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Speaker 1: Hey, Daniel, when you are teaching, are you the kind

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Speaker 1: of professor that assigns super hard homework in your classes?

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Speaker 1: You mean, like, find the motion of a banana tied

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Speaker 1: to a string held by a squirrel riding on a

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Speaker 1: roller coaster, all of that in orbit around a black hole?

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Speaker 1: Like that kind of problem? What are you, professor, Rube Goldberg? No,

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Speaker 1: that was just a joke. I actually like to make

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Speaker 1: the homework just a little bit harder than what we

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Speaker 1: work on in class. You know, that's where the concepts

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Speaker 1: really come together in your mind. Right, right, you're an

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Speaker 1: evil professor. Basically you never assigned unsolved research problems to

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Speaker 1: first year students. Know that only happens in the movies. Man,

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Speaker 1: Goodwill Hunting is not a documentary. You're not Matt Damon.

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Speaker 1: I don't have the looks for it. Yes, there's always

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Speaker 1: room for improvement. Hi am more hamming cartoonists and the

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Speaker 1: creator of PhD comics. I'm Daniel. I'm a particle physicist,

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Speaker 1: and I've never solved an outstanding math problem. Not yet,

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Speaker 1: do you mean? Right? Like if you had solved it, it

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Speaker 1: it wouldn't be an an outstanding math problem. That's true. Yeah,

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Speaker 1: there are these famous, outstanding problems, and it's cool when

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Speaker 1: they stand for hundreds of years and then somebody comes

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Speaker 1: along and figures them out. What do you think happens?

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Speaker 1: Like somebody just comes up with the right way to

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Speaker 1: look at it, or like they see something nobody else

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Speaker 1: has seen before, or the history was just waiting for

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Speaker 1: the right intellect. Yeah, sometimes it's a slow construction of

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Speaker 1: ideas over hundreds of years. When you look at the

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Speaker 1: history of it and be like, problem proposed in sixteen nineteen,

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Speaker 1: progress has made in eighteen fourteen, and then Samantha figures

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Speaker 1: it out, and it's pretty awesome to see the stretch

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Speaker 1: of history there. I'm waiting for people to solve some

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Speaker 1: pretty intractable parenting problems. Didn't sometimes they had Those are eternal, man,

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Speaker 1: they will never be solved. They will never be solved.

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Speaker 1: It's part of being human, I guess. Welcome to our

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Speaker 1: podcast Daniel and Jorge Explain the Universe, a production of

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Speaker 1: our Heart Radio in which we tackle the hardest problem,

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Speaker 1: which is understanding the nature of this universe we find

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Speaker 1: ourselves in. How does it work, where did it come from,

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Speaker 1: why is it the way that it is, and is

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Speaker 1: it even possible to understand it. We dive right into

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Speaker 1: the biggest, hardest, deepest questions. We explain the answers and

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Speaker 1: our ignorance to you. What if that's the harder problem,

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Speaker 1: Daniel explaining something to other people. We do our best here,

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Speaker 1: but um, it's pretty hard to wrap your head around

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Speaker 1: all the amazing and incredible stuff that is happening in

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Speaker 1: the universe. And one of my favorite things about doing

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Speaker 1: this podcast is exercising that part of my brain that

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Speaker 1: translates these ideas from like the cutting edge of physics,

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Speaker 1: two things everybody can understand, because to do that you

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Speaker 1: have to have a really good grasp on what's going on. See,

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Speaker 1: you actually have to understand it first before explaining into people.

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Speaker 1: So what am I doing here? Then? Well, sometimes when

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Speaker 1: you try to explain something, you realize whole lot of second,

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Speaker 1: I don't really understand how this works as well as

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Speaker 1: I thought it did sometimes only sometimes, though that never

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Speaker 1: happens on our podcast. It happens to me all the

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Speaker 1: time when I'm teaching and also on this podcast, And

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Speaker 1: that's one reason why it's so fun, because not only

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Speaker 1: are we explaining stuff, we're also learning as we go.

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Speaker 1: But that is a pretty good parenting lesson. Also, it's

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Speaker 1: good to share what you know when you learn what

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Speaker 1: you love about this crazy beautiful costmas. Yeah, how does

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Speaker 1: that help you with your parenting? Well, it's just good

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Speaker 1: to share. I think it's good. Well, you have to

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Speaker 1: share with your children. I think it's a law, that

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Speaker 1: is a rule. But it's also good to teach it

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Speaker 1: to share, you know. It's just everyone's more generous with

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Speaker 1: their what they have in their knowledge. We're all happy.

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Speaker 1: I thought you were going to use the wondering glamor

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Speaker 1: of the universe to convince your kids to do their chores,

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Speaker 1: like take out the trash because stars are amazing? Are

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Speaker 1: you are insignificant in this universe? You're a tiny speck

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Speaker 1: of dust in the floating and vast vacuum of perhaps

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Speaker 1: infinite space, and therefore you should do your homework. I

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Speaker 1: think that will work against you. So then why should

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Speaker 1: I bother taking out the trash if nothing matters? Because

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Speaker 1: if nothing matters children, everything matters. Like that that trended

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Speaker 1: philosophical use that PhD for something. But anyways, we do

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Speaker 1: like to talk about not only what scientists know about

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Speaker 1: this universe and all of the wonderful stuff in it,

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Speaker 1: but also what scientists are struggling with understanding about how

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Speaker 1: things work. That's right, because we have this amazing mental

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Speaker 1: machinery of science that lets us build up a body

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Speaker 1: of knowledge. Things we do understand about the universe has

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Speaker 1: a machinery to it, and that machinery is mathematical. It's

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Speaker 1: incredible in me sometimes that mathematics can describe the way

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Speaker 1: the world works at all. You know, you throw a

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Speaker 1: baseball and it follows a parabola, which is a very

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Speaker 1: simple mathematical relationship. So it's incredible when you can use

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Speaker 1: mathematics to describe what's really very complex behavior, all sorts

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Speaker 1: of zillions of particles moving through the air altogether. But

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Speaker 1: sometimes it's easier than other times. And the cool thing

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Speaker 1: about sciences is that it's always at the sort of

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Speaker 1: the leading edge of human knowledge, right, Like that's what

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Speaker 1: science is. It's sort of like asking the questions nobody's

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Speaker 1: ever asked, or finding the answers nobody that has so far.

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Speaker 1: And so sometimes you run into things that are just

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Speaker 1: really really extra hard or maybe even impossible. Yeah, and

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Speaker 1: sometimes they are impossible because the physics is really hard,

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Speaker 1: and sometimes they're impossible because we just don't have the

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Speaker 1: mathematics yet. Like, there's been lots of times in history

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Speaker 1: when mathematicians have developed tools, not because they thought they

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Speaker 1: were gonna be useful for physics, but just because they

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Speaker 1: thought it was fun, and then later on physicists were

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Speaker 1: like a whold on a second. That totally helps me

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Speaker 1: solve this problem I've been struggling with for twenty years.

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Speaker 1: A great example is general relativity, which is built on geometry,

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Speaker 1: which was developed just ten years before. Without all that

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Speaker 1: work developing geometry, there's no way Einstein could have developed relativity.

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Speaker 1: Is this really fascinating dance between mathematics and physics? Yeah?

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Speaker 1: What kind of dance? How would you describe that dance?

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Speaker 1: Is it like a Charleston or more like a waltz?

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Speaker 1: Or like hip hop breakdancing competition? What would you call it?

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Speaker 1: The mathematicians carefully build their tools and we just sneak

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Speaker 1: in and steal them, So maybe it's more like a

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Speaker 1: cat Burglar dance. Oh man, I can't wait for that,

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Speaker 1: you know, interpretive dance History of Science Broadway play that

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Speaker 1: you're working on. Yeah, you know, I wish it was

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Speaker 1: more back and forth. Sometimes I feel like, shouldn't the

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Speaker 1: mathematicians be excited when their tools actually get used to

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Speaker 1: describe the real universe? But a lot of times they

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Speaker 1: don't seem to care at all, and they're like, whatever,

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Speaker 1: who cares about the real universe? I'm walking the halls

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Speaker 1: of truth. You're selling their halls with like reality and

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Speaker 1: like red and dirt, Like that's just dirt. Adams are

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Speaker 1: just dirt. If they cared about getting dirty, they would

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Speaker 1: have been physicists instead of mathematicians. I see, physicis are

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Speaker 1: are the down and dirty of of scientists. I think

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Speaker 1: physicists are to mathematicians what engineers are to physicists. Oh,

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Speaker 1: I see the better the better people, right, the true

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Speaker 1: heroes on the hierarchy of useless pure the hierarchy of usefulness.

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Speaker 1: You mean, depending on what you put in the top? Yes,

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Speaker 1: exactly right. Yes, if you turn upside down, we're actually

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Speaker 1: at the top. Yes, it's all about your perspective, that's right.

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Speaker 1: There is no up in space anyway. Well, there are

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Speaker 1: interesting problems in physics, some of them which are even intractable,

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Speaker 1: and so in this episode we'll be talking about one

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Speaker 1: such problem that maybe affects are very movement through space,

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Speaker 1: and it affects how planets revolve around their suns, and

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Speaker 1: which we may never find the answer for. So to

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Speaker 1: be on the podcast, we'll be asking the question, what's

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Speaker 1: so hard about the three body problem? Now, Daniel, this

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Speaker 1: is not something that's not safe for work, is it?

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Speaker 1: I mean, I see something here at three bodies? Is

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Speaker 1: this about? You know? No, this is not about being

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Speaker 1: exploratory in your relationships at all. It's what's so mathematically

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Speaker 1: difficult about three gravitationally attracting objects? Is the safe preparatory

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Speaker 1: in the heavenly bodies relationships? You know, some bodies here

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Speaker 1: on Earth are quite heavenly as well, but we're talking

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Speaker 1: about celestial bodies, that's right, the real stars. Alright, So

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Speaker 1: the three button. More specifically, this is kind of about

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Speaker 1: what is the three body problem at all? Because I

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Speaker 1: imagine that a lot of people have heard of him,

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Speaker 1: although it is the title of sort of a well

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Speaker 1: known science fiction novel out there, right, that's fairly recent,

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Speaker 1: that's right. Yeah, it's like one of the biggest novels

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Speaker 1: in the last few years. It's a whole trilogy written

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Speaker 1: by a fantastic Chinese author. A lot of people are

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Speaker 1: really into this book, and a lot of our listeners

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Speaker 1: have written in asking us to talk about this book.

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Speaker 1: But I thought, first maybe be more fun to talk

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Speaker 1: about like the physics problem that's at the heart of

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Speaker 1: the novel, that we can talk about the actual problem itself. Yeah,

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Speaker 1: I think. I try to read the novel. It's it's

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Speaker 1: pretty dense, it's kind of thick. Yeah, there's a lot

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Speaker 1: of physics in that book, which is pretty fun for

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Speaker 1: people who like really well thought out physics novels. And

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Speaker 1: so it's a good idea to try to get an

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Speaker 1: understanding for like what is the underlying problem at the

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Speaker 1: core of the story? Right? And it was like a

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Speaker 1: bestseller and want all the awards right in science fiction.

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Speaker 1: M So you can check that out if you like.

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Speaker 1: But the title of it refers to kind of an

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Speaker 1: old and famous problem in physics about I imagine three bodies.

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Speaker 1: That's right, it's really old problem, and old problems are

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Speaker 1: the funniest problems because it means that like a lot

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Speaker 1: of smart people have been butting their heads against this

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Speaker 1: problem for decades or even centuries, and nobody has figured

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Speaker 1: it out. And doesn't mean it's impossible. There are other

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Speaker 1: mathematical problems that have existed for hundreds of years and

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Speaker 1: then all of a sudden, some dude in a cabin

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Speaker 1: in Russia comes out with like a hundred page proof

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Speaker 1: of it. So it might be possible to be solved,

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Speaker 1: but nobody's cracked this one. Yeah, just a book on Airbnb,

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Speaker 1: that cabin in Russia, and you know, book it for

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Speaker 1: for a couple of years, and that you might solve

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Speaker 1: a famous problem. That's the real answer. That wasn't a metaphor.

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Speaker 1: That was that really happened to you, not to me. No,

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Speaker 1: there really is a Russian mathematician who worked all by

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Speaker 1: himself for a decade and saw the famous problem in math,

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Speaker 1: the remon conjecture. Wow. And he was in a cabin,

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Speaker 1: using a cabin. He worked all by himself, and he

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Speaker 1: just sent in the solution and they tried to give

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Speaker 1: him the Fields Medal for it and he wouldn't even

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Speaker 1: show up. Wow. That feels like such a fine line

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Speaker 1: between like, you know, genius and you know, socially unacceptable behavior.

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Speaker 1: He's well on one side of that line. But anyways,

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Speaker 1: let's talk about this problem, the three body problem. And so,

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Speaker 1: as usually we were wondering how many people out there

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Speaker 1: we knew what this was, if they had heard of

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Speaker 1: it before beyond the novel, or how important it is

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Speaker 1: to sort of predicting the movement of our planets in

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Speaker 1: our solar system. So Daniel as usually went out there

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Speaker 1: into the wilds of the internet to ask people what

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Speaker 1: is the three body problem? So, while we are still

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Speaker 1: pandemically shut down, I am very grateful to all of

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Speaker 1: you who are willing to participate via email on the

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Speaker 1: person on the virtual street interviews. So if you would

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Speaker 1: like to participate and hear your speculation on the podcast,

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Speaker 1: please don't be shy. Send us a message to questions

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Speaker 1: at Daniel and Jorge dot com. Think about it for

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Speaker 1: a second. Do you know what the three body problem is?

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Speaker 1: Here's what people have to say. I don't know what

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Speaker 1: the three body problem is, I'm afraid so I'm barely

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Speaker 1: aware of what the three body problem is. I did

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Speaker 1: read as you should use three body problem trilogy. My

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Speaker 1: understanding is that it's a problem with how three bodies

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Speaker 1: orbit one another and how it could continue to do

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Speaker 1: that and be stable without cuestion into one another. A

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Speaker 1: lot of people spend a fair amount of time calculating

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Speaker 1: how two massive bodies interacts due to the gravitational field

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Speaker 1: surrounding them. But actually, if you add a third body,

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Speaker 1: the system becomes unstable, it becomes chaotic, so you can't

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Speaker 1: determine an exact solution. And also if you make a

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Speaker 1: small change let's say in the initial positions of the bodies, um,

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Speaker 1: you can't actually determine how let's say the forces between

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Speaker 1: the three bodies will be affected. I think that's to

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Speaker 1: do when you've got three bodies that rotatue interacts, usually

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Speaker 1: like the Sun, the Earth and the Moon, for example,

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Speaker 1: would be that would be three bodies, and I think

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Speaker 1: you can solve two bodies. Any more than a few

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Speaker 1: more and you can't solve it. I think is it

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Speaker 1: is one of the issues. Wow, that is something I

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Speaker 1: am not sure where it is. I don't know what

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Speaker 1: the three body problem is m unless it's relating to

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Speaker 1: a previous question where if you have three bodies acting

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Speaker 1: on each other gravitationally, um, you haven't got sort of

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Speaker 1: one orbiting another or one with a joint orbit with

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Speaker 1: another that that will be probably quite at random implication

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Speaker 1: to their orbits. I have never heard of the three

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Speaker 1: body problem before. But if I were to guess, I

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Speaker 1: think it is three bodies interacting with each other, and

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Speaker 1: something unusual happens, like something that doesn't happen between two

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Speaker 1: bodies of four bodies. It just happens between these three

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Speaker 1: bodies for some reason, and for some reason the number

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Speaker 1: is three. Actually, I've studied physics before, so I know

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Speaker 1: that the three body problem is this problem where if

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Speaker 1: you have two objects pulling on each other, then those

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Speaker 1: equations can be solved pretty easily. But if you add

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Speaker 1: in a third body, now you have three different interactions

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Speaker 1: between A B, A C and C B. And when

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Speaker 1: you have interactions of that order that that many interactions,

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Speaker 1: it becomes sort of an unsolvable math problem. And so

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Speaker 1: we don't have like good solutions for those sort of situations.

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Speaker 1: We have to essentially come up with approximations and simulate it.

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Speaker 1: All right, There not a lot of knowledge about this,

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Speaker 1: But someone did read the True Gene. Yeah, exactly three

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Speaker 1: books in the three Body Problem trilogy. It's nice. It

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Speaker 1: must have been good because he read all three or

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Speaker 1: I wonder if your completest, you know, tendencies would kick

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Speaker 1: in after you rerund well, I can't just read one

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Speaker 1: three body problem book. I gotta read all three depends

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Speaker 1: if they leave a cliffhanger at the end of the

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Speaker 1: first novel. You should title all your trilogies with the

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Speaker 1: number three in it. But it seems like most people

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Speaker 1: here are guessing it has to do with bodies in

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Speaker 1: space and then specifically three bodies of course, But a

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Speaker 1: lot of people are saying maybe it's about it becoming

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Speaker 1: unsolvable or chaotic or unstable. Are they sort of in

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Speaker 1: the right track. They are exactly on the right track.

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Speaker 1: It's really interesting. There's a problem which is easy if

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Speaker 1: there's only two objects involved, and then becomes basically unsolvable

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Speaker 1: if you have three objects involved, right, like real human relationships,

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Speaker 1: which can be tricky even when there are two bodies involved,

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Speaker 1: even if everyone is open minded, it gets tricky. Al Right, Well,

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Speaker 1: let's dig into Daniel, how would you describe the three

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Speaker 1: body problems? I think the best way to describe it

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Speaker 1: is to first talk about what we can do and

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Speaker 1: simply said, if you have two objects in space, and

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Speaker 1: you know where they are, how heavy they are, and

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Speaker 1: the direction they're going in, then you can predict their motion.

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Speaker 1: You can say at some time in the future, I

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Speaker 1: know where they are going to be. So, for example,

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Speaker 1: imagine just the Sun and the Earth. These are two

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Speaker 1: objects that pull on each other. There are forces involved.

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Speaker 1: And if you know where the Sun and the Earth

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Speaker 1: are at some moment in time, in which direction they're heading,

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Speaker 1: and their masses, you can write down a very simple

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Speaker 1: formula that will tell you where they will be in

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Speaker 1: the future. Like you say, where will the sun be

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Speaker 1: in a year, or in a thousand years or in

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Speaker 1: a million years. It's like a very simple mathematical expression.

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Speaker 1: You plug in the time, it tells you where the

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Speaker 1: Sun will be. So that's the two body problem, and

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Speaker 1: we have a solution for that. We can crank through

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Speaker 1: the mathematics and get a very nice simple formula that

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Speaker 1: tells us where they will be at any moment in

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Speaker 1: the future. Right, But you have to kind of assume

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Speaker 1: that they're alone in the in the whole universe, like

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Speaker 1: there's nothing else in the universe pulling on them. Right,

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Speaker 1: that's right, only two bodies. And as usual, you know,

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Speaker 1: physics is telling a story, and that story is always approximate.

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Speaker 1: The reality never matches the approximate stories we try to

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Speaker 1: use when we tell physics stories because in reality, there's

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Speaker 1: an infinite number of bodies out there in space, and

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Speaker 1: gravity works for over infinite distances, and so everything in

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Speaker 1: the universe is hugging on things all the time. But

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Speaker 1: usually you can get away with disregarding that. You don't

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Speaker 1: have to care about what's happening in Andromeda when you're

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Speaker 1: doing in the calculation of whether your satellite is going

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Speaker 1: to go around the Earth, because it's basically zero contribution.

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Speaker 1: So here we're talking about the scenario where you have

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Speaker 1: two bodies and everything else can be ignored without changing

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Speaker 1: anything down to like, you know, the tenth decimal place

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Speaker 1: or something. Yes, so in the sort of simplified universe

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Speaker 1: of exactly two things in your universe, you can predict

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Speaker 1: the motion of two objects, all right, So then I'm

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Speaker 1: guessing when you get to three bodies, it gets a

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Speaker 1: little harder. When you get to three bodies, it doesn't

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Speaker 1: just get a little harder, it becomes impossible. If you

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Speaker 1: know where three objects are. You know, so you have,

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Speaker 1: for example, the Sun, the Earth, and then another object.

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Speaker 1: Now you just have three objects and you know exactly

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Speaker 1: where they are, what direction they're going in, and you

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Speaker 1: know their masses. You cannot write down a simple formula

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Speaker 1: that tells you where they're going to be in a week,

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Speaker 1: or in a year or in a thousand years. Well,

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Speaker 1: it gets really complicated. Suddenly, it gets really complicated. We

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Speaker 1: don't have a solution. Now, we have an understanding for

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Speaker 1: what's going on, Like we know the forces involved, We

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Speaker 1: know what the gravity is between two objects given their distance. Right,

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Speaker 1: that's a pretty simple formula. Newton told us how to

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Speaker 1: do that. But that doesn't mean we know how to

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Speaker 1: find the solution. Doesn't mean we can take those forces

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Speaker 1: and predict the motion. Right. Well, I think this might

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Speaker 1: be kind of a subtle subject for a lot of

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Speaker 1: people out there, which is like what you mean in

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Speaker 1: physics as a solution, because it doesn't mean that you

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Speaker 1: can't predict where they're going to be. You just don't

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Speaker 1: have an easy solution to the equations to predict this. Right.

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Speaker 1: It means that we know what the constraints are. Like

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Speaker 1: physics tells you what the rules are, tells you like,

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Speaker 1: for example, how two objects pull on each other. It

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Speaker 1: doesn't tell you how those objects are going to move.

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Speaker 1: To figure out how the objects are to move, which

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Speaker 1: is what you need to predict their emotion. You need

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Speaker 1: to be able to solve all of those equations and

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Speaker 1: get the answer out. So physics gives you, like all

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Speaker 1: the equations you need to solve. It doesn't mean you

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Speaker 1: know how to solve the equations, Like not every equation

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Speaker 1: you get is solvable, or we don't necessarily have the

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Speaker 1: mathematical tools to solve an arbitrary equation. Turns out, in

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Speaker 1: physics there are only like five problems we do know

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Speaker 1: how to solve and everything else is intractable. Well, that

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Speaker 1: probably makes for a short workday there free. But I

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Speaker 1: think what you mean is, like, for example, like a ball,

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Speaker 1: if I throw a ball here at my son in

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Speaker 1: our backyard here, like I know that that ball, I

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Speaker 1: know the constraints on it, like I know the forces

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Speaker 1: pulling on it, the force of gravity, and I know

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Speaker 1: that F equals m A for example. So I can solve,

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Speaker 1: for example, for its exceloration very easily. But maybe getting

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Speaker 1: like a formula for what its position is going to

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Speaker 1: be is a little tricky. It's different than knowing what

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Speaker 1: it's acceleration is going to be exactly. The acceleration just

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Speaker 1: tells you how is momentums and change in a given moment.

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Speaker 1: Right to know where it's going to be, you need

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Speaker 1: to then solve the equations of motion, which incorporate all

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Speaker 1: these forces and is affected by that acceleration. But it

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Speaker 1: requires actually solving the equation. You know. It's like if

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Speaker 1: I have an equation that says X plus five equals ten. Right,

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Speaker 1: that's an equation that constrains X. It limits what X

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Speaker 1: can be, but it's not actually the solution. The solution

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Speaker 1: is X equals five. That's a very simple one, right.

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Speaker 1: You know exactly how to go from the equation X

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Speaker 1: plus five equals tend to the solution, But you don't

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Speaker 1: necessarily know how to do that for an arbitrary equation.

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Speaker 1: Take another simple example, like X squared equals forty nine.

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Speaker 1: How do you find the solution to that? You know

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Speaker 1: off the top of your head that x equals seven works,

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Speaker 1: You can plug it in and check it. But how

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Speaker 1: do you find the solution? If I tell you X

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Speaker 1: square equals an arbitrary number? How do you find the

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Speaker 1: square root of an arbitrary number? There actually is no

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Speaker 1: way to do that. There is no mechanism for solving

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Speaker 1: that equation other than guessing and checking us like my

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Speaker 1: parenting strategy right there. And I think what you mean is, like,

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Speaker 1: you know, in physics, you have equations to tell you,

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Speaker 1: for example, like the acceleration of x, which is like

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Speaker 1: how the velocity changes, which is like how the position

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Speaker 1: is changing. Like you have equations for that. But to

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Speaker 1: actually get the pocsisition, you have to kind of backtrack

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Speaker 1: from acceleration to velocity to position. And that's where the

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Speaker 1: trickiness comes from, right yeah, because the acceleration changes through time,

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Speaker 1: and so to figure out how all those accelerations add

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Speaker 1: up to describe the motion of the object is not

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Speaker 1: always easy. And then what you want is a simple

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Speaker 1: formula that describes it, and that doesn't necessarily exist, right

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Speaker 1: because I guess when you go from two bodies to

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Speaker 1: three bodies, then the formula just get too complicated. The

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Speaker 1: formula gets too complicated. Exactly, the system gets really complicated

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Speaker 1: because now you have these three different objects pulling on

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Speaker 1: each other, and it actually becomes chaotic. All right, Well,

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Speaker 1: let's dig into why exactly it is so hard and

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Speaker 1: how it becomes pure chaos when you add a third

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Speaker 1: cell steel body into the mix, and what consequences it

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Speaker 1: has for our ability to predict the universe. But first,

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Speaker 1: let's take a quick break. All right, Daniel, we're talking

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Speaker 1: about the three body problem, and I guess we're not

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Speaker 1: just talking about like what happens if your spouse moves

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Speaker 1: to another city, right, this is more cosmic. I can't

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Speaker 1: solve that problem for you. There is no equation that

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Speaker 1: tells you how to live your life. That's the one

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Speaker 1: body problem is already pretty hard. Now we're talking about

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Speaker 1: the three body problem. One is the loneliest number. But

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Speaker 1: this is not a relationship helpline, and this is not

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Speaker 1: a podcast about human emotions. We are trying to solve

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Speaker 1: the much easier problem of motion of objects through space.

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Speaker 1: And so you're saying that when I have two objects

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Speaker 1: in space, it's easy enough to sort of predict where

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Speaker 1: they're going to be once you have three. It because

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Speaker 1: there's no easy solution to that problem. Yeah, there's no

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Speaker 1: easy solution. There's no like short mathematical answer when you

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Speaker 1: like is something like x f T or x is

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Speaker 1: the position of the object, and then a simple formula

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Speaker 1: where you can plug in the time and it will

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Speaker 1: tell you exactly the position of the object. That's what

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Speaker 1: you're looking for because you'd like to be able to

429
00:22:15,800 --> 00:22:18,080
Speaker 1: take that system and say, I want to know where

430
00:22:18,119 --> 00:22:19,399
Speaker 1: the moon is going to be, where I want to

431
00:22:19,480 --> 00:22:20,920
Speaker 1: know where the sun is going to be in a

432
00:22:21,000 --> 00:22:23,360
Speaker 1: thousand years. The problem is that there is no such

433
00:22:23,440 --> 00:22:25,879
Speaker 1: simple formula. We haven't found one at least, and we

434
00:22:25,960 --> 00:22:28,800
Speaker 1: suspect that it might not exist because the system of

435
00:22:28,920 --> 00:22:32,240
Speaker 1: three objects is much much more complicated than a system

436
00:22:32,280 --> 00:22:35,120
Speaker 1: of just two objects, right, And it gets really complicated

437
00:22:35,119 --> 00:22:38,240
Speaker 1: because now you have three objects in three D? Is

438
00:22:38,280 --> 00:22:40,200
Speaker 1: it kind of about going to the third dimension? That

439
00:22:40,280 --> 00:22:42,080
Speaker 1: makes it hard because I imagine if you have two

440
00:22:42,119 --> 00:22:44,440
Speaker 1: bodies in space, you can just treat him as like

441
00:22:44,480 --> 00:22:46,920
Speaker 1: a two D problem, right, like you just imagine the

442
00:22:47,000 --> 00:22:48,879
Speaker 1: plane where these two bodies are. But once you have

443
00:22:49,000 --> 00:22:51,240
Speaker 1: three and then it's like, now it's a three D problem.

444
00:22:51,359 --> 00:22:53,359
Speaker 1: It's true that two objects in space you can always

445
00:22:53,359 --> 00:22:55,480
Speaker 1: define a plane between them. You can also put three

446
00:22:55,560 --> 00:22:58,320
Speaker 1: objects on a plane though, right, three points define a plane,

447
00:22:58,440 --> 00:23:00,679
Speaker 1: so there's always a plane for three jects. I think

448
00:23:00,720 --> 00:23:03,040
Speaker 1: the problem is that when you have three objects, a

449
00:23:03,200 --> 00:23:07,320
Speaker 1: small change in their location leads to a big change

450
00:23:07,640 --> 00:23:09,320
Speaker 1: in where they're going to be in the future. At

451
00:23:09,400 --> 00:23:12,760
Speaker 1: least for gravitational interactions, whereas if you have two objects,

452
00:23:13,040 --> 00:23:15,000
Speaker 1: a small change and where the Earth is going to be,

453
00:23:15,280 --> 00:23:17,879
Speaker 1: it will mostly settle back into the same answer. And

454
00:23:18,000 --> 00:23:20,879
Speaker 1: so in terms of like finding an equation that describes it,

455
00:23:21,080 --> 00:23:24,240
Speaker 1: there's a whole family of equations that can describe stable solutions.

456
00:23:24,640 --> 00:23:27,400
Speaker 1: We don't really have functions that are very good describing

457
00:23:27,640 --> 00:23:31,399
Speaker 1: chaotic situations, whereas very small change in the angle or

458
00:23:31,440 --> 00:23:34,440
Speaker 1: the velocity of the moon means it's now suddenly over here,

459
00:23:34,560 --> 00:23:36,120
Speaker 1: or it's suddenly on the other side of the sun,

460
00:23:36,240 --> 00:23:39,040
Speaker 1: or it flies off in a completely different direction. Our

461
00:23:39,040 --> 00:23:42,359
Speaker 1: equations are not good at describing chaotic mathematics. But I

462
00:23:42,359 --> 00:23:44,399
Speaker 1: guess maybe the question is, like, what is it that

463
00:23:44,480 --> 00:23:47,480
Speaker 1: about going from two to three that actually makes the

464
00:23:47,600 --> 00:23:51,760
Speaker 1: equations unsolvable? Like before, with two, I can solve the equations,

465
00:23:51,840 --> 00:23:54,480
Speaker 1: but with three, there's no solution for them. Does it

466
00:23:54,560 --> 00:23:57,480
Speaker 1: become nonlinear? Is that what it is? It's already nonlinear,

467
00:23:57,600 --> 00:24:00,119
Speaker 1: right that even with an equals to it's nonlinear as

468
00:24:00,160 --> 00:24:03,400
Speaker 1: these distances go like one over radius squared, so there's

469
00:24:03,400 --> 00:24:06,480
Speaker 1: an inverse are squared there, So it's already nonlinear. I

470
00:24:06,560 --> 00:24:08,880
Speaker 1: think something you said earlier is really the right way

471
00:24:08,920 --> 00:24:11,200
Speaker 1: to think about it. We know the forces F and

472
00:24:11,240 --> 00:24:13,760
Speaker 1: the mass M, and we have F equals m A,

473
00:24:14,080 --> 00:24:16,960
Speaker 1: so we can get the acceleration. That's a very simple formula.

474
00:24:17,160 --> 00:24:19,680
Speaker 1: But how do you go from knowing the acceleration, which

475
00:24:19,720 --> 00:24:22,639
Speaker 1: is how much the speed is changing, to knowing the

476
00:24:22,760 --> 00:24:25,439
Speaker 1: actual location. What you have to do is add up

477
00:24:25,480 --> 00:24:29,000
Speaker 1: the effects of lots of little accelerations over time, which

478
00:24:29,080 --> 00:24:32,280
Speaker 1: means you have to integrate. You have to use calculus.

479
00:24:32,600 --> 00:24:35,040
Speaker 1: But just like there aren't that many physics problems that

480
00:24:35,080 --> 00:24:38,920
Speaker 1: are solvable, not every function can be integrated, at least

481
00:24:39,200 --> 00:24:41,720
Speaker 1: not into a simple formula you can write down. So

482
00:24:41,920 --> 00:24:44,560
Speaker 1: just because you know the force and the acceleration doesn't

483
00:24:44,640 --> 00:24:47,760
Speaker 1: mean you know how to integrate it into getting the location.

484
00:24:48,119 --> 00:24:49,960
Speaker 1: And we can go a little bit further if you

485
00:24:50,040 --> 00:24:52,719
Speaker 1: look at the structure of the problem. Mathematicians call these

486
00:24:52,760 --> 00:24:56,560
Speaker 1: problems non integrable, which just means that, like the possible

487
00:24:56,600 --> 00:25:00,240
Speaker 1: trajectories for these objects in this three D space don't

488
00:25:00,240 --> 00:25:04,240
Speaker 1: follow simple paths right like, they diverge very quickly. It's

489
00:25:04,240 --> 00:25:06,320
Speaker 1: not like it can be easily simplified from a whole

490
00:25:06,359 --> 00:25:08,920
Speaker 1: big set of possible solutions down to just a few,

491
00:25:09,119 --> 00:25:11,080
Speaker 1: and with any equals too. With the two body problem,

492
00:25:11,359 --> 00:25:13,480
Speaker 1: there are a bunch of simplifications you can make that

493
00:25:13,640 --> 00:25:17,000
Speaker 1: separate the problem so that, for example, the distance between

494
00:25:17,040 --> 00:25:20,480
Speaker 1: the objects is independent of their relative angle, because for

495
00:25:20,600 --> 00:25:23,240
Speaker 1: two objects, you know, the angle doesn't really matter. What

496
00:25:23,440 --> 00:25:26,120
Speaker 1: only matters is really just the distance. But for three

497
00:25:26,200 --> 00:25:28,840
Speaker 1: objects you have not just the relative distances, but you

498
00:25:28,960 --> 00:25:31,720
Speaker 1: also have the relative angles. And so now all the

499
00:25:31,800 --> 00:25:34,320
Speaker 1: problems are still tied together. You know, when you try

500
00:25:34,359 --> 00:25:36,600
Speaker 1: to solve a set of equations, sometimes it's helpful to

501
00:25:36,640 --> 00:25:39,440
Speaker 1: try to separate them and solve them independently, but that's

502
00:25:39,480 --> 00:25:42,080
Speaker 1: not always possible, and when they're all entangled up with

503
00:25:42,160 --> 00:25:44,960
Speaker 1: each other, you can't always find a solution. Now, I see,

504
00:25:45,000 --> 00:25:47,280
Speaker 1: there's something sort of magical about the number two that

505
00:25:47,480 --> 00:25:49,520
Speaker 1: then you lose once you get more than two, right,

506
00:25:49,560 --> 00:25:51,720
Speaker 1: because it's not just three bodies that are hard, it's

507
00:25:51,720 --> 00:25:54,200
Speaker 1: also four and five and six and infinite. Right. Yes,

508
00:25:54,320 --> 00:25:56,360
Speaker 1: you might have thought, oh, well, two bodies are solvable,

509
00:25:56,440 --> 00:25:59,080
Speaker 1: so then why not three? It's actually the other direction.

510
00:25:59,200 --> 00:26:02,360
Speaker 1: Two is the the one that is solvable. Right. All

511
00:26:02,440 --> 00:26:05,560
Speaker 1: the problems are unsolvable except for this one magic special

512
00:26:05,720 --> 00:26:08,680
Speaker 1: case of two bodies which we have been able to

513
00:26:08,760 --> 00:26:12,240
Speaker 1: separate using this special trick and solve. So it's sort

514
00:26:12,240 --> 00:26:14,639
Speaker 1: of lucky that any of them are solvable. Well, the

515
00:26:15,000 --> 00:26:18,480
Speaker 1: zero body problem is solvable too, and the one body problem,

516
00:26:18,560 --> 00:26:21,280
Speaker 1: I imagine is solvable. It's just that it's just gets

517
00:26:21,320 --> 00:26:24,840
Speaker 1: more complicate. Real equations start to like interact with each other,

518
00:26:24,920 --> 00:26:27,719
Speaker 1: and then you can't like fit a simple formula as

519
00:26:27,760 --> 00:26:31,080
Speaker 1: a solution, right, yeah, exactly. And in addition, there's something

520
00:26:31,160 --> 00:26:34,880
Speaker 1: about chaos here, right, that's right, The results become chaotic.

521
00:26:35,080 --> 00:26:37,359
Speaker 1: As we said before, if you change a little bit

522
00:26:37,400 --> 00:26:39,680
Speaker 1: the initial conditions, if Earth is a little bit further

523
00:26:39,800 --> 00:26:43,119
Speaker 1: away or pointing in a slightly different direction, you can

524
00:26:43,160 --> 00:26:46,959
Speaker 1: get completely different outcomes. So Earth can be like tossed

525
00:26:46,960 --> 00:26:49,400
Speaker 1: out of the Solar System, or it can fall into

526
00:26:49,440 --> 00:26:52,040
Speaker 1: another orbit or something like that. Whereas if you just

527
00:26:52,160 --> 00:26:54,879
Speaker 1: have two bodies, things tend to be pretty stable. That

528
00:26:55,000 --> 00:26:57,520
Speaker 1: means that if you perturb it, something comes along, gives

529
00:26:57,560 --> 00:26:59,840
Speaker 1: the Earth a little push, will probably roll back into

530
00:26:59,880 --> 00:27:03,040
Speaker 1: a initial orbit, whereas in a three body system, things

531
00:27:03,119 --> 00:27:05,600
Speaker 1: get out of hand very quickly. And that's you know,

532
00:27:05,720 --> 00:27:08,639
Speaker 1: not just like is it complicated motion. That's one of

533
00:27:08,680 --> 00:27:11,760
Speaker 1: the reasons why we don't have a simple formula because

534
00:27:11,760 --> 00:27:15,040
Speaker 1: we don't have functions that describe that, like sign and

535
00:27:15,200 --> 00:27:18,560
Speaker 1: co sign and logarithm. These things are mostly well behaved,

536
00:27:18,640 --> 00:27:22,399
Speaker 1: and so it's very difficult to describe chaotic motion using

537
00:27:22,440 --> 00:27:25,119
Speaker 1: the sort of mathematical language that we have developed. Oh,

538
00:27:25,280 --> 00:27:28,800
Speaker 1: I see, because there's no function that is chaotic kind

539
00:27:28,840 --> 00:27:31,639
Speaker 1: of is that what you're saying, like, chaotic motion is

540
00:27:31,760 --> 00:27:35,480
Speaker 1: not easily kind of captured in a formula. Yeah, it's

541
00:27:35,480 --> 00:27:38,359
Speaker 1: not easily captured in a formula. It's possible to describe

542
00:27:38,440 --> 00:27:42,760
Speaker 1: chaotic motion, but usually our solutions there are numerical, they're approximate,

543
00:27:43,000 --> 00:27:46,879
Speaker 1: use simulations. You know, we can describe chaotic systems like

544
00:27:47,280 --> 00:27:50,080
Speaker 1: you build a computer system, you put three objects in it,

545
00:27:50,440 --> 00:27:52,280
Speaker 1: and then what you do is you say, all right,

546
00:27:52,359 --> 00:27:54,960
Speaker 1: what happens in the first second, and you say, well,

547
00:27:55,000 --> 00:27:56,760
Speaker 1: the Earth's gonna move this way, the Sun is gonna

548
00:27:56,760 --> 00:27:58,119
Speaker 1: move that way, and the moon is going to move

549
00:27:58,200 --> 00:28:00,399
Speaker 1: this other direction, and then you update everything and then

550
00:28:00,440 --> 00:28:02,639
Speaker 1: you do it again. So you slice the problem in

551
00:28:02,720 --> 00:28:04,680
Speaker 1: time and you say, what if I only want to

552
00:28:04,760 --> 00:28:07,720
Speaker 1: predict a half second from now or a milli second

553
00:28:07,800 --> 00:28:10,600
Speaker 1: from now, then you can really simplify and say I

554
00:28:10,720 --> 00:28:12,399
Speaker 1: know what to do for a half second. Then you

555
00:28:12,480 --> 00:28:14,320
Speaker 1: just do that over and over and over again. That's

556
00:28:14,359 --> 00:28:16,520
Speaker 1: the way we can describe a chaotic system is like

557
00:28:16,800 --> 00:28:19,440
Speaker 1: slicing it in time and then try to move our

558
00:28:19,520 --> 00:28:23,359
Speaker 1: stimulation forward, just one time slice at a time. But

559
00:28:23,480 --> 00:28:25,359
Speaker 1: that doesn't mean that we can then look at that

560
00:28:25,440 --> 00:28:27,600
Speaker 1: motion and say, oh, look it follows a sign wave,

561
00:28:27,720 --> 00:28:30,040
Speaker 1: or oh look it follows a logarithm of a sign wave.

562
00:28:30,400 --> 00:28:33,160
Speaker 1: We can't find a solution. We can't find a mathematical

563
00:28:33,240 --> 00:28:35,840
Speaker 1: description of the motion, even if we can describe it

564
00:28:35,920 --> 00:28:39,400
Speaker 1: in the simulation I see. So like we can maybe

565
00:28:39,520 --> 00:28:41,560
Speaker 1: predict what the system is going to do, what these

566
00:28:41,880 --> 00:28:43,520
Speaker 1: three bodies are going to do, but we have to

567
00:28:43,560 --> 00:28:45,960
Speaker 1: do it step by step. We can't just say, like, hey,

568
00:28:46,040 --> 00:28:47,560
Speaker 1: twenty years from now, this is what it's going to be.

569
00:28:47,960 --> 00:28:50,080
Speaker 1: There's no formula that will tell you that. You have

570
00:28:50,200 --> 00:28:52,240
Speaker 1: to like simulate it a little by little until you

571
00:28:52,320 --> 00:28:54,520
Speaker 1: get to ten years from now. Yeah, and even those

572
00:28:54,600 --> 00:28:58,480
Speaker 1: simulations are difficult because it's chaotic. Like if you don't

573
00:28:58,560 --> 00:29:02,040
Speaker 1: make those calculations very very very precise, then your simulation

574
00:29:02,160 --> 00:29:03,880
Speaker 1: is going to be wrong. As you try to predict

575
00:29:03,960 --> 00:29:07,960
Speaker 1: further and further into the future, because small mistakes really

576
00:29:08,000 --> 00:29:11,080
Speaker 1: add up the snowball into big mistakes. It's just like

577
00:29:11,200 --> 00:29:14,240
Speaker 1: you know, the butterfly problem. Butterfly flaps its wings in

578
00:29:14,360 --> 00:29:17,720
Speaker 1: China and that has cascading effects on the weather, which

579
00:29:17,800 --> 00:29:21,000
Speaker 1: causes eventually a storm in Central Park in New York.

580
00:29:21,120 --> 00:29:23,720
Speaker 1: And these things are real. They're real physical systems that

581
00:29:23,880 --> 00:29:26,080
Speaker 1: behave this way where if you give them a very

582
00:29:26,200 --> 00:29:29,080
Speaker 1: small nudge, it can have a very big effect downstream.

583
00:29:29,280 --> 00:29:32,000
Speaker 1: And that makes them very very challenging even to simulate,

584
00:29:32,080 --> 00:29:34,320
Speaker 1: as we talked about, because if you get something wrong

585
00:29:34,800 --> 00:29:38,080
Speaker 1: very early on, your results in ten years are nonsense.

586
00:29:38,440 --> 00:29:40,719
Speaker 1: We much prefer to have like a simple we call

587
00:29:40,760 --> 00:29:43,840
Speaker 1: it an analytical formula, like a very short math expression

588
00:29:44,080 --> 00:29:45,920
Speaker 1: that we can just plug numbers into, because it can

589
00:29:45,960 --> 00:29:47,800
Speaker 1: be exact and it can tell us exactly what's going

590
00:29:47,840 --> 00:29:50,000
Speaker 1: to happen in ten years or in a hundred years.

591
00:29:50,160 --> 00:29:52,600
Speaker 1: I think what you're saying is that these numerical approaches

592
00:29:52,760 --> 00:29:56,440
Speaker 1: or simulations, they're just an approximation basically, right Like you're

593
00:29:56,640 --> 00:29:58,960
Speaker 1: looking at the equations like the f equals amaze or

594
00:29:59,040 --> 00:30:01,920
Speaker 1: the you know, the horses between the three bodies, and

595
00:30:02,000 --> 00:30:04,280
Speaker 1: you're saying, well, let's not try to get the exact solution.

596
00:30:04,360 --> 00:30:07,600
Speaker 1: Let's just pretend that for the next millisecond everyone has

597
00:30:07,640 --> 00:30:10,560
Speaker 1: the same acceleration or something like that. Exactly. You make

598
00:30:10,600 --> 00:30:12,600
Speaker 1: a bunch of simplications and you say, well, I only

599
00:30:12,640 --> 00:30:14,920
Speaker 1: want to predict a millisecond in the future, so can

600
00:30:14,960 --> 00:30:17,080
Speaker 1: I do that? And then you just keep doing that

601
00:30:17,240 --> 00:30:19,600
Speaker 1: over and over again. You're saying that if I'm wrong

602
00:30:19,640 --> 00:30:21,960
Speaker 1: a little bit because of that implication, then in a

603
00:30:22,040 --> 00:30:25,400
Speaker 1: chaotic system, I could be really wrong. Yeah, and that's

604
00:30:25,400 --> 00:30:27,680
Speaker 1: a big deal. If you're doing something like planning a

605
00:30:27,800 --> 00:30:31,560
Speaker 1: trip to the stars or sending your probe to Jupiter

606
00:30:31,800 --> 00:30:34,520
Speaker 1: or whatever, you definitely want to get that right right, Yeah.

607
00:30:34,560 --> 00:30:37,000
Speaker 1: You don't want to be off by a few light years. Yeah.

608
00:30:37,080 --> 00:30:39,120
Speaker 1: Or even if you're just flying through the Solar System,

609
00:30:39,520 --> 00:30:41,360
Speaker 1: if you get it wrong, you could end up crashing

610
00:30:41,400 --> 00:30:44,120
Speaker 1: into the Sun or getting tossed out of the Solar

611
00:30:44,160 --> 00:30:46,080
Speaker 1: System in the wrong direction. You're trying to make it

612
00:30:46,160 --> 00:30:49,040
Speaker 1: to Pluto from here, right, Pluto is very far away

613
00:30:49,040 --> 00:30:52,000
Speaker 1: in a very very small target. Imagine firing a gun

614
00:30:52,560 --> 00:30:54,920
Speaker 1: from l A to New York and trying to hit

615
00:30:55,040 --> 00:30:57,400
Speaker 1: a tiny and the tiny target, it's very difficult. They're

616
00:30:57,480 --> 00:31:00,640
Speaker 1: very small. If you're off by a tiny little angle

617
00:31:00,960 --> 00:31:02,640
Speaker 1: in l A, you're definitely not going to hit that

618
00:31:02,720 --> 00:31:04,480
Speaker 1: target in New York. But I guess that. You know,

619
00:31:04,640 --> 00:31:07,320
Speaker 1: we are pretty good these days with you know, supercomputers,

620
00:31:07,360 --> 00:31:10,600
Speaker 1: we are pretty good at simulating things and kind of predicting.

621
00:31:10,720 --> 00:31:12,720
Speaker 1: You know, maybe not the storm that comes from the

622
00:31:12,800 --> 00:31:14,920
Speaker 1: butterfly wings, but you know, the weather is you know,

623
00:31:15,040 --> 00:31:17,520
Speaker 1: predictable sort of up to like a week, right or

624
00:31:18,000 --> 00:31:20,760
Speaker 1: a couple of weeks, which is super impressive because they

625
00:31:20,800 --> 00:31:23,960
Speaker 1: have to simulate all of those you know, air molecules

626
00:31:24,000 --> 00:31:25,920
Speaker 1: and pockets of hot air that are out there in

627
00:31:25,960 --> 00:31:28,920
Speaker 1: the atmosphere. It's not that it makes the problem impossible,

628
00:31:29,040 --> 00:31:32,120
Speaker 1: it's just makes it harder. Or you know kind of storms,

629
00:31:32,120 --> 00:31:33,880
Speaker 1: how much we can predict it. Yeah, if you had

630
00:31:33,880 --> 00:31:36,960
Speaker 1: an infinitely powerful computer, then we could solve these problems

631
00:31:37,200 --> 00:31:39,840
Speaker 1: because we could simulate them with really high resolution. We

632
00:31:39,880 --> 00:31:43,200
Speaker 1: could take like really really short time steps in our simulation.

633
00:31:43,400 --> 00:31:45,760
Speaker 1: Instead of stepping forward a millisecond, we could step forward

634
00:31:45,800 --> 00:31:48,680
Speaker 1: in nanosecond and then correct. And so if you had

635
00:31:48,840 --> 00:31:51,920
Speaker 1: infinite computing resources, you could do these things very effectively.

636
00:31:52,080 --> 00:31:54,320
Speaker 1: And some of the reasons why these problems which seem

637
00:31:54,400 --> 00:31:56,840
Speaker 1: to be impossible for a long time, like predicting the weather,

638
00:31:57,400 --> 00:31:59,680
Speaker 1: seem to be getting easier, and not because humans are

639
00:31:59,680 --> 00:32:02,840
Speaker 1: getting smarter, but because our computers are getting more powerful,

640
00:32:03,160 --> 00:32:05,360
Speaker 1: and so now we have a lot more computing power

641
00:32:05,400 --> 00:32:08,320
Speaker 1: available to do things like predicting the weather and trying

642
00:32:08,320 --> 00:32:11,560
Speaker 1: to predict earthquakes and all these really really hard problems

643
00:32:11,600 --> 00:32:14,719
Speaker 1: that are really important. Like today we can predict how

644
00:32:14,800 --> 00:32:16,960
Speaker 1: the whole Solar system works, right, We mostly can, And

645
00:32:17,000 --> 00:32:19,320
Speaker 1: a lot of that is because mostly the Solar system

646
00:32:19,400 --> 00:32:21,880
Speaker 1: is a bunch of two body problems, like the Earth

647
00:32:22,000 --> 00:32:24,800
Speaker 1: moving around the Sun. Technically it's you know, it's an

648
00:32:24,840 --> 00:32:27,120
Speaker 1: eight body problem because the Earth is pulled on by

649
00:32:27,160 --> 00:32:29,840
Speaker 1: the Moon and Jupiter and Neptune and whatever. But mostly

650
00:32:29,880 --> 00:32:32,840
Speaker 1: it's just the Sun. You can ignore everything else when

651
00:32:32,880 --> 00:32:35,480
Speaker 1: you're calculating the Earth to some degree. If you want

652
00:32:35,480 --> 00:32:37,720
Speaker 1: to get it exactly right, then yes, you need to

653
00:32:37,800 --> 00:32:40,600
Speaker 1: include effects from Mars and Venus, and then you can't

654
00:32:40,680 --> 00:32:43,320
Speaker 1: use Kepler's laws. You can't use the simple formulas that

655
00:32:43,400 --> 00:32:45,520
Speaker 1: we have for a two body problem. You have to

656
00:32:45,560 --> 00:32:48,600
Speaker 1: get down and dirty and do the simulations using very

657
00:32:48,680 --> 00:32:50,920
Speaker 1: powerful computers. But then I guess, would you say that

658
00:32:51,000 --> 00:32:53,840
Speaker 1: our Solar system is chaotic as well? Like is our

659
00:32:53,960 --> 00:32:56,560
Speaker 1: Solar system a chaotic system? Because it seems sort of

660
00:32:56,600 --> 00:32:59,880
Speaker 1: stable right now, but are you saying maybe, like if

661
00:33:00,040 --> 00:33:01,520
Speaker 1: you give it enough time, it is kind of a

662
00:33:01,560 --> 00:33:04,960
Speaker 1: little unpredictable. Yeah, definitely, the Solar System is chaotic, but

663
00:33:05,240 --> 00:33:08,400
Speaker 1: on the cosmological time scales, not on like a year

664
00:33:08,840 --> 00:33:11,920
Speaker 1: or ten years, but unlike millions and billions of years,

665
00:33:12,360 --> 00:33:14,480
Speaker 1: and it was more chaotic in the beginning. We sort

666
00:33:14,520 --> 00:33:17,640
Speaker 1: of settled into something that's more stable. But when the

667
00:33:17,720 --> 00:33:19,880
Speaker 1: Solar System began, it was a big hot mess and

668
00:33:19,920 --> 00:33:23,280
Speaker 1: things were flying everywhere. Planets were colliding into each other

669
00:33:23,400 --> 00:33:26,040
Speaker 1: and making new planets and throwing things out of the

670
00:33:26,080 --> 00:33:29,080
Speaker 1: Solar System. We probably had a different number of planets

671
00:33:29,240 --> 00:33:32,320
Speaker 1: a billion or two billion years ago. People suspect there

672
00:33:32,400 --> 00:33:35,600
Speaker 1: might have been like another giant planet which was tossed

673
00:33:35,640 --> 00:33:38,680
Speaker 1: out of the Solar System by Jupiter and Saturn. So, yeah,

674
00:33:38,720 --> 00:33:41,280
Speaker 1: that sounds pretty chaotic to me. Solar system was like,

675
00:33:41,600 --> 00:33:43,280
Speaker 1: you know, I have enough to deal with with the

676
00:33:43,880 --> 00:33:46,920
Speaker 1: nine bodies, possibly eight, let's get someone out. But you

677
00:33:47,040 --> 00:33:49,480
Speaker 1: can take a very complicated system like the Solar system

678
00:33:49,760 --> 00:33:53,400
Speaker 1: and find approximately stable solutions things which will last for

679
00:33:53,480 --> 00:33:56,160
Speaker 1: a long long time. But how stable are they? Something

680
00:33:56,240 --> 00:33:58,480
Speaker 1: which flies through the Solar system can perturb it a

681
00:33:58,560 --> 00:34:00,880
Speaker 1: little bit, and then things can very quickly go out

682
00:34:00,960 --> 00:34:03,360
Speaker 1: of whack. So if you have like another star and

683
00:34:03,440 --> 00:34:06,040
Speaker 1: that gets a little close to our Solar system, it

684
00:34:06,080 --> 00:34:08,399
Speaker 1: could change the orbit of Jupiter, which could have knock

685
00:34:08,440 --> 00:34:10,680
Speaker 1: on effects about changing the orbit of Saturn, and then

686
00:34:10,760 --> 00:34:13,359
Speaker 1: the asteroid belt and Mars, and pretty soon we could

687
00:34:13,400 --> 00:34:16,960
Speaker 1: have craziness. All right, Well, let's get into that craziness

688
00:34:17,120 --> 00:34:19,719
Speaker 1: of our Solar system and what the consequences are of

689
00:34:19,800 --> 00:34:24,040
Speaker 1: this three body problem and our ability to understand the

690
00:34:24,760 --> 00:34:27,799
Speaker 1: rest of the cosmos. But first let's take another quick break.

691
00:34:40,640 --> 00:34:44,080
Speaker 1: All right, we're talking about the three body problem, and

692
00:34:44,320 --> 00:34:48,239
Speaker 1: it's hard to find an analytical solution to it, as

693
00:34:48,280 --> 00:34:50,279
Speaker 1: opposed to the two body problem, which you can find

694
00:34:50,320 --> 00:34:52,759
Speaker 1: a nice, neat formula for it. But I wonder then

695
00:34:52,760 --> 00:34:55,000
Speaker 1: if this is sort of like a physicist frustration, because

696
00:34:55,040 --> 00:34:57,640
Speaker 1: as an engineer, I'm pretty much used to like things

697
00:34:57,680 --> 00:35:00,719
Speaker 1: not having an analytical solution, like from day one, like

698
00:35:00,880 --> 00:35:02,960
Speaker 1: nothing only like throwing a ball up in the air

699
00:35:03,000 --> 00:35:05,080
Speaker 1: has an analytical solution. Everything else you have to do

700
00:35:05,200 --> 00:35:08,920
Speaker 1: with numerical simulations or approximating, you know, the Navy, your

701
00:35:08,920 --> 00:35:12,040
Speaker 1: Stokes equations and having non linear stuff that you can't solve,

702
00:35:12,560 --> 00:35:14,600
Speaker 1: and so you know like it. As an engineer you

703
00:35:14,640 --> 00:35:17,560
Speaker 1: always rely on simulations, but maybe in physics you get

704
00:35:17,640 --> 00:35:20,560
Speaker 1: more frustrated for not having like a neat, you know,

705
00:35:21,320 --> 00:35:23,839
Speaker 1: clean formula to predict the future. Well, the thing that's

706
00:35:23,880 --> 00:35:26,520
Speaker 1: tantalizing is that there are a few cases when you

707
00:35:26,719 --> 00:35:29,000
Speaker 1: can find a neat formula where you can start with

708
00:35:29,200 --> 00:35:32,640
Speaker 1: just pencil and paper, describe the pushing and the pulling

709
00:35:32,680 --> 00:35:35,279
Speaker 1: of your system, and then get out a formula that

710
00:35:35,360 --> 00:35:37,719
Speaker 1: tells you where everything is going to be basically for

711
00:35:37,960 --> 00:35:41,520
Speaker 1: all time. That's amazing, it's beautiful, and it's tempting. It

712
00:35:41,600 --> 00:35:43,840
Speaker 1: makes you think, Wow, why can't I do this for

713
00:35:44,000 --> 00:35:47,080
Speaker 1: other systems? Why can't I do this for every system? Right?

714
00:35:47,120 --> 00:35:49,560
Speaker 1: Because if they exist for some systems, it gives you

715
00:35:49,640 --> 00:35:51,960
Speaker 1: the sense that, like, if we had the right mathematics,

716
00:35:52,040 --> 00:35:55,080
Speaker 1: if we knew the right language to talk about this stuff,

717
00:35:55,360 --> 00:35:58,920
Speaker 1: maybe even really complicated problems would be simpler. So it's

718
00:35:58,960 --> 00:36:01,600
Speaker 1: sort of aspirational yeah, I can imagine that frustration. You're

719
00:36:01,640 --> 00:36:04,600
Speaker 1: in your cabin in the middle of Russia, in Siberia,

720
00:36:04,640 --> 00:36:06,240
Speaker 1: in the middle of nowhere, and you're like, oh, shoot,

721
00:36:06,800 --> 00:36:09,480
Speaker 1: I need a computer I didn't bring one, or oh shoot,

722
00:36:09,520 --> 00:36:11,640
Speaker 1: I need to talk to somebody else, I don't have

723
00:36:11,719 --> 00:36:15,279
Speaker 1: a phone. That's frustrating, right, It is frustrating. And you know,

724
00:36:15,400 --> 00:36:18,760
Speaker 1: it's something funny about teaching freshman physics. I teach mechanics

725
00:36:18,920 --> 00:36:21,839
Speaker 1: often here you see irvine, and you know there are

726
00:36:21,960 --> 00:36:24,680
Speaker 1: not a lot of problems that really are solvable, like

727
00:36:24,960 --> 00:36:27,400
Speaker 1: very few problems can you actually sit down with pencil

728
00:36:27,440 --> 00:36:30,480
Speaker 1: and paper and say, here's the situation, here's the solution.

729
00:36:30,640 --> 00:36:32,720
Speaker 1: And so, in teaching this class for like almost twenty

730
00:36:32,800 --> 00:36:36,000
Speaker 1: years now, I've noticed that basically every physics Hormemork problem

731
00:36:36,080 --> 00:36:39,160
Speaker 1: in every textbook is one variation on like one of

732
00:36:39,239 --> 00:36:41,960
Speaker 1: these five solvable problems. And so as soon as you

733
00:36:42,000 --> 00:36:44,200
Speaker 1: look at when you're like, oh, this is that one problem,

734
00:36:44,360 --> 00:36:46,359
Speaker 1: or this is a problem number four, except they're using

735
00:36:46,400 --> 00:36:48,759
Speaker 1: a squirrel instead of a ball of rolling down a

736
00:36:48,840 --> 00:36:51,120
Speaker 1: plane or something, and so it all boils down to

737
00:36:51,239 --> 00:36:54,080
Speaker 1: like a few solvable problems because there are only a

738
00:36:54,160 --> 00:36:56,799
Speaker 1: few that can actually be solved. I mean, there's an

739
00:36:56,840 --> 00:36:59,920
Speaker 1: analytical simple solutions to what Professor Whitesen is gonna have.

740
00:37:00,120 --> 00:37:02,879
Speaker 1: But on the final test, I hope students are taking notes.

741
00:37:03,520 --> 00:37:05,439
Speaker 1: I say, if you take my class for twenty years,

742
00:37:05,480 --> 00:37:09,640
Speaker 1: it becomes pretty easy. I guess even physics professors are predictable.

743
00:37:09,680 --> 00:37:13,160
Speaker 1: Is that what you're saying they're going to do. It's

744
00:37:13,200 --> 00:37:16,600
Speaker 1: hard to invent new solvable problems in physics. And you

745
00:37:16,680 --> 00:37:20,120
Speaker 1: know it's not just like motion of two objects. There

746
00:37:20,160 --> 00:37:22,200
Speaker 1: are lots of places in physics where the problems are

747
00:37:22,239 --> 00:37:25,440
Speaker 1: not solvable. Einstein developed general relativity, right, which means he

748
00:37:25,520 --> 00:37:29,880
Speaker 1: wrote down the equations for how space curves when masses around.

749
00:37:30,239 --> 00:37:32,560
Speaker 1: He wrote down the equations, which means those are the

750
00:37:32,600 --> 00:37:35,759
Speaker 1: constraints that space has to follow. It doesn't mean he

751
00:37:35,880 --> 00:37:39,399
Speaker 1: can tell you how space behaves when masses around. Those

752
00:37:39,440 --> 00:37:42,920
Speaker 1: are the solutions to the Einstein equation. And he couldn't

753
00:37:42,960 --> 00:37:45,680
Speaker 1: solve his own equations. Like he developed general relativity and

754
00:37:45,719 --> 00:37:47,759
Speaker 1: he's like, here the equations, I don't know how to

755
00:37:47,800 --> 00:37:50,280
Speaker 1: solve this. He wasn't even the first person to solve

756
00:37:50,360 --> 00:37:53,520
Speaker 1: the Einstein equation that was short styled. Because these equations

757
00:37:53,560 --> 00:37:56,640
Speaker 1: are like famously impossible to solve. Now, if you have

758
00:37:56,760 --> 00:37:59,120
Speaker 1: a solution, you can check it. You can say I

759
00:37:59,239 --> 00:38:02,200
Speaker 1: think space ends in this way when there's massed around.

760
00:38:02,400 --> 00:38:04,279
Speaker 1: You can plug it into the equations, and if it works,

761
00:38:04,320 --> 00:38:06,560
Speaker 1: you're like, cool, I found it. But again, just because

762
00:38:06,600 --> 00:38:08,600
Speaker 1: you have the equations doesn't mean you know how to

763
00:38:08,680 --> 00:38:12,759
Speaker 1: find the solution. Anybody who's done differential equations knows that's true.

764
00:38:12,800 --> 00:38:15,920
Speaker 1: We have like no general mechanism for saying, here's a

765
00:38:15,920 --> 00:38:18,520
Speaker 1: differential equation, I can go from the equation to finding

766
00:38:18,600 --> 00:38:21,480
Speaker 1: the solution. And so there's lots of places in physics

767
00:38:21,800 --> 00:38:23,640
Speaker 1: where we just don't know how to solve these things.

768
00:38:23,760 --> 00:38:26,200
Speaker 1: Even still for general relativity, we only know how to

769
00:38:26,239 --> 00:38:29,680
Speaker 1: solve it for a few cases, like an empty universe,

770
00:38:29,920 --> 00:38:33,560
Speaker 1: a universe that's smoothly filled with matter like no lumps

771
00:38:33,600 --> 00:38:37,520
Speaker 1: at all, or a black hole. Basically everything else is unsolvable.

772
00:38:37,719 --> 00:38:40,080
Speaker 1: Then that's why before Sheeld found right like Evan found

773
00:38:40,120 --> 00:38:43,200
Speaker 1: the solution for general relativity in the case of a

774
00:38:43,280 --> 00:38:45,759
Speaker 1: simple black hole. Yeah, exactly. He was the first person

775
00:38:45,840 --> 00:38:48,400
Speaker 1: to ever solve these equations, and he actually did it

776
00:38:48,719 --> 00:38:51,120
Speaker 1: while he was a soldier in World War One. What

777
00:38:51,760 --> 00:38:54,239
Speaker 1: was he like fighting in a cabin in Russia. Also,

778
00:38:55,200 --> 00:38:57,719
Speaker 1: never fight a land war in Russian man, especially while

779
00:38:57,719 --> 00:39:02,360
Speaker 1: you're trying to solve question. Extra difficulty points. Unless he

780
00:39:02,480 --> 00:39:04,759
Speaker 1: was fighting for the Russians. Maybe I don't know, maybe

781
00:39:04,760 --> 00:39:06,799
Speaker 1: he's Russian, and then he had a lot of time

782
00:39:06,840 --> 00:39:10,000
Speaker 1: because the other team was doomed. No, but it's a

783
00:39:10,040 --> 00:39:12,040
Speaker 1: great story. You should look up how short Starts solved

784
00:39:12,080 --> 00:39:14,680
Speaker 1: this problem. I see. So it's not he solved general

785
00:39:14,680 --> 00:39:17,360
Speaker 1: relativity for all time in all cases. He just found

786
00:39:17,400 --> 00:39:20,440
Speaker 1: a solution for general relativity in this special case of

787
00:39:20,520 --> 00:39:22,560
Speaker 1: a simple black hole. Yeah, of a universe that has

788
00:39:22,680 --> 00:39:25,480
Speaker 1: nothing but a black hole in it. He figured out

789
00:39:25,560 --> 00:39:28,719
Speaker 1: the solution how space bends in that scenario. And then

790
00:39:28,840 --> 00:39:31,279
Speaker 1: later people figured out, Okay, well, if I assume that

791
00:39:31,360 --> 00:39:34,239
Speaker 1: the universe is totally empty, can I solve the equations? Oh,

792
00:39:34,400 --> 00:39:36,240
Speaker 1: I can do that? Or if I assume the universe

793
00:39:36,360 --> 00:39:39,000
Speaker 1: is like filled smoothly with matter, can I do that?

794
00:39:39,160 --> 00:39:42,480
Speaker 1: But like, nobody has solved general relativity for like our

795
00:39:42,600 --> 00:39:45,200
Speaker 1: solar system, or even just for like the Sun and

796
00:39:45,280 --> 00:39:48,480
Speaker 1: the Earth together. It's too complicated. Nobody has figured out

797
00:39:48,640 --> 00:39:51,359
Speaker 1: how to go from those equations to say, here's how

798
00:39:51,520 --> 00:39:55,200
Speaker 1: space has to bend in this situation. Oh wait, so

799
00:39:55,440 --> 00:39:57,920
Speaker 1: not even like the two body problem has a solution

800
00:39:58,000 --> 00:40:01,000
Speaker 1: in general relativity. Yeah, that's right. General auctivity much much

801
00:40:01,080 --> 00:40:05,480
Speaker 1: harder than Newtonian mechanics. We can do things like numerical relativity,

802
00:40:05,520 --> 00:40:07,960
Speaker 1: like we can describe how black holes orbit each other

803
00:40:08,040 --> 00:40:11,120
Speaker 1: and collide and generally gravitational waves. Because we can do

804
00:40:11,200 --> 00:40:15,040
Speaker 1: it numerically, we can use computers to do approximate solutions

805
00:40:15,080 --> 00:40:17,680
Speaker 1: to these things. But nobody can like write down simple

806
00:40:17,760 --> 00:40:20,279
Speaker 1: formulas to tell you like how black holes orbit each

807
00:40:20,280 --> 00:40:23,120
Speaker 1: other and collapse. Oh, I see. All this time we've

808
00:40:23,120 --> 00:40:25,879
Speaker 1: been talking about the two body probably being solvable. It's

809
00:40:25,920 --> 00:40:28,800
Speaker 1: only solvable in the Newtonian case, right, Like if you

810
00:40:28,840 --> 00:40:33,319
Speaker 1: assume the simplest or the simple physics of Newton, then

811
00:40:33,480 --> 00:40:35,840
Speaker 1: you can find a solution, but not for three. But

812
00:40:35,920 --> 00:40:38,200
Speaker 1: if you assume, like what we actually know what's going

813
00:40:38,239 --> 00:40:40,920
Speaker 1: on general relativity, then it's we can't even start, Like

814
00:40:41,400 --> 00:40:44,319
Speaker 1: there's no solution, Yeah exactly. You know, Einstein lays out

815
00:40:44,360 --> 00:40:46,800
Speaker 1: the equations the constraints, but he doesn't tell you, and

816
00:40:46,880 --> 00:40:49,520
Speaker 1: he doesn't know how to go from the constraints to

817
00:40:49,719 --> 00:40:52,080
Speaker 1: a solution. You know, it's sort of like if you're

818
00:40:52,400 --> 00:40:54,319
Speaker 1: driving down the highway with your family and you ask

819
00:40:54,320 --> 00:40:56,440
Speaker 1: somebody what they want for dinner, and everybody says, I

820
00:40:56,520 --> 00:40:58,319
Speaker 1: want a salad, or I want pizza, or I want

821
00:40:58,360 --> 00:41:01,280
Speaker 1: hot dogs, Like those are the con straints. Doesn't necessarily

822
00:41:01,320 --> 00:41:03,759
Speaker 1: mean you know how to find a restaurant that satisfies

823
00:41:03,880 --> 00:41:07,080
Speaker 1: those constraints, right, Having the constraints doesn't tell you how

824
00:41:07,160 --> 00:41:10,000
Speaker 1: to find a solution. Wow, it sounds like something from

825
00:41:10,080 --> 00:41:13,600
Speaker 1: personal experience with data. You're trying to events, Yes, I'm

826
00:41:13,640 --> 00:41:17,160
Speaker 1: looking for a restaurant the search salads and hotdogs and pizza.

827
00:41:18,120 --> 00:41:21,000
Speaker 1: Let me know if you find one that's not even

828
00:41:21,040 --> 00:41:23,719
Speaker 1: the general relativity solution. Like if you add relatives to

829
00:41:23,880 --> 00:41:27,279
Speaker 1: this card, right, then it gets impossible, right, because then

830
00:41:27,360 --> 00:41:31,880
Speaker 1: you have all these relative dynamics exactly, very chaotic, very quickly. Well,

831
00:41:31,920 --> 00:41:34,160
Speaker 1: I think what's interesting is that this is not just

832
00:41:34,680 --> 00:41:38,240
Speaker 1: difficult for us as physicists to like predict these things

833
00:41:39,080 --> 00:41:41,120
Speaker 1: and kind of like know what's going to happen, but

834
00:41:41,200 --> 00:41:42,880
Speaker 1: it's also kind of hard for the universe to know

835
00:41:42,920 --> 00:41:45,000
Speaker 1: what's going to happen. Right, Like, if something is chaotic,

836
00:41:45,120 --> 00:41:48,600
Speaker 1: it also means that things are kind of unpredictable in general,

837
00:41:48,719 --> 00:41:51,319
Speaker 1: like crazy things can happen in our solar system. Yes,

838
00:41:51,480 --> 00:41:54,759
Speaker 1: systems with three objects don't last very long because they

839
00:41:54,840 --> 00:41:57,880
Speaker 1: are chaotic. They don't tend to fall into stable patterns

840
00:41:58,000 --> 00:42:00,560
Speaker 1: and survive for very long. So if you have like

841
00:42:01,040 --> 00:42:04,960
Speaker 1: three stars orbiting each other, then pretty quickly two of

842
00:42:05,040 --> 00:42:08,080
Speaker 1: them will eject the third one out into the universe.

843
00:42:08,320 --> 00:42:11,279
Speaker 1: Because there are not very many stable solutions to the

844
00:42:11,400 --> 00:42:13,839
Speaker 1: three body problem. And this is different from like can

845
00:42:14,040 --> 00:42:17,560
Speaker 1: human mathematicians write down a simple formula to predict what

846
00:42:17,680 --> 00:42:20,680
Speaker 1: will happen? That's one question. Another question is like how

847
00:42:20,840 --> 00:42:23,560
Speaker 1: long can three stars orbit each other before two of

848
00:42:23,600 --> 00:42:25,640
Speaker 1: them kick out the other one. I guess you mean

849
00:42:25,719 --> 00:42:28,680
Speaker 1: like three stars of about the same size, right, Yeah,

850
00:42:28,920 --> 00:42:30,960
Speaker 1: three stars about the same size and about the same

851
00:42:31,040 --> 00:42:33,720
Speaker 1: distance from each other at a real like three body system.

852
00:42:33,960 --> 00:42:36,400
Speaker 1: Because the only way for that to really happen, for

853
00:42:36,480 --> 00:42:38,759
Speaker 1: it to become stable is to sort of turn it

854
00:42:38,920 --> 00:42:42,840
Speaker 1: into a double two body system. Take your three stars,

855
00:42:43,320 --> 00:42:46,000
Speaker 1: group two of them together, make them really close, and

856
00:42:46,080 --> 00:42:48,440
Speaker 1: put them far away from the third star, and then

857
00:42:48,480 --> 00:42:50,520
Speaker 1: what you have is like a little two body system

858
00:42:50,520 --> 00:42:53,520
Speaker 1: of two stars. And then you have that two body system.

859
00:42:53,560 --> 00:42:55,440
Speaker 1: You can treat it sort of like as a single

860
00:42:55,560 --> 00:42:58,320
Speaker 1: object when you're talking about the third star which is

861
00:42:58,360 --> 00:43:01,000
Speaker 1: now orbiting that pair. And so when we do find

862
00:43:01,160 --> 00:43:04,400
Speaker 1: trinary systems out there in the universe, they're typically this

863
00:43:04,600 --> 00:43:07,040
Speaker 1: like two body system. In a hierarchy, we have a

864
00:43:07,120 --> 00:43:09,640
Speaker 1: two body system, and then one of those bodies turns

865
00:43:09,680 --> 00:43:11,920
Speaker 1: out to have two things inside of it, right, And

866
00:43:12,160 --> 00:43:14,040
Speaker 1: I think this hierarchy we sort of talked about it

867
00:43:14,160 --> 00:43:17,400
Speaker 1: in the last podcast, but it's acidly with distance, right, Like,

868
00:43:17,640 --> 00:43:20,760
Speaker 1: if two of them are out here, you know, interacting

869
00:43:20,800 --> 00:43:23,919
Speaker 1: and orbiting around each other, then to another body that's

870
00:43:24,320 --> 00:43:27,840
Speaker 1: fairly far away, our two little bodies here, I feel

871
00:43:27,880 --> 00:43:30,600
Speaker 1: like one. And so then that makes it more stable. Exactly, if,

872
00:43:30,640 --> 00:43:32,800
Speaker 1: for example, we had two sons at the center of

873
00:43:32,840 --> 00:43:35,359
Speaker 1: our solar system, if they were really close to each other,

874
00:43:35,640 --> 00:43:37,800
Speaker 1: and they were much closer to each other than we

875
00:43:38,000 --> 00:43:40,400
Speaker 1: were to them, we could treat it like it was

876
00:43:40,520 --> 00:43:42,800
Speaker 1: just one object. It wouldn't matter to us that it

877
00:43:42,920 --> 00:43:45,359
Speaker 1: was two objects. But if we got closer to them,

878
00:43:45,440 --> 00:43:47,560
Speaker 1: or if we even like trying to get between them,

879
00:43:47,640 --> 00:43:50,160
Speaker 1: then it would make a big difference on our trajectory

880
00:43:50,480 --> 00:43:52,520
Speaker 1: that there were two objects instead of one, and so,

881
00:43:52,640 --> 00:43:54,960
Speaker 1: for example, in that novel we talked about at the

882
00:43:55,040 --> 00:43:57,520
Speaker 1: top of the episode, that's exactly what's going on. There's

883
00:43:57,520 --> 00:44:00,440
Speaker 1: a solar system with two stars and a plan that's

884
00:44:00,480 --> 00:44:03,040
Speaker 1: whizzing all around right through them in a very crazy,

885
00:44:03,200 --> 00:44:05,759
Speaker 1: unstable orbit. And so not only does it have like

886
00:44:05,960 --> 00:44:08,120
Speaker 1: really weird night and day patterns, but it has a

887
00:44:08,280 --> 00:44:12,800
Speaker 1: very chaotic trajectory, and so you can't necessarily predict exactly

888
00:44:12,880 --> 00:44:14,480
Speaker 1: where it's going to be. It's kind of like a

889
00:44:14,560 --> 00:44:17,840
Speaker 1: real couples, I guess, you know, like from a distance,

890
00:44:18,000 --> 00:44:20,200
Speaker 1: you can sort of assume they think and act as one,

891
00:44:20,440 --> 00:44:22,520
Speaker 1: but once you get go up close to them easily,

892
00:44:22,520 --> 00:44:24,839
Speaker 1: there's a lot of disagreement there. But you never want

893
00:44:24,880 --> 00:44:27,839
Speaker 1: to get between them exactly. That's right. It soundstable. Yeah,

894
00:44:27,840 --> 00:44:29,880
Speaker 1: you don't want to be the third body there, you

895
00:44:30,000 --> 00:44:31,919
Speaker 1: definitely don't. You can get tossed out of your solar

896
00:44:32,000 --> 00:44:37,960
Speaker 1: system or maybe eject the one of the others. But then, yes,

897
00:44:38,160 --> 00:44:40,480
Speaker 1: it sounds like we're writing a romcom now involving a

898
00:44:40,560 --> 00:44:42,880
Speaker 1: trip to the woods in Russia. All right, Well, this

899
00:44:43,040 --> 00:44:45,560
Speaker 1: is kind of an interesting question here, and an interesting

900
00:44:45,640 --> 00:44:47,560
Speaker 1: problem because it doesn't just tell you that some things

901
00:44:47,600 --> 00:44:50,319
Speaker 1: are hard to solve in nature, but some things are

902
00:44:51,120 --> 00:44:55,160
Speaker 1: hard and unpredictable themselves in nature, right, Like some of

903
00:44:55,239 --> 00:44:58,000
Speaker 1: these things out in nature they just don't last long

904
00:44:58,080 --> 00:45:01,040
Speaker 1: they been out of control, or they a settle into

905
00:45:01,120 --> 00:45:04,799
Speaker 1: things that are more stable, like to body solar systems. Yeah,

906
00:45:04,920 --> 00:45:07,360
Speaker 1: and it could be that in the future somebody events

907
00:45:07,440 --> 00:45:10,800
Speaker 1: mathematics that makes it easier to describe that crazy chaotic

908
00:45:10,880 --> 00:45:13,120
Speaker 1: motion and that you know, in twenty years or in

909
00:45:13,160 --> 00:45:15,560
Speaker 1: fifty years, we have like a a new basic function,

910
00:45:15,800 --> 00:45:17,680
Speaker 1: you know, like we have signed and coson. These were

911
00:45:17,760 --> 00:45:21,200
Speaker 1: invented functions by human mathematicians. Somebody might come up with

912
00:45:21,280 --> 00:45:23,800
Speaker 1: a new function which turns out to be really useful

913
00:45:23,880 --> 00:45:27,000
Speaker 1: to describing three body motion and and allows us to

914
00:45:27,200 --> 00:45:31,120
Speaker 1: find some expression. A lot of mathematicians are skeptical because

915
00:45:31,200 --> 00:45:33,880
Speaker 1: they can sort of express these solutions is like an

916
00:45:33,920 --> 00:45:36,880
Speaker 1: infinite series, and they showed that it's very complicated, and

917
00:45:37,000 --> 00:45:39,520
Speaker 1: they suspect that there isn't a simple function. But you know,

918
00:45:39,760 --> 00:45:43,200
Speaker 1: future mathematicians are usually smarter than today's mathematicians, and so

919
00:45:43,520 --> 00:45:45,760
Speaker 1: I hold out hope or maybe like there are aliens

920
00:45:45,800 --> 00:45:48,239
Speaker 1: who have figured this out, you know, like they'll come

921
00:45:48,280 --> 00:45:49,800
Speaker 1: to us and be like, yes sign and cosap we

922
00:45:49,880 --> 00:45:53,360
Speaker 1: don't have, you know, chaos sign or something that describes

923
00:45:53,440 --> 00:45:57,200
Speaker 1: chaos motion. Yeah, exactly, And maybe somewhere some mathematicians is

924
00:45:57,280 --> 00:45:59,719
Speaker 1: developing the tools and they don't even realize how it's

925
00:45:59,719 --> 00:46:02,800
Speaker 1: going to useful. I love those stories of mathematicians developing

926
00:46:02,840 --> 00:46:06,640
Speaker 1: these ideas and then them later being co opted by physicists.

927
00:46:06,680 --> 00:46:09,160
Speaker 1: And so maybe those ideas exist right now and all

928
00:46:09,200 --> 00:46:10,560
Speaker 1: you have to do is go out and read the

929
00:46:10,680 --> 00:46:13,280
Speaker 1: right math paper and you're like, oh, this is exactly

930
00:46:13,360 --> 00:46:15,800
Speaker 1: the hammer we need to hit this physics nail. Or

931
00:46:15,840 --> 00:46:18,279
Speaker 1: maybe the answer is in some cabin in Russia, but

932
00:46:18,440 --> 00:46:20,600
Speaker 1: the you know, the poor soul ran out of food

933
00:46:20,680 --> 00:46:24,560
Speaker 1: or something and it's lost to us, but it's written

934
00:46:24,600 --> 00:46:26,800
Speaker 1: down on a frozen sheet of paper in that cabin.

935
00:46:27,520 --> 00:46:31,000
Speaker 1: It exists. But anyways, I guess the good news is

936
00:46:31,080 --> 00:46:33,240
Speaker 1: that it's an open problem and there could be somebody

937
00:46:33,360 --> 00:46:35,759
Speaker 1: listening to this podcast right now that might solve it

938
00:46:35,840 --> 00:46:38,120
Speaker 1: in the future, maybe even you. Well we hope you

939
00:46:38,239 --> 00:46:41,239
Speaker 1: enjoyed that. Thanks for joining us, see you next time.

940
00:46:49,120 --> 00:46:51,960
Speaker 1: Thanks for listening, and remember that Daniel and Jorge explained

941
00:46:51,960 --> 00:46:54,840
Speaker 1: the universe is a production of I heart Radio. For

942
00:46:55,000 --> 00:46:57,919
Speaker 1: more podcast from My heart Radio, visit the I heart

943
00:46:58,000 --> 00:47:01,560
Speaker 1: Radio app, Apple Podcasts, or wherever you listen to your

944
00:47:01,640 --> 00:47:02,360
Speaker 1: favorite shows.