Modern Understanding of Chaos Theory

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What's in your wallet? Terms apply. See capital one dot com slash bank Capital one in A member FDIC. Hey everybody, Chuck here and welcome to our sciencey playlist. suuper excited about this one And I'm going to kick it off everybody with this episode on how Chaos Theory changed the universe Welcome to Stuff You should Know Ir from Houseuffworks. 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 a you ever seen a vvent horizon I did, Not bad. Great movie. Are you crazy? I't think it was great. Oh, it was so imaginative. I thought it was okay. It was like a love crafting thing in outer space. Yeah. Loved it. It was all right. I love crafted it. Yeah. I liked it U That's what I think of when I think of chaos. 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 Yeah to see the chaos underneath and I should check that out again I should. I think about Jurassic Park. And Jeff Gobblum as the creep Mr Malcolm explaining chaos Yeah in the the little auto driving SUV or whatever that was. Right. Yeah. That's why it was called in the script, the auto dririving SUV scene. Yeah. And you know what? I actually rewatched that scene and it confirmed two things. One is that he actually did a pretty decent job for a Hollywood movie a very rudimentary explanation of chaos. Yeah. And you watched it for this? Yeah Yeah, just that scene. Yeah. And then it also confirmed of what a creep that character was. Yeah. If you watch that scene, he's like You know, he was all gross and flirty with her right in front of herer ex. right But there's this, 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. Really? 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 Goldlum. 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 out in the manner in which he speaks, but I don't think he's a creep Do you Wow. I've got no nothing against Jeff Gold. Okay. I think he's a u I think he's doing Jeff Goldbun It was also a sign of the times. like if that movie were made today after u What was her name in the movie? Ellie Sattler, I think. Yeah, dor. Stler would be like, it's very inappropriate to stroke my hair, dude. Yeah. Like don't touch me. Right This was the nineties. nineties? free wheeling It was eight No it was nineties. It was the the early mid nineties, I think Yeah, ninety two, ninety three, ninety four. The book came out in nineteen ninety and in the book. Ian Malcolm, who's a ician. Yeah, a petician. Right. He u 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 Park. Yeah, me too, probably. And It really It was really misleading. I think the entire Term chaos It's very misleading as far as the general public goes 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 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 basically the idea that like systems Do not behave in very neat ways that we easily grasp, understand or measure Right, and not even Even simple systems don't sometimes. It doesn't always have to be complex. but I want to give a shout out in addition to our own article. Oh to you know, when it comes to stuff like this, the brain brereaking stuff for me. Man, this is a brainbreaker. You know, 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 barom ABA RIM publications turns out to be website about biblical patterns sandwiched in the middle there is a really great, easy to understand. series of pages on chaos there. Nice So I was like, manan, I get it now M in a rudimentary way. Right. Well, yeah, yeah I think even a lot of Pe who deal with systems that chaotic behavior, which I guess is to say basically all systems eventually under the right conditions. Yeah don't necessarily understand chaos. Yeah, and they define a complex system as specifically. It doesn't mean just like, oh, it's Complex I mean, it is. But specifically, they define it in a way that helped me understand. It's a system that has so much motion 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. Right So before computers came around we before the quantum mechanical revolion it was It was a lot more basic. It was like what comes up must come down L 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? Yeah So prior to the scientific revolution. everyverybody was like, oh, well, it's God The Eth is at the center of the universe and God is spinning everything around like a top, right? Yeah It was all a theistic explanation. Then the scientific revolution happens and people start applying things like math and making like mathematical discoveries and figuring out that they are Oder They're finding order in patterns and predictability to the universe.. If you can apply mathematics to it. Yes, specifically if you can apply mathematics to the starting point Right, rightight. So if you can if you can figure out how a system works, mathematically speaking, right? Yeah. You can go in and plug in whatever coordinates you want to Yeah and watch it go. You can predict what the outcome' going to be What this is is that it's based on What at the time was a totally revolutionary idea U by initially I think Cart was the first one to kind of say Cause and effect is a pretty big part of our universe, right? Yeah, it was sort of like where this is the sixteen hundreds where early science met philosophy. Right. They kind of complelimmented one another as far as something that's We werere 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, 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 scientists that's changed the world more than Newton has. Maybe He's he's got legs. People shouted out others in email, but um 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, Newton, I think. And anyt timee hed donunked to'd be like creream. Yeah You just got creamed. Oh 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 as a B baller. Yeah So u Man, that threw me off a little bit. That's right. The cream. Yeah, the cream comes along and He basically says, W this, dudes, this cause and effect thing you're talking about I can express it in quantifiable terms And he comes up with all these great laws and basically sets the stage, the foundation for science for the next three centuries or so. Yeah, these laws that were so rock solid and powerful scientists kind of got ahead of themselves a little and said we're done like with Newton's laws, we can predict U we can predict everything if we have a good enough beginning accurate value to plug into his equations. And they weren't I think it was a little hubris and a little just excitement about like, well, we figured it all out. Right, that you could take Newton's laws and if you had accurate enough measurements. you could predict 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 they're 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. They figured out and 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 how a system is going to change over time using differential equations, right So this is what Newton comes along and figures out that you can describe the universe in these mathematical terms using differential equations. And Like you said, there was a tremendous amount of hubris and Well, I think you said there was some hubris. I think there was 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 Yeah. becausecause again, the hallmark of determinism is that if you have exact measurements, you can predict an outcome accurately 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 Right. So you have that Beautiful little diamond Yeah set up. You got your cue ball put that cue ball and you crack it with the cue and if you are super accurate with your initial measurements. you should be able to mathematically plot out 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 variables temperature if there's wind in the room. like the felt on the table 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 pull table will look exactly the same after the break. Yeah, which is 's pretty much impossible for like a human to do with their hands Sure. But the idea at the time of science was that if you could build a perfect machine that could recreate these conditions, it will happen the same way every time, right And this, I mean, this led to They had hubriss, but you could understand it when Like literally in eighteen forty six To people predicted tune exist Yeah within months not would exist, but does exist.. And this is not by looking up in the sky. like they did it with math. R. And they were right. Yeah. So imagine in eighteen forty six, when that happens, they're like Yeah, we kind of 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 U that this stuff really panned out, It held true for everything from you know the investigation into electricity to new chemical reactions and understanding those. Yeah. 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 it is understandable how science kind of was like, we got it all figured out. Well, and like you said, they u even Galileo was smart enough to know There's uncertainty in these measurements, like precision is key. So they spent What does the article say a lot of the Much of the nineteenth and twentieth 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. Yeah The problem is they Like you said, Galileo knew that there was some sort of There were there were going to be some flaws in measurement that we just didn't have those great scientific instruments yet, right? Yeah, it's called the uncertainty Pinciple. Okay Promets accuracy But The idea is that if you have a good enough instruments you can overcome that. and that the the more you shrink the u error in measuring the initial conditions Yeah the the more you're going to shrink the error in the outcome. Yeah, it'd be proportionate, right? They were correct. The thing is They were also aware but ignoring in a a lot of ways. some Outstanding problems spepecifically 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. bathroom. Okay and we'll be back Hey everybody, hereere's a fact for you. 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Yeah, how this came about was in eighteen eighty five there was King Oscar to of Sweden and Norway Yeah L about Norway. bothoth U 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 mostost brilliant minds on planet Earth got together and tried to do this. U with mathematical proofs and no one could do it Uh, and then a dude named Hony. You got to help me there with that Ponar Mmm Say the whole thing. Henriie Poncar. Very nice. He was French. belieelve it or not And he was a mathematician and he said, you know what I'm not going to look at this big picture of all the planets in the suun and all their orbits. You'd have to be a fool to try that. Sure. He said, I'm going to shrink this down. Like we talked about, shrinking that initial value and that initial condition. and he shrunk it down. He said, I'm going to look at just a couple of bodies orbiting one another Uh with a common center of gravity. And I'm going to look at this And this was called the in body problem. Yeah, which was smart to do because The more variables you factor into a nonlinear equation like that just the harder it's going to be. S he shrunk it down. So the end body problem has to do with Three or more celestial bodies orbiting one another. So Pan Car said, I'll just start with three. Yeah And what he found from doing his equations for this King Oscar, the Squel Prize Um was that shrinking the initial conditions, measurement or rate of error. Right? Yeah 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 differences in the initial conditions fed into a system? Yeah. produced Wildly different outcomes. Yeah. after a fairly short time. Yeah, like let me just round off the mass of this planet at like the eighth decimal point Right. cares Who cares at that point? Yeah. I me just round that one to a two.. And that would throw everything off at at a pretty high rate R. And he said Wait a minute, I think this contest is in Possble Right. He said there is no way to 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 Yeah among celestial bodies. Yeah, it's such a complex system. There are far too many variables that it's impossible to start with something so minute to get the equation whatever the sum that you want at end. Well, not only that Not a sum, I guess, but the result. Not only that and this is what really undermined determinism was that he figured out that you would have to have Infinitely precise measurements whichich even if you built a perfect machine that could take the infinitely perfect machine that could take a measurement of like the movement of a celestial body around another Yeah it's literally impossible to get infite an infinitely precise measurement, which means that we could never predict out to a certain degree the movement of these celestial bodies. L he was saying like No, you can't get You can't build a machine there that gets measurements enough that we can overcome this Terminism is wrong Like you can't just say 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 Bring me another rack of lamb and here's your prize. Yeah and he won by proving that it was impossible, which is pretty interesting. utterly and completely changed Not just math, but like 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 They didn't have super computers at the time. so it would be a little while, aboutbout seventy years at MIT until U we could actually kind of feed these things into machines capable of plotting these things out in a way that we could see. Right Really incredible. So there was this dude seventy years later Uh name. Edward Lawrence or Lauren. Yeah. Well, first of all, we should set the stage. The reason this guy He was a meteorologist and scientist.. Not that those are not the same thing. right He's a scientist who sabble the meteorology.. He was a mathematician. Yeah Uh, but he was really into meteorology because it was a there was a weir are juxtaposition at the time where sending people in outer space, but we couldn't predict the weather Yeah, and it was it was definitely a blot on the field of meteorology.. P people were like, Do you guys know what you're doing and meteorologists are like, you have no idea how hard this is. Yeah. Like, yeah, we can predict it a couple days out, but after that, it's just It's totally unpredictable. It drives us mad. And it's not it wasn't just their u Their reputations that were at stake. like people were losing their lives because of it, right? Yeah, in nineteen sixty two, there were two notorious storms, one on the east cooast and one on the west the Ash Wednesday storm in the east and the big blow in the West that killed a lot of people, cost hundreds of millions of dollars in damage And people are like, you know, we need to be able to see these things coming a little more Right? because it's problem. And meteorologists were like, whyy don't 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. Yeah. it was amazing. and they 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 bytes a second Yeah, that we had the abacus and then the supercomuter, Nothing in between U I looked up the computer that Laurence was working with. Was the Whopper? A Royal McBe. What was the whopper? War games Was it called the Whopper? Yeah WPR. Right I can't believe they called it that. I pretty soon. So the guy just nicknamed it Joshua No, Joshua was the Software Falcon was the old man who designed all the stuff and his son was Joshua, and that was the password to get in. Oh, that was the password. Yeah I guess I was too young to understand what a password was. Yeah. Okay. You didn't even there weren't passwords at the time. No. passw shouted at the computer and they were like, okay, access granted. Yeah ill that movie holds Does it really? Oh, totally. Youotta check it out. Yeah, still very, very fun Young Allie Sheety boy had a crush on her rom that movie? She was great. Yeah. What else was she in recently Wn't she in something? Well, I mean she She kind of went away for a while and then had her big comeback with that indie movie High Art. But that was a while ago Has she been in anything else recently I think I saw something in something recently and I didn't realize it was her. I was she looks familiar. I was like, oh, that's Ally Sheety I. T I could look it up, but I won't It doesn't matter. Anyway, I still crush on her. So the Royal McBee was Not quite the whopper. You could actually sit down at it. The Royal McBe. That's the name of That sounds like a hamburger too. It was by the Royal ror company And they got into computers for a second. And this is the kind of computer that Laurerence was working with. And it was A huge deal, like you were saying, Abacus supercomputer Yeah U, but it was still pretty Dumb as far as what we have today is concerned. But it was enough that Lawrenn was like, Lawn's in his ilk We're 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 a computational model of twelve Meteorological, meteorological. I like how you said it. Calculations, which is very basic. because they're infinite meteorological calculations probably. Yeah. Depending to to say it wrong again? No, no,. L 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. So that's very basic, but he wanted to start out, you know with something attainable.. So he narrowed it down to twelve conditions, basically, twelve calculations that had, you know, temperature, wind speed pressure, stuff like that. startarted forecasting weather. U and then he said, you know, it'd be great if you could see this So I'm going to spit it into my Wonder machine the McWopper was the Royal McB Royal McB And I'm going to get a print out So you can visualize what this looks like right So things were going well and you had this print out and everyone was amazed because these calculations never seem to repeat themselves He was making like, um word art You remember that? that was the first thing anybody did on a computer. Oh yeah, yeah. was to make word art like a butterfly or something. Right. You would print out I never could do that I couldn't eith They have to be able to visualize things spatially You have to that right kind of brain for that. Right? Or you have to be following a guide book that tells you how to do it. True. Have you ever seen M you and everyone we know Yeah, I love that movie. That's a great movie. Yeah. Th those little kids in there, they were doing that. Oh yeah, yeah Forever back and forth So I haven't seen that since it came out. It's been a while. Oh, you gott to see it again. Yeah. Great movie v Ally Sheeti's not in it. No. It's Miranda July. Right. And she like wrote and directed too, right? She did a great job. was It's one of those rare movies where There's just the right amount of whimsy Because Wimsy so easily overpowers everything else and becomes like ye. Yeah, yeah This is like the most perfectly balanced amount of like whimsy I've ever seen in a movie. Yeah, if there's too much whimsy I just like Terrible, Garden state. I just wan to punch it in the face. Terrible Although I like Garden State but I haven' seen it since it came out. It hasn't aged well. Yeah It's just when you look at it now it's just so Cut and whimsical. Ohes, like, ah come on. 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. It is. I'm dreading it. That's why I'm stalling. U 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 nineteen sixty one this output. he noticed was interesting. So he said, you know, I'm going to repeat this calculation, see it again But I'm going to save time I'm just gonna to kind of pick up in the middle And I'm not going to input as many numbers But I'm still using the same values just I'm not going out to six decimal points. So the printout he had went to three decimal points. Yeah. So he was working from the printout. and didn't take into account that the computer accepted six decimal points. So he was just putting in three cororrect and expecting that the outcome would be the same, right? Yes, But the outcome was way different.ight. And he went whoa, whoa. What? Yeah What's going on here It was a big deal. I mean, someone would have come up with this eventually probably Yeah 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 chos 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. Lauren starts looking at this and he's like, Wait a minute, is this is weird. This is worth investigating And like, u, like uh What was his name Pon Caret? Yeah 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. I'm just going to takeake one. pect of weather call 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 into to fill that vacuum this left And that creates a rolling are vertically based Convection current. Yeah, okay? You could I would describe it as oven Ovin Boiling water, Yeah, cup of coffee. Sure. Wherever there's a temperature differential based on a vertical alignment, you're going to have a rolling convection current, o Yeah, it sounds complex, but he just picked out one thing basically, one condition. Right. And this is the one he picked out. But had you seen my hands moving listeners, you would be like, oh yeah, I know it' your tongue. He made little rollle motions. So he's like, okay, I can figure this out. So he comes up with three Three formula that kind of describe a rolling convection current. And he starts trying to figure out how to describe this rolling convection current. And so like I said, he got these three formula, which were basically three variables that he calculated over time. And he plugged them 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 they'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. Right because it's easier for people to understand. He wass a very visual guy. Totally. All of a sudden it made this crazy graph where the line as it progressed forward through time went all over the place. It went from this axis to another axis 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 convection current changes over time, right? Yeah Lorenza is looking at this He was expecting these three things to equalize and eventually form a line. Yeah. 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. No. And what he discovered was what Pont Cart 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 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 going to slip outside those curves every time unless you're A robot? sureure U and that's what it ended up looking like. Yeah, yeah, it never retraced the same path twice ever 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 Lauren who was curious enough to be like, what is going on here? againg, he sat down and started to do the math and thinking about this and especially how it applied to the weather, right? Yeah And he came up with Something very famous. Yes, the butterfly effect. Yes. Uh A This thing kind of look like butterfly wings a little bit. Yeah and B, when he went to present his findings, He basically had the notion, he's like, I'm going I'm going to wow these people in the crowd in nineteen seventy two conference that I'm going to. And I'm going I'm going to say something like, you know The seagull flaps its wings and it starts a small turbulence that can one that can affect weather on the other side of the world. R. small little thing will just grow and grow. and snowball and effective things. And he had a colleague who wass like Seagull wings, That's nice. right. And he said, how about this? and this is the title they ended up with. Predictability, Cullen Does the flap of a butterfly's wings in Brazil set off a tornado in Texas Everyone was like Whoa, whoa. Mind's blown. Yeah Should we take a break? Yes. All right, we'll be right back Hey everybody. hereere's a fact for you. In the United States, there is a break in every twenty six seconds and that means that somewhere right now, an intruder is getting closer. And the problem with most security systems is that they only alert you after the break in has started and that's too late. Well, that's what makes SimplySafe different. They use alerts. SimpllySafe's US based live agents, they identify threats on your property and help deter them before they actually break in. 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I have no idea the gender neutral Narrator They said he said right, Th about a town that has like ten thousand people living in it. to make that town work, you got to have like a gas station, a grocery store, A library whatever you need to sustain that town. Okay. So all these things are built, everyveryone's happy. you have equilibrium He said, So that's great then let's say, You build some someone comes and builds a factory on the outskirts of that town. And there's going to be ten thousand more people living there. Right. And they don't go to church Maybe so. Uh Did I say church, they needed a church? No, no. okay. I was just assuming this was what called bibical web equilibrium. No, no But you just have more people. so there's you need another gas station, 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. I see equilibrium is called an attractor Okay So then he said It 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 ten thousand. let's say three thousand those people just up and leave one day. Okay. And the grocery store guy says, well, there's only seven thousand people here. We need eight thousand people living here to make a profit So I'm shutting down this grocery store Th then all of a sudden you have demand for groceries. So things go on for 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. someomeone else comes along because the demand. And it is this search for equilibrium this Dynet well, you reach equilibrium here and there as the store opens. Periods of stability. Periods of stability. And that dynamic equilibrium is called a strange attractor So an a attractor is the state which a system settles on, strange 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 surely can add Now, you're going to add to it That's it. No, I mean, like it Yeah, and a att trractor is where if you graph 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 a trractor. I can't I can't top that. All right. Grocery store, small town. That was great So Lorenza's strrange attractor was named a Lorenza attractor, named after him. Big deal. They weren't using the word chaos yet No, but published that paper about butterfly wings, right? Yeah. The butterfly effect. and cououpled with his picture the picture of a strange dractor, which is almost the Aside from fractals Almost the u the yeah, the um emblem or the logo for Chaos theory, the Lord is detractor is and It got attention off the bat. It wasn't like Poincaret's findings where it got neglected for seventy years. almost immediately everybody was talking about this. because again, what Laorenta had uncovered, which is the same thing that Poincaret 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. Yeah. 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 nature. Yeah. And I think as far as we're concerned is a really important point too, Chuck. because It doesn't mean that nature is unstable, Chaotic It means that ucture of what we understand as order doesn't jibe with how the universe actually functions. Yeah It's just our understanding of it. Yeah. And we're just so anthropocentric We see it as chaos and disorder and something to be feared. Right. When really it's just complexity that we don't have the capability of predicting. Yeah 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 likeber Robert Hume who I understand was a philosopher, but he was a philosopher scientist. Sure. His whole jam was like, cause and effect is an illusion that like we all we it's just an assumption like that If you drop a pencil, it will always fall down. It's an illusion. and this is pre gravity, understanding gravity But he makes a good point gravity when everyone's just floating around. Yeah. going this pencil has got me wacky. Yeah. But But the point was that you know, we are we base A lot of our assumptions And 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 cause and effect is an illusion. I love that guy. this definitely supports that idea For sure Sorry, I'm excited about Chaos theory. C believe it? Well, I mean I like that I'm able to understand it in enough of a rudimentary way that I can talkk about it at a dinner party. Well, thank your Bible website Well, once you take the formulas out, Yeah, for people like us We're like, oh okay, we can understand chaos. Yeah. Then when somebody says, goodood, do a differential equation, you're just like, So what? A different equation.. All right, so earlier I said that chaos had not been used the word chaos to describe all this junk. and that didn't happen until later on. and well actually later on aboutout ten years. Yeah, But it was kind of at the same time this other stuff was going on with Lorenz late sixties, early seventies There' wass a guy named Stehven Smail U Fields medal recipient. so you know, he's good at math And, um he describbe something that we now know The Sail horseshoe And it goes a little something like this. Bom boom U so all right, take a piece of dough like bread dough. and you smash it out into a big flat rectangle. Can do. 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 put a little rosemary on it. Yeah, maybe so. Wellil, sea salt? Yeah. And then lick it before you bake it so you know it's yours. No one else can have it Uh, so you you have that flat rectangle of dough, you roll it up. into a tube Th then you smash that down kind of flat And then you bend that down to where it eventually looks like a horseshoe. Okay So now you take that horseshoe, you take another rectangle of de and you throw that horseshoe ono that And then you do the same thing The snail horseshoe basically says You cannot predict where the two points of that horseshoe will end up Yeah, you can roll it a million times and it'll end up in a million different places Totally random different places too. 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? Iitate forcecps? Sure. And I can't do that. That's fine. He's not one he's not on my repertoire 'sine. 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 been a better movie Like all of that coincidence stuff that Oh I love that. so And he also did the smile t shirt like It was just too much. like he really hammered it too much. I liked it That 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. ckis. You know, it was a good Tom Hanks movie that was overlooked. road to perition No that. This's a good one Great Sam Mendez Oh man, that guy's awesome. Yeah. Oh, what is he going to do? He might do something He did the James Ba, He did Skyfall. Yeah, yeah, know. he's Al that last one that wasn't so great. He's got a potential project coming up and he would be amazing for it. I don't remember what it was. Did you see Revolutionary Road? Yes, God It was just like You want to jump off a bridge? Yeah, see that movie like every five minutes during that movie. That was hardcore. It is U 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. 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. Yeah Watch Joe versus the Volcano instead. Great movie Uh Where was I? Smail 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. Oh no, no, no. York was Tom York's dad Yeah, you're right. He wasn't the first person. You're correct. But Mail's horseshoe illustrates a really good point, Chuck. Is it Tom York's dad? No okay No, but they're both British Yorkies. Actually one's Australian They're British. So those two points which should which started out right by each other and then end up in two totally different places. Yeah. That applies not just to bread dough but also to things like water molecules. that are right next to each other at some point And then a month later, they're in two different oceans. Yeah. Even though you would assume that they would go through all the same motions and everything. Oh sure. But they're not. There's so many different variables with things like ocean currents two water molecules that were once side by side end up in totally random different places. Yeah And that's part of chaos. It's basically chaos personified. Yeah Chaos molecule fide So we mentioned York, where I was going with that was 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. so he started using theseese equations, these differential equations And he came up with a formula known as the logistic difference equation. basically enled him to predict these animal populations pretty well. And it was working pretty well for a while, but he noticed something really, really weird, right? Yeah He had this formula The logistic difference equation? Yeah is the name of it. Sure. Okay. So we had that formula and He figured out that if you took R, which in this case was the reproductive rate of a animal population. pushed it past three, the number three. So that meant that the average animal in this population of animals. Three. offspring in its lifetime. or in a season, whatever Yeah If you push to past three, all of a sudden, the number of the population. Diverge. Yeah, if you pushed it equal to three actually or more. Right, it would diverge Yeah whichich is weird because a population of animals can't be two different numbers, you know, likeike that herd of antelope is not There's not thirty, but there's also forty five of them at the same time. Yeah. That's called a superposition and that has to do with quantum states not. herds of antelopes, sure That was kind of weird And then he found if you pushed it a little further, if you made the reproductive 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 o yeah, millionths of a degree Um It all of a sudden it would turn into four So there'd be four different numbers for that was the animal population. And then it 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