The Stuff You Should Know Doin’ Science Playlist: How Chaos Theory Changed the Universe

Hey, everybody.

Chuck here and welcome to our sciencey playlist. Super 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 from HowStuffWorks dot Com.

Hey, and welcome to the podcast. I'm Josh Clark with Charles W. Chuck Bryant, and there's Jerry over there. So this is Stuff you should Know, the podcast about chaos theory. Like, have you ever seen Event Horizon?

I did not bad?

Great movie?

Are you crazy? Do you think it was great?

Oh? It was so imaginative.

I thought it was okay.

It was like a LOVECRAFTI and thing in outer space. Yeah, I loved it.

It was all right.

I love crafted it.

Yeah, I liked it.

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, to see the chaos underneath.

And I should check that out again.

Yeah.

I think about Jurassic Park and Jeff Goldblum as the creep doctor Malcolm explaining chaos in the little auto driving.

Suv or whatever that was.

Yeah, that's what I was calling the script, the auto driving suv scene.

Yeah, and you know what, he actually rewatched that scene and it confirmed two things. One is that he actually did a pretty decent job for a Hollywood movie of a very rudimentary explanation of chaos.

And you watched it for this.

Yeah, yeah, just that scene. And then it also confirmed of what a creep that character was. Yeah, if you watch that scene, he's like, you know, he was all gross and flirty with her right in front of her ex but there's this you know, he's talking to her. I didn't even know 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.

Hu 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 groady, And I love Jeff Goldblum. It's not a reflection on him.

He was basically doing Jeff Goldbloom.

Well that's what he Yeah, sure he's Jeff Goldbloom, but I don't.

Think that's how in the manner in which he speaks. But I don't think he's a creep, do you.

Wow, I've got nothing against Jeff gold Okay, I think he's a I think he's doing Jeff Goldblum.

It was also a sign of the times, like if that movie were made today, doctor.

What was her name in the movie, at least Satler, I think.

Yeah, doctor Satler would be like, it's very inappropriate to stroke my hair, dude.

Yeah, like, don't touch me, right.

But this was the nineties or yeah, nineties. Free Wheeling was eight, No, it was nineties.

It was the early mid nineties, I think, yeah, ninety twee ninety four. The book came out in nineteen ninety and in the book Ian Malcolm, who's a Chaotician.

Yeah, a cre chaotian, right he.

He goes into even more depth about chaos there. But that was I mean, that was the first time I ever heard of chaos theory was from Jurassic Part 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 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 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 when you know, when it comes to stuff like this, the brain breaking stuff.

For me, man, this was a brain breaker.

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 a barm Aba Rim Publications, which turns out to be a website about biblical patterns and sandwiched in the middle, there is a really great, easy to understand series of pages on chaos.

They're nice, So.

I was like, man, I get it now. I mean in a rudimentary way.

Right, Well, yeah, yeah, I think even a lot of people who deal with that display 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 defined a complex system as specifically. It doesn't mean just like, oh it's complex, I mean it is, right, but specifically they define it in a way that helped me understand it's a system that has so much motion, so many elements that are in.

Motion, moving parts.

Yeah, that it takes like a computer to calculate all the possibilities of like what that could look like five minutes from now, ten years from now. So before computers came around, before the quantum mechanical revolution, it was 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 uni versus leading up to the discovery of chaos. Right, So, prior to the the scientific revolution, everybody was like, oh, well it's God, the Earth is at the center of the universe and God is spinning everything around like a top. Right, Yeah,

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, you can go in and plug in whatever coordinates you want to and watch it go. You can predict what the outcome is going to be. And what this is that it's base don what at the time was a totally revolutionary idea by Initially, I think Descartes 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 sixteen hundred's where early science met philosophy, Right, they kind of complimented one another as far as something that's we're talking about determinism.

Right, So that was the kind of the seeds of determinism was the scientific revolution, and like you said, where philosophy and science came together in the form of Descartes.

Right.

Yeah.

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 got.

Legs people shouted out others an email, but I'll just say he's at the near the top for sure with some other people.

The Cream. Yeah, so Newton came along and knew and said.

That was his name, Isaac the Kream Newton.

Right. I think anytime he dunked 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 baller.

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, does 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 done with Newton's laws. We can predict we can predict everything if we have a good enough beginning accurate value to plug into his equations, and they weren't. I think there was a little hubris and a little just excitement about like, will 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 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.

And 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, Yeah, 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

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 cueball, you put that que ball, and you crack it with the queue. And if you are super accurate with your initial measurements, you should be able to mathematically plot out via angles where the balls will end up.

Right exactly, Like you can say, this is what the table will look like after the break, if you know the force, the angle, all those little.

Variable temperature, if there's wind in the room, sure, 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 was 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 this, I mean this led to they had hubris, but you could understand it when like literally in eighteen forty six, two people predicted Neptune would exist.

Yeah, within months of 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 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 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, and 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 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 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, and 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 there are gonna be some flaws and measurement that we just didn't have those great scientific instruments yet.

Right, Yeah, it's called the uncertainty principle. Okaybi of its accuracy.

Right, But the idea is that if you have a good enough instruments, you can overcome that, and that the the more you shrink the error in measuring the initial conditions. Yeah, the more you're going to shrink the error in the outcome be proportionate.

Right. They were correct.

The thing is they were also aware but ignoring in a lot of ways some out standing problems, specifically something called the N body problem.

Yet, you know what, I'm so excited about this. I need to take a break.

I think that's a good idea.

I need to go check out my end body in the bathroom.

Okay, and we'll be back, all.

Right, Chuck, We're back. So there's some there's some issues right with determinism. There's some some weird problems out there that are saying like, hey, pay attention to me because I'm not sure determinism works. Right, And one is the N body problem.

Yeah.

How this came about was in eighteen eighty five. That was King Oscar number two of Sweden and Norway.

Yeah, don't want to leave out Norway.

Both he said, you know what, let's offer a prize to anyone who can prove the stability of the Solar system, something that has been stable for a long time before that. And a lot of the most brilliant minds on planet Earth got together and tried to do this with mathematical proofs, and no one could do it. And then a dude name Henri. You got to help me there with that? Oh, say the whole thing.

Henri pon Care 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.

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, right, you know, 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 end 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, so he shrunk it down. So the n body problem has to do with three or more celestial bodies orbiting one another. So Plonkarre said, let's just start with three.

Yeah, smart.

And what he found from doing his equations for this king Oscar the sequel prize, was that shrinking the initial conditions measurements or rate of error, right, yeah, did not really shrink 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 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, and you.

Know who cares? Who cares at that point?

I mean just round that one to a two, and that would throw everything off at a pretty high rate. And he said, wait a minute, I think this contest is impossible.

Right, He said, there is no way to prove the stability of the Solar System because he just uncovered the idea that it's impossible for us to predict the rate of change 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 that you want.

Right, well, not only that, but the result.

Not only that. And this is what really undermined determinism was that he figured out that you would have to have an infinitely precise measurement, which even if you build a perfect machine that could take the infinitely or a perfect machine that could take a measurement of like the the movement of a celestial body around another, it's literally impossible to get infinite an infinitely precise measurement, which means that we could never predict out to a certain degree

Yeah, and King Oscar the sequel said you win, 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 they 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 earthshaking.

Yeah, he discovered dynamical instability or chaos. And they didn't have supercomputers at the time, so it would be a little while, 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 was this dude seventy years later named Edward Lawrence or Lorenz.

Yeah.

Well, first of all, we should set the stage the reason this guy he was a meteorologist, yeah, and scientists, right, not that those are not the same thing, right. He's a scientist who dabbled a meteorology. He was a mathematician, yeah, but he was really into meteorology because it was there was a weird juxtaposition at the time where we were sending people into outer space but we couldn't predict the weather.

Yeah, and it was it was definitely a blot on the field of meteorology. People were like, do you guys know what you're doing? Yeah, And meteorologists, you're like, you have no idea how hard this is? Yeah, Like, yeah, we can predict it a couple of days out, but after that, it's just it's totally unpredictable. It drives us mad. And it wasn't just their their reputations that were at stake, like people were losing their lives because of it.

Right, Yeah, nineteen sixty two there were two notorious 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 and damage, and people were like, you know, we need to be able to see these things coming a little more, right, because it's a problem.

And meteorologists were like, why did you do it?

Then?

So they thought the key was these big supercomputers. Remember the supercomputers. When they came out the big rooms full of hardware, it was amazing, and they were finally able to do like these incredible calculations that we could never do before.

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

Yeah, we had the abacus and then the supercomputer. There's nothing in between.

I looked up the computer that Lareen's was working.

Was it the Whopper?

A Royal McBee? What was the Whopper?

War Games?

Was it called the Whopper?

Yeah?

Wopright, I can't believe they called it that.

So the guy just nicknamed it Joshua.

No, Joshua was the h 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, okay, you didn't even there weren't passwords at the time.

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

Yeah.

Still that movie holds up, does it really? Oh? Totally?

You got to check it out.

Yeah. Still very very fun. Young Ali sheety boy had a crush on her from that movie.

She was great.

Yeah.

What else was she in recently? Wasn't she in something?

Well?

I mean she kind of went away for a while and then had her big comeback with that indie movie High Art, But that was a while ago.

Has she been in anything else? Recently.

Sure, I think I saw something and something recently and I didn't realize that was her. Oh rightly, she looks familiar. I was like, oh, that's Ali sheety.

I don't know all right, I could look it up, but I won't. It doesn't matter anyway. I still crush on her.

So the the Royal McBee was not quite the whopper. You could actually sit.

Down the Royal McBee.

That's the name of it.

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 Lawrence was like, Lawrence 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 twelve meteorological meteorological I liked how you said it calculations, which is very basic because they're infinite meteorological calculations. Probably, yeah, depending to say it wrong again.

No, no, like it sounds like you're about to say it wrong and then you pull it out at the last second. Maybe it's really impressive.

But 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, 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 McWhopper, the Royal McBee, and I'm going to get a print

He was making like like like word art. You remember that, Like that was the first thing anybody did on a computer. Oh yeah, yeah, it was to make word art like a butterfly or.

Something, right, you would print out. Yeah, I never could do that.

I couldn't either.

Like you have to be able to visualize things spatially. You have to have that right kind of brain.

For that, right or you have to be following a guide book.

True.

Have you ever seen me? You and everyone? We know?

Yeah? I love that movie.

That's a great movie.

Yeah.

Those little kids in there, they were doing that. Oh yeah yeah, the forever back and forth poop boy.

I haven't 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.

Ali Sheet he's not in it. No, it's a Miranda in July.

Right, and she like wrote and directed too. Right.

She did a great job. It's like it's one of those rare movies where like there's just the right amount of whimsy, because whimsy so easily overpowers everything else and becomes.

Like yeah, yeah, yeah.

This is like the most perfectly balanced amount of like whimsy you 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 do a lot of movies today.

Oh yeah, well 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 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 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 points.

So the print out he had went to three decimal points. Yeah, so he was working from the print out and didn't take into account that the computer accepted six decimal points. So he was just 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 scientists basically. So I mean, the guy's got an attractor named after him, you know what I mean.

Yeah, well, let's get to that.

So Lorenz starts looking at this and he's like, wait a minute, this is this is weird, this is worth investigating, and like, what was his name, puon Carre. 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 take one aspect of weather called the rolling convection current, and I'm going to see how I can write it down

Yeah, okay, you could.

I would describe it as oven.

Oven, boiling water, 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.

He made little rolling motions.

So he's like, okay, I can figure this out. So he comes up with three three formulae 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 him in and he found three variables

Again, he wanted to just be able to visualize this, right, because it's easier for people to understand.

He was a very visual guy.

Totally.

All of a sudden, it made this crazy graph that 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, And Lorenzo.

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 point care A discovered, which was that some systems, even relatively simple systems, exhibit very complex, unpredictable behavior, which you could call chaos.

Yeah.

And when you say things were going all over like if you look at the graph, it it's not just lines going in straight lines bouncing all over the place randomly, like there was an order to it, but the lines were not on top of one another. Like let's say you draw a figure eight with your pencil and then you continue drawing that figure eight.

It's going to.

Slip outside those curves right every time unless you're a robot.

Sure, And that's what it ended up looking like.

Yeah.

Yeah, 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, A, this thing kind of looked 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 gonna I'm gonna wow these people in the crowd in nineteen seventy two. It's a conference that I'm going to and I'm gonna I'm gonna say something like, you know, the seagull flaps his wings and it starts a small turbulence that can one that

Should we take a break? All right, We'll be right back, all right.

So the Lorens Attractor is that picture that he ended up with, The Lorens Attractor. And this biblical pattern website that I found described attractors and strange attractors in a way that even dumb old me could understand what you got. So if I may, he says, all right, here's the cycle of chaos. He said, I actually I don't know who wrote this. A woman could have been a small child, Noah.

Of undetermined gender. I have no idea the gender neutral narrator, they said.

He said, right, think 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, 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 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 is what's equilibrium.

No, no, no, but you just have more people. So there's you need another gas station and another grocery store. Let's say so they build all these things and then you reach equilibrium. Again, it's maintained because you build all these other systems.

Up.

I see that equilibrium. It's 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 factory being built and you have those original ten thousand, let's say three thousand. Those people just up and leave one day, and the grocery store guy says, well, there's only seven thousand people here. We need eight thousand people living here to make a profit, so I'm shutting down this grocery store. Then all of a sudden, you have demand for groceries. So things go on for a little while, and someone comes in and say, hey, this town needs

Periods of stability, periods.

Of stability, and that dynamic equilibrium is called a strange attractor. So an attractor is the state which the system settles on. Stranger attractor is the trajectory on which it never settles down but tries to reach the equilibrium with periods of stability.

Does that make.

Sense that Bible based explanation was dynamite. I understand it better than I did before, and I understood it okay before. That's great.

Surely can add yeah, yeah, no, you're gonna add to it. No, that's it.

No, I mean like it. Yeah. An attractor is where if you graph something and eventually it reaches equilibrium, it's a regular attractor. If 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 Lorenz's strange attractor was named a Lorenz attractor named after him. Big deal.

They weren't using the word chaos yet.

No, but he published that paper about butterfly wings, right, yeah, the butterfly effect, and it coupled with his picture is the picture of a strange attractor, which is almost the aside from fractals, almost the the emblem or the logo for chaos theory, the Lorens attractor is. It got attention off the bat. It wasn't like puant Caret's findings where

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 Robert Hume, who I know, 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, 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.

Price gravity when everyone's just floating around.

Yeah, going this pencils got me wacky. Yeah, but the point was that you know, we are we base a lot of our assumptions or a lot of stuff that we take a law are actually based on assumptions that are made from observations over time, and that we're just making predictions that cause and effect as an illusion. I love that guy, and this definitely supports that idea for sure. Sorry, I'm excited about chaos theory.

Can believe it?

Well, I mean I like that I'm able to understand it in enough of a rudimentary way that I can talk about it at a dinner party.

Well, thank your Bible website. Well once you take the formulas out, Yeah, for people like us, we're like, oh, okay, we can understand chaos.

Yeah.

Then when somebody says, good, do a differential equation, You're just like.

What what a different equation? 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, well actually about ten years, you know, but it was kind of.

At the same time this other stuff was going on with Lorenz. Yeah, late sixties, early seventies. There's a guy named Stephen Smale, Fields metal recipient, so you know, he's good at math, and he described something that we now know as the Smale horseshoe. And it goes a little something like this. So, all right, take a piece of dough like bread dough, and you smash it out into a big flat rectangle.

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 go a little roseberry on it, yeah, maybe so well sea salt.

Yeah, and then lick it before you bake it so you know it's yours. No one else can have it.

So you have that flat rectangle of dough, you roll it up into a tube and then you smash that down kind of flat, and then you bend that down to where it eventually looks like a horseshoe. Okay, so now you take that horseshoe, you take another rectangle 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

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 imitate Forrest Gump? Sure, I can't do that.

That's fine.

He's not one. He's not in my repertoire.

That's fine.

Although I did see that again part of it recently.

Does it hold up well?

I mean, take out forty minutes of it and it would have been a better movie, like all of that.

Coincidence stuff that.

Oh I love that.

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.

You know. It was a good Tom Hanks movie. That was overlooked A Road to Perdition.

Yeah, this is 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 Bar he did Skyfall. Yeah, yeah, no, he's gonna also that last one that wasn't so great.

He's got a potential project coming up and he would be amazing for it. I don't remember what it was.

Did you see Revolutionary Road?

Yes?

God how it was just like.

Yeah, you want to jump off a bridge?

Yeah? Movie like every five minutes during that movie.

That was hardcore.

It is.

Uh 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 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.

No, No, No, York was Tom York's dad.

Yeah, you're right, he wasn't the first person York correct.

But SMaL's horseshoe illustrates a really good point.

Chuck, is it Tom York's dad?

No, Okay, no, but they're both British, Sure, Yorky's actually one's Australian. Nope, 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 too 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, 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 one side by side end up in totally random different places. Yeah, and that's part of chaos. It's basically chaos personified yea, 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, so he was using math to model how animal populations would change over time giving certain starting conditions. So he started using these equations as 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. 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 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. If you pushed it 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 diverge. 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 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, 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 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, and then we would turn into sixteen. And then all of a sudden, after a certain point, it would turn into chaos. The number would be everything at once, all over the place, just totally random numbers that it oscillated between.

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 eight sixteen chaos two four sixteen two four eight sixteen chaos all before you even got to the number four of the reproductive rate.

Yeah, And he was working with mister 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 nineteen seventy five they co authored a paper called Period three Implies Chaos and man, finally somebody said the word I kept thinking it was all these other people.

Yeah, And this paper where they first debuted the name chaos. They they based it Tom York's dead based it on Edward Lawrence's paper.

Yeah.

He was like, you know what, I have a feeling that has something to do with the Lawrens attractor.

So that.

Provided chaos to the world. And it was the basically the third the third time a scientist had said we don't understand the universe like we think we do, and determinism is based on an illusion like don't you get it of order in a really chaotic universe? And this established chaos. It took off like a rocket in the eighties and the nineties. You know, as you know from Jurassic Park, chaos was everything everybody's like chaos, this is

Yeah, like don't throw everything out the windows. No, you can still try and predict weather and still try and build more accurate instruments and get you know, decent results. But you can't with absolute perfection predict 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 equations and saying like, if the ocean temperature is this at this time of year and the fish population is this at that time, then this is how many offspring this fish stop, this fish population is going to have. Say okay, here is the fish population, Here is the ocean temperature, here are

Yeah, And that's why, like when you see things like you know, fifty years ago they predicted this animal be its extinct and it's not. Well, it's because the variations were too complex, right, They tried to predict And that's why if you look at a ten day forecast, you, sir, are a fool, Right, it's true, Well, ten days from now it 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

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 data could have been off slightly this one value, and then you have more buffalo than you think.

Yeah, sure you got buffaloed by chaos.

And we're not even getting into fractals. That's a whole other thing.

And we did a whole other podcast in June twenty twelve about fractals and the mandal while mandel Brett mendel Brett, Mandelbrot, Yeah, and go listen to that one and hear me clinging to the edge of a clift.

Yet, man, we should end this. But first I want to say, there is a really interesting article it's pretty understandable on Quanta magazine about a guy named George Sugihara and he is a chaos theory dude who's got a whole lab and is applying it to real life. So it's a really good picture of chaos theory and action. Go check it out. Okay, if you want to know more about chaos theory, I hope your brain's not broken.

Yeah, go take some LSD and look at fractals. Don't do that.

You can type those words into how stuff works in the search bar any of those fractals, LSD chaos. It'll bring up some good stuff. And since I said good stuff, it's time for a listener mail.

I'm gonna call this rare shout out get requests all the time.

And bet I know each one really Yeah dude and his 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 this date. My first time listening was during my first deployment.

Yeah yeah, yeah, when.

I listened to your list on famous and influential films, I was hooked after that. Since I came back stateside, have 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.

That's good.

Even my girlfriend Rachel has warmed up to you dudes, which was not a pleasant I'm sorry, which was a pleasant shock to me. 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 that 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 uh, thanks for listening.

Yeah, man, thank you, that is a great email. I love that one.

Glad we don't give you a headache. Rachel, Yeah for real, she listens to this one, She's.

Like, Okay, oh yeah, everybody's gonna get a headache from this one. Like I came to hate the sound of my own voice from this one.

Ah, you'll be right.

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