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Speaker 1: When you pop a piece of cheese into your mouth,

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Speaker 3: Everyone loves getting good advice and staying in the know.

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Speaker 3: There's nothing like getting a heads up on something before

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Speaker 4: Hey Daniel, when you are teaching, are you the kind

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Speaker 4: 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

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Speaker 1: hole like that kind of problem.

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Speaker 4: What are you, professor, Rube Goldberg.

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Speaker 1: No, that was just a joke. I actually like to

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

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

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Speaker 1: concepts really come together in your mind.

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Speaker 4: Right, right, you're an evil professor. Basically you never assigned

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Speaker 4: unsolved research problems to first year students.

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Speaker 1: No, that only happens in the movies. Man, Goodwill Hunting

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Speaker 1: is not a documentary.

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Speaker 4: You're not Matt Damon.

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Speaker 1: I don't have the looks for it.

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Speaker 4: Yes, there's always room for improvement. M orgem a cartoonist

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Speaker 4: and the creator of PhD comics.

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Speaker 1: Hi, I'm Daniel. I'm a particle physicist, and I've never

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Speaker 1: solved an outstanding math problem.

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Speaker 4: Not yet. Do you mean right? If you had solved it,

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Speaker 4: it wouldn't be an outstanding math problem.

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Speaker 1: That's true. Yeah, there are these famous outstanding problems, and

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Speaker 1: it's cool when they stand for hundreds of years and

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Speaker 1: then somebody comes along and figures them out.

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Speaker 4: Wow, what do you think happens? Like somebody just comes

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Speaker 4: up with the right way to look at it, or

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Speaker 4: like they see something nobody else had seen before. Or

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Speaker 4: the history was just waiting for the right intellect.

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Speaker 1: Yeah. Sometimes it's a slow construction of ideas over hundreds

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Speaker 1: of years, and you look at the history of it

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Speaker 1: and be like, problem proposed in sixteen nineteen, progress is

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Speaker 1: made in eighteen fourteen, and then twenty seventeen Samantha figures

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

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Speaker 1: of history there.

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Speaker 4: I'm waiting for people to solve some pretty intractable parenting

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Speaker 4: problems that sometimes I have.

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Speaker 1: Those are eternal, man, they will never be solved.

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Speaker 4: This will never be solved. It's part of being human,

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Speaker 4: I guess. But welcome to our podcast Daniel and Jorge

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Speaker 4: Explain the Universe, a production of iHeartRadio in which.

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Speaker 1: We tackle the hardest problem, which is understanding the nature

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Speaker 1: of this universe. We find ourselves in how does it work?

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Speaker 1: Where did it come from? Why is it the way

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Speaker 1: that it is? And is it even possible to understand it?

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Speaker 1: We dive right into the biggest, hardest, deepest questions. We

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Speaker 1: explain the answers and our ignorance to you.

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Speaker 4: I wonder if that's the harder problem Daniel explaining something

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Speaker 4: to other people. We do our best here but it's

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Speaker 4: pretty hard to sort of wrap your head around all

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Speaker 4: the amazing and incredible stuff that is happening in the universe.

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Speaker 1: And one of my favorite things about doing this podcast

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Speaker 1: is exercising that part of my brain that translates these

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Speaker 1: ideas from like the cutting edge of physics to things

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

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

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Speaker 4: Oh, I see, you actually have to understand it first

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Speaker 4: before it'splaining it to people. So what am I doing here?

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Speaker 2: Then?

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Speaker 1: Are Well, sometimes when you try to explain something, you

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Speaker 1: realize whole lot a second, I don't really understand how

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Speaker 1: this works as well as.

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Speaker 4: I thought it did sometimes only sometimes, though that never

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Speaker 4: happens time on our podcast.

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Speaker 1: It happens to me all the time when I'm teaching

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Speaker 1: and also on this podcast, And that's one reason why

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Speaker 1: it's so fun, because not only are we explaining stuff,

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Speaker 1: we're also learning as we go.

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Speaker 4: That is a pretty good parenting lesson. Also, it's good

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Speaker 4: to share what you know. When you learn what you

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Speaker 4: love about this crazy beautiful.

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Speaker 1: Cosmos, Yeah, how does that help you with your parenting?

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Speaker 4: Well, it's just good to share. I think it's good. Well,

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Speaker 4: you have to share with your children. I think that's

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Speaker 4: a law, that is a rule, But it's also good

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Speaker 4: to teach it to share.

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Speaker 2: You know.

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Speaker 4: Just if everyone's more generous with their what they have

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Speaker 4: in their knowledge, we're all happy.

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Speaker 1: I thought you were going to use the wonder and

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Speaker 1: glamour of the universe to convince your kids to do

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Speaker 1: their chores, like take out the trash, because stars are amazing.

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Speaker 4: Or you are insignificant in this universe. You're a tiny

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Speaker 4: speck of dust and the floating and vast vacuum of

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Speaker 4: perhaps infinite space, and therefore you should do your homework.

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

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

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Speaker 4: Because if nothing matters children, everything matters.

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Speaker 1: I like that.

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Speaker 4: I like that trendid philosophical use that PhD for something.

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Speaker 4: But anyways, we do like to talk about not only

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Speaker 4: what scientists know about this universe and all of the

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Speaker 4: wonderful stuff in it, but also what scientists are struggling

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Speaker 4: with understanding about how things work.

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Speaker 1: That's right, because we have this amazing mental machinery of

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

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Speaker 1: things we do understand about the universe. It has a

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

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Speaker 1: to me sometimes that mathematics can describe the way the

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

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

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

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

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

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Speaker 1: sometimes it's easier than other times.

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Speaker 4: Yeah, the cool thing about science is that it's always

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Speaker 4: at this sort of the leading edge of human knowledge, right,

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Speaker 4: Like that's what science is. It's sort of like asking

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Speaker 4: the questions nobody's ever asked, or finding the answers nobody

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Speaker 4: that has so far. And so sometimes you run into

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Speaker 4: things that are just really really extra hard or maybe

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Speaker 4: even impossible.

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Speaker 1: Yeah, And sometimes they are impossible because the physics is

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Speaker 1: really hard, and sometimes they're impossible because we just don't

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Speaker 1: have the mathematics yet. Like, there have been lots of

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Speaker 1: times in history when mathematicians have developed tools, not because

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Speaker 1: they thought they were going to be useful for physics,

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Speaker 1: but just because they thought it was fun, and then

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Speaker 1: later on physicists were like, hold on a second, that

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Speaker 1: totally helps me solve this problem I've been struggling with

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Speaker 1: for twenty years. A great example is general relativity, which

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Speaker 1: is built on geometry, which was developed just ten years before.

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Speaker 1: Without all that work developing geometry, there's no way Einstein

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Speaker 1: could have developed relativity. It's this really fascinating dance between

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Speaker 1: mathematics and physics.

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Speaker 4: Yeah, what kind of dance? How would you describe it dance?

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Speaker 4: Is it like a Charleston or more like a waltz?

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Speaker 4: Or is it like a hip hop breakdancing competition? What

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Speaker 4: 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.

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Speaker 4: Oh man, I can't wait for that, you know, interpretive

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Speaker 4: dance History of Science Broadway play that you're working on.

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Speaker 1: Yeah, you know, I wish it was more back and forth.

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Speaker 1: Sometimes I feel like, shouldn't the mathematicians be excited when

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Speaker 1: their tools actually get used to describe the real universe?

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Speaker 1: But a lot of times they don't seem to care

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Speaker 1: at all, and they're like whatever, who cares about the

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Speaker 1: real universe. I'm walking the halls of truth.

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Speaker 4: You're selling their halls with like reality and like real

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Speaker 4: mud and dirt, Like that's just dirt, just dirt.

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Speaker 1: Yeah, if they cared about getting dirty, they would have

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Speaker 1: been physicists instead of mathematicians.

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Speaker 4: I see. Physicists are the down and dirty of scientists.

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Speaker 1: I think physicists are to mathematicians what engineers are to physicists.

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Speaker 4: Oh, I see, the better, the better people, right, the

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Speaker 4: true heroes.

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Speaker 1: I'm the hierarchy of useless purity.

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Speaker 4: The hierarchy of usefulness.

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

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Speaker 1: exactly right.

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Speaker 4: Yes, if you turn upside down, we're actually at the top. Yes,

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Speaker 4: it's all about your perspective.

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Speaker 1: That's right. There is no up in space anyway.

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Speaker 4: Well, there are interesting problems in physics, some of them

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Speaker 4: which are even intractable, and so in this episode we'll

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Speaker 4: be talking about one such problem that maybe affects our

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Speaker 4: very movement through space, and it affects how planets revolve

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Speaker 4: around their suns, and which we may never find the

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Speaker 4: answer for. So to the end the podcast, we'll be

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Speaker 4: asking the question, what's so hard about the three body problem. Now, Daniel,

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Speaker 4: this is not something that's not safe for work, is it.

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Speaker 4: I mean, I see something here. Three bodies? Is this about?

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

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Speaker 1: your relationships at all. It's what's so mathematically different about

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Speaker 1: three gravitationally attracting objects.

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Speaker 4: Is the safe for labratory in the heavenly bodies relationships?

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Speaker 1: You know, some bodies here on Earth are quite heavenly

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Speaker 1: as well, but we're talking about celestial bodies.

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Speaker 4: That's right, the real stars, all right, So the three

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Speaker 4: More specifically, this is kind of about what is this

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Speaker 4: three body problem at all? Because I imagine not a

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Speaker 4: lot of people have heard of them, although it is

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Speaker 4: the title of a sort of a well known science

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Speaker 4: 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 it'd be more fun to

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

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Speaker 1: of the novel that we can talk about the actual

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Speaker 1: problem itself.

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Speaker 4: Yeah, I think I try to read the novel. It's

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Speaker 4: pretty dense, it's kind of thick.

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Speaker 1: Yeah, there's a lot of physics in that book, which

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Speaker 1: is pretty fun for people who like really well thought

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Speaker 1: out physics novels. And so it's it's a good idea

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Speaker 1: to try to get an understanding for like what is

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Speaker 1: the underlying problem at the core of the story?

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Speaker 4: Right, And it's like a bestseller won all the awards

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Speaker 4: right in science fiction.

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Speaker 5: Mm hmmm.

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Speaker 4: So you can check that out if you like. But

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Speaker 4: the title of it refers to kind of an old

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Speaker 4: and famous problem in physics about I imagine three bodies.

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

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Speaker 1: are the funnest problems because it means that like a

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

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Speaker 1: this problem for decades or even centuries, and nobody's figured

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Speaker 1: it out, and does just mean it's impossible. There are

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

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

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Speaker 1: cabin in Russia comes out with like one hundred page

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Speaker 1: proof of it, so it might be possible to be solved,

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Speaker 1: but nobody's cracked this one.

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Speaker 4: Yeah, just a book on Airbnb, that cabin in Russia,

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Speaker 4: and you know, book it for a couple of years,

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Speaker 4: and you might solve a famous problem. That's the real answer.

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Speaker 1: That wasn't a metaphor, that was that really happened to you,

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Speaker 1: not to me. No, there really is a Russian mathematism

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Speaker 1: who worked all by himself for a decade and solved

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Speaker 1: a famous problem in math, the Remond conjecture.

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Speaker 4: Wow.

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Speaker 1: And he was in a cabin, he used in a cabin,

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Speaker 1: he worked all by himself, and he just sent in

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Speaker 1: the solution and they tried to give him the fields

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Speaker 1: metal for it and he wouldn't even show up.

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Speaker 4: Wow. That feels like such a fine line between like,

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Speaker 4: you know, genius and you know, socially unacceptable behavior.

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

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Speaker 4: But anyways, let's talk about this problem, the three body problem.

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Speaker 4: And so, as usually, we were wondering how many people

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Speaker 4: out there we knew what this was, if they had

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Speaker 4: heard of it before beyond the novel, or how important

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Speaker 4: it is to sort of predicting the movement of our

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Speaker 4: planets in our solar system. So Daniel, as usually went

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Speaker 4: out there into the wilds of the internet to ask

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Speaker 4: people what is the three body problem?

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Speaker 1: So, while we are still pandemically shut down, I am

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Speaker 1: very grateful to all of you who are willing to

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Speaker 1: participate via email on the person on the virtual street.

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Speaker 1: So if you would like to participate and hear your

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Speaker 1: speculation on the podcast, please don't be shy. Send us

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Speaker 1: a message to questions at Danielandjorge dot com.

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Speaker 4: Think about it for a second. Do you know what

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Speaker 4: the three body problem is? Here's what people have to say.

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Speaker 1: I don't know what the three body problem is. I'm

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Speaker 1: afraid so.

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Speaker 6: I'm really aware of what the three body problem is.

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Speaker 6: I did read as you should lose three Body problem trilogy.

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Speaker 6: My understanding is that it's a problem with how three

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Speaker 6: bodies orbit one another and how it could continue to

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Speaker 6: do that be stable without crashing into one another.

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Speaker 7: A lot of people spend a fair amount of time

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Speaker 7: calculating how two massive bodies interact due to the gravitational

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Speaker 7: field surrounding them, but actually, if you add a third body,

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Speaker 7: the system becomes unstable, it becomes chaotic. So you can

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Speaker 7: determine an exact solution. And also if you make a

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Speaker 7: small change let's say in the initial positions of the bodies,

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Speaker 7: you can't actually determine how let's say the forces between

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Speaker 7: the three bodies will be affected.

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Speaker 5: I think that's the do when you've got three bodies

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Speaker 5: that grotatically interactions like the Sun, the Earth and the Moon,

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Speaker 5: for example, would be it would be three bodies. And

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Speaker 5: I think you can solve two bodies, and can any

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Speaker 5: more than a fee more and you can't solve it.

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Speaker 5: I think it's one of the issues.

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Speaker 8: Oh wow, that is something I am not sure what

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Speaker 8: it is.

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Speaker 9: I don't know what the three body problem is unless

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Speaker 9: it's relating to a previous question where if you have

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Speaker 9: three bodies acting on each other gravitationally, you haven't got

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Speaker 9: sort of one orbiting another or one with a joint

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Speaker 9: orbit with another, that there'll be probably quite at random

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Speaker 9: to their rule bees.

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Speaker 10: I have never heard of the three body problem before,

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Speaker 10: but if I were to guess, I think it is

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Speaker 10: three bodies interacting with each other and something unusual happens,

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Speaker 10: like something that doesn't happen between two bodies or four bodies.

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Speaker 10: It just happens between these three bodies for some reason,

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Speaker 10: and for some reason the number is three.

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Speaker 11: Actually, I've studied physics before, so I know that the

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Speaker 11: three body problem is this problem where if you have

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Speaker 11: two objects pulling on each other, then those equations can

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Speaker 11: be solved pretty easily. But if you add in a

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Speaker 11: third body, now you have three different interactions between ab

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Speaker 11: AC and CB. And when you have interactions of that

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Speaker 11: order that many interactions, it becomes sort of an unsolvable

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Speaker 11: math problem. And so we don't have like good solutions

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Speaker 11: for those sort of situations. We have to essentially come

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Speaker 11: up with approximations and simulate it.

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Speaker 4: All right, it's not a lot of knowledge about this,

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Speaker 4: but someone did read the trilogy.

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Speaker 1: Yeah, exactly three books in the three Body Problem trilogy.

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Speaker 1: It's nice.

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Speaker 4: It must have been good because he read all three.

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Speaker 4: Or I wonder if your completest, you know, tendencies would

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Speaker 4: kick in after you rerun. Well, I can't just read

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Speaker 4: one three body problem book. I gotta read all three.

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

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Speaker 1: the first novel.

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Speaker 4: You should title all your trilogies with the number three

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Speaker 4: in it. But it seems like most people here are

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Speaker 4: guessing it has to do with bodies in space and

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Speaker 4: the specifically three bodies of course, but a lot of

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Speaker 4: people are saying maybe it's about it becoming unsolvable or

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Speaker 4: chaotic or unstable. Are they sort of in the right track.

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Speaker 1: They are exactly on the right track. It's really interesting.

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Speaker 1: There's a problem which is easy if there's only two

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Speaker 1: objects involved, and then becomes basically unsolvable if you have

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Speaker 1: three objects involved.

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Speaker 4: Right, like real human relationships.

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Speaker 1: Which can be tricky even when there are two bodies.

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Speaker 4: Involved, even if everyone is open minded, it gets tricky.

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Speaker 4: All right, Well, let's dig into it, Daniel, how would

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Speaker 4: you describe the three body problems?

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Speaker 1: I think the best way to describe it is to

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Speaker 1: first talk about what we can do and simply said,

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Speaker 1: if you have two objects in space and you know

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Speaker 1: where they are, how heavy they are, and the direction

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Speaker 1: they're going in, then you can predict their emotion. You

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

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

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

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

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

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Speaker 1: at some moments in time, and 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.

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Speaker 4: Right, But you have to kind of assume that they're

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Speaker 4: alone in the whole unit, like there's nothing else in

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Speaker 4: the universe pulling on them.

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Speaker 1: Right, It'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 tugging 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 the calculation of whether your satellite is going to

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

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

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

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Speaker 1: down to like, you know, the tenth decimal place or something. Yeah,

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Speaker 1: so in the sort of simplified universe of exactly two

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Speaker 1: things in your universe, you can predict the motion of

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Speaker 1: two objects.

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Speaker 4: All right, So then I'm guessing when you get to

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Speaker 4: three bodies, it gets a little harder.

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Speaker 1: When you get to three bodies, it doesn't just get

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Speaker 1: a little harder, it becomes impossible. If you know where

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

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Speaker 1: the Sun, the Earth, and then another object. Now you

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Speaker 1: just have three objects, and you know exactly where they are,

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Speaker 1: what direction they're going in, and you know their masses.

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Speaker 1: You cannot write down a simple formula that tells you

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Speaker 1: where they're going to be in a week, or in

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Speaker 1: a year or in a thousand years.

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Speaker 12: Well, it gets really complicated. Suddenly, it gets really complicated.

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Speaker 12: We don't have a solution. Now we have an understanding

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Speaker 12: for what's going on, Like we know the forces involved,

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Speaker 12: we know what the gravity is between two objects given

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Speaker 12: their distance. Right, that's a pretty simple formula. Newton told

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Speaker 12: us how to do that. But that doesn't mean we

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Speaker 12: know how to find the solution. Doesn't mean we can

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Speaker 12: take those forces and predict the motion.

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Speaker 4: Right. Well, I think this might be kind of a

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Speaker 4: subtle subject for a lot of people out there. Which

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Speaker 4: is it like what you mean in physics as a solution,

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Speaker 4: because it doesn't mean that you can't predict where they're

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Speaker 4: going to be. You just don't have an easy solution

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Speaker 4: 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 going to move,

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Speaker 1: which is what you need to predict their emotion, you

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

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

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

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

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

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

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

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

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Speaker 4: Well, that probably makes for a short work day there

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Speaker 4: for you. But I think what you mean is like,

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Speaker 4: for example, like a ball, if I throw a ball

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Speaker 4: here at my son in our backyard here, like I

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Speaker 4: know that Doug ball. I know the constraints in it,

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Speaker 4: like I know the forces pulling on it, the force

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Speaker 4: of gravity, and I know that F equals M for example.

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Speaker 4: So I can solve, for example, for its acceleration very easily,

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Speaker 4: but maybe getting like a formula for what its position

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Speaker 4: is going to be is a little tricky. It's different

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Speaker 4: than knowing what it's accele is going to be exactly.

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Speaker 1: The acceleration just tells you how is momentums in change

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Speaker 1: in a given moment right to know where it's going

441
00:21:07,119 --> 00:21:09,679
Speaker 1: to be, you need to then solve the equations of

442
00:21:09,720 --> 00:21:12,480
Speaker 1: motion which incorporate all these forces and is affected by

443
00:21:12,480 --> 00:21:16,679
Speaker 1: that acceleration. But it requires actually solving the equation. You know.

444
00:21:16,720 --> 00:21:19,040
Speaker 1: It's like if I have an equation that says X

445
00:21:19,080 --> 00:21:22,879
Speaker 1: plus five equals ten. Right, that's an equation that constrains X.

446
00:21:22,880 --> 00:21:25,600
Speaker 1: It limits what X can be, but it's not actually

447
00:21:25,640 --> 00:21:28,760
Speaker 1: the solution. The solution is X equals five. That's a

448
00:21:28,840 --> 00:21:30,760
Speaker 1: very simple one, right. You know exactly how to go

449
00:21:30,840 --> 00:21:34,600
Speaker 1: from the equation X plus five equals ten to the solution,

450
00:21:34,840 --> 00:21:36,359
Speaker 1: But you don't necessarily know how to do that for

451
00:21:36,400 --> 00:21:40,160
Speaker 1: an arbitrary equation. Take another simple example, like X squared

452
00:21:40,200 --> 00:21:43,239
Speaker 1: equals forty nine. How do you find the solution to that?

453
00:21:43,320 --> 00:21:45,679
Speaker 1: You know off the top of your head that x

454
00:21:45,720 --> 00:21:48,159
Speaker 1: equals seven works, You can plug it in and check it.

455
00:21:48,359 --> 00:21:50,880
Speaker 1: But how do you find the solution? If I tell

456
00:21:50,920 --> 00:21:54,040
Speaker 1: you X squared equals an arbitrary number, how do you

457
00:21:54,119 --> 00:21:56,640
Speaker 1: find the square root of an arbitrary number? There actually

458
00:21:56,960 --> 00:21:59,520
Speaker 1: is no way to do that. There is no mechanism

459
00:21:59,560 --> 00:22:03,200
Speaker 1: for solve that equation other than guessing and checking.

460
00:22:03,320 --> 00:22:06,920
Speaker 4: Sounds like my parenting strategy right there. And I think

461
00:22:06,920 --> 00:22:08,960
Speaker 4: what you mean is, like, you know, in physics you

462
00:22:09,000 --> 00:22:11,840
Speaker 4: have equations to tell you, For example, like the acceleration

463
00:22:12,000 --> 00:22:15,000
Speaker 4: of X, which is like how the velocity is changed,

464
00:22:15,000 --> 00:22:17,080
Speaker 4: which is like how the position is changing. Like you

465
00:22:17,119 --> 00:22:19,240
Speaker 4: have equations for that, but to actually get the position,

466
00:22:19,359 --> 00:22:22,200
Speaker 4: you have to kind of backtrack from acceleration to velocity

467
00:22:22,280 --> 00:22:25,720
Speaker 4: to position. And that's where the trickiness comes from, right.

468
00:22:25,760 --> 00:22:28,960
Speaker 1: Yeah, because the acceleration changes through time, and so to

469
00:22:29,000 --> 00:22:31,800
Speaker 1: figure out like how all those accelerations add up to

470
00:22:31,880 --> 00:22:34,679
Speaker 1: describe the motion of the object is not always easy.

471
00:22:35,040 --> 00:22:37,439
Speaker 1: And then what you want is a simple formula that

472
00:22:37,480 --> 00:22:40,640
Speaker 1: describes it, and that doesn't necessarily exist.

473
00:22:40,480 --> 00:22:42,560
Speaker 4: Right because I guess when you go from two bodies

474
00:22:42,560 --> 00:22:46,159
Speaker 4: to three bodies, then the formula just get too complicated.

475
00:22:46,280 --> 00:22:49,920
Speaker 1: The formula gets too complicated. Exactly, the system gets really

476
00:22:49,960 --> 00:22:53,480
Speaker 1: complicated because now you have these three different objects pulling

477
00:22:53,520 --> 00:22:56,200
Speaker 1: on each other, and it actually becomes chaotic.

478
00:22:56,320 --> 00:22:58,879
Speaker 4: All right, Well, let's dig into why exactly it is

479
00:22:58,920 --> 00:23:02,159
Speaker 4: so hard and how it becomes pure chaos when you

480
00:23:02,359 --> 00:23:05,640
Speaker 4: add a third celestial body into the mix, and what

481
00:23:05,680 --> 00:23:09,640
Speaker 4: consequences it has for our ability to predict the universe.

482
00:23:09,880 --> 00:23:11,680
Speaker 4: But first, let's take a quick break.

483
00:23:15,960 --> 00:23:18,879
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Speaker 1: of cheese into your mouth or enjoy a rich spoonful

533
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Speaker 1: of Greek yogurt, you're probably not thinking about the environmental

534
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Speaker 1: impact of each and every bite, But the people in

535
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Speaker 1: the dairy industry are. US dairy has set themselves some

536
00:25:59,080 --> 00:26:03,600
Speaker 1: ambitious sustainability goals, including being greenhouse gas neutral by twenty

537
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538
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539
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Speaker 1: drive down greenhouse gas emissions. Take water, for example, most

540
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541
00:26:15,680 --> 00:26:18,800
Speaker 1: water cools the milk, cleans equipment, washes the barn, and

542
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543
00:26:22,480 --> 00:26:25,479
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550
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551
00:26:53,200 --> 00:26:55,800
Speaker 4: All right, Daniel, we're talking about the three body problem.

552
00:26:55,920 --> 00:26:58,080
Speaker 4: And I guess we're not just talking about what happens

553
00:26:58,080 --> 00:27:00,439
Speaker 4: if your spouse moves to another city, right, this is

554
00:27:00,480 --> 00:27:01,080
Speaker 4: more cosmic.

555
00:27:01,280 --> 00:27:02,919
Speaker 1: I can't solve that problem for you. There is no

556
00:27:03,000 --> 00:27:05,359
Speaker 1: equation that tells you how to live your life.

557
00:27:07,080 --> 00:27:09,879
Speaker 4: That's the one body problem is already pretty hard. Now

558
00:27:09,920 --> 00:27:11,600
Speaker 4: we're talking about the three body problem.

559
00:27:11,640 --> 00:27:13,800
Speaker 1: One is the loneliest number. But this is not a

560
00:27:13,840 --> 00:27:17,480
Speaker 1: relationship helpline, and this is not a podcast about human emotions.

561
00:27:17,720 --> 00:27:20,359
Speaker 1: We are trying to solve the much easier problem of

562
00:27:20,560 --> 00:27:22,119
Speaker 1: motion of objects through space.

563
00:27:22,240 --> 00:27:24,640
Speaker 4: And so you're saying that when I have two objects

564
00:27:24,680 --> 00:27:27,360
Speaker 4: in space, it's easy enough to sort of predict where

565
00:27:27,359 --> 00:27:29,760
Speaker 4: they're going to be. Well, once you have three, there's

566
00:27:29,760 --> 00:27:31,720
Speaker 4: no easy solution to that problem.

567
00:27:31,800 --> 00:27:35,560
Speaker 1: Yeah, there's no easy solution. There's no like short mathematical answer.

568
00:27:35,760 --> 00:27:38,399
Speaker 1: When you'd like is something like xft, where x is

569
00:27:38,440 --> 00:27:40,920
Speaker 1: the position of the object, and then a simple formula

570
00:27:41,080 --> 00:27:43,160
Speaker 1: where you can plug in the time and it'll tell

571
00:27:43,200 --> 00:27:46,120
Speaker 1: you exactly the position of the object. That's what you're

572
00:27:46,160 --> 00:27:48,640
Speaker 1: looking for, because you'd like to be able to take

573
00:27:48,680 --> 00:27:50,800
Speaker 1: that system and say, I want to know where the

574
00:27:50,800 --> 00:27:52,199
Speaker 1: moon is going to be, or I want to know

575
00:27:52,200 --> 00:27:54,359
Speaker 1: where the sun is going to be in a thousand years.

576
00:27:54,440 --> 00:27:56,720
Speaker 1: The problem is that there is no such simple formula.

577
00:27:56,760 --> 00:27:59,119
Speaker 1: We haven't found one at least, and we suspect that

578
00:27:59,200 --> 00:28:02,200
Speaker 1: it might not exist because the system of three objects

579
00:28:02,320 --> 00:28:05,159
Speaker 1: is much much more complicated than a system of just

580
00:28:05,200 --> 00:28:06,560
Speaker 1: two objects.

581
00:28:06,240 --> 00:28:08,359
Speaker 4: Right, And it gets really complicated because now you have

582
00:28:08,520 --> 00:28:11,560
Speaker 4: three objects in three D? Is it kind of about

583
00:28:11,560 --> 00:28:13,680
Speaker 4: going to that third dimension? That makes it hard because

584
00:28:13,720 --> 00:28:16,000
Speaker 4: I imagine, if you have two bodies in space, you

585
00:28:16,040 --> 00:28:18,200
Speaker 4: can just treat them as like a two D problem, right,

586
00:28:18,240 --> 00:28:20,960
Speaker 4: like you just imagine the plane where these two bodies are.

587
00:28:20,960 --> 00:28:22,800
Speaker 4: But once you have three and then it's like not

588
00:28:22,880 --> 00:28:23,879
Speaker 4: it's a three D problem.

589
00:28:23,920 --> 00:28:25,920
Speaker 1: It's true that two objects in space you can always

590
00:28:25,960 --> 00:28:28,120
Speaker 1: define a plane between them. You can also put three

591
00:28:28,119 --> 00:28:30,959
Speaker 1: objects on a plane, though right three points define a plane,

592
00:28:31,040 --> 00:28:33,280
Speaker 1: so there's always a plane for three objects. I think

593
00:28:33,320 --> 00:28:35,679
Speaker 1: the problem is that when you have three objects, a

594
00:28:35,800 --> 00:28:39,959
Speaker 1: small change in their location leads to a big change

595
00:28:40,240 --> 00:28:41,920
Speaker 1: in where they're going to be in the future, at

596
00:28:41,960 --> 00:28:45,400
Speaker 1: least for gravitational interactions, whereas if you have two objects,

597
00:28:45,640 --> 00:28:47,680
Speaker 1: a small change and where the Earth is going to be,

598
00:28:47,880 --> 00:28:50,520
Speaker 1: it will mostly settle back into the same answer. And

599
00:28:50,560 --> 00:28:53,560
Speaker 1: so in terms of like finding an equation that describes it,

600
00:28:53,640 --> 00:28:56,880
Speaker 1: there's a whole family of equations that can describe stable solutions.

601
00:28:57,200 --> 00:28:59,440
Speaker 1: We don't really have functions that are very good at

602
00:28:59,480 --> 00:29:03,520
Speaker 1: describing chaotic situations, where it's very small change in the

603
00:29:03,520 --> 00:29:06,040
Speaker 1: angle or the velocity of the moon means it's now

604
00:29:06,160 --> 00:29:08,320
Speaker 1: suddenly over here, or it's suddenly on the other side

605
00:29:08,360 --> 00:29:10,280
Speaker 1: of the sun, or it flies off in a completely

606
00:29:10,320 --> 00:29:14,680
Speaker 1: different direction. Our equations are not good at describing chaotic mathematics.

607
00:29:14,760 --> 00:29:16,760
Speaker 4: But I guess maybe the question is, like, what is

608
00:29:16,800 --> 00:29:19,040
Speaker 4: it that about going from two to three that actually

609
00:29:19,160 --> 00:29:23,800
Speaker 4: makes the equations unsolvable? Like beforeward two I can solve

610
00:29:23,800 --> 00:29:26,560
Speaker 4: the equations, but with three, there's no solution for them,

611
00:29:26,840 --> 00:29:28,840
Speaker 4: does it become nonlinear? Is that what it is?

612
00:29:28,920 --> 00:29:31,400
Speaker 1: It's already nonlinear, right that Even with N equals too,

613
00:29:31,440 --> 00:29:35,200
Speaker 1: it's nonlinear because these distances go like one over radius squared,

614
00:29:35,560 --> 00:29:38,920
Speaker 1: so there's an inverse R squared there, So it's already nonlinear.

615
00:29:39,040 --> 00:29:41,280
Speaker 1: I think something you said earlier is really the right

616
00:29:41,280 --> 00:29:43,640
Speaker 1: way to think about it. We know the forces F

617
00:29:43,720 --> 00:29:46,560
Speaker 1: and the mass M, and we have F equals maa,

618
00:29:46,680 --> 00:29:49,520
Speaker 1: so we can get the acceleration. That's a very simple formula.

619
00:29:49,760 --> 00:29:52,280
Speaker 1: But how do you go from knowing the acceleration, which

620
00:29:52,320 --> 00:29:55,320
Speaker 1: is how much the speed is changing, to knowing the

621
00:29:55,400 --> 00:29:58,040
Speaker 1: actual location. What you have to do is add up

622
00:29:58,080 --> 00:30:01,640
Speaker 1: the effects of lots of little accelerations over time, which

623
00:30:01,680 --> 00:30:04,960
Speaker 1: means you have to integrate. You have to use the calculus.

624
00:30:05,200 --> 00:30:07,640
Speaker 1: But just like there aren't that many physics problems that

625
00:30:07,640 --> 00:30:11,600
Speaker 1: are solvable, not every function can be integrated, at least

626
00:30:11,840 --> 00:30:14,360
Speaker 1: not into a simple formula you can write down. So

627
00:30:14,560 --> 00:30:17,200
Speaker 1: just because you know the force in the acceleration doesn't

628
00:30:17,240 --> 00:30:20,280
Speaker 1: mean you know how to integrate it into getting the location.

629
00:30:20,680 --> 00:30:22,600
Speaker 1: And we can go a little bit further if you

630
00:30:22,600 --> 00:30:25,320
Speaker 1: look at the structure of the problem. Mathematicians call these

631
00:30:25,360 --> 00:30:29,160
Speaker 1: problems non integrable, which just means that, like the possible

632
00:30:29,200 --> 00:30:32,760
Speaker 1: trajectories for these objects in this three D space don't

633
00:30:32,800 --> 00:30:36,840
Speaker 1: follow simple paths right like, they diverge very quickly. It's

634
00:30:36,840 --> 00:30:38,920
Speaker 1: not like it can be easily simplified from a whole

635
00:30:38,920 --> 00:30:41,560
Speaker 1: big set of possible solutions down to just a few,

636
00:30:41,680 --> 00:30:43,720
Speaker 1: and with any equals too. With a two body problem,

637
00:30:43,960 --> 00:30:46,120
Speaker 1: there are a bunch of simplifications you can make that

638
00:30:46,240 --> 00:30:49,640
Speaker 1: separate the problem so that, for example, the distance between

639
00:30:49,640 --> 00:30:53,120
Speaker 1: the objects is independent of their relative angle, because for

640
00:30:53,160 --> 00:30:55,920
Speaker 1: two objects, you know, the angle doesn't really matter. What

641
00:30:56,040 --> 00:30:58,760
Speaker 1: only matters is really just the distance. But for three

642
00:30:58,840 --> 00:31:01,479
Speaker 1: objects you have not just the relative distances, but you

643
00:31:01,560 --> 00:31:04,320
Speaker 1: also have the relative angles, and so now all the

644
00:31:04,360 --> 00:31:06,920
Speaker 1: problems are still tied together. You know, when you try

645
00:31:06,960 --> 00:31:09,200
Speaker 1: to solve a set of equations, sometimes it's helpful to

646
00:31:09,240 --> 00:31:12,000
Speaker 1: try to separate them and solve them independently, but that's

647
00:31:12,080 --> 00:31:14,720
Speaker 1: not always possible, and when they're all entangled up with

648
00:31:14,760 --> 00:31:17,000
Speaker 1: each other, you can't always find a solution.

649
00:31:17,280 --> 00:31:19,320
Speaker 4: I see, there's something sort of magical about the number

650
00:31:19,320 --> 00:31:22,080
Speaker 4: two that then you lose once you get more than two, right,

651
00:31:22,160 --> 00:31:24,320
Speaker 4: because it's not just three bodies that are hard. It's

652
00:31:24,320 --> 00:31:26,520
Speaker 4: also four and five and six in infinite right.

653
00:31:26,680 --> 00:31:29,000
Speaker 1: Yes, you might have thought, oh, well, two bodies are solvable,

654
00:31:29,040 --> 00:31:31,640
Speaker 1: so then why not three. It's actually the other direction.

655
00:31:31,760 --> 00:31:35,000
Speaker 1: Two is the only one that is solvable. Right. All

656
00:31:35,000 --> 00:31:38,240
Speaker 1: the problems are unsolvable except for this one magic special

657
00:31:38,320 --> 00:31:41,320
Speaker 1: case of two bodies, which we have been able to

658
00:31:41,360 --> 00:31:44,840
Speaker 1: separate using this special trick and solve. So it's sort

659
00:31:44,840 --> 00:31:46,800
Speaker 1: of lucky that any of them are solvable.

660
00:31:46,960 --> 00:31:49,960
Speaker 4: Well, the zero body problem is solvable too, and the

661
00:31:50,040 --> 00:31:53,160
Speaker 4: one body problem, I imagine is solvable. It's just that

662
00:31:53,280 --> 00:31:55,840
Speaker 4: it just gets more complicate, relic like the equations start

663
00:31:55,880 --> 00:31:58,360
Speaker 4: to like interact with each other, and then you can't

664
00:31:58,400 --> 00:32:00,520
Speaker 4: like fit a simple format as.

665
00:32:00,360 --> 00:32:02,160
Speaker 1: A solution, right, yeah, exactly.

666
00:32:02,280 --> 00:32:05,320
Speaker 4: And in addition, there's something about chaos here, right.

667
00:32:05,240 --> 00:32:08,480
Speaker 1: That's right, The results become chaotic. As we said before,

668
00:32:08,560 --> 00:32:11,080
Speaker 1: if you change a little bit the initial conditions, if

669
00:32:11,080 --> 00:32:13,720
Speaker 1: Earth is a little bit further away or pointing in

670
00:32:13,760 --> 00:32:17,680
Speaker 1: a slightly different direction, you can get completely different outcomes.

671
00:32:17,960 --> 00:32:20,600
Speaker 1: So Earth can be like tossed out of the Solar System,

672
00:32:21,080 --> 00:32:23,680
Speaker 1: or it can fall into another orbit or something like that.

673
00:32:23,920 --> 00:32:26,120
Speaker 1: Whereas if you just have two bodies things tend to

674
00:32:26,120 --> 00:32:28,800
Speaker 1: be pretty stable. That means that if you perturb it,

675
00:32:29,000 --> 00:32:31,040
Speaker 1: something comes along and gives the Earth a little push,

676
00:32:31,120 --> 00:32:33,960
Speaker 1: it'll probably roll back into its initial orbit, whereas in

677
00:32:34,000 --> 00:32:37,240
Speaker 1: a three body system things get out of hand very quickly.

678
00:32:37,600 --> 00:32:40,960
Speaker 1: And that's not just like is it complicated motion. That's

679
00:32:41,000 --> 00:32:44,080
Speaker 1: one of the reasons why we don't have a simple formula,

680
00:32:44,120 --> 00:32:47,480
Speaker 1: because we don't have functions that describe that, like sine

681
00:32:47,600 --> 00:32:51,200
Speaker 1: and cosine and logarithm. These things are mostly well behaved

682
00:32:51,200 --> 00:32:55,000
Speaker 1: and so it's very difficult to describe chaotic motion using

683
00:32:55,040 --> 00:32:57,400
Speaker 1: the sort of mathematical language that we have developed.

684
00:32:57,600 --> 00:33:00,640
Speaker 4: Oh, I see, because there's no function that then is

685
00:33:00,720 --> 00:33:03,560
Speaker 4: chaotic kind of Is that what you're saying, Like, chaotic

686
00:33:03,600 --> 00:33:07,560
Speaker 4: motion is not easily kind of captured in a formula.

687
00:33:07,680 --> 00:33:10,480
Speaker 1: Yeah, it's not easily captured in a formula. It's possible

688
00:33:10,560 --> 00:33:14,480
Speaker 1: to describe chaotic motion, but usually our solutions there are numerical,

689
00:33:14,520 --> 00:33:17,680
Speaker 1: there are approximate. We use simulations. You know, we can

690
00:33:17,840 --> 00:33:21,480
Speaker 1: describe chaotic systems like you build a computer system, you

691
00:33:21,560 --> 00:33:23,840
Speaker 1: put three objects in it, and then what you do

692
00:33:23,920 --> 00:33:26,720
Speaker 1: is you say, all right, what happens in the first second,

693
00:33:27,040 --> 00:33:28,680
Speaker 1: and you say well, the Earth's going to move this way,

694
00:33:28,760 --> 00:33:30,240
Speaker 1: the Sun's going to move that way, and the moon

695
00:33:30,320 --> 00:33:31,760
Speaker 1: is going to move this other direction, and then you

696
00:33:31,840 --> 00:33:34,280
Speaker 1: update everything, and then you do it again. So you

697
00:33:34,320 --> 00:33:36,440
Speaker 1: slice the problem in time, and you say, what if

698
00:33:36,480 --> 00:33:39,280
Speaker 1: I only want to predict a half second from now

699
00:33:39,400 --> 00:33:42,360
Speaker 1: or a millisecond from now, then you can really simplify

700
00:33:42,360 --> 00:33:44,240
Speaker 1: it and say I know what to do for a

701
00:33:44,240 --> 00:33:45,800
Speaker 1: half second, and then you just do that over and

702
00:33:45,840 --> 00:33:47,920
Speaker 1: over and over again. That's a way we can describe

703
00:33:47,920 --> 00:33:50,520
Speaker 1: a chaotic system is like slicing it in time and

704
00:33:50,560 --> 00:33:54,240
Speaker 1: then try to move our simulation forward, just one time

705
00:33:54,360 --> 00:33:56,920
Speaker 1: slice at a time. But that doesn't mean that we

706
00:33:57,000 --> 00:33:58,960
Speaker 1: can then look at that motion and say, oh, look

707
00:33:59,040 --> 00:34:01,880
Speaker 1: it follows a sign. Oh look it follows the logarithm

708
00:34:01,920 --> 00:34:04,560
Speaker 1: of a sine wave. We can't find a solution. We

709
00:34:04,560 --> 00:34:07,680
Speaker 1: can't find a mathematical description of the motion, even if

710
00:34:07,720 --> 00:34:09,239
Speaker 1: we can describe it in the simulation.

711
00:34:09,800 --> 00:34:12,840
Speaker 4: I see. So like we can maybe predict what the

712
00:34:12,880 --> 00:34:15,120
Speaker 4: system is going to do, what these three bodies are

713
00:34:15,120 --> 00:34:16,680
Speaker 4: going to do, but we have to do it step

714
00:34:16,719 --> 00:34:19,080
Speaker 4: by step. We can't just say, like, hey, twenty years

715
00:34:19,120 --> 00:34:20,799
Speaker 4: from now, this is what it's going to be. There's

716
00:34:20,800 --> 00:34:22,920
Speaker 4: no formula that will tell you that. You have to

717
00:34:22,960 --> 00:34:25,200
Speaker 4: like simulate it little by little till you get to

718
00:34:25,440 --> 00:34:26,160
Speaker 4: ten years from now.

719
00:34:26,320 --> 00:34:29,920
Speaker 1: Yeah, and even those simulations are difficult because it's chaotic,

720
00:34:30,040 --> 00:34:33,600
Speaker 1: Like if you don't make those calculations very very precise,

721
00:34:33,920 --> 00:34:35,880
Speaker 1: then your simulation is going to be wrong as you

722
00:34:35,920 --> 00:34:38,720
Speaker 1: try to predict further and further into the future, because

723
00:34:38,800 --> 00:34:42,920
Speaker 1: small mistakes really add up the snowball into big mistakes.

724
00:34:43,239 --> 00:34:46,240
Speaker 1: It's just like you know the butterfly problem. Butterfly flaps

725
00:34:46,320 --> 00:34:49,560
Speaker 1: its wings in China and that has cascading effects on

726
00:34:49,600 --> 00:34:52,880
Speaker 1: the weather, which causes eventually a storm in Central Park

727
00:34:52,960 --> 00:34:55,120
Speaker 1: in New York. And these things are real. The real

728
00:34:55,160 --> 00:34:58,200
Speaker 1: physical systems that behave this way where if you give

729
00:34:58,200 --> 00:35:00,359
Speaker 1: them a very small nudge, it can have a very

730
00:35:00,400 --> 00:35:03,640
Speaker 1: big effect downstream. And that makes them very very challenging

731
00:35:03,760 --> 00:35:06,319
Speaker 1: even to stimulate, as we talked about, because you get

732
00:35:06,360 --> 00:35:09,880
Speaker 1: something wrong very early on, your results in ten years

733
00:35:09,920 --> 00:35:13,000
Speaker 1: are nonsense. We much prefer to have like a simple

734
00:35:13,040 --> 00:35:15,520
Speaker 1: we call it an analytical formula, like a very short

735
00:35:15,600 --> 00:35:18,280
Speaker 1: math expression that we can just plug numbers into, because

736
00:35:18,320 --> 00:35:20,080
Speaker 1: it can be exact and it can tell us exactly

737
00:35:20,120 --> 00:35:21,960
Speaker 1: what's going to happen in ten years or in one

738
00:35:22,040 --> 00:35:22,640
Speaker 1: hundred years.

739
00:35:22,760 --> 00:35:25,200
Speaker 4: I think what you're saying is that these numerical approaches

740
00:35:25,320 --> 00:35:29,080
Speaker 4: or simulations, they're just an approximation basically, right, Like you're

741
00:35:29,200 --> 00:35:31,560
Speaker 4: looking at the equations like the f equals maas or

742
00:35:31,600 --> 00:35:35,200
Speaker 4: the forces between the three bodies, and you're saying, well,

743
00:35:35,280 --> 00:35:37,319
Speaker 4: let's not try to get the exact solution. Let's just

744
00:35:37,400 --> 00:35:40,520
Speaker 4: pretend that for the next millisecond everyone has the same

745
00:35:40,560 --> 00:35:41,920
Speaker 4: acceleration or something like that.

746
00:35:42,120 --> 00:35:44,960
Speaker 1: Exactly. You make a bunch of simplifications and you say, well,

747
00:35:44,960 --> 00:35:46,880
Speaker 1: I only want to predict a millisecond in the future,

748
00:35:47,160 --> 00:35:49,359
Speaker 1: so can I do that? And then you just keep

749
00:35:49,360 --> 00:35:50,640
Speaker 1: doing that over and over again.

750
00:35:50,920 --> 00:35:53,200
Speaker 4: You're saying that if I'm wrong a little bit because

751
00:35:53,200 --> 00:35:55,719
Speaker 4: of that simplication, then in a chaotic system, I could

752
00:35:55,760 --> 00:35:56,600
Speaker 4: be really wrong.

753
00:35:56,960 --> 00:35:59,479
Speaker 1: Yeah, and that's a big deal. If you're doing something

754
00:35:59,560 --> 00:36:02,880
Speaker 1: like plain ending a trip to the stars or sending

755
00:36:02,920 --> 00:36:05,680
Speaker 1: your probe to Jupiter or whatever, you definitely want to

756
00:36:05,680 --> 00:36:06,480
Speaker 1: get that right.

757
00:36:06,600 --> 00:36:08,520
Speaker 4: Right, Yeah, you don't want to be off by a

758
00:36:08,560 --> 00:36:09,280
Speaker 4: few light years.

759
00:36:09,400 --> 00:36:11,760
Speaker 1: Yeah, Or even if you're just flying through the Solar System,

760
00:36:12,120 --> 00:36:13,960
Speaker 1: if you get it wrong, you could end up crashing

761
00:36:14,000 --> 00:36:16,720
Speaker 1: into the Sun or getting tossed out of the Solar

762
00:36:16,719 --> 00:36:18,759
Speaker 1: System in the wrong direction. You're trying to make it

763
00:36:18,760 --> 00:36:21,640
Speaker 1: to Pluto from here, right, Pluto is very far away

764
00:36:21,640 --> 00:36:24,720
Speaker 1: in a very very small target. Imagine firing a gun

765
00:36:25,120 --> 00:36:28,080
Speaker 1: from La to New York and trying to hit a tiny,

766
00:36:28,320 --> 00:36:31,640
Speaker 1: tiny target. It's very difficult. They're very small. If you're

767
00:36:31,680 --> 00:36:34,720
Speaker 1: off by a tiny little angle in LA, you're definitely

768
00:36:34,719 --> 00:36:36,200
Speaker 1: not going to hit that target in New York.

769
00:36:36,239 --> 00:36:38,000
Speaker 4: But I guess that. You know, we are pretty good

770
00:36:38,000 --> 00:36:40,560
Speaker 4: these days with you know, supercomputers, We are pretty good

771
00:36:40,560 --> 00:36:43,880
Speaker 4: at simulating things and kind of predicting. You know, maybe

772
00:36:43,920 --> 00:36:46,239
Speaker 4: not the storm that comes from the butterfly wings, but

773
00:36:46,320 --> 00:36:48,640
Speaker 4: you know, the weather is you know, predictable sort of

774
00:36:48,880 --> 00:36:51,279
Speaker 4: up to like a week, right or a couple of weeks,

775
00:36:51,320 --> 00:36:54,279
Speaker 4: which is super impressive because they have to simulate all

776
00:36:54,320 --> 00:36:57,560
Speaker 4: of those you know, air molecules and pockets of hot

777
00:36:57,560 --> 00:36:59,680
Speaker 4: air that are out there in the atmosphere. It's not

778
00:36:59,719 --> 00:37:02,439
Speaker 4: that it it makes the problem impossible. It just makes

779
00:37:02,480 --> 00:37:05,000
Speaker 4: it harder or you know kind of shorings. How much

780
00:37:05,040 --> 00:37:05,719
Speaker 4: we can predict it.

781
00:37:05,840 --> 00:37:08,440
Speaker 1: Yeah, if you had an infinitely powerful computer, then we

782
00:37:08,480 --> 00:37:11,000
Speaker 1: could solve these problems because we could simulate them with

783
00:37:11,239 --> 00:37:14,280
Speaker 1: really high resolution. We could take like really really short

784
00:37:14,360 --> 00:37:17,680
Speaker 1: time steps in our simulation. Instead of stepping forward a millisecond,

785
00:37:17,680 --> 00:37:20,440
Speaker 1: we could step forward a nanosecond and then correct. And

786
00:37:20,560 --> 00:37:23,359
Speaker 1: so if you had infinite computing resources, you could do

787
00:37:23,400 --> 00:37:25,799
Speaker 1: these things very effectively. And some of the reasons why

788
00:37:25,840 --> 00:37:28,439
Speaker 1: these problems which seem to be impossible for a long time,

789
00:37:28,560 --> 00:37:31,400
Speaker 1: like predicting the weather, seem to be getting easier, and

790
00:37:31,480 --> 00:37:34,239
Speaker 1: not because humans are getting smarter, but because our computers

791
00:37:34,239 --> 00:37:36,799
Speaker 1: are getting more powerful, and so now we have a

792
00:37:36,840 --> 00:37:40,080
Speaker 1: lot more computing power available to do things like predicting

793
00:37:40,120 --> 00:37:42,759
Speaker 1: the weather and trying to predict earthquakes and all these

794
00:37:42,840 --> 00:37:45,120
Speaker 1: really really hard problems that are really important.

795
00:37:45,360 --> 00:37:48,920
Speaker 4: Like today we can predict how the whole Solar system works, right.

796
00:37:48,800 --> 00:37:50,480
Speaker 1: We mostly can, And a lot of that is because

797
00:37:50,600 --> 00:37:53,560
Speaker 1: mostly the Solar system is a bunch of two body problems,

798
00:37:53,680 --> 00:37:57,080
Speaker 1: like the Earth moving around the Sun. Technically it's you know,

799
00:37:57,120 --> 00:37:59,399
Speaker 1: it's an eight body problem because the Earth is pulled

800
00:37:59,400 --> 00:38:01,680
Speaker 1: on by the Moon and Jupiter or a neptune and whatever,

801
00:38:01,880 --> 00:38:04,920
Speaker 1: but mostly it's just the Sun. You can ignore everything

802
00:38:04,960 --> 00:38:07,799
Speaker 1: else when you're calculating the Earth to some degree. If

803
00:38:07,840 --> 00:38:10,040
Speaker 1: you want to get it exactly right, then yes, you

804
00:38:10,080 --> 00:38:12,839
Speaker 1: need to include effects from Mars and Venus. And then

805
00:38:12,880 --> 00:38:15,200
Speaker 1: you can't use Kepler's laws. You can't use the simple

806
00:38:15,280 --> 00:38:17,840
Speaker 1: formulas that we have for a two body problem. You

807
00:38:17,920 --> 00:38:20,480
Speaker 1: have to get down and dirty and do the simulations

808
00:38:20,640 --> 00:38:22,239
Speaker 1: using very powerful computers.

809
00:38:22,400 --> 00:38:24,080
Speaker 4: But then, I guess, would you say that our Solar

810
00:38:24,080 --> 00:38:27,280
Speaker 4: system is chaotic as well? Like? Is our Solar system

811
00:38:27,440 --> 00:38:30,120
Speaker 4: a chaotic system? Because it seems sort of stable right now,

812
00:38:30,560 --> 00:38:33,040
Speaker 4: But are you saying maybe, like if you give it

813
00:38:33,120 --> 00:38:35,040
Speaker 4: enough time, it is kind of a little unpredictable.

814
00:38:35,120 --> 00:38:39,839
Speaker 1: Yeah, definitely, the Solar system is chaotic, but on cosmological timescales,

815
00:38:40,000 --> 00:38:42,760
Speaker 1: not on like a year or ten years, but onlike

816
00:38:42,880 --> 00:38:46,160
Speaker 1: millions and billions of years, and it was more chaotic

817
00:38:46,200 --> 00:38:49,040
Speaker 1: in the beginning. We sort of settled into something that's

818
00:38:49,040 --> 00:38:51,520
Speaker 1: more stable. But when the Solar system began, it was

819
00:38:51,560 --> 00:38:54,400
Speaker 1: a big hot mess and things were flying everywhere. Planets

820
00:38:54,440 --> 00:38:57,640
Speaker 1: were colliding into each other and making new planets and

821
00:38:57,680 --> 00:39:00,040
Speaker 1: throwing things out of the Solar system. We probably I

822
00:39:00,040 --> 00:39:02,719
Speaker 1: had a different number of planets a billion or two

823
00:39:02,800 --> 00:39:05,640
Speaker 1: billion years ago. People suspect there might have been like

824
00:39:05,719 --> 00:39:08,880
Speaker 1: another giant planet which was tossed out of the Solar

825
00:39:08,920 --> 00:39:12,080
Speaker 1: System by Jupiter and Saturn. So yeah, that sounds pretty

826
00:39:12,120 --> 00:39:12,799
Speaker 1: chaotic to me.

827
00:39:13,000 --> 00:39:15,160
Speaker 4: Solar system was like, you know, I have enough to

828
00:39:15,200 --> 00:39:18,560
Speaker 4: deal with with the A nine bodies, possibly eight, let's

829
00:39:18,600 --> 00:39:19,239
Speaker 4: kick someone out.

830
00:39:19,320 --> 00:39:21,400
Speaker 1: But you can take a very complicated system like the

831
00:39:21,440 --> 00:39:25,640
Speaker 1: Solar system and find approximately stable solutions, things which will

832
00:39:25,680 --> 00:39:28,359
Speaker 1: last for a long long time. But how stable are they?

833
00:39:28,520 --> 00:39:31,000
Speaker 1: Something which flies through the Solar System can perturb it

834
00:39:31,040 --> 00:39:33,279
Speaker 1: a little bit, and then things can very quickly go

835
00:39:33,360 --> 00:39:35,879
Speaker 1: out of whack. So if you have like another star

836
00:39:36,040 --> 00:39:38,680
Speaker 1: that gets a little close to our Solar system, it

837
00:39:38,680 --> 00:39:41,000
Speaker 1: could change the orbit of Jupiter, which could have knock

838
00:39:41,000 --> 00:39:43,279
Speaker 1: on effects about changing the orbit of Saturn, and then

839
00:39:43,360 --> 00:39:46,000
Speaker 1: the asteroid belt and Mars, and pretty soon we could

840
00:39:46,000 --> 00:39:47,000
Speaker 1: have craziness.

841
00:39:47,200 --> 00:39:50,000
Speaker 4: All right, Well, let's get into that craziness of our

842
00:39:50,040 --> 00:39:52,799
Speaker 4: Solar system and what the consequences are of this three

843
00:39:52,840 --> 00:39:57,640
Speaker 4: body problem and our ability to understand the rest of

844
00:39:57,640 --> 00:39:59,960
Speaker 4: the cosmos. But first, let's take another.

845
00:40:00,160 --> 00:40:06,640
Speaker 1: Great When you pop a piece of cheese into your mouth,

846
00:40:06,719 --> 00:40:09,880
Speaker 1: or enjoy a rich spoonful of Greek yogurt, you're probably

847
00:40:09,920 --> 00:40:13,960
Speaker 1: not thinking about the environmental impact of each and every bite,

848
00:40:14,000 --> 00:40:16,640
Speaker 1: But the people in the dairy industry are. US Dairy

849
00:40:16,680 --> 00:40:20,960
Speaker 1: has set themselves some ambitious sustainability goals, including being greenhouse

850
00:40:21,000 --> 00:40:23,560
Speaker 1: gas neutral by twenty to fifty. That's why they're working

851
00:40:23,600 --> 00:40:25,960
Speaker 1: hard every day to find new ways to reduce waste,

852
00:40:26,000 --> 00:40:30,200
Speaker 1: conserve natural resources, and drive down greenhouse gas emissions. Take water,

853
00:40:30,280 --> 00:40:33,360
Speaker 1: for example, most dairy farms reuse water up to four

854
00:40:33,400 --> 00:40:36,880
Speaker 1: times the same water cools the milk, cleans equipment, washes

855
00:40:36,920 --> 00:40:39,720
Speaker 1: the barn, and irrigates the crops. How is US Dairy

856
00:40:39,719 --> 00:40:43,480
Speaker 1: tackling greenhouse gases. Many farms use anaerobic digestors that turn

857
00:40:43,520 --> 00:40:47,440
Speaker 1: the methane from maneure into renewable energy that can power farms, towns,

858
00:40:47,440 --> 00:40:49,560
Speaker 1: and electric cars. So the next time you grab a

859
00:40:49,560 --> 00:40:51,600
Speaker 1: slice of pizza or lick an ice cream cone, know

860
00:40:51,640 --> 00:40:54,359
Speaker 1: that dairy farmers and processors around the country are using

861
00:40:54,360 --> 00:40:57,879
Speaker 1: the latest practices and innovations to provide the nutrient dense

862
00:40:58,000 --> 00:41:00,719
Speaker 1: dairy products we love with less of an impact. Visit

863
00:41:00,800 --> 00:41:03,560
Speaker 1: usdairy dot com slash sustainability to learn more.

864
00:41:04,640 --> 00:41:08,120
Speaker 8: There are children, friends and families walking, riding on paths

865
00:41:08,120 --> 00:41:10,600
Speaker 8: and roads every day. Remember they're real people with loved

866
00:41:10,600 --> 00:41:12,799
Speaker 8: ones who need them to get home safely. Protect our

867
00:41:12,800 --> 00:41:16,360
Speaker 8: cyclists and pedestrians because they're people too. Go safely California

868
00:41:16,400 --> 00:41:18,600
Speaker 8: from the California Office of Traffic Safety and Caltrans.

869
00:41:18,680 --> 00:41:21,640
Speaker 14: Hey there, it's Ryan seacrests for Safeway. After a summer

870
00:41:21,640 --> 00:41:23,919
Speaker 14: of fun, it's time to get your home ready for fall.

871
00:41:23,960 --> 00:41:26,160
Speaker 14: There's nothing better than stocking up on all your favorite

872
00:41:26,200 --> 00:41:29,239
Speaker 14: household items and saving now through October. First shop in

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Speaker 4: All Right, we're talking about the three body problem and

890
00:42:30,040 --> 00:42:34,000
Speaker 4: it's hard to find an analytical solution to it, as

891
00:42:34,000 --> 00:42:36,040
Speaker 4: opposed to the two body problem, which you can find

892
00:42:36,080 --> 00:42:38,480
Speaker 4: a nice, neat formula for it. But I wonder then

893
00:42:38,520 --> 00:42:40,759
Speaker 4: if this is sort of like a physicist frustration, because

894
00:42:40,760 --> 00:42:43,360
Speaker 4: as an engineer, I'm pretty much used to, like thinks,

895
00:42:43,440 --> 00:42:46,520
Speaker 4: not having an analytical solution, like from day one, like

896
00:42:46,600 --> 00:42:48,719
Speaker 4: nothing only like throwing a ball up in the air

897
00:42:48,719 --> 00:42:50,840
Speaker 4: has an analytical solution. Everything else you have to do

898
00:42:50,920 --> 00:42:55,000
Speaker 4: with numerical simulations or approximating, you know, Navy your Stokes

899
00:42:55,040 --> 00:42:57,800
Speaker 4: equations and having non linear stuff that you can solve

900
00:42:58,280 --> 00:43:00,879
Speaker 4: and so, you know, like any you you always rely

901
00:43:00,960 --> 00:43:04,319
Speaker 4: on simulations. But maybe in physics you get more frustrated

902
00:43:04,400 --> 00:43:07,840
Speaker 4: for not having like a neat, you know, clean formula

903
00:43:07,880 --> 00:43:08,680
Speaker 4: to predict the future.

904
00:43:08,880 --> 00:43:11,120
Speaker 1: Well, the thing that's tantalizing is that there are a

905
00:43:11,160 --> 00:43:13,960
Speaker 1: few cases when you can find a neat formula where

906
00:43:13,960 --> 00:43:17,319
Speaker 1: you can start with just pencil and paper, describe the

907
00:43:17,400 --> 00:43:19,759
Speaker 1: pushing and the pulling of your system, and then get

908
00:43:19,800 --> 00:43:22,440
Speaker 1: out a formula that tells you where everything is going

909
00:43:22,520 --> 00:43:26,320
Speaker 1: to be basically for all time. That's amazing. It's beautiful,

910
00:43:26,400 --> 00:43:28,960
Speaker 1: and it's tempting. It makes you think, Wow, why can't

911
00:43:29,000 --> 00:43:31,080
Speaker 1: I do this for other systems? Why can't I do

912
00:43:31,160 --> 00:43:32,480
Speaker 1: this for every system?

913
00:43:32,680 --> 00:43:32,839
Speaker 13: Right?

914
00:43:32,880 --> 00:43:35,319
Speaker 1: Because if they exist for some systems, it gives you

915
00:43:35,360 --> 00:43:37,759
Speaker 1: the sense that, like, if we had the right mathematics,

916
00:43:37,800 --> 00:43:40,880
Speaker 1: if we knew the right language to talk about this stuff,

917
00:43:41,080 --> 00:43:44,680
Speaker 1: maybe even really complicated problems would be simpler. So it's

918
00:43:44,680 --> 00:43:45,720
Speaker 1: sort of aspirational.

919
00:43:45,880 --> 00:43:47,960
Speaker 4: Yeah, I can imagine that frustration. You're in your cabin

920
00:43:48,080 --> 00:43:50,680
Speaker 4: in the middle of Russia, in Siberia, in the middle

921
00:43:50,719 --> 00:43:52,880
Speaker 4: of nowhere, and you're like, oh shoot, I need a

922
00:43:52,920 --> 00:43:55,480
Speaker 4: computer I didn't bring one, or oh shoot, I need

923
00:43:55,520 --> 00:43:57,880
Speaker 4: to talk to somebody else I don't have a phone.

924
00:43:58,520 --> 00:43:59,719
Speaker 4: That's frustrating, right it is.

925
00:44:00,680 --> 00:44:03,560
Speaker 1: And you know it's something funny about teaching freshman physics.

926
00:44:03,600 --> 00:44:06,920
Speaker 1: I teach mechanics often here at you see Irvine and

927
00:44:07,000 --> 00:44:09,040
Speaker 1: you know there are not a lot of problems that

928
00:44:09,120 --> 00:44:12,280
Speaker 1: really are solvable, like very few problems can you actually

929
00:44:12,320 --> 00:44:15,000
Speaker 1: sit down with pencil and paper and say, here's the situation,

930
00:44:15,360 --> 00:44:17,680
Speaker 1: here's the solution. And so, in teaching this class for

931
00:44:17,719 --> 00:44:20,680
Speaker 1: like almost twenty years now, I've noticed that basically every

932
00:44:20,680 --> 00:44:24,279
Speaker 1: physics homework problem and every textbook is one variation on

933
00:44:24,440 --> 00:44:27,279
Speaker 1: like one of these five solvable problems. And so as

934
00:44:27,280 --> 00:44:28,600
Speaker 1: soon as you look at one and you're like, oh,

935
00:44:28,760 --> 00:44:31,319
Speaker 1: this is that one problem, or this is problem number four,

936
00:44:31,400 --> 00:44:34,240
Speaker 1: except they're using a squirrel instead of a ball rolling

937
00:44:34,280 --> 00:44:36,640
Speaker 1: down a plane or something, and so it all boils

938
00:44:36,680 --> 00:44:39,319
Speaker 1: down to like a few solvable problems because there are

939
00:44:39,440 --> 00:44:41,840
Speaker 1: only a few that can actually be solved.

940
00:44:42,000 --> 00:44:44,800
Speaker 4: You mean, there's an analytical, simple solutions to what Professor

941
00:44:44,840 --> 00:44:47,319
Speaker 4: Whitson is going to put on the final test. I

942
00:44:47,320 --> 00:44:48,680
Speaker 4: hope students are taking notes.

943
00:44:49,239 --> 00:44:51,160
Speaker 1: I say, if you take my class for twenty years,

944
00:44:51,200 --> 00:44:52,160
Speaker 1: it becomes pretty easy.

945
00:44:52,320 --> 00:44:55,560
Speaker 4: Yeah. I guess even physics professors are predictable. Is that

946
00:44:55,600 --> 00:44:58,000
Speaker 4: what you're saying, Yes, exactly, take what they're going to do.

947
00:44:58,719 --> 00:45:02,279
Speaker 1: It's hard to invent new solvable problems in physics. And

948
00:45:02,320 --> 00:45:05,600
Speaker 1: you know, it's not just like motion of two objects.

949
00:45:05,760 --> 00:45:07,800
Speaker 1: There are lots of places in physics where the problems

950
00:45:07,840 --> 00:45:11,000
Speaker 1: are not solvable. Einstein developed general relativity, right, which means

951
00:45:11,120 --> 00:45:14,759
Speaker 1: he wrote down the equations for how space curves when

952
00:45:14,840 --> 00:45:17,600
Speaker 1: mass is around. He wrote down the equations, which means

953
00:45:17,880 --> 00:45:20,600
Speaker 1: those are the constraints that space has to follow. It

954
00:45:20,640 --> 00:45:24,200
Speaker 1: doesn't mean he can tell you how space behaves when

955
00:45:24,200 --> 00:45:27,360
Speaker 1: mass is around. Those are the solutions to the Einstein equation.

956
00:45:27,680 --> 00:45:30,680
Speaker 1: And he couldn't solve his own equations. Like he developed

957
00:45:30,680 --> 00:45:32,920
Speaker 1: general relativity and he's like, here are the equations. I

958
00:45:32,960 --> 00:45:34,920
Speaker 1: don't know how to solve this. He wasn't even the

959
00:45:34,920 --> 00:45:38,239
Speaker 1: first person to solve the Einstein equation. That was short style,

960
00:45:38,400 --> 00:45:42,000
Speaker 1: because these equations are like famously impossible to solve. Now,

961
00:45:42,040 --> 00:45:43,840
Speaker 1: if you have a solution, you can check it. You

962
00:45:43,840 --> 00:45:46,840
Speaker 1: can say, hmm, I think space bends in this way

963
00:45:46,960 --> 00:45:49,000
Speaker 1: when there's mass around. You can plug it into the

964
00:45:49,000 --> 00:45:51,440
Speaker 1: equations and if it works, you're like, cool, I found it.

965
00:45:51,480 --> 00:45:53,799
Speaker 1: But again, just because you have the equations doesn't mean

966
00:45:53,880 --> 00:45:56,439
Speaker 1: you know how to find the solution. Anybody who's done

967
00:45:56,560 --> 00:45:59,960
Speaker 1: differential equations knows that's true. We have like no general

968
00:46:00,200 --> 00:46:03,040
Speaker 1: mechanism for saying here's a differential equation, I can go

969
00:46:03,080 --> 00:46:05,919
Speaker 1: from the equation to finding the solution. And so there's

970
00:46:05,960 --> 00:46:08,440
Speaker 1: lots of places in physics where we just don't know

971
00:46:08,440 --> 00:46:11,080
Speaker 1: how to solve these things. Even still, for general relativity,

972
00:46:11,160 --> 00:46:13,560
Speaker 1: we only know how to solve it for a few cases,

973
00:46:13,760 --> 00:46:17,960
Speaker 1: like an empty universe, a universe that's smoothly filled with

974
00:46:18,080 --> 00:46:21,040
Speaker 1: matter like no lumps at all, or a black hole.

975
00:46:21,440 --> 00:46:23,319
Speaker 1: Basically everything else is unsolvable.

976
00:46:23,440 --> 00:46:26,240
Speaker 4: Then that's why Schortshield found right, he found a solution

977
00:46:26,360 --> 00:46:29,799
Speaker 4: for general plativity in the case of a simple black hole.

978
00:46:29,960 --> 00:46:32,240
Speaker 1: Yeah, exactly. He was the first person to ever solve

979
00:46:32,239 --> 00:46:35,080
Speaker 1: these equations. And he actually did it while he was

980
00:46:35,120 --> 00:46:36,560
Speaker 1: a soldier in World War One?

981
00:46:36,760 --> 00:46:39,480
Speaker 4: What was he in fighting in a cabin in Russia?

982
00:46:39,719 --> 00:46:43,080
Speaker 1: Also, never fight a land war in Russia, man, especially

983
00:46:43,280 --> 00:46:43,960
Speaker 1: while you're trying.

984
00:46:43,840 --> 00:46:48,120
Speaker 4: To solve physish questions. It's extra difficulty points. Unless he

985
00:46:48,200 --> 00:46:50,480
Speaker 4: was fighting for the Russians. Maybe I don't know, Maybe

986
00:46:50,520 --> 00:46:52,520
Speaker 4: he's Russian and then he had a lot of time

987
00:46:52,600 --> 00:46:54,400
Speaker 4: because the other team was doomed.

988
00:46:55,200 --> 00:46:56,799
Speaker 1: No, but it's a great story. You should look up

989
00:46:56,840 --> 00:46:58,280
Speaker 1: how Schwartz I'd solved this problem.

990
00:46:58,360 --> 00:47:01,319
Speaker 4: I see. So it's not he solved general relativity for

991
00:47:01,400 --> 00:47:03,720
Speaker 4: all time in all cases. He just found a solution

992
00:47:03,840 --> 00:47:06,720
Speaker 4: for general relativity in this special case of a simple

993
00:47:06,760 --> 00:47:07,160
Speaker 4: black hole.

994
00:47:07,239 --> 00:47:10,040
Speaker 1: Yeah, a universe that has nothing but a black hole

995
00:47:10,040 --> 00:47:12,920
Speaker 1: in it. He figured out the solution how space bends

996
00:47:13,160 --> 00:47:16,120
Speaker 1: in that scenario, and then later people figured out, Okay, well,

997
00:47:16,280 --> 00:47:18,799
Speaker 1: if I assume that the universe is totally empty, can

998
00:47:18,840 --> 00:47:21,000
Speaker 1: I solve the equations? Oh? I can do that. Or

999
00:47:21,000 --> 00:47:24,120
Speaker 1: if I assume the universe is like filled smoothly with matter,

1000
00:47:24,239 --> 00:47:26,800
Speaker 1: can I do that? But like, nobody has solved general

1001
00:47:26,800 --> 00:47:29,920
Speaker 1: relativity for like our solar system, or even just for

1002
00:47:30,040 --> 00:47:32,960
Speaker 1: like the Sun and the Earth together. It's too complicated.

1003
00:47:33,120 --> 00:47:35,759
Speaker 1: Nobody has figured out how to go from those equations

1004
00:47:35,920 --> 00:47:39,200
Speaker 1: to say, here's how space has to bend in this situation.

1005
00:47:39,480 --> 00:47:42,760
Speaker 4: Oh wait, so not even like the two body problem

1006
00:47:43,000 --> 00:47:44,799
Speaker 4: has a solution in general relativity.

1007
00:47:44,840 --> 00:47:48,640
Speaker 1: Yeah, that's right. General relativity much much harder than Newtonian mechanics.

1008
00:47:48,760 --> 00:47:51,640
Speaker 1: We can do things like numerical relativity, like we can

1009
00:47:51,680 --> 00:47:54,360
Speaker 1: describe how black holes orbit each other and collide and

1010
00:47:54,440 --> 00:47:57,840
Speaker 1: generally gravitational waves. Because we can do it numerically, we

1011
00:47:57,880 --> 00:48:00,880
Speaker 1: can use computers to do a proc submit solutions to

1012
00:48:00,960 --> 00:48:04,040
Speaker 1: these things, but nobody can like write down simple formulas

1013
00:48:04,080 --> 00:48:06,200
Speaker 1: to tell you, like how black holes orbit each other

1014
00:48:06,280 --> 00:48:06,920
Speaker 1: and collapse.

1015
00:48:07,280 --> 00:48:09,439
Speaker 4: Oh, I see. All this time we've been talking about

1016
00:48:09,480 --> 00:48:12,440
Speaker 4: the two body probably being solvable. It's only solvable in

1017
00:48:12,480 --> 00:48:15,160
Speaker 4: the NEWTONI in case, right, Like, if you assume the

1018
00:48:15,239 --> 00:48:19,279
Speaker 4: simplest stuff or the simple physics of Newton, then you

1019
00:48:19,320 --> 00:48:21,799
Speaker 4: can find a solution, but not for three. But if

1020
00:48:21,800 --> 00:48:24,080
Speaker 4: you assume, like what we actually know what's going on

1021
00:48:24,160 --> 00:48:27,359
Speaker 4: general relativity, then it's we can't even start, Like there's

1022
00:48:27,360 --> 00:48:27,880
Speaker 4: no solution.

1023
00:48:28,080 --> 00:48:31,480
Speaker 1: Yeah, exactly. You know, Einstein lays out the equations the constraints,

1024
00:48:31,480 --> 00:48:33,839
Speaker 1: but he doesn't tell you, and he doesn't know how

1025
00:48:33,880 --> 00:48:36,480
Speaker 1: to go from the constraints to a solution. You know.

1026
00:48:36,560 --> 00:48:39,040
Speaker 1: It's sort of like if you're driving down the highway

1027
00:48:39,040 --> 00:48:40,799
Speaker 1: with your family and you ask everybody what they want

1028
00:48:40,800 --> 00:48:43,000
Speaker 1: for dinner and everybody says, I want a salad, or

1029
00:48:43,000 --> 00:48:45,200
Speaker 1: I want pizza or I want hot dogs, Like, those

1030
00:48:45,200 --> 00:48:47,680
Speaker 1: are the constraints. Doesn't necessarily mean you know how to

1031
00:48:47,719 --> 00:48:51,360
Speaker 1: find a restaurant that satisfies those constraints, right, Having the

1032
00:48:51,400 --> 00:48:53,640
Speaker 1: constraints doesn't tell you how to find a solution.

1033
00:48:54,080 --> 00:48:56,800
Speaker 4: Wow, it sounds like something from personal experience with that,

1034
00:48:56,960 --> 00:48:58,600
Speaker 4: and you're trying to vent peraps.

1035
00:48:58,880 --> 00:49:01,400
Speaker 1: Yes, I'm looking for a rest thrown the search salads

1036
00:49:01,440 --> 00:49:04,400
Speaker 1: and hot dogs and pizza. Let me know if you

1037
00:49:04,440 --> 00:49:06,799
Speaker 1: find one.

1038
00:49:06,200 --> 00:49:08,640
Speaker 4: That's not even the general relativity solution. Like if you

1039
00:49:08,640 --> 00:49:12,600
Speaker 4: add relatives to this card, right, then it gets impossible, right,

1040
00:49:12,640 --> 00:49:14,440
Speaker 4: because then you have all this relative.

1041
00:49:14,120 --> 00:49:17,360
Speaker 1: Dynamics exactly, very chaotic, very quickly.

1042
00:49:17,560 --> 00:49:19,799
Speaker 4: Well, I think what's interesting is that this is not

1043
00:49:20,040 --> 00:49:23,600
Speaker 4: just difficult for us as physicists to like predict these

1044
00:49:23,640 --> 00:49:26,720
Speaker 4: things and kind of like know what's going to happen,

1045
00:49:26,800 --> 00:49:28,560
Speaker 4: but it's also kind of hard for the universe to

1046
00:49:28,600 --> 00:49:30,760
Speaker 4: know what's going to happen, right, Like if something is chaotic,

1047
00:49:30,840 --> 00:49:34,400
Speaker 4: it also means that things are kind of unpredictable in general,

1048
00:49:34,440 --> 00:49:37,080
Speaker 4: Like crazy things can happen in our solar system yees.

1049
00:49:37,200 --> 00:49:40,520
Speaker 1: Systems with three objects don't last very long because they

1050
00:49:40,560 --> 00:49:43,680
Speaker 1: are chaotic. They don't tend to fall into stable patterns

1051
00:49:43,719 --> 00:49:46,400
Speaker 1: and survive for very long. So if you have like

1052
00:49:46,760 --> 00:49:50,719
Speaker 1: three stars orbiting each other, then pretty quickly two of

1053
00:49:50,760 --> 00:49:53,840
Speaker 1: them will eject the third one out into the universe.

1054
00:49:54,040 --> 00:49:57,080
Speaker 1: Because there are not very many stable solutions to the

1055
00:49:57,080 --> 00:49:59,640
Speaker 1: three body problem. And this is different from like can

1056
00:50:00,000 --> 00:50:03,319
Speaker 1: in mathematicians write down a simple formula to predict what

1057
00:50:03,400 --> 00:50:06,520
Speaker 1: will happen? That's one question. Another question is like how

1058
00:50:06,600 --> 00:50:09,319
Speaker 1: long can three stars orbit each other before two of

1059
00:50:09,320 --> 00:50:10,680
Speaker 1: them kick out the other one.

1060
00:50:10,840 --> 00:50:13,040
Speaker 4: I guess you mean like three stars of about the

1061
00:50:13,040 --> 00:50:14,360
Speaker 4: same size, right.

1062
00:50:14,200 --> 00:50:16,440
Speaker 1: Yeah, three stars about the same size and about the

1063
00:50:16,480 --> 00:50:18,680
Speaker 1: same distance from each other, right, a real like three

1064
00:50:18,719 --> 00:50:22,040
Speaker 1: body system. Because the only way for that to really happen,

1065
00:50:22,080 --> 00:50:24,399
Speaker 1: for it to become stable, is to sort of turn

1066
00:50:24,440 --> 00:50:28,640
Speaker 1: it into a double two body system. Take your three stars,

1067
00:50:29,040 --> 00:50:31,799
Speaker 1: group two of them together, make them really close, and

1068
00:50:31,840 --> 00:50:34,200
Speaker 1: put them far away from the third star, and then

1069
00:50:34,239 --> 00:50:36,240
Speaker 1: what you have is like a little two body system

1070
00:50:36,280 --> 00:50:39,240
Speaker 1: of two stars. And then you have that two body system.

1071
00:50:39,280 --> 00:50:41,200
Speaker 1: You can treat it sort of like as a single

1072
00:50:41,280 --> 00:50:44,080
Speaker 1: object when you're talking about the third star which is

1073
00:50:44,120 --> 00:50:46,800
Speaker 1: now orbiting that pair. And so when we do find

1074
00:50:46,920 --> 00:50:50,160
Speaker 1: triary systems out there in the universe, there're typically this

1075
00:50:50,400 --> 00:50:52,800
Speaker 1: like two body system. In a hierarchy, we have a

1076
00:50:52,840 --> 00:50:55,400
Speaker 1: two body system and then one of those bodies turns

1077
00:50:55,400 --> 00:50:57,320
Speaker 1: out to have two things inside of it.

1078
00:50:57,360 --> 00:50:59,440
Speaker 4: Right, And I think this hierarchy we sort of talked

1079
00:50:59,480 --> 00:51:02,160
Speaker 4: about it in last podcast. But it has to do

1080
00:51:02,200 --> 00:51:04,879
Speaker 4: with distance, right, Like, if two of them are out here,

1081
00:51:05,680 --> 00:51:08,520
Speaker 4: you know, interacting and orbiting around each other, then to

1082
00:51:08,560 --> 00:51:12,560
Speaker 4: another body that's fairly far away, our two little bodies

1083
00:51:12,600 --> 00:51:15,080
Speaker 4: here feel like one, and so then that makes it

1084
00:51:15,120 --> 00:51:15,640
Speaker 4: more stable.

1085
00:51:15,719 --> 00:51:18,200
Speaker 1: Exactly, if, for example, we had two sons at the

1086
00:51:18,200 --> 00:51:20,600
Speaker 1: center of our solar system, if they were really close

1087
00:51:20,640 --> 00:51:22,719
Speaker 1: to each other, and they were much closer to each

1088
00:51:22,719 --> 00:51:25,520
Speaker 1: other than we were to them, we could treat it

1089
00:51:25,760 --> 00:51:28,040
Speaker 1: like it was just one object. It wouldn't matter to

1090
00:51:28,120 --> 00:51:30,319
Speaker 1: us that it was two objects. But if we got

1091
00:51:30,320 --> 00:51:32,360
Speaker 1: closer to them, or if we even like trying to

1092
00:51:32,400 --> 00:51:34,719
Speaker 1: get between them, then it would make a big difference

1093
00:51:34,960 --> 00:51:37,960
Speaker 1: on our trajectory that there were two objects instead of one.

1094
00:51:38,080 --> 00:51:40,520
Speaker 1: And so, for example, in that novel we talked about

1095
00:51:40,520 --> 00:51:43,000
Speaker 1: at the top of the episode, that's exactly what's going on.

1096
00:51:43,040 --> 00:51:45,920
Speaker 1: There's a solar system with two stars and a planet

1097
00:51:45,960 --> 00:51:48,840
Speaker 1: that's whizzing all around right through them in a very crazy,

1098
00:51:48,960 --> 00:51:51,560
Speaker 1: unstable orbit. And so not only does it have like

1099
00:51:51,680 --> 00:51:53,920
Speaker 1: really weird night and day patterns, but it has a

1100
00:51:54,040 --> 00:51:58,520
Speaker 1: very chaotic trajectory, and so you can't necessarily predict exactly

1101
00:51:58,600 --> 00:51:59,440
Speaker 1: where it's going to be.

1102
00:51:59,480 --> 00:52:02,359
Speaker 4: It's kind of real couples, I guess. You know, like

1103
00:52:02,840 --> 00:52:05,120
Speaker 4: from a distance you can sort of assume they think

1104
00:52:05,160 --> 00:52:07,600
Speaker 4: and act as one. But once you like GetUp close

1105
00:52:07,640 --> 00:52:09,560
Speaker 4: to them, you see there's a lot of disagreement there.

1106
00:52:09,840 --> 00:52:11,880
Speaker 1: But you never want to get between them exactly.

1107
00:52:12,120 --> 00:52:14,120
Speaker 4: That's right. It's unstable. Yeah, you don't want to be

1108
00:52:14,160 --> 00:52:15,120
Speaker 4: the third body.

1109
00:52:14,880 --> 00:52:17,279
Speaker 1: There, you definitely don't. You can get tossed out of

1110
00:52:17,280 --> 00:52:18,279
Speaker 1: their solar system.

1111
00:52:19,719 --> 00:52:22,080
Speaker 4: Or maybe e check to one or the others.

1112
00:52:22,400 --> 00:52:24,799
Speaker 1: Then I guess, yes, it sounds like we're writing a

1113
00:52:24,840 --> 00:52:27,759
Speaker 1: rom com now involving a trip to the woods in Russia.

1114
00:52:27,800 --> 00:52:30,680
Speaker 4: All right, well, this is kind of an interesting question here,

1115
00:52:30,719 --> 00:52:32,719
Speaker 4: and an interesting problem because it doesn't just tell you

1116
00:52:32,760 --> 00:52:35,319
Speaker 4: that some things are hard to solve in nature, but

1117
00:52:35,400 --> 00:52:40,399
Speaker 4: some things are hard and unpredictable themselves in nature. Right,

1118
00:52:40,480 --> 00:52:43,000
Speaker 4: Like some of these things out in nature, they just

1119
00:52:43,000 --> 00:52:45,839
Speaker 4: don't last long. They spin out of control, or they

1120
00:52:46,239 --> 00:52:49,160
Speaker 4: settle into things that are more stable, like two body

1121
00:52:49,400 --> 00:52:50,200
Speaker 4: solar systems.

1122
00:52:50,320 --> 00:52:52,720
Speaker 1: Yeah, and it could be that in the future somebody

1123
00:52:52,760 --> 00:52:56,040
Speaker 1: events mathematics that makes it easier to describe that crazy

1124
00:52:56,120 --> 00:52:58,800
Speaker 1: chaotic motion and that you know, in twenty years or

1125
00:52:58,880 --> 00:53:01,280
Speaker 1: fifty years, we have like a a new basic function,

1126
00:53:01,520 --> 00:53:03,440
Speaker 1: you know, like we have sign and cosign. These were

1127
00:53:03,480 --> 00:53:06,960
Speaker 1: invented functions by human mathematicians. Somebody might come up with

1128
00:53:07,040 --> 00:53:09,520
Speaker 1: a new function which turns out to be really useful

1129
00:53:09,600 --> 00:53:13,280
Speaker 1: to describing three body motion and allows us to find

1130
00:53:13,360 --> 00:53:17,080
Speaker 1: some expression. A lot of mathematicians are skeptical because they

1131
00:53:17,080 --> 00:53:20,520
Speaker 1: can sort of express these solutions as like an infinite series,

1132
00:53:20,560 --> 00:53:23,360
Speaker 1: and they show that it's very complicated, and they suspect

1133
00:53:23,400 --> 00:53:25,800
Speaker 1: that there isn't a simple function. But you know, future

1134
00:53:25,800 --> 00:53:29,360
Speaker 1: mathematicians are usually smarter than today's mathematicians, and so I

1135
00:53:29,440 --> 00:53:30,480
Speaker 1: hold out hope.

1136
00:53:30,360 --> 00:53:32,600
Speaker 4: Or maybe like there are aliens who have figured this out,

1137
00:53:33,000 --> 00:53:34,799
Speaker 4: you know, like they'll come to us and be like, yes,

1138
00:53:34,840 --> 00:53:37,160
Speaker 4: sign and cost and we don't have you know, Chao

1139
00:53:37,320 --> 00:53:39,799
Speaker 4: sign or something that describes chaos motion.

1140
00:53:40,040 --> 00:53:43,560
Speaker 1: Yeah, exactly, And maybe somewhere some mathematician is developing the

1141
00:53:43,600 --> 00:53:45,759
Speaker 1: tools and they don't even realize how it's going to

1142
00:53:45,760 --> 00:53:48,759
Speaker 1: be useful. I love those stories of mathematicians developing these

1143
00:53:48,760 --> 00:53:52,360
Speaker 1: ideas and then them later being co opted by physicists.

1144
00:53:52,400 --> 00:53:54,920
Speaker 1: And so maybe those ideas exist right now, and all

1145
00:53:54,960 --> 00:53:56,320
Speaker 1: you have to do is go out and read the

1146
00:53:56,400 --> 00:53:59,040
Speaker 1: right math paper and you're like, oh, this is exactly

1147
00:53:59,080 --> 00:54:01,319
Speaker 1: the hammer we need to hit this physics nail.

1148
00:54:01,480 --> 00:54:03,640
Speaker 4: Or maybe the answer is in some cabin in Russia,

1149
00:54:04,000 --> 00:54:06,480
Speaker 4: but the the poor soul ran out of food or

1150
00:54:06,480 --> 00:54:09,360
Speaker 4: something and it's lost to us forever.

1151
00:54:09,600 --> 00:54:11,880
Speaker 1: But it's written down on a frozen sheet of paper

1152
00:54:11,920 --> 00:54:12,560
Speaker 1: in that cabin.

1153
00:54:13,239 --> 00:54:16,759
Speaker 4: It exists. But anyways, I guess the good news is

1154
00:54:16,800 --> 00:54:19,080
Speaker 4: that it's an open problem and there could be somebody

1155
00:54:19,120 --> 00:54:21,600
Speaker 4: listening to this podcast right now that might solve it.

1156
00:54:21,560 --> 00:54:22,960
Speaker 1: In the future, maybe even you.

1157
00:54:23,360 --> 00:54:25,640
Speaker 4: Well, we hope you enjoyed that. Thanks for joining us,

1158
00:54:26,239 --> 00:54:27,000
Speaker 4: See you next time.

1159
00:54:34,840 --> 00:54:37,640
Speaker 1: Thanks for listening, and remember that Daniel and Jorge Explain

1160
00:54:37,719 --> 00:54:40,960
Speaker 1: the Universe is a production of iHeart Radio. For more

1161
00:54:41,040 --> 00:54:45,680
Speaker 1: podcasts from iHeart Radio, visit the iHeartRadio app, Apple Podcasts,

1162
00:54:45,800 --> 00:54:48,160
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1163
00:54:59,520 --> 00:55:01,959
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Speaker 1: When you pop a piece of cheese into your mouth,

1172
00:55:31,520 --> 00:55:34,799
Speaker 1: you're probably not thinking about the environmental impact. But the

1173
00:55:34,840 --> 00:55:37,720
Speaker 1: people in the dairy industry are. That's why they're working

1174
00:55:37,760 --> 00:55:40,360
Speaker 1: hard every day to find new ways to reduce waste,

1175
00:55:40,480 --> 00:55:44,600
Speaker 1: conserve natural resources, and drive down greenhouse gas emissions. How

1176
00:55:44,680 --> 00:55:48,600
Speaker 1: is us dairy tackling greenhouse gases? Many farms use anaerobic

1177
00:55:48,640 --> 00:55:52,360
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1178
00:55:52,440 --> 00:55:56,000
Speaker 1: that can power farms, towns, and electric cars. Visit you

1179
00:55:56,080 --> 00:55:59,040
Speaker 1: as dairy dot COM's Last Sustainability to learn more.

1180
00:56:00,600 --> 00:56:04,040
Speaker 8: There are children, friends, and families walking, riding on paths

1181
00:56:04,080 --> 00:56:06,560
Speaker 8: and roads every day. Remember they're real people with loved

1182
00:56:06,560 --> 00:56:08,719
Speaker 8: ones who need them to get home safely. Protect our

1183
00:56:08,760 --> 00:56:10,799
Speaker 8: cyclists and pedestrians because they're people too.

1184
00:56:11,120 --> 00:56:11,680
Speaker 1: Go safely.

1185
00:56:11,760 --> 00:56:14,600
Speaker 8: California From the California Office of Traffic Safety and Caltrans