This episode of Stuff You Should Know is sponsored by Squarespace. Whether you need a landing page, a beautiful gallery of professional blogger and online store, it's all possible with the Squarespace website. Go to squarespace dot com and set your website apart. Welcome to Stuff you Should Know from House Stuff Works dot com. Hey, and welcome to the podcast. I'm Josh Clark with Charles W. Chuck Bryant, and there's Jerry over there. So this is Stuff you Should Know, the podcast about chaos theory. Like, uh, have you ever seen Event Horizon? I did not bad great movie? Are you crazy? I don't think it was great? Oh so imagine it it. I thought it was okay. It was like a love crafty and thing in our space. Loved it all right, I love crafted it. I liked it. Um. That's what I think of when I think of k US. You know, there's that one part where they kind of give you like a glimpse behind, like the dimension that this action is taking place in, to see the chaos underneath, and you should check that out again. I think about Jurassic Park and Jeff Goldblum as as the creep. Dr Malcolm explaining chaos in the little auto driving suv or whatever that was. Yeah, that's what it was called in the script, the auto driving suv scene. Yeah, and you know what, he actually rewatched that scene and it confirmed two things. One is that he uh, he actually did a pretty decent job for a Hollywood movie with a very rudimentary explanation of chaos. Um, and you watched it for this Yeah, yeah, just that scene. And then it also confirmed of what a creep that character was. Yeah, if you watched that scene, he's like, you know, he's all gross and flirty with her right in front of her ex but there's just you know, he's talking to her. I didn't even notice this at first. He like he just like touches her hair out of nowhere for no reason. He's just talking to her and he just like grabs her hair and touches it. And I'm like, what a creep. I know, if you look closely, you can see the hormones emerging through his chest hair. Yeah, and I love Jeff Goldblum. It's not a reflection on him. He was basically doing Jeff Goldblum. Well that's what Yeah, sure he's Jeff Goldblum, but I don't think that's how in the manner in which he speaks. But I don't think he's a creep, do you. Wow, I've got nothing against Jeff gold Okay, I think he's a I think he's doing Jeff Goldblum. It was also a sign of the times, like if that movie were made today, doctor what was her name in the movie? Yeah, Dr Sutler would be like, it's very inappropriate to stroke my hair, like, don't touch me. But this was the nineties. Was eight No, it was nineties. It was the early mid ninety. Other thing, the book came out and in the book, uh Ian Malcolm, who's a Kayetician creep Kaetician? Right he um he he goes into even more depth about chaos. But that was I mean, that was the first time I ever heard of chaos theory was from Jurassic Parks, and um it really it was really misleading. I think the entire term chaos is very misleading as far as the general public goes as from what I researched in this this for this article. Well, yeah, I mean you hear the word chaos as an English speaker and you think frenetic and crazy, out of control. Yeah, and that's not what it means in terms of science like this, right. What it means, I guess we can say up front is is basically the idea that complex systems do not behave in very neat ways that we can easily grasp, understand, ander measure, right, and not even even simple systems don't. Sometimes it doesn't always have to be complex. But um, I want to give a shout out in addition to our own article to UH when you know, when it comes to stuff like this, the brain breaking stuff. For me, this is a breaker. You know how I always go to like blank blank for kids because it always helps. If there's a dinosaur mascot on the page, it's a sure thing we can understand it. But the best explanation for all this stuff that I found on the internet was from a website called a bar Um A B A R I. M. Publications, which turns out to be a website about biblical patterns and sandwiched in the middle, there is a really great, easy to understand UH series of pages on chaos there. So I was like, man, I get it now in a rudimentary way, right, Well, yeah, um, I think even a lot of people who deal with systems that display chaotic behavior, which I guess is to say basically all systems eventually under the right conditions, Um, don't necessarily understand chaos. Yeah, And they defined a complex system is specifically. It doesn't mean just like, oh it's complex, I mean it is, but specifically, Um, they define it in a way that helped me understand it's a system that has so much motion, so many elements that are in motion, moving parts. Yeah, that it takes like a computer to calculate all the possibilities of like what that could look like five minutes from now, ten years from now. So before computers came around, we before the quantum mechanical revolution, it was there's a lot more basic. It was like what comes up must come down, stuff like that. Let's talk about that, Chuckers, because when you're talking about chaos theory, it helps to understand how it revolutionized the universe by getting a clear picture of how we understood the universe leading up to the discovery of chaos. Right, So, prior to the um the scientific revolution, everybody was like, oh, well, it's it's God. The Earth is at the center of the universe and God is spinning everything around like a top right, it was all a theistic explanation. Then the scientific revolution happens and people start applying things like math and making like mathematical discoveries and and and figuring out that there are there's order. They're finding order in patterns and predictability to the universe if you can apply mathematics to it, specifically, if you can apply mathematics to the starting point, right, right, So if you can, if you can um figure out how a system works mathematically speaking, right, you can go in and plug in whatever coordinates you want to and watch it go. You can predict what what the outcomes can be and what this is the it's based on what at the time was a totally revolutionary idea um By Initially, I think the cart was the first one to kind of say, causing effect is a pretty big part of our universe, right. Yeah. It was sort of like where this is sixteen hundreds, where early science met philosophy. They kind of complimented one another as far as something that's we're talking about determinism, right, So that was the kind of the seeds of determinism. Was the scientific revolution, And like you said, where philosophy and science came together in the form of Descartes, right, and then Newton came along and we did a whole episode on him. Yeah, January of this year. That was a good one. It was really good. Like I think you said in that episode that there's possibly no scienists that changed the world more than Newton has. He's he's got legs. People shouted out others and email, but I'll just say he's at the near the top for sure with some other people. The Cream. Yeah, so Newton came along and Newton said that was his name, Isaac the Cream new anytime he don't to be like cream. Yeah, you just got creamed. I thought he was a boxer. He's a basketball player. He was much more well known as a boxer, but he definitely could dunk as a as a B baller. So, um man, that threw me off a little bit. Yeah, the Cream comes along and uh, he basically says, watch this, dude, this causing effect thing you're talking about, I can express it in quantifiable terms. And he comes up with all of these great laws and and basically sets the stage the foundation for science for the next three centuries or so. Yeah, these these laws that were so rock solid and powerful that scientists kind of got ahead of themselves a little and said we're done. Like with Newton's laws, we can predict, uh, we can predict everything if we have a good enough beginning accurate value to plug into his equations, and they weren't. I think there was a little hubrius and a little just excitement about like, well we figured it all out right that that you could take Newton's laws and if you had accurate enough measurements, uh, you could predict what the outcome would be of that system that you plug those measurements into using these formula. And at the time, a lot of this was like planetary, like, well, we know that these planets are here and they're moving and their orbiting, So if we know these things, we can plug it into an equation and we can figure out what it's going to be like in a hundred years exactly. And they figured out the basis of determinism is what we just said, that if you have accurate measurements, you can take those measurements and use them to predict um how a system is going to change over time using differential equations. Right, yeah, so this is what this is what Newton comes along and figures out that you can describe the uni us in these mathematical terms using differential equations and um like, you said there was a tremendous amount of hubris, and well, I think you said there's some hubris. I think there's a tremendous amount of hubris where science basically said, we've mastered the universe, We've uncovered the blueprint of the universe, and now we understand everything. It's just a matter now of getting our scientific measurements more and more and more exact. Because again, the hallmark of determinism is that if you have exact measurements, you can predict an outcome accurately, like the pool queue example or the pool table example. Right right, So if you've got a pool table, let's say you're playing some nine ball. You have that beautiful little diamond set up, you got your cue ball, you put that cue ball, and you you crack it with the queue, and if you are super accurate with your initial measurements, you should be able to mathematically plot out via angles where the balls will end up, right exactly, like you can say, this is what the table will look like after the break. If you know the force the angle, all those little variable temperature, if there's wind in the room, like the felt on the table, like everything. The more specific you are, the more accurate your end result will be. Right. And then one of the other hallmarks of determinism is that if you take those exact same initial conditions and do them again, the table, the pool table will look exactly the same after the break, which is pretty much impossible for like a human to do with their hands. Sure, but the idea at the time of science is that if you could build a perfect machine, sure that could recreate these conditions, it will happen the same way every time. Right, And this, I mean this led to they had hubris, but you could understand it when like literally in two people predicted Neptune would exist within months, that would exist, but does exist. And this is not by looking up in the sky like they did it with math and they were right. So imagine in eighty when that happens, they're like, yeah, we kinda we've got the math down, so we're pretty much all knowing well. Plus also, for the most part, these not just with Neptune, they were finding um that this stuff really panned out. It held true for everything from um you know, the investigation into electricity to new chemical reactions and understanding those and it it laid the scientific revolution, laid the basis for the industrial revolution, and just the change that came out of the world like that. It definitely there. It is understandable how science kind of was like we got it all figured out well, and like you said, they even Galileo was smart enough to know there's uncertainty in these measurements, like the precision is key. So they spent what does the article say, a lot of the much of an enth and twenty century just trying to build better instrumentation to get more and more smaller and smaller and more precise measurements. Right, That was like basically the goal of it, right, Yeah, which was the right direction. That's like exactly what they should have been doing. The problem is there, Like you said, Galileo knew that there was some sort of there there gonna be some flaws and measurement that we just didn't have those great scientific instruments yet. It's called the uncertainty principle. It's accuracy, right, But the idea is that if you have a good enough instruments, you can overcome that, and that the the more you shrink the um error in measuring the initial conditions, the more you're gonna shrink the error in the outcome. It would be proportionate. Right. They were correct. The thing is they were also aware but ignoring in a lot a lot of ways some outstanding problems, specifically something called the end body problem. You know what, I'm so excited about this. I need to take a break. I think that's a good idea. I need to go check out my end body in the bathroom. Okay, and we'll be back. All right, check, we're back. So there's some there's some issues right with determinism. There's some some weird problems out there that are saying like, hey, pay attention to me because I'm not sure determinism works. Uh. And one of the one is the end body problem. Yeah. How this came about was that was King Oscar number two of Sweet and Norway. Yeah, I don't want to leave out Norway both. Uh. He said, you know what, let's offer a prize to anyone who can prove the stability of the solar system something that has been stable for a long time before that and a lot of the most brilliant minds on planet Earth got together and tried to do this, uh with mathematical proofs, and no one could do it. Uh. And then a dude name Honoree. You gotta help me there with that, Oh, say, the whole thing very nice. He was French, believe it or not, and he was a mathematician, and he said, you know what, I'm not gonna look at this big picture of all the planets in the sun and all their orbits. You'd have to be a fool to try that. Sure, he said, I'm gonna shrink this down, Like we talked about shrinking that initial value, you know, and um, that initial condition. He shrunk it down. He said, I'm gonna look at just a couple of bodies orbiting one another, uh, with a common center of gravity. And I'm gonna look at this. And this was called the N body problem. Yeah, which was smart to do, because the more variables you factor into um a nonlinear equation like that, just the harder it's gonna be. So he shrunk it down. So the N body problem has to do with three or more celestial bodies orbiting one another. So Plank said, I'll just start with three. Smart and what he found from doing his equations for this this King Oscar. The sequel prize um was that shrinking the initial conditions um measurement or rate of error right, did not really shrink the the error in the outcome, which flies in the face of determinism. What he found was that just very very minute different is in the initial conditions fed into a system produced wildly different outcomes after a fairly short time. Yeah, like, let me just round off the mass of this planet at like the eighth decimal point, and you know who cares? Who cares at that point? Let me just round that one to a two, and that would throw everything off at a at a pretty high rate. And he said, wait a minute, I think this contest is in polsib right, He said, there is no way to prove prove, to prove the stability of the Solar system, because he just uncovered the idea that it's impossible for us to predict the the the rate of change among celestial bodies. Yeah, it's such a complex system. There are far too many variables that, uh, it's impossible to start with something so minute to get the equation whatever the sum that you want. Well, not only that, but the result, not only that and this is what really undermined determinism was that he figured out that you would have to have an infinitely precise measurement, which even if you build a perfect machine that could take the infinitely or a perfect machine that could take a measurement of like the the movement of a celestial body around another, you, it's literally impossible to get infinite and infinitely precise measurement, which means that we could never predict out to a certain degree the movement of the celestial bodies. Like he was saying, like, no, you you can't get You can't build a machine that that gets measurements enough that we can overcome this, like determinism is wrong, Like you can't just say, uh, we have the understanding to predict everything. There's a lot of stuff out there that we're not able to predict. And he uncovered it trying to figure out this end body problem. Yeah, and King Oscar the sequel said you win, Yeah, bring me another rack of lamb and uh, here's your prize. And he won by proving that it was impossible, which is pretty interesting. And they utterly and completely changed not just math, but like our our our understanding of the universe, and our understanding of our understanding of the universe, which is even more kind of earth shaking. Yeah, he discovered dynamical instability or chaos, and um, they didn't have supercomputers at the time, so it would be a little while, about seventy years at m I T until uh we could actually kind of feed these things into machines capable of plotting these things out in a way that we could see, which was really incredible. So there is this dude um seven years later, uh named um Edward Lawrence Lawrence. Yeah. Well, first of all, we should set the stage the reason this guy he was a meteorologist and scientists, right, not that those are not the same thing, right, He's a scientist who dabbled the meteorology. Here was a mathematician, Yeah, but he was really into meteorology because it was there was a weird juxtaposition at the time where we were sending people into outer space but we couldn't predict the weather. Yeah, and it was it was definitely a blot on the field of meteorology. People were like, do you guys know what you're doing? And and meteorologists are like, you have no idea how hard this is? Like yeah, we can predict it a couple of days out, but after that, it's just it's totally unpredictable. It drives as mad and it's not. It wasn't just there. Um, their reputations that were at stake, like people were losing their lives because of it, right, Yeah. N two there were two notorious storms, one on the East coast and one on the west. Uh, the ash Wednesday storm in the East and the big blow on the West that of a lot of people, cost hundreds of millions of dollars in damage. And people were like, you know, we need to be able to see these things coming a little more because it's a problem. And meteorologists were like, why did you do it then? So they thought the key was these big supercomputers. Remember the supercomputers. When they came out the big rooms full of hardware, it was amazing, and they were finally able to do like these incredible calculations that we could never do before. I know, they were able to like crunch sixty four bites a second. Yeah, we had the advocates and then the supercomputer. There was nothing in between. Um. I looked up the computer that Lawrence was working with the Whopper Royal McBee. What was the Whopper board games? Was it? It called the Whopper w a PR I can't believe they called it that. So the guy just nicknamed it Joshua. No, Joshua was the the software Falcon was the old man who designed all the stuff up and his son was Joshua. And that was the password. Oh, that was the password. Yeah, I guess I was too young to understand what a password was. Okay, you didn't even there weren't passwords at the time. Shouted it at the computer and they're like, okay, access granted. Yeah. Still that movie holds up. Does it really check it out? Yeah, it's still very very fun. Young Ali Sheety boy had a crush on her from that movie. She was great. Yeah. What else was she in recently? Wasn't she in something? Well? I mean she kind of went away for a while and then had her big comeback with the indie movie High Art, But that was a while ago. Has she been in anything else recently? Sure? I think I saw something and something recently and I didn't realize that was her. She looks familiar and I was like, oh, that's Ali Sheety. I don't know, all right, I could look it up, but I won't. It doesn't matter anyway. I still crushed on her. So the the Royal mcbeebe was not quite the whopper. You could actually sit down at it. The Royal McBee that's the name of that sounds like a hamburger too. It was by the Royal Typewriter Company. And they got into computers for a second. And this is the kind of computer that Lawrence was working with, and it was a huge deal, Like you were saying, Avacus supercomputer. Um. But it was still pretty dumb as far as what we have today is concerned. But it was enough that Lawrence is like Lawrence and his ILK, where like, finally we can start running models and actually predict the weather. Yeah, he started doing just that. He did. So he started off with UM, a computational model of twelve meteorological meteorological I like how you calculations, which is very basic because they're infinite meteorological calculations, probably depending to stay wrong again, like it sounds like you're about to say it wrong and then you pull it out at the last second. Maybe it's really impressive, but uh so that's very basic. But he wanted to start out you know with something at Hannibal. So he narrowed it down to twelve conditions, basically twelve calculations that had you know, temperature, wind, speed, pressure, stuff like that started forecasting weather. Uh. And then he said, you know, it'd be great if you could see this, So I'm gonna spit it into my wonder machine, the McWhopper Royal MCB, and I'm gonna get a print out so you can visualize what this looks like. So things were going well and you had this print out, and everyone was amazed because these these calculations never seemed to repeat themselves. He was making like, um, like like word art. You remember that. That was the first thing anybody did on a computer. Oh yeah, it was to make word art like a butterfly, right you would print out. Yeah. I never could do that. I couldn't either, Like you have to be able to visualize things spatially that you have to that right kind of brain for that, right or you have to be following a guy book that you have you ever seen? Me? You and everyone we know. Yeah, I love that movie. That's a great movie. Those little kids in there they were doing that. Oh yeah, yeah, forever, back and forth, poop. Well, I haven't. I haven't seen that since it came out. It's been a while. Oh you gotta see it again? Yeah, great movie. Ali's not in it. It's a Miranda July right, and she like wrote and directed to right. She did a great job. It's like it's one of those rare movies where like there's just the right amount of whimsy, because whimsy so easily overpowers everything else and becomes like, yeah, this is like the most perfectly balanced amount of like whimsy you've ever seen in a movie. Yeah, there's too much whimsy. I just like terrible Garden State. I just want to punch in the face terrible. Although I like Garden State, but I haven't seen it since it came out. It hasn't aged. Well, it's just when you look at it now, it's just so cute and whimsical. Oh yeah, it's like come on, yeah, boy, we're getting to a lot of movies today. Oh yeah, well we're stalling. We haven't even talked about butterfly Effect yet, which is coming and I'm dreading it. That's why I'm stalling. All right, So where were we? He was running his calculations, printing out his values so people could see it, and then he got a little lazy one day. In this output he noticed was interesting, so he said, you know, I'm gonna repeat this calculation see it again, but I'm gonna save time. I'm just gonna kind of pick up in the middle, and I'm not gonna input as many numbers, but I'm still using the same values, just I'm not going out to six decimal points. So the print out he had went to three decimal points. So he was working from the print out and didn't take into account that the computer accepted six decimal points, so he was just getting in three correct and expecting that the outcome would be the same, right, yes, but the outcome was way different. He went, whoa, whoa what? Yeah, he's like, what's going on here? It was a big deal. I mean, someone would have come up with this eventually, probably, yeah, but I sort of accidentally came upon it. It's neat that this guy did this because it changed his career. I think he went from emphasis on meteorology to an emphasis on chaos math to stud scientists basically. So look, I mean, the guy's got an attractor named after him, you know what I mean. Yeah, Well, let's get to that. So Lorenz starts looking at this and he's like, wait a minute, this is this is weird, this is worth investigating, and like uh, like uh, what was his name? Plankara? He said, I need fewer variables, So I'm not going to try to predict weather with these twelve differential equations that you have to take into Account'm just gonna take one aspect of weather called the rolling convection current, and I'm going to see how I can write it down in formula form. So a rolling convection current, chuck, is where you know, how the wind is created where air at the surface is heated and then starts to rise and suddenly cool air from higher above comes in to fill that that vacuum that's left, and that creates a rolling um or vertically based convection current. Okay you could. I would describe it as oven oven boiling water, a cup of coffee. Wherever there's a temperature differential based on a vertical alignment, you're going to have a rolling convection current. Okay, yeah, it sounds complex, but he just picked out one thing, basically, one condition, and this is the one he picked out. But had you seen my hands moving listeners, you would be like, oh, yeah, I know. So um He's like, okay, I can figure this out. So he comes up with three three formula that kind of describe a rolling invection current, and he starts trying to figure out how to describe this rolling convection current. Right, and so, like I said, he got this these three formula, which we're basically three variables that he calculated over time, and he plugged him in and he found three variables that changed over time. And he found that after a certain point, when you graph these things out, and since there're three, you graph them out on a three dimensional graph. So x, Y and Z. Again, he wanted to just be able to visualize this because it's easier for people to understand. He was a very visual guy. All of a sudden, it made this crazy graph that where the the line as it progressed forward through time, went all over the place. It went from this access to another access to the other axis, and it would spend some time over here, and then it would suddenly loop over to the other one, and it followed no rhyme or reason. It never retraced its path. And it was describing how a convey action current changes over time, right, and Lorenz is looking at this, he was expecting these three things to equalize and eventually form a line, because that's what determinism says, things are going to fall into a certain amount of equilibrium and just even out over time. That is not what he found now, And what he discovered was what pan quar A discovered, which was that some systems, even relatively simple systems, exhibit very complex, unpredictable behavior, which you could call chaos. Yeah. And when you say things were going all over like if you look at the graph, it it's not just lines going in straight lines bouncing all over the place randomly, like there was an order to it, but the lines were not on top of one another. Like let's say you draw a figure eight with your pencil, and then you continue drawing that figure eight, it's gonna slip outside those curves every time unless you're a robot. Um. And that's what it ended up looking like. Yeah, yeah, it never retraced the same path twice ever. Um. It had a lot of really surprising properties, and at the time it just fell completely outside the understanding of science, right. Yeah. Luckily this happened to Lawrence, who was curious enough to be like, what is going on here? And again he sat down and started to do the math and thinking about this and especially how it applied to the weather right, and he came up with something very famous. Yes, the butterfly effect. Yes, uh a, this thing kind of looked like butterfly wings a little bit, uh and be When he went to present his findings, he basically had the notion He's like, I'm gonna I'm gonna wile these people in the crowd in No, it's a conference that I'm going to and I'm gonna I'm gonna say something like, you know, the seagull flaps his wings and it starts a small turbulence that can one that can affect whether on the other side the world, the small little thing will just grow and grow in snowball and effective things. And he had a colleague goes like, seagull wings, that's nice, and he said, how about this, and this is the title. They ended up with, predictability Colin does the flap of a butterfly's wings in Brazil set off a tornado and Texas and everyone was like, WHOA mind's blown? Should we take a break? All right, We'll be right back, all right. So the lawns attractor. Uh, is that picture that he ended up with? The Laurens attractor? And this biblical pattern website that I found described attractors and strange attractors in a way that even dumb old me could understand. So if I may, he says, all right, here's the cycle of chaos. He said, Actually, I don't know who wrote this. A woman could have been a small child, could have been no of undetermined gender. I have no idea. So the gender neutral narrator, they said, he's sorry. I think about a town that has like ten thousand people living in it. To make that town work, you gotta have like a gas station, a grocery store, a library, um, whatever you need to sustain that town. So all these things are built, everyone's happy. You have equilibrium, he said. So that's great. Then let's say you build some Someone comes and build a factory on the outskirts of that town, and there's gonna be ten thousand more people living there and they don't go to church. Maybe so, uh, did I say church? They needed a church? Okay? I was just assuming this is what's called no. But you just have more people. So there's you need another gas station and another grocery store. Let's say, so they build all these things, and then you reach equilibrium. Again, it's maintained because you build all these other systems up. That equilibrium is called an attractor. Okay, so then he said it's said, they said he capital he the royal. He said, all right, now, let's say instead of that that factory being built, and you have those original tin bowls, and let's say three thousand those people just up and leave one day, and the grocery store guy says, well, there's only seven thousand people here. We need eight thousand people living here to to make a profit. So I'm shutting down this grocery store. Then all of a sudden, you have demand for groceries. So things go on a little while, and someone comes in and say, hey, this town needs a grocery store. They build a grocery store, they can't sustain, they shut down. Someone else comes along because the demand and it is this search for equilibrium, this dyna Well, you reach equal delibrium here and there as the store opens, periods of stability, periods of stability, and that dynamic equilibrium is called a strange attractor. So, an attractor is the state which a system settles on. Stranger attractor is the trajectory on which it never settles down but tries to reach the equilibrium with periods of stability. Does that make sense that Bible based explanation was dynamite. I understand it better than I did before, and I understood it okay before. That's great. Surely can add yeah, yeah, now you're gonna add to it. No, that's it, No, I mean like it. Yeah. An attractor is where if you raft something and eventually it reaches equilibrium, it's a regular attractor. If it never reaches equilibrium, is constantly trying to and has periods of stability. Strange attractor. I can't. I can't top that, alright, grocery store, small town. That was great. So um Lorenz, a strange attractor was named a Lorenz attractor named after him. Big deal. They weren't using the word chaos yet. No. But he published that paper about butterfly wings, right, the butterfly effect, and it coupled with his pictures the picture of a strange attractor, which is almost the aside from fractals, almost the the the um emblem or the logo for chaos theory. The Laurens attractor is um. It got attention off the bat. It wasn't like plan cares findings where he got neglected for seventy years. Almost immediately everybody was talking about this because again, what Lorenz had uncovered, which is the same thing that plan Care had uncovered, is that determinism is possibly based on an illusion that the universe isn't stable, that the universe isn't predictable, and that what we are seeing as stable and predictable are these little periods windows of stability that are found in strange attractor graphs, that that's what we think the order of the universe is, but that that is actually the abnormal aspect of the universe, and that instability unpredictability, as far as we're concerned, is the actual state of affairs in in nature. And I think as far as we're concerned, is a really important point to Chuck, because it doesn't mean that nature is unstable chaotic. It means that our picture of what we understand as order doesn't jibe with how the universe actually functions. It's just our understanding of it, and we're's just so um anthropocentric that you know, we we see it as chaos and disorder and something to be feared, when really it's just complexity that we don't have the capability of predicting after a certain degree. Yeah, I think that makes me feel a little better, because when you read stuff like this, you start to feel like, well, the Earth could just throw us all off of its face at any moment because it starts spinning so fast that gravity becomes undone. And I know that's not right. By the way, I've always loved that kind of science that shows we don't know anything. Like Robert Hume, who I know, I understand was a philosopher, but he was a philosopher scientist. Um. His whole jam was like causing effect as an illusion that like we all we it's it's just an assumption, like that if you drop a pencil, it will always fall down, and it's an illusion. And this is pretty um gravity understanding gravity. But he makes a good pet gravity when everyone's just floating around. Yeah, going this pencils got me wacky. But but the point was that you know, we we are. We base a lot of our assumptions um or a lot of stuff that we take as law are actually based on assumptions that are made from observations over time, and that we're just making predictions that causing effect as an illusion. I love that guy, and this this definitely supports that idea for sure. Yeah. Sorry, I'm I'm excited about chaos theory. Believe it. Well, I mean I like that I'm able to understand it and enough of a rudimentary way that I can talk about it at a dinner party. Well, thank your Bible website. Well, once you take the formulas out for people like us, we're like, okay, we can understand chaos. Then when somebody says, good, do a differential equation, just like, what a different equation? Right? All right? So earlier I said that chaos had not been used the word chaos to describe all this junk, uh, And that didn't happen until later on and well actually about ten years, you know, but it was kind of at the same time this other stuff was going on with rinds. Yeah, late sixties, early seventies. There was a guy named Steven Smile Uh fields metal recipients. So you know, he's good at math, and um, he describes something that we now know as the small horseshoe, and it goes a little something like this. Uh So, all right, take a piece of dough with like bread dough, and you smash it out into a big flat rectangle. So you're looking at that thing and you're like, boy, I hope this makes some good bread. This is gonna be so good. So then you do a little rosemary on it. Yeah maybe so yeah, and then um lick it before you bake it, so you know it's yours. No one else can happen. Uh So, you you have that flat rectangle of dough, you roll it up into a tube, and then you smash that down kind of flat, and then you bend that down to where it eventually looks like a horse shoe. So now how you take that horseshoe. You take another rectangle of dough and you throw that horseshoe onto that, and then you do the same thing. The smell horseshoe basically says you cannot predict where the two points of that horseshoe will end up. You can roll it a million times and they'll end up in a million different places, totally random, different places to totally random. You never know. It's like a box of chocolates. You never know what you're gonna get. You have to say it, and that became known. You have to say it. Oh what imitate Forrest Gumps? Now I can't do that. That's fine. He's not one. He's not in my repertoire. That's fine. Although I did see that again part of it recently. Does it hold up well? I mean, take out forty minutes of it and it would have been a better movie, like all of that coincidence stuff that that and he also did the smile t shirt like it was just too much, Like he really hammered it too much was the basis of the movie. I know. But see it again and I guarantee you, like an hour and a half into it, you'll be like, I get it. You know. It was a good Tom Hanks movie that was overlooked. Road to Perdition, Yeah, that was a good one. Great Sam Indees. Oh man, that guy is awesome. Yeah, Oh what is he gonna do? He might do something he did the James bo he did Skyfall. Yeah, yeah, I know he's gonna also that last one that wasn't so great. He's got a potential project coming up and he would be amazing for and I don't remember what it was. Did you see Revolutionary Road? Yes? God have it was just like, yeah, you want to jump off a bridge like every five minutes during that movie. That was hardcore. H he did that one too. Huh yeah, And don't see that if you're like engaged to be married or thinking about it, yeah, or if you're blue already. I'm yeah, just take a really good good mood and be like I'm sick of being in a good mood, sit down and watch Revolutionary Road. Watch Joe Versus of Volcano instead. Uh? Where was I smell? Horseshoe? Is what that's called? And? Um? That was he was the first person to actually use the word chaos. Oh he was? I think so? No? No, No, York was Tom York's dad. Yeah, you're right, he wasn't the first person York correct. But it's male's horseshoe. Illustrates a really good point, Chuck, is it Tom York's dad? No? But they're both British, sure, York. Actually one's Australian. No, they're British. Um. So those two points, which should which started out right by each other and then end up in two totally different places. That applies not just a bread dough, but also too, things like water molecules that are right next to each other at some point and then months later they're in two different oceans, even though you would assume that they would go through all the same motions and everything, but they're not. There's so many different variables with things like ocean currents that two water molecules that were once side by side end up in totally random different places. And that's part of chaos. It's basically chaos personified or chaos molecule fied. So we mentioned York. Where I was going with that was, Um, there was an Australian named Robert May and he was a population biologist. So he was using math to model how animal populations would change over time, giving certain starting conditions. Uh. So he started using uh these equations is differential equations, and he came up with a formula known as the logistic difference equation that basically enabled him to predict these animal populations pretty well. Yeah, and it was working pretty well for a while, but he noticed something really really weird, right, Yeah, he had this formula. Um, the logistic difference equation is the name of it. Sure, Okay, So we had of that formula, and he figured out that if you took our which in this case was the reproductive rate of a animal population, and you pushed it past three, the number three, so that meant that the average animal in this population of animals had three offspring in its lifetime or in a season, whatever. If you pushed the past three, all of a sudden, the number of the population would diverge. If you pushed it equal to three, actually or more, it would diverge, which is weird because a population of animals can't be two different numbers, you know, like that herd of antelope is not there's not thirty, but there's also forty five of them at the same time. That's called the superposition, and that has to do with quantum states, not herds of antelopes. That was kind of weird. And then he found if you pushed it a little further, if you made the productive rate like three point oh five seven or something like that. I think it was a different number, but you just tweaked it a little bit, not even to four. We're talking like millions of a of a of a degree um, all of a sudden it would turn into four so there'd be four different numbers for that was the animal population, and then would turn into sixteen, and then all of a sudden, after a certain point, it would turn into chaos. The number would be everything at once, all over the place, just totally random numbers that it oscillated between. But in all that chaos, there would be periods of stability. Right, you push it a little further, and all of a sudden it would just go to two again. But beyond that it didn't go back to the original two numbers. It went to another two. So if you looked at it on a graph, it went line divided into two, divided into four eight sixteen chaos, two four sixteen sixteen chaos, all before you even got to the number four of the reproductive right. And he was working with Mr York because he was a little confounded, so he was a mathematician buddy of his, James Yorke from the University of Maryland, so they worked together on this. In the nine they co authored a paper called Period three implies Chaos and man, finally somebody said the word. I kept thinking it was all these other people. Yeah, and the this this paper where they first debut the name chaos. Um. They they based it. UM. Tom York's Dead based it on Edward Lawrences paper. He was like, you know what, I have a feeling that has something to do with the Lawrens attractor. So that, um, that that provided chaos to the world. And it it was the basically the third the third time a scientist had said we don't understand the universe like we think we do, and determinism is based on an illusion of order, a really chaotic universe. And this, uh, this established chaos. It took off like a rocket. And the eighties and the nineties, you know, as you know from Jurassic Park, chaos was everything. Everybody's like, chaos, this is totally awesome. It's the new frontier science. And then it just went It just went away, And a lot of people said, well, it was a little overhyped, but I think more than anything, and I think this is kind of the current understanding of chaos because it didn't actually go away. It became a deeper and deeper field. As you'll see, Um, people mistook what chaos meant. It wasn't the a new the new type of science. It was a new understanding of the universe. It was saying like, yes, you can still use new Tony in physics, like don't throw everything out the window. You can still try and predict weather and still try and build more accurate instruments and get you know, decent results. But you can't with absolute perfection. Complex systems like determinism. The the ultimate goal of determinism is false. It can never be it can never be done because we can't have an infinitely precise measurement for every variable or any variable. Therefore, we can't predict these outcomes. Right, So you would expect science to be like, what's the point, what's the point of anything? Well, some some chaos people have said, no, this is this is great, this is good. We'll take this. Will take the universe as it is, rather than trying to force it into our pretty little equations and saying like if the ocean temperature is this at this time of year, uh, and the fish population is this at that time, then this is how many offspring this fish stole. This fish population is going to have. Um, say, okay, here is the fish population, here is the ocean temperature, here all these other variables. Let's feed it into a model and see what happens. Not this is going to happen. What happens instead? And this is kind of the understanding of chaos theory. Now. It's taking raw data, as much data as you can possibly get your hands on, as precise data as you could possibly get your hands on, and just feeding it into a model and seeing what patterns emerge. Rather than making assumptions, it's saying, what's the outcome? What comes out of this model? Yeah, And that's why, like when you see some things, like you know, fifty years ago they predicted this animal be its extinct and it's not. Well, it's because the variations were too complex they tried to predict. Uh. And that's why if you look at a ten day forecast, you, sir, are a fool. All right, Well, ten days from now says it's going to rain in the afternoon. Come on. But if you take if you took enough variables for weather for like a city, and fed it into a model of the weather for that city, you could find, uh, you could find a time when it was similar to what it is now, and you could conceivably make some assumptions based on that. You can say, well, actually we can we can predict a little further out than we think. But um, it's it's based on this, this theory, this understanding of chaos, of unpredictability, of not just not forcing nature into our formulas, but putting data into a model and seeing what comes out of it. Yeah, and then at the end of that you learn like when that animal is not extinct like you thought it would be, you go back and look at the original thing and you have a more accurate picture of how the you know, data could have been off slightly this one value, and then you have more buffalo than you think. Yeah, sure you got buffaloed by chaos. And we're not even getting into fractals. It's a whole other thing. And we did a whole other podcast in June about fractals and Mandel Bena, mandel Brett, mendel Brett, mandel Brett. Yeah, and go listen to that one and hear me clinging to the edge of a clift. Man. We we should end this, but first, um, I want to say, there is a really interesting article it's pretty understandable on Quanta magazine about a guy named George and he is a chaos theory dude who's got a whole lab and is applying it to real life. So it's a really good picture of chaos theory and action. Go check it out. Okay, Uh, if you want to know more about chaos theory, I hope your brain is not broken. Yeah, go take some LSD and look attical that. Um, you can type those words into how stuff works in the search bar any of those fractals LSD chaos. It'll bring up some good stuff. And since I said good stuff, it's time for a listener. Now, I'm gonna call this rare shout out get requests all the time. I bet I know which one is really dude his girlfriend? Yeah no, so far, so good. Hey, guys, just want to say I think you're doing a wonderful job with the show. To this date. My first time listening was during my first deployment. Uh yeah, when I listened to your list on famous and influential films and I was hooked after that. Since I came back State Side has spent many hours driving to and fro uh see my girlfriend, to my barracks, and I can happily say that they've been made all the more enjoyable by listening to you guys. Even my girlfriend Rachel has warmed up to you dudes, which was not a pleasant I'm sorry, which was a pleasant shock to me that she has told me repeatedly that she cannot listen to audiobooks because quote hearing people talk on the radio gives me a headache end quote. Anyway, I hope you guys continue to make awesome podcasts as I'm headed out on my next deployment. And if you could give a show it out to Rachel, I'm sure it would make her feel a little better that I got the pleasant people on the podcast to reaffirm how much I love her. That is John Rachel hanging there, John, be safe and thanks for listening. Yeah, man, thank you. That is a greed email. I love that one. Glad we don't give you a headache. Rachel. Yeah. For she listened to this son, and she's like, okay, oh yeah, everybody's gonna get a headache from this one. Like I came to hate the sound of my own voice from this one. You'll be right. 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