If you do it that way, suddenly you have a very different view that has a million decimal places and they differ like that. There is no noise in the system, this is not variability, this is intrinsic to the system and the fact that this will now spread and amplify the consequences is why the entire system is unpredictable due to these butterfly effects. Well, let me think about the critical point. In this strange realm of TR, not only is there no predictability, that's an important point and the closer you look, you'll still see the same degree of noise variability.

Noise is not something that disappears, but almost philosophically this critical point in a system is linear. boring system with an attractor this is the answer in chaotic systems there is no real answer and if you are here it does not mean that you are not right you are not quite there there is no there is no the notion that there is a solution in the center is a invention of the data that oscillates there, there is no correct idealized answer there, this is the idealized answer, which is a completely unpredictable system. Well, what's intrinsic to this now is the fact that, even though it seems like an order now. magnitude closer there is still this variability that can be amplified like a butterfly effect and make a big difference and you look an order of magnitude closer and there is still a butterfly effect potentially and it doesn't matter how many digits you go down how close Look how good your tools are reductively, the variability will still exist there and the way to describe this here is, therefore, this is a scale-free system, the nature of the variability is exactly the same if you are looking at an integer. or if you're looking at a number pulled to three decimal places or three flexible places from Google and that kind of thing that's independent of how many steps down you're looking at the system, the fact that there will still be the difference and it can still work its way up to make a difference, that means that all of this is scale-free, no matter how closely you look at it, in other words, the whole reductive philosophy that the closer you look, the better your measurement tools will be.

Greater variability will disappear in a scale-free chaotic system, regardless of the degree of reduction or the degree of detail the system was looking at, the amount of noise will remain proportionally the same because it is not noise. That's the system, so don't have this reductionist notion that all we need to do is get better tools and look closer and closer and the noise will disappear because it's not noise, this is the phenomenon at whatever scale you look at it. and this introduces the notion of what a fractal is because a fractal is a complex pattern a visual pattern an equation that produces a pattern things of that type where it has no scale its appearance is the same no matter what scale you look at the complexity is the same no matter how closely you look at it the degree of variability is the same because it is not variability it is intrinsic to the system good ways to define a fractal because it has become a very fashionable topic and There are several different ways to think about it more formal.

What a fractal is is information that encodes a pattern where, for example, you can encode a pattern that is a line, a line, and therefore is a one-dimensional object, but where the line is moving with such complexity with a such an infinite amount of complexity because even if you look closer it will be just as proportionally complex, look closer and closer, in other words it will be an infinitely long line in a finite space that starts to make it sound more eventually this starts to look more like a two-dimensional object what a fractal is is some object some property that is a fraction of a dimension if this continues infinitely it is a line but in reality it is much more than a line but it is not completely two-dimensional, it has 1.3 dimensions, it is a fractal, a fractal is a system that has fractional dimensions, where the infinite amount of complexity, the closer you look at it, it will remain that way, means that this is a line like no other. line is one that has an infinite length in a finite space it is more than a line but it is not completely two-dimensional it is a fraction it is a fraction of a dimension that is the formal mathematical definition of a fractal for our purposes, however, neither is it en No matter how close or how far you look at it, the amount of variability is the same and therefore we have an absolutely classic fractal system, whether it is channels on Mars or whether it is the dendrites of a single neuron, regardless what dimension and without what. uh resolution you were looking at it with the degree of complexity the degree of variability remains proportionally constant it is a fraction the systems that bifurcate are classic fractals and the variability within the system is constant regardless of the scale you were looking at and therefore it tells you the variability is not and is not variability, it is rather what the system is really about, so I look here, well, so you can see these fractal properties, the circulatory system is a fractal with approximately the same degree of complexity as the pulmonary system at their branch points.

In the dendrites of a single neuron, such as the branches of a tree, they are all fractals, their complexity, their variability is independent of the scale, this is what is beginning to be seen in all these physiological systems, these fractals that have equivalent scales of complexity. infinitely different, very different magnifications and as a clue to where we're headed on Friday, what that begins to tell you is that you can solve this coding problem for these hugely bifurcated systems where they're made of a billion cells and this is a A single cell can use some very similar rules and all the rule has to be is scale free.

We'll see exactly what I mean by that on Friday, but this starts to solve the problem that there aren't enough genes there and what this introduces is the notion that there are fractal genes, genes that give instructions that are independent of scale, we'll see. a lot more on that on Friday, so we have these fractal systems all over the place where the point over and over and over again is variability. It's not variability noise, that's what the system is about, there is no absolute state that the closer you get to it, the more suddenly it will seem clean and unchanging.

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 college student I've ever met in all my years here at Stanford, which was cool because the study was only possible because he was crazy,obsessive, well, this is what the study was about. I was thinking about all this fractal chaos in the midst of all of us running on a standard model that God, if we could just measure this down to the single cell level, then we would really know what's going on because that's going to be so much better than blood. values ​​because it's noisy to work with that model - the more reductive you are, the cleaner the data will be and then here's this whole other world of these non-linear fractal systems.

It shouldn't work that way, so I thought of doing 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 with the variability and the point here was to make it as controlled as possible for some topic that was a kind of Bio 150 was related and The idea occurred to you that it would be interesting to look at what the effects of testosterone are on behavior, just taking any kind of question like that from this course, what are the effects and you can answer that at the level of societies, okay?

People who are farmers tend to have different testosterone levels than hunters. All of that, how does that affect things like behavior? You can ask that, at the level of a single individual, what do a person's testosterone levels tell you about behavior? You can ask at a system level, what's happening with blood pressure throughout the body and brain oxygen delivery as a function of the system, down to a single organ, what's happening to the brain, down to a single cell molecule, until the end, you see the logic of this, so what we did and I use it in the most parasitic way possible, what we did was go to the literature, the scientific literature, and for a reason we chose a literature which was not contemporary at the time, but was 10 years old and we looked at all the magazines.

So it occurred to us that there were once articles in the area of ​​what could be interpreted as the effects of testosterone on behavior, from comparisons of anthropology journals between different groups to people performing X-ray crystallography on testosterone receptors. Testosterone and what this madness. The man I was dating at the time was going through each of those documents and first classifying whether this is an organism is this one multiorganism is this a cellular is this a subcellular all that and then measure how variable If the data from that study were a pain because what they had to do was right, so there would be a number in one of these articles that would look like this and what this tells you is that for this group here is the average and this is a measure of how much variability there was and this tells you that there was a lot more variability in this measurement than in this one, all of that you could think of something and not worry about the details here, something called coefficient of variation, which is what you ask how much variability there is in relation to size total of this and therefore what you will get is, for example, the circumstance if this is 100 units high and in this case it is 10 units high and in this case it is 50 units high, in this case its coefficient of the variation would be 50%, your variance is half the size of what you are studying and in this case the coefficient of variation would only be 10%, it is much less noisy data, so what he did was his little rule there and the next three and A2. years with nothing else to do, he went through these hundreds of articles and for each figure he measured what was the mean and what was the error bar on each finger and therefore what was the coefficient of iation for that error for that piece of information. of data for that figure for that entire article that would have 110 different data bars in there and he's measuring and going crazy about this and eventually what he was able to do was include the average coefficient of variation across all the articles in the organisms category and all the articles in the cellular category and even reductive science what is the prediction as we go from the big articles on organisms to the submolecular and subcellular the noise the variability the coefficient of variation should be decreasing as you become 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's intrinsic beneath the oscillatory matter, which is the system rather than the discrepancy of the system would predict that the relative amount of noise, the variability, the coefficient of variation shouldn't tend to decrease, there really shouldn't be a relationship between the level at which you were examining the phenomenon and the amount of variability, so it's an incredible amount of work. later, this was his.

What happened in the early 1990s producing this figure here, this was it, we cried with pride and happiness when we finally saw that this was about this is the coefficient of variation of all the data and all the documents that year that were in the organism level around a coefficient of variation of 18% organ system a single organ multicellular unicellular subcellular is there a trend towards variability decreasing absolutely no, it is not going anywhere, it remains fairly constant looking at scales of increases ranging from societies to crystallography on individual molecules, the data does not become cleaner, it does not become less variable because it is a fractal system.

An additional possibility was that you would know some of what was going on if you were looking at all the literature from that year and you know, as we all know, some of those articles are kind of rubbish and not very good scientists, maybe that's the noise in the system and there is enough noise flooding it at each of these levels. This was the advantage we had. I had been looking at articles published 10 years earlier, I could now see how many times that article was cited in the next 10 years; in other words, I could find the articles that people in that field considered really good versus the ones that were garbage now they did all the analysis only on the articles that were in the top 10th percentile of influence, the best article in the field and it ends up looking exactly like that, it's a fractal system as you get closer and closer to measuring what's really happening. whereas at the level of individual molecules you don't get clearer data because it's a fractal system, it's a chaotic fractal system, so it was really interesting, what was even more interesting was after that, when we tried to publish the paper, so that we put it together. and we wrote this article and we submitted it to one of my favorite neuroscience journals and after a couple of weeks the editor responded saying this is totally cool stuff, this is really interesting, this has really made me rethink some things, this is very Exciting stuff, although I don't see what it has to do with our journal so we can't really publish it, so I sent it to my favorite Endocrinology journal and two weeks later I get a letter from the editor saying, "Wow, totally cool ".

They come to dinner and bring that piece of paper, but I don't quite see what it has to do with our field and going our way up and down all the different relevant journals and those different disciplines and every time they come back. "Say, wow, it's not that interesting. I can't wait to tell my friend who the social anthropologist or the X-ray crystallographer is. It's not that, but I don't see what it has to do with our particular field here and we could." I didn't publish it in a specialized journal at any of these levels, so we finally published it in this journal as a kind of philosophical proceedings of medicine and biology.

As far as I know, I was the first person under 80 to publish a The article in that magazine is the Diary of elderly and somewhat demented professors who are now writing their philosophical articles because they no longer generate data, as if I broke the barrier of age in that magazine and they published there and in the years since. it had zero impact on the literature in terms of anyone citing it in terms of anyone actually citing it that's not true there's a mathematician in Moscow this guy started writing to me about two months after the article came out and he basically said that This was the most wonderful thing I had ever read and I had transformed his life and he loved me and he has been writing about once every 3 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 C on that, but as far as I know, that's the only person who noticed that they're making this point, but what does it have to do with our discipline? So what we see here is an advantage for Friday. What do fractals do? Destroy the notion that they become even more reductive than in the 16th century and we will get better data. It doesn't get better because it's the same degree of variability because variability is whoa, where does variability go? system rather than system discrepancy, fractals show that also what we'll start to see on Friday is how fractal systems could now be used to solve some of those missing neurons and genes problems, okay, so in the first past what it looked like today It's about this endless destruction of reductionist science and you know that's how you fix a broken clock, but the world of really interesting things is like broken clouds and they are non-linear AP periodic systems that are just as interesting and complex regardless of the scale at which you dedicate yourself. look at them today most of science doesn't make any sense to us we are the Vanguard okay that's a drag because that doesn't really accomplish much because what there has to be is a substitution, so where is the real predictability? the real Insight comes from and that's what Friday is about, which is this whole emergence field of complexity that we'll see there, but the last point here ends up being okay, great, you've convinced me that you've trashed linear additive periodic systems and It is necessary to burn 500 years of science books at the stake.

Is classical reductionism good for anything? Yes, we already know. It's good for when watches break. No no. I mean, is it good for anything in the realm of things we need? I'm interested in how biology works and how behavior works. All that and what you get is that it is very useful and very effective if you are not very demanding if you are not very precise. An example that there is a miserable disease out there. killing people left and right and it's this viral disease and you're trying to figure out how to find a vaccine for it and you finally find a vaccine and you start distributing it to people and what you see is exactly what Jonah's opinion was that It did wonders to prevent polio, but one in every 560 children would suffer the worst case of polio, so now a very reductive question could be asked: this vaccine, what happened to that child and what will we see?

At that level, if you're trying to ask that's not going to be the case, if we understand what happened to that child, we're going to have to understand the individual cells of him all the way and get better and better numbers because that's okay. We have just entered a world where it is actually a non-linear chaotic system where reduction is useful on average. It is much better for children to receive this vaccine than not to receive the vaccine you want. Classic reductive, dead white man. Predictable reduction. The science is that if you have a community of children who are injected with this versus a community who are not, they are going to be healthier, don't ask me about a particular individual, let the immune system of a particular individual, reductionism collapses there, but If science is satisfactory to you, count, do you tend to be healthier than them?

The reduction is excellent, that's enough. Let's assume your question is a good one. Is there a certain time of year? What is the likely weather in January versus June? It will never go. have reducing tools that can tell you on any particular day what the temperature will be in 3 years, but if all you want to know is that it is generally warmer in June than in January, the reducing tools that exist now are sufficient and when Look at what people do in their research in laboratories and places like this in my laboratory, all that when you sit there and say wow, we just learned when they try to discover the cure for some disease by finding the mutation.

Wow, that's really a reductionist approach and we just learned that it's nonsense. Wow, everyone dismisses what he does. It's actually quite useful because you're not too picky about what you want out of it. My lab, for example, studies what happens in the brain after a stroke. and we're trying to figure out gene therapy things that can be done and we can't tell you why one rat in eight won't get help with this procedure, while three rats will do wonderfully, so, oh, I know, let's look at their molecules. Individuals, that is. I'm not going to do it, reductionism breaks, but it's perfectly fine at the level that's useful here, which is on average, is this a plausible thing that you might want to do to humans at some point later, most of whichdeals with scientific research and when? look at the labs around here and look at the labs you work in, those of you who do research, your reductionism is a perfectly good thing to use because you're not too picky about what you don't want to propose. an explanation of how every neuron and every developing grasshopper on Earth branches at this point, you want to know generally about 3 to 4 hours after the egg hatches or the grasshopper's parents meet and fall in love or whatever.

So that's generally when you start to get differentiation here, your science is great, as long as most of what we're asking is this kind of science where you just need to have a general predictive sense, reductionism is fine, but Anyway, deep down, when I really want to understand systems, it's anything but reductionism and probably the most important philosophical point is that when you look at these interesting complex systems, there is no answer, there is no solution to what this wheels. hydraulics is going to be doing and therefore, all of us who do not agree with the perfect answer are not that we are deviating from what is the real answer what is supposed to be the real norm the variation is what is supposed to be all the things that are interesting When you measure them and they look like that, it's not because they're not what they're supposed to be and they don't match the norm.

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