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Hey, everybody, it's me, Josh, your old pal, and for this week's Spy Case Selex, I've chosen how chaos theory changed. The Universe first came out in July of 2016. And I have to say, I think it's one of the better science stuff you should know episodes of all time. There's just something about this that grabbed me and Chuck by the callers and said, I'm interesting, aren't I? And we said, yes, you definitely are.

And this one has everything. It has science. It has philosophy. It has our understanding of the universe is just an all around good episode. So I hope you enjoy it as much as I did listening to it.

Again, welcome to Stuff You Should Know. A production of I Radio's HowStuffWorks. Hey, and welcome to the podcast, I'm Josh Clark with Charles W.. Chuck Bright, and there's Gerri over there. So this is stuff you should know the podcast about chaos theory. Like, have you ever see an event horizon? I did. Not bad. Great movie. Are you crazy? I didn't think it was great. Oh, so imaginative. I thought it was OK.

It was like a Lovecraftian thing in outer space. Yeah. Loved it. All right. I love crafted it. Yeah, I like that.

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 you should check that out again. Yeah, I should. I think about Jurassic Park and Jeff Goldblum as the creep. Dr. Malcolm explaining chaos in the the little auto driving SUV or whatever that was, right? Yeah, that's what I was calling the script, the auto driving SUV thing. Yeah.

And, you know, I actually watch that scene and it confirmed two things. One is that he he actually did a pretty decent job for a Hollywood movie, a very rudimentary explanation of chaos. Yeah. And you watched it for this year. OK, yeah. Just that scene. Yeah. And then it also confirm 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 her ex, right.

But there's this, you know, he's talking to her. I don'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, it's Crowdie. And I love Jeff Goldblum. It's not a reflection on him. He was basically doing Jeff Goldblum. Well, that's what he. 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 nothing against Jeff Gold. OK, 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?

Sattler.

Yeah, Dr. Sattler would be like, it's very inappropriate to stroke my hair, but yeah.

Like, don't touch me. Right. But this was the 90s, Freewheelin I was 18, I was 19. It was the the early mid 90s, I think 92, 93, 94. The book came out in 1990. And in the book, Ian Malcolm, who's a petition.

Yeah. ACRI petition. Right. He he he goes into even more depth about chaos, I'm sure. 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 is very misleading as far as the general public goes, as from what I researched in 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 of science like this. Right.

What it means. I guess we can say up front is basically the idea that complex systems do not behave in very neat ways that we can 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 to one, you know, when it comes to stuff like this, the brain breaking stuff for me, man, this is a brain 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 Bahram I Am 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 Theory. So I was like, man, I get it now. My in a rudimentary way, right? Oh, yeah. Yeah. 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.

I don't necessarily understand chaos.

Yeah. And they define a complex system as specifically. Does it mean just like. Oh, it's. Complex, I mean, it is right, but specifically they define it in a way that help me understand it's a system that has so much emotion, so many elements that are in motion moving parts. Yeah. That it takes like a computer to calculate all the possibilities. Right. Of like what that could look like five minutes from now. 10 years from now.

Right. So before computers came around, we before the quantum mechanical revolution, it was 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. Yeah.

So prior to the, um, the scientific revolution, everybody was like, oh, well, it's got the earth 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 there are there's order.

They're finding order in patterns and predictability to the universe. Yeah. If you can apply mathematics to it.

Yes. Specifically if you can apply mathematics to the starting point.

Right. Right. 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 outcomes going to be and what this is that it's based on what at the time was a totally revolutionary idea. By initially I think Descartes was the first one to kind of say, uh, cause and effect is a pretty big part of our universe, right?

Yeah, it was sort of like where it's a six hundreds where early science met philosophy. Right. They kind of complemented one another as far as something. That's where 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? Yeah. And then Newton came along and we did a whole episode on him.

Yeah. January of this year. It was a good one. It was really good. Like I think you said in that episode that there's possibly no scientist that changed the world more than Newton has.

Maybe is he's got legs. People shouted out others in email. But I'll just say he's at 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. Right. I think any time is going to be like cream. 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 a as a B ball. Yeah. So.

Man, that threw me off a little bit. That's right. The cream, yeah, the cream comes along and he basically says, watch this dude's this cause and effect thing you're talking about.

I can express it in quantifiable terms. And he comes up with all of these great laws 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, we can predict everything if we have a good enough beginning accurate value. Right. To plug into his equations. Yeah, and they weren't I think there 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 what the outcome would be of that system, that you plug those measurements into using this 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. Right. 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 100 years.

Exactly. And they they've 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 how a system is going to change over time using differential equations, right? Yeah. So this is 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 is a tremendous amount of hubris and well, I think you said there is 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, because, again, the hallmark of determinism is that if you have exact measurements, you can predict an outcome accurately, like the the pool Q example, the pool table example. Right, right.

So if you've got a pool table, let's say you're playing some nine ball. Right. You have that beautiful little diamond. Yeah. Set up. You got your cue ball, you put that cue ball and you crack it with the Q and if you are super accurate with your initial measurements, you should be able to mathematically plot out the 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 red shirt 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.

Yeah. 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? Yeah.

And I mean, this led to they had hubris, but you could understand it when, like, literally in 1846, two people predicted Neptune would exist. Yeah. Within months that would exist but does exist. Right. And this is not by looking up in the sky like they did it with math. Right. And they were right. Yeah.

So imagine in 1846 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 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. And it it laid the scientific revolution, laid the basis for the industrial revolution. Yeah. And just the change that came out of the world like that, it definitely 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 the 19th and 20th century just trying to build better instrumentation to get more and more and smaller and smaller and more precise measurements. Right. That was basically the goal of. All 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 is some sort of there they're 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 Principle, OK? It's accuracy, right. But the idea is that if you have a good enough instrument, you can overcome that. And that the the more you shrink the. Error in measuring the initial conditions? Yeah, the the more you're going to shrink the error in the outcome. Yeah, it'd be proportional, right? They were correct. The thing is, they were also aware, but ignoring in 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 own body in the bathroom, OK? And we'll be back.

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That see? Hey there, it's LeAnn Rimes. You know, these days, it's pretty easy to feel way too overwhelmed and disconnected not only from each other, but ourselves. My new podcast, Wholly Human Focus, is on living our best fullest lives by expanding into our most complete and whole selves. I'd love you to join me as I sit down with people who I've found to be some of the world's most inspiring and enlightening motivators. Healers and wise souls together will make more sense of this crazy existence.

We all share ourselves and each other. Listen and follow. Holy Human with me. LeAnn Rimes on the I Heart radio app, Apple podcast or wherever you listen to podcasts. All right, check her 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. Right. And one is the anybody problem.

Yeah. How this came about was in 1885, that was King Oscar number two of Sweden and Norway. Yeah. To Norway both. He said, you know what, let's offer a prize to anyone who can prove the stability of the solar system. Yeah. 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.

And then a dude named Honoree, you got to help me there with that one car. Oh, say the whole thing on repond car. Very nice. He was French, believe 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 sun and all their orbits either 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.

Right, you know, yeah, and that initial condition, he shrunk it down, he said, I'm going to look at just a couple of bodies orbiting one another 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, the just the harder it's going to be sure he shrunk it down. So the body problem has to do with three or more celestial bodies orbiting one another. So Poincaré said, I'll just start with three.

Yeah, smart. And what he found from doing his equations for this this King Oscar, the sequel prize, was that shrinking the initial conditions, measurement, error rate of error, right? Yeah. Did not really shrink the the error in the outcome. Right. Which flies in the face of determinism. What he found was that just very, very minor differences in the initial conditions fed into his 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. And like, you know, who cares.

Who cares at that point. Yeah. I mean, just around that one to a two. All right. And that would throw everything off at a at a pretty high rate. Right. And he said, wait a minute, I think this contest is impossible. Right. He said there is no way to 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 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, Manute, to get the equations or whatever the the sum that you want it to end.

Well, not only that as some 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 an infinitely precise measurement.

Yeah. Which even if you built a perfect machine that could take the infinitely perfect machine, that could take a measurement of like the the the movement of a celestial body around another. Yeah. You it's literally impossible to get infinite, an infinitely precise measurement now, which means that we could never predict out to a certain degree the movement of these celestial bodies, like he was saying, like, no, you you can't get you can't build a machine that gets measurements enough that we can overcome this.

Like determinism 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 body problem.

Yeah, and King Oscar, the sequel, said U.N.. Yeah, 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.

And that utterly and completely changed, not just math, but like our our understanding of the universe and our understanding of our understanding of the universe, which is even more kind of earthshaking. Yeah. He discovered dynamical instability or chaos and they didn't have supercomputers at the time. So it would be a little while, right about seventy years at MIT until we could actually kind of feed these things into machines capable of plotting these things out in a way that we could see.

Right. Which was really incredible. So there is this dude, 70 years later named Edward Lawrence Lawrence. Yeah.

Well, first of all, we should set the stage. The reason this guy, he was a meteorologist and scientist. Right. Not that those are not the same thing. All right. He's a scientist who dabbled in meteorology. Right? He was a mathematician. Yeah.

But he was really into meteorology because it was a there was a weird juxtaposition at the time where we were 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. People were like, do you guys know what you're doing? Yeah.

And meteorologists are like, you have no idea how hard this is. Yeah. Like, yeah, we can predict that a couple of days out, but after that, it just it's totally unpredictable. It drives us mad. And it's not it wasn't just their their reputations that were at stake, but people were losing their lives because of it. Right. Yeah. In 1962 there were two Notre.

Three storms, one on the East Coast and one on the west, the Ash Wednesday storm in the east and the big blow on the west that killed a lot of people, cost hundreds of millions of dollars in damage. Right. And people are like, you know, we need to be able to see these things coming a little more. Right, because it's a problem. The meteorologists were like, why 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 can never do before.

I know they were able to, like, crunch 64 bytes a second.

You know, we had the abacus and then the supercomputer. Right. There's nothing in between. I looked up the computer that Lawrence was working was the Whopper or Royal McBee. What was the whopper wargames? Was it called the Whopper? Whopper? All right. I can't believe they call it that pretty. So the guy just nicknamed it Joshua.

Now, Joshua was the the. Software Falcon was the old man who designed all this 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. OK, you didn't even there weren't passwords at the time.

No password shouted it at the computer and they're like, OK, access granted.

Yeah. Still that movie holds up does it really. Oh totally. Got to check it out. Yes. Still very, very fun. Young Ali City boy had a crush on her from that movie. She was great. Yeah. What else was she in recently? When she and something well, I mean, 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.

She'd been in anything else recently? Sure. I think I saw something in something recently and I didn't realize it was her. Oh, really? She looks familiar. I was like, Oh, that's Sheedy. I don't know. All right, I could look it up, but I won't as the matter anyway. I still crush on her. So the the Royal McBee was not quite the whopper. You could actually sit down at the Royal McBee.

That's the name. 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, Abacus supercomputer. Yeah, but it was still pretty dumb as far as what we have today is concerned. But it was enough that Lorens is like Lorenzen and his ilk were 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 12 Meteorological Meteorological. I like to use calculations, which is very basic because there are infinite meteorological calculations, probably depending the wrong.

Again, like you, 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 so that's very basic. But he wanted to start out, you know, with something attainable. So he narrowed it down to 12 conditions, basically 12 calculations that had, you know, temperature, wind speed, pressure, stuff like that. Right. Started forecasting weather. 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 the WOPR was the royal mic, the Royal McVee, and I'm going to get a printout so you can visualize what this looks like.

Right. So things were going well and he had this printout and everyone was amazed because these these calculations never seem to repeat themselves. He was making like like like word art. You remember that that was the first thing anybody did on a computer. Oh, yeah. To what's the word? Like a butterfly. Right. You would print out. Yeah, I never could do that. I couldn't either. I kept to be able to visualize things spatially.

You have to have that right kind of brain for that. Right. Or you have to be following a guidebook through. Have you ever seen me, you and everyone we know. Yeah. Love that movie. That's a great movie. Yeah. There's little kids in there. They are doing that. Oh yeah. Yeah. The forever back and forth poop. But I haven't seen that since it came out. It's been a while. Oh you got to see it again.

Yeah. Great movie. Good movie. Al Qaeda is not in it. No, it's a Miranda July. Right. And she like wrote and directed to write. She did a great job.

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, yeah, yeah, this is like the most perfectly balanced amount of, like, whimsy I've ever seen in a movie. Yeah, there's too much whimsy. I just like terrible Garden State. I just want to punch it in the face. Terrible.

Although I like Garden State, but I haven't 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 cutesy and whimsical. Oh yeah. It's like come on. Yeah.

Boy we're getting to a lot of movies today. Oh yeah. We're stalling. We haven't even talked about Butterfly Effect yet, which is coming.

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 1961. 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 going 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 point.

So the pruno, he had went to three decimal point. Yeah. So he was working from the printout and didn't take into account that the computer accepted six decimal point. So he was just putting in three. Correct. And expecting that the outcome would be the same. Right. Yes. But the outcome was way different. Right.

And 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 an emphasis on meteorology to an emphasis on chaos, math to stud scientist, basically.

So, I mean, the guy's got an Attracta named after him, you know what I mean? Yeah, well, let's get to that. So Lawrence starts looking at this and he's like, wait a minute, this is this is weird. This is worth investigating. And like like what was his name? Poincaré. Yeah. He said I need fewer variables. So I'm not going to try to predict weather with these 12 differential equations that you have to take into account.

I'm just going to take one aspect of weather called the rolling convection current, and we're going to see how I can write it down in formula form. So rolling convection current, Chuck, is where you know how the wind is created, where air at the surface is heated and starts to rise. Yeah. And suddenly cool air from higher above comes in to fill that that vacuum that's left. And that creates a rolling whole or vertically based convection current.

Yeah. OK, you could I would describe it as oven oven. Boiling water. Yeah. 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. 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. I'm sure he made literally 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. Right, correct.

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 there are 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.

Here's a very visual guy. Totally. All of a sudden, it made this crazy graph that were the the line as it progressed forward through time, went all over the place. It went from this axis 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 convection current changes over time, right?

Yeah. And Llorens 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 now. And what he discovered was what Poincaré 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, draw a figure eight with your pencil and then you continue drawing that figure eight. It's going to slip outside those curves, right? Every time, unless you're a robot.

Sure. And that's what I 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 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? 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 to you know, while these people in the crowd in 1972, it's a conference that I'm going to and I'm going to I'm going to say something like, you know, the seagull flaps his wings and it starts a small turbulence that can one that can affect weather on the other side of the world.

Right. Small little thing will just grow and grow and snowball and affect things. And he had a colleague who was like seagull wings. That's nice. All 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? And everyone was like, whoa, whoa. Minds blown. Yeah. So we take a break, yes. All right, we'll be right back.

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All right.

So the Lauryn's Attracta.

Is that picture that he ended up with, right, that Karaf, the Lauryn's Attracta and this biblical pattern Web site that I found described attractors in strange attractors in a way that even dumble me could understand what you got. So if I may. He says, all right, here's the cycle of chaos, he said. Except I don't know who wrote this 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 thing about a town that has like 10000 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. OK, 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 builds a factory on the outskirts of that town and there's going to be 10000 more people living there.

Right. And they don't go to church maybe. So that I say church. They needed a church. No, no. OK, I was just assuming this is a biblical equilibrium, 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. I see that equilibrium. It's called an attractor.

OK, 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 had those original ten thousand let's say three thousand, those people just up and leave one day, OK. And the grocery store guy says, well, there's only 7000 people here. We need eight thousand people living here to to make a profit. So I'm shutting down this grocery store. Hmm.

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. Right. They can't sustain. They shut down. Someone else comes along because the demand and it is this search for equilibrium, this dinette, 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 when a tractor is the state which a system settles on a stranger, a tractor is the trajectory on which it never settles down, but tries to reach the equilibrium with periods of stability. So that makes sense.

That Bible based explanation was dynamite. I understand it better than I did before, and I understood it OK before. That's great. Sure, we can add. Yeah, yeah, now you're going to add to it. No, that's it. No, I mean, like it. Yeah. And attractors where if you graph something and eventually it reaches equilibrium, it's a regular tractor, it never reaches equilibrium and is constantly trying to and has periods of stability.

Strange attractor.

I can't I can't top that. All right. Grocery store, small town.

That was great. So Lorenza Strange, a tractor was named a Lorenza tractor named after him.

Big deal. They weren't using the word chaos yet. No, but he published that paper about butterfly wings, right? Yeah. The Butterfly Effect. And it coupled with his picture is the picture of a strange tractor, which is almost the aside from fractals, almost the the the emblem or the logo for chaos theory, the detractors, it got attention off the bat.

It wasn't like plonkers findings where it got neglected for 70 years. Almost immediately. Everybody was talking about this because, again, what Lawrence had uncovered, which is the same thing that Poincaré discovered, 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. Yeah. 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 in nature. Yeah. 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. Right. Chaotic. It means that our picture of what we understand is 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 that, you know, 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 like Robert Hume, who I know I understand was a philosopher, but he was a force for scientists. Sure. His whole jam was like cause and effect is an illusion that like we all it's just an assumption like that. If you drop a pencil, it will always fall down. It's an illusion. And this is pretty gravity, understanding gravity. But he makes a good point.

Gravity when everyone's just floating around. Yeah, go in this pencil. Got me wacky. Yeah.

But the point was that, you know, we, we are we base a lot of our assumptions 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. And this this definitely supports that idea for sure.

Sorry, I'm excited about chaos theory.

Yeah, well, I mean, I like that I'm able to understand it enough of a rudimentary way that I can talk about it at a dinner party. Well, thank you. Bible website. Well, once you take the formulas out. Yeah. For people like us we're like, oh OK. We can understand chaos. Yeah.

Then when somebody says good, do a differential equations just like a 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. Right. 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 Llorens. Yeah, late 60s, early 70s, there was a guy named Stephen Smale, uh, Fields medal recipient.

So, you know, he's good at math and. He describes something that we now know as the Smale horseshoe, and it goes a little something like this boom, boom.

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, oh, boy, I hope this makes some good bread.

This can be so good. So then you just little rosemary on it. Yeah, maybe so. Well see salt. Yeah. And then lick it before you bake it so you know it's yours no one else can have.

And so you have that flat rectangle of dough, you roll it up into a tube and then he smash that down kind of flat and then he bean that down to where it eventually looks like a horseshoe. OK, so now 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 Smale 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 to totally random.

You never know.

It's like a box of chocolates. You never know what you're going to get. You have to say it. And that became known. You have to say, oh what. Imitate Forrest Gump. Sure, I can 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 40 minutes of it and it would have been a better movie.

Yeah. Like all of that coincidence stuff that. Oh, I love that.

And he also did that smile shirt like it was just too much like he really hammered it too much like that.

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, Zemeckis, you know, is it good Tom Hanks movie that was overlooked? A Road to Perdition? Yeah, that was a good one. Great Sam Mendes. Oh, man, that guy's awesome. Yeah. Oh, what is he going to do? He might do something. He did the James Bond.

He did Skyfall. Yeah. Yeah, I know he's going to do 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 have. Just like. Yeah. You want to jump off a bridge. Yeah.

That movie like every five minutes during that movie, it was hardcore. It is. He did that one too huh. Yeah.

And don't see that if you're like engaged to be married you're thinking about it. Yeah.

Or if you're blue already. Yeah 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. Yeah.

Watch Joe versus the Volcano instead. Great movie. Uh where was I. Smale Horseshoe is what that's called and. That was he was the first person to actually use the word chaos. Oh, he was? I think so. Oh, no, no, no. Your York was Tom dead? Yeah, you're right.

He wasn't the first person. New York. Correct.

But it smells horseshoe. Illustrates a really good point.

Chuck, is it Tom York's dad? No. OK, no. But they're both British. Sure. Yorkeys actually. One's Australian. No, they're British. All right. So those two points, which should which started out right by each other and 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 that 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. Or chaos molecule fied.

So we mentioned York, where I was going with that was there was an Australian named Robert May and he was a population biologist. Yeah. So he was using math to model how animal populations would change over time, giving certain starting conditions. So he started using 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. The logistic difference in equation is the name of it. OK, so we had that formula and he figured out that if you took ah. Which in this case was the reproductive rate of an animal population. Yeah. 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.

Yeah. If you push the past three, all of a sudden the number of the population would diverge. Yeah. If you pushed it equal to three actually or more. Right. It would divert. Yeah. 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 30, but there's also 45 of them at the same time. Yeah. That's called the superposition and that has to do with quantum states, not herds of antelope.

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, oh, yeah, millions of of a of a degree. All of a sudden it would turn into four.

So there'd be four different numbers for that was the animal population then would turn into 16 and then all of a sudden after a certain point, it would turn into chaos. Yes, the number would be everything at once all over the place, just totally random numbers that it oscillated between.

Yeah, 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. Yeah, 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 a16 chaos two four six two four eight six in chaos. Yeah.

All before you even got to the number four of the reproductive rate. Yeah. And he was working with Mr York because he was a little confounded. So he was a mathematician buddy of his James York from the University of Maryland. So they worked together on this. And in 1975 they co-authored a paper called Period three implies chaos.

And man, finally somebody said the word, yeah. I kept thinking it was all these other people. Yeah. And this this paper where they first debut, the the name Chaos, they they based it. Thom Yorke said based it on Edward Lawrence's paper. Yeah. He was like, you know what, I have a feeling this has something to do with the Lauryn's Attracta so that 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. Yeah. And determinism is based on an illusion like that. You get it out of order. Yeah. In a really chaotic universe. And this disestablished chaos took off like a rocket in the 80s and the 90s.

As you know from Jurassic Park, chaos was everything, everybody's like chaos. This is totally awesome. It's the new frontier of science. And then it just 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, people mistook what chaos meant. It wasn't the a new the new type of science. Yeah. It was a new understanding of the universe. It was saying, like, yes, you can still use Newtonian physics. Yeah. Like, don't throw everything out the window.

You can still try and predict weather and still try and build more accurate instruments. Right. And get, you know, decent results. But you can't with absolute perfection, 100 percent predict. Right. Complex systems like determinism.

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? No, not science. Well, some some chaos. People have said, no, this is this is great. This is good. We'll take this. We'll take the universe as it is, rather than trying to force it into our pretty little equation and saying, like, if the ocean temperatures this at this time of year in the fish population, is this at that time, then this is how many offspring, this fish stock, this fish population is going to have to say, OK, 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. Right. 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 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 I like when you see things like, you know, 50 years ago they predicted this animal would be extinct and it's not.

Well, that's because the variations were too complex, right? They tried to predict, and that's why if you look at a 10 day forecast, you, sir, are a fool. Right. It's true. Well, 10 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 you could find a time when it was similar to what it is now. Yeah. 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 it's based on 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. Yeah. This one value. Right. And then you have more buffalo than you think. Yeah. I'm sure you got buffaloed by chaos and we're not even getting into fractals.

That's a whole other thing. And we did a whole other podcast. Yeah. In June 2012 about fractals and Mandell. Benoit Mandelbrot. Yeah. Mendel, Brett Mandelbrot. Yeah. And go listen to that one and hear me clinging to the edge of a cliff. Yeah. Clift Man, we should end this.

But first I want to say there is a really interesting article. It's pretty understandable on Quantum magazine about a guy named George Huguely Sugihara. Mm hmm. And he is a chaos theory, dude. There is he'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.

OK, if you wanna know more about chaos theory, I hope your brain's not broken.

Yeah, go take some LSD and fractals. Don't do that. You can type those words into HowStuffWorks in the search for any of those fractals, LSD chaos. It'll bring up some good stuff. And this is good stuff. It's time for listening.

Now I'm going to call this rare shout out. You get requests all the time. I bet I know which one this is. Really? Yeah, it's girlfriend. Yeah. No, so far so good.

Hey, guys, just wanted to say I think you're doing a wonderful job with the show to the state. My first time listening was during my first deployment. Yeah. And now when I listen to your list on famous and influential films, I was hooked after that. Since I came back stateside, I spent many hours driving to and fro to 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, because even my girlfriend Rachel is warmed up to you dudes, which was not a pleasant I'm sorry, which was a pleasant shock to me, as 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 shout out to Rachel, I'm sure it would make her feel a little better. But I got the pleasant people on the podcast to reaffirm how much I love her. That is John. Rachel, hang in there. John, be safe. And thanks for listening. Yeah. I mean, thank you. That's a great email.

I love that one. But we don't give you a headache, Rachel. Yeah. For she listen to this song, she's like, oh yeah. Everybody's going to get a headache from this one. Like I came to hate the sound of my own voice from this one. Oh, you'll be all right.

If you want to get in touch with us, you can hang out with us on Twitter as well as keep podcasting goes for Instagram. You can hang out with this on Facebook, dot com slash stuff. You should know you can send us an email to Stuff podcast, the HowStuffWorks dot com. And as always, join us at our home on the Web stuff you should know dot com. Stuff you should know is a production of radios HowStuffWorks for more podcasts, my radio.

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