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Hey, everybody.
Chuck here, and welcome to our Sciency 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.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.
Have you ever seen Event Horizon?
I did.
Not bad.
Great movie.
Are you crazy?
I don't think it was great.
Oh, it was so imaginative.
I thought it was okay.
It was like a Lovecraftian thing in outer space.
Yeah.
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.
Yeah.
To see the chaos underneath.
I should check that out again.
Yeah, I think you should.
I think about Jurassic Park and Jeff Goldblum as the creep.
Dr. Malcolm explaining chaos in the little auto-driving SUV or whatever that was.
Right.
That's what it was called in the script, the auto-driving SUV scene.
Yeah, and you know what?
I actually re-watched 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.
Yeah.
Oh, you watched it for this?
Yeah.
Okay.
Yeah, just that scene.
Yeah.
And then it also confirmed of what a creep that character was.
Yeah.
If you watch that scene, he's like...
You know, he was all gross and flirty with her right in front of her ex.
Right.
But there's this, you know, he's talking to her.
I didn't even notice this at first.
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 grody.
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 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 Goldblum.
Oh, okay.
I think he's doing Jeff Goldblum.
It was also a sign of the times.
Like if that movie were made today, Dr. What was her name in the movie?
Ellie Sattler, I think.
Yeah, Dr. Sattler would be like, it's very inappropriate to stroke my hair, dude.
Yeah.
Like, don't touch me.
Right.
But this was the 90s.
Or was it the 90s?
Yeah, it was freewheeling.
Or was it, no, it was 90s.
It was the early, mid-90s, I think.
Yeah.
92, 93, 94.
The book came out in 1990.
And in the book, Ian Malcolm, who's a chaotician.
Yeah, a creep chaotician.
Right.
He goes into even more depth about chaos theory.
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.
From what I researched 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, 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 it comes to stuff like this, the brain breaking stuff for me,
Man, this was a brain breaker.
You know how I always go to 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 Abarim A-B-A-R-I-M Publications, which turns out to be a website about biblical patterns, and sandwiched in the middle there is a really great, easy to understand series of pages on Chaos Theory.
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 systems 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 define 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 to calculate all the possibilities of what that could look like five minutes from now, 10 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 universe leading up to the discovery of chaos, right?
Yeah.
So prior to 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.
It was all a theistic explanation.
Then the scientific revolution happens and people start applying things like math and making mathematical discoveries and figuring out that 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 figure out how a system works, mathematically speaking, right?
Yeah.
You can go in and plug in whatever coordinates you want to.
Yeah.
And watch it go.
You can predict what the outcome is going to be.
And what this is, it's based on what at the time was a totally revolutionary idea.
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 1600s, where early science met philosophy.
Right.
They kind of complemented 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.
I think you said in that episode that there's possibly no scientist that's changed the world more than Newton has.
Maybe.
He's got legs.
People shouted out others in email, but I'll just say he's near the top.
For sure.
With some other people.
The cream.
Yeah.
So Newton came along and Newton said.
That was his name, Isaac the Cream Newton.
Right.
I think.
Anytime he dunked, he'd 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 b-baller.
So, man, that threw me off a little bit.
That's all right.
The cream.
Yeah, the cream comes along.
And he basically says watch this, dudes.
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 laws that were so rock, solid and powerful that scientists kind of got ahead of themselves a little and said we're done.
Done.
With Newton's laws we can predict everything if we have a good enough beginning accurate value 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 right.
Yeah, 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.
Yeah.
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 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?
So this is what Newton comes along and figures out that you can describe the universe in these mathematical terms using differential equations.
And, like you said, there was a tremendous amount of hubris.
And Well, I think you said there was some hubris.
I think there was a tremendous amount of hubris where science basically said we've mastered the universe.
We've uncovered the blueprint of the universe, and now we understand everything.
It's just a matter now of getting our scientific measurements more and more and more exact.
Yeah.
Because again, the hallmark of determinism is that if you have exact measurements, you can predict an outcome accurately.
Like the pool cue example, or the pool table example, right?
Right.
So if you've got a pool table, let's say you're playing some nine ball.
Right.
So you have that beautiful little diamond set up.
You got your cue ball.
You put that cue ball and you crack it with the cue.
And if you are super accurate with your initial measurements, you should be able to mathematically plot out the angles where the balls will end up.
Right, exactly.
You can say this is what the table will look like after the break, if you know the force, the angle, all those little variables.
The temperature, if there's wind in the room, the felt on the table, everything.
The more specific you are, the more accurate your end result will be.
Right.
And then, one of the other hallmarks of determinism is that if you take those exact same initial conditions and do them again, the pool table will look exactly the same after the break.
Yeah, which is pretty much impossible for a human to do with their hands.
Sure, but the idea at the time of science was that if you could build a perfect machine that could recreate these conditions, it will happen the same way every time, right?
Yeah.
And this 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 of each other.
Not would exist, but does exist.
Right.
And this is not by looking up in the sky.
They did it with math.
Right.
And they were right.
Yeah.
So imagine in 1846.
When that happens, they're like yeah, we've got the math down, so we're pretty much all knowing.
Right.
Well, plus also for the most part, not just with Neptune.
They were finding that this stuff really panned out.
It held true for everything from the investigation into electricity to new chemical reactions and understanding those.
And the scientific revolution laid the basis for the industrial revolution.
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, 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 smaller and smaller and more precise measurements.
Right.
That was basically the goal of it, right?
Yeah, which was the right direction.
That's exactly what they should have been doing.
Yeah.
The problem is, like you said, Galileo knew that there was some sort of, there were going to be some flaws in measurement, that we just didn't have those great scientific instruments yet, right?
Yeah, it's called the uncertainty principle.
Okay.
It prohibits accuracy.
Right.
But the idea is that if you have good enough instruments, you can overcome that.
And that the more you shrink the in measuring the initial conditions, the more you're going to shrink the error in the outcome.
It'd be proportionate, 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 N-body problem.
Yeah, 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 in-body in the bathroom.
Okay.
And we'll be back.
All right, Chuck, we're back.
So there's some issues, right, with determinism.
There's 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 end body problem.
Yeah.
How this came about was in 1885, there 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.
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 with mathematical proofs, and no one could do it.
And then a dude named Henri, you gotta help me there with that last name.
Say the whole thing.
Henri Poincaré.
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.
And that initial condition.
And he shrunk it down.
He said I'm going to look at just a couple of bodies orbiting one another with a common center of gravity.
And I'm going to look at this.
And this was called the in-body problem.
Yeah, which was smart to do, because the more variables you factor into a nonlinear equation like that, just the harder it's going to be.
So he shrunk it down.
So the n-body problem has to do with three or more celestial bodies orbiting one another.
So Poincaré said, oh, I'll just start with three.
Yeah.
And what he found from doing his equations for this King Oscar, the sequel prize, was that shrinking the initial conditions, measurement or rate of error right 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 his system produced wildly different outcomes after a fairly short time.
Yeah, like let me just round off the mass of this planet at like the eighth decimal point.
Right.
And like, you know, who cares?
Who cares?
At that point.
Yeah.
Let me just round that one to a two.
Right.
And that would throw everything off at a pretty high rate.
Right.
And he said, wait a minute, I think this contest is impossible.
Yeah.
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 sum that you want at the end.
Well, not only that.
Not a sum, I guess, but the result.
Not only that, and this is what really undermined determinism was that he figured out that you would have to have an infinitely precise measurement which, even if you built a perfect machine that could take the infinitely, or a perfect machine that could take a measurement of the movement of a celestial body around another, it's literally impossible to get an infinitely precise measurement, which means that we could never predict out, to a certain degree, the movement of these celestial bodies.
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 end body problem.
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 that...
Utterly and completely changed not just math, but our understanding of the universe and our understanding of our understanding of the universe, which is even more kind of earth-shaking.
Yeah, he discovered dynamical instability or chaos.
Yeah.
They didn't have supercomputers at the time.
So it would be a little while about 70 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 Lorenz, or Lorenz.
Yeah, well, first of all, we should set the stage.
The reason this guy, he was a meteorologist and scientist.
Not that those are not the same thing.
He's a scientist who dabbled in meteorology.
Right.
He was a mathematician.
Yeah.
But he was really into meteorology because 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 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 it a couple of days out.
But after that, it's just it's totally unpredictable.
It drives us mad.
And it's not it wasn't just their their reputations that were at stake.
Like people were losing their lives because of it.
Right.
Yeah, in 1962, 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 in damage.
Right.
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 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 were finally able to do these incredible calculations that we could never do before.
I know.
They were able to crunch 64 bytes a second.
Yeah.
We had the abacus and then the supercomputer.
Right.
There was nothing in between.
Yeah.
I looked up the computer that Lorenz was working with.
Was it the Whopper?
A Royal McBee.
What was the Whopper?
War Games.
Was it called the Whopper?
Yeah.
W-O-P-R.
Right.
I can't believe they called it that.
I know.
Pretty stupid.
So the guy just nicknamed it Joshua?
No, Joshua was the...
Software?
Falcon was the old man who designed all this stuff, and his son was Joshua, and that was the password to get into the system.
Oh, that was the password.
Yeah.
I guess I was too young to understand what a password was.
Yeah.
Okay.
There weren't passwords at the time.
No.
And you just shouted it at the computer, and they were like, okay, access granted.
Yeah.
Still, that movie holds up.
Does it really?
Oh, totally.
I gotta check it out.
Yeah, still very, very fun.
Young Ally Sheedy, boy, I 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 her in something recently and I didn't realize that was her.
Oh, really?
She looks familiar.
I was like, oh, that's Ally Sheedy.
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 Royal McBeeb was not quite the Whopper.
You could actually sit down at it.
The Royal McBeeb?
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.
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.
He started doing just that.
He did.
So he started off with a computational model of 12 meteorological calculations, which is very basic because there are infinite meteorological calculations, probably.
Did I say it wrong again?
No, no.
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.
Right.
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 McWhopper.
What was it?
The Royal McBee.
The Royal McBee.
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 calculations never seemed to repeat themselves.
He was making like word art.
You remember that?
That was the first thing anybody did on a computer.
Oh, yeah, yeah.
Was to make word art, like a butterfly or something.
Right, you would print out.
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 guidebook that tells you how to do it.
True.
Have you ever seen Me, You, and Everyone We Know?
Yeah, I love that movie.
That's a great movie.
Those little kids in there, they were doing that.
Oh, yeah, yeah.
The forever back and forth poop.
Well, I haven't seen that since it came out.
It's been a while.
Oh, you gotta see it again.
Great movie.
Good movie.
Ally Sheedy's not in it.
No.
It's Miranda July.
Right, and she wrote and directed too, right?
She did a great job.
It was her show.
It's one of those rare movies where There's just the right amount of whimsy.
Because whimsy so easily overpowers everything else and becomes like bleh.
Yeah, yeah.
This is like the most perfectly balanced amount of whimsy I've ever seen in a movie.
Yeah, if there's too much whimsy, I just like 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, oh, 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.
It is.
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, 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 printout he had went to three decimal points.
Yeah.
So he was working from the printout and didn't take into account that the computer accepted six decimal points.
So he was just putting in three.
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.
He sort of accidentally came upon it.
It's neat that this guy did this because it changed his career.
I think he went from emphasis on meteorology to an emphasis on chaos math.
To stud scientists.
Basically.
So, 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 weird.
This is worth investigating.
And like, what was his name, Poincaré?
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 I'm 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 vacuum that's left and that creates a rolling vertically-based convection current.
Yeah.
Okay?
I would describe it as oven convection.
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 what you're talking about.
Sure.
He made little rolly motions.
So he's like, okay, I can figure this out.
So he comes up with 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 formulas, which were basically three variables that he calculated over time.
And he plugged them in, and he found three variables that changed over time.
And he found that, after a certain point, when you graph these things out and since they're three, you graph them out on a three-dimensional graph, so X, Y and Z.
Again, he wanted to just be able to visualize this.
Right.
Because it's easier for people to understand.
He was a very visual guy.
All of a sudden it made this crazy graph where the line as it progressed forward through time went all over the place.
It went from this axis to another axis, to the other axis, and it would spend some time over here and then it would suddenly loop over to the other one and it followed no rhyme or reason.
It never retraced its path and it was describing how a convection current changes over time, right?
And Lorenz was looking at this.
He was expecting these three things to equalize and eventually form a line, because that's what determinism says.
Things are going to fall into a certain amount of equilibrium and just even out over time.
That is not what he found.
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, if you look at the graph it's not just lines going in straight lines bouncing all over the place randomly.
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 every time unless you're a robot.
Sure.
And that's what it ended up looking like.
Yeah, yeah.
It never retraced the same path twice, ever.
It had a lot of really surprising properties.
And at the time, it just fell completely outside the understanding of science, right?
Yeah.
Luckily, this happened to Lorenz, 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.
A, this thing kind of looked like butterfly wings a little bit.
And B.
When he went to present his findings he basically had the notion he's like I'm gonna wow these people in the crowd in 1972.
It's a conference that I'm going to.
And I'm gonna say something.
Like you know, the seagull flaps its wings and it starts a small turbulence that can affect weather on the other side of the world.
A small little thing will just grow and grow and snowball and affect things.
And he had a colleague who was like, eh.
Seagull wings, that's nice.
And he said, how about this?
And this is the title they ended up with.
Predictability, colon, 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.
Should we take a break?
Yes.
All right, we'll be right back.
All right, so the Lorenz Attractor. is that picture that he ended up with.
Right, that graph.
It's called the Lorenz 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, actually, I don't know who wrote this.
Could have been a woman, could have been a small child.
Could have been Noah.
Of undetermined gender, I have no idea.
To the gender neutral narrator.
They said, he said, all right, think about a town that has like 10,000 people living in it.
To make that town work, you gotta have like a gas station, a grocery store, a...
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 10000 more people living there.
Right, and they don't go to church.
Maybe so.
Did I say church?
They needed a church?
No, no.
Oh, okay.
I was just assuming this was going to break the equilibrium.
No, no, no.
But you just have more people, so 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 is called an attractor.
Okay.
So then he said, it said, they said.
He, capital he.
The royal.
He said, all right now, let's say, instead of that factory being built, and you had those original 10000, let's say 3000, of those people just up and leave one day.
Okay.
And the grocery store guy says, well, there's only 7,000 people here.
We need 8,000 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 a grocery store.
They build a grocery store.
They can't sustain.
They shut down.
Someone else comes along because of the demand.
And it is this search for equilibrium, this dynamic.
Well, you reach equilibrium here and there as the store opens.
Periods of stability.
Periods of stability.
And that dynamic equilibrium is called a strange attractor.
So an attractor is the state which a system settles on.
Strange attractor is the trajectory on which it never settles down but tries to reach the equilibrium with periods of stability.
Man.
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 you can add.
Yeah?
Yeah.
No, you're going to add to it?
No.
That's it?
No.
I mean like yeah, an attractor is where, if you graph something and eventually it reaches equilibrium, it's a regular attractor.
If it never reaches equilibrium, it's constantly trying to and has periods of stability strange attractor.
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?
The butterfly effect.
And it coupled with his picture, the picture of a strange attractor which is almost the aside from fractals, almost the emblem or the logo for chaos theory, the Lorentz attractor.
It got attention off the bat.
It wasn't like Poincaré's findings where it got neglected for 70 years.
Almost immediately.
Everybody was talking about this because again, what Lorenz had uncovered, which is the same thing that Poincaré had uncovered, is that determinism is possibly based on an illusion that the universe isn't stable, that the universe isn't predictable, and that what we are seeing as stable and predictable are these little periods, windows of stability that are found in strange attractor graphs.
That that's what we think the order of the universe is, but that that is actually the abnormal aspect of the universe.
And that instability unpredictability, as far as we're concerned, is the actual state of affairs in nature.
Yeah.
And I think, as far as we're concerned, is a really important point too Chuck, because it doesn't mean that nature is unstable and chaotic.
It means that our picture of what we understand as order doesn't jibe with how the universe actually functions.
Yeah.
It's just our understanding of it.
And we're just so anthropocentric that we see it as chaos and disorder and something to be feared.
When really it's just complexity that we don't have the capability of predicting after a certain degree.
Yeah, I think that makes me feel a little better, because when you read stuff like this, you start to feel like well, the Earth could just throw us all off of its face at any moment, because it starts spinning so fast that gravity becomes undone.
And I know that's not right, by the way.
I've always loved that kind of science that shows we don't know anything.
Like Robert Hume, who I understand was a philosopher, but he was a philosopher scientist.
Sure.
His whole jam was like cause and effect is an illusion.
It's just an assumption that if you drop a pencil, it will always fall down.
It's an illusion.
And this is pre-gravity, understanding gravity.
But he makes a good point.
It's pre-gravity when everyone's just floating around.
Yeah.
Going, this pencil's got me wacky.
But the point was that 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.
Pretty cool.
And this definitely supports that idea.
For sure.
Sorry, I'm excited about chaos theory.
Can you 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 for people like us, we're like oh okay, we can understand chaos.
Then when somebody says, good, do a differential equation, you're just like, what?
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.
Well, actually, not later on.
About 10 years.
Yeah, but it was kind of at the same time this other stuff was going on with Lorenz.
Yeah.
Late 60s, early 70s.
There was a guy named Stephen Smale, Fields Medal 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
Boom, boom, da-choo, 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, boy, I hope this makes some good bread.
This is going to be so good.
Put a little rosemary on it.
Yeah, maybe so.
Olive oil, 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 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, too.
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 it.
Oh, what?
Imitate Forrest Gump?
Sure.
No, I can't do that.
That's fine.
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.
I thought that was so charming.
And he also did the smile t-shirt.
Sure.
It was just too much.
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 an hour and a half into it, you'll be like, I get it.
Zemeckis.
You know what was a good Tom Hanks movie that was overlooked?
Road to Perdition.
Yeah, not bad.
It 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, no, he's going to do... And also that last one that wasn't so great.
He's got a potential project coming up and he would be amazing for it, and I don't remember what it was.
Did you see Revolutionary Road?
Yes, God.
It was just like...
Yeah, you want to jump off a bridge and see 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 engaged to be married or thinking about it.
Yeah, or if you're blue already.
Yeah.
Just take a really good mood and be like, I'm sick of being in a good mood.
Sit down and watch Revolutionary Road.
Yeah.
Watch Joe vs. the Volcano instead.
Great movie.
Where was I?
Smale Horseshoe is what that's called.
That was, he was the first person to actually use the word chaos.
Oh, he was.
I think so.
Oh, no, no, no.
York was.
Tom York's dad.
Yeah, you're right.
He wasn't the first person.
You are correct.
But Smale's Horseshoe illustrates a really good point, Chuck.
Is it Tom York's dad?
No.
Oh, okay.
No, but they're both British.
Sure.
Yorkies.
Actually, one's Australian.
No, they're British.
So those two points which started out right by each other and then end up in two totally different places.
Yeah, that applies not just to bread dough, but also to things like water molecules that are right next to each other at some point and then a month later they're in two different oceans.
Even though you would assume that they would go through all the same motions and everything.
But they're not.
There's so many different variables with things like ocean currents that two water molecules that were once side by side end up in totally random different places.
And that's part of chaos.
It's basically chaos personified.
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.
So he was using math to model how animal populations would change over time, given certain starting conditions.
So he started using these equations, these 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, it was working pretty well for a while, but he noticed something really, really weird, right?
Yeah.
He had this formula, the logistic difference equation is the name of it.
Sure.
Okay, so he 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 30, but there's also 45 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 3057 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 millionths of a degree.
All of a sudden, it would turn into four.
So there'd be four different numbers that was the animal population.
And then it would turn into 16.
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 16 chaos.
Two, four 16, two four, eight 16 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 3 Implies Chaos.
And man, finally, somebody said the word.
Yeah.
I kept thinking it was all these other people.
Yeah, and this paper where they first debut the name Chaos they based it, Tom Yorkstead 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 Lawrence Attractor.
So that provided chaos to the world.
And it was basically 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 80s and the 90s, as you know from Jurassic Park.
Chaos was everything.
Everybody was like, chaos, this is totally awesome.
It's the new frontier of science.
And then it just went away.
And a lot of people said, well, it was a little over-hyped.
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 new type of science.
It was a new understanding of the universe.
It was saying like, yes, you can still use Newtonian physics.
Don't throw everything out the window.
You can still try and predict weather and still try and build more accurate instruments and get decent results, but you can't, with absolute perfection 100 predict complex systems.
Like determinism, the ultimate goal of determinism is false.
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?
Yeah.
What's the point of anything?
No, not science.
Well, some chaos people have said, no, this is great, this is good.
We'll take the universe as it is, rather than trying to force it into our pretty little equations and saying 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 population is going to have.
Say, okay, here is the fish population.
Here is the ocean temperature.
Here are all these other variables.
Let's feed it into a model and see what happens.
Not this is going to happen.
What happens instead?
And this is kind of the understanding of chaos theory now.
It's taking raw data as much data as you can possibly get your hands on, as precise data as you could possibly get your hands on and just feeding it into a model and seeing what patterns emerge.
Rather than making assumptions, it's saying, what's the outcome?
What comes out of this model?
Yeah, and that's why, when you see things like, 50 years ago they predicted this animal would be extinct and it's not.
Well, that's because the variations were too complex.
They tried to predict, and that's why if you look at a 10-day forecast, you, sir, are a fool.
Well, 10 days from now, it says it's going to rain in the afternoon.
Come on.
But 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 and you could conceivably make some assumptions based on that.
You can say, well, actually, 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 data could have been off slightly.
Yeah.
This one value.
Right.
And then you have more buffalo than you think.
Yeah.
Sure.
You got buffaloed by chaos.
And we're not even getting into fractals.
It's a whole other thing, and we did a whole other podcast in June 2012 about fractals and Benoit Mandelbrot.
Yeah.
Mandelbrot?
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 that'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 in action.
Go check it out.
Okay, if you want to know more about chaos theory hope your brain's not broken yeah, go take some lsd and look at fractals.
Don't do that.
Um, you can type those words into how stuff works in the search bar.
Any of those fractals lsd, chaos.
It'll bring up some good stuff.
And since i said good stuff, it's time for listener mail.
I'm going to call this Rare Shoutout.
I get requests all the time.
I'll bet I know which one this is.
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.
Yes, the one.
Yeah?
Yeah.
That's good.
That's good. 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 thanks for listening.
Yeah, man.
Thank you.
That was a great email.
I love that one.
Glad we don't give you a headache, Rachel.
Yeah, for real.
She listens 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.
You'll be all right.
If you want to get in touch with us, you can hang out with us on Twitter at SYSK Podcast.
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