WEBVTT - Why is the three-body problem so hard? 0:00:08.360 --> 0:00:10.760 Hey, Daniel, when you are teaching, are you the kind 0:00:10.760 --> 0:00:14.400 of professor that assigns super hard homework in your classes? 0:00:14.600 --> 0:00:17.720 You mean, like, find the motion of a banana tied 0:00:17.760 --> 0:00:20.439 to a string held by a squirrel riding on a 0:00:20.520 --> 0:00:23.360 roller coaster, all of that in orbit around a black hole? 0:00:23.480 --> 0:00:29.720 Like that kind of problem? What are you, professor, Rube Goldberg? No, 0:00:29.920 --> 0:00:31.920 that was just a joke. I actually like to make 0:00:31.960 --> 0:00:34.720 the homework just a little bit harder than what we 0:00:34.840 --> 0:00:37.199 work on in class. You know, that's where the concepts 0:00:37.200 --> 0:00:40.320 really come together in your mind. Right, right, you're an 0:00:40.320 --> 0:00:44.839 evil professor. Basically you never assigned unsolved research problems to 0:00:44.960 --> 0:00:47.960 first year students. Know that only happens in the movies. Man, 0:00:48.000 --> 0:00:51.800 Goodwill Hunting is not a documentary. You're not Matt Damon. 0:00:51.920 --> 0:00:55.160 I don't have the looks for it. Yes, there's always 0:00:55.200 --> 0:01:12.959 room for improvement. Hi am more hamming cartoonists and the 0:01:12.959 --> 0:01:16.800 creator of PhD comics. I'm Daniel. I'm a particle physicist, 0:01:16.880 --> 0:01:20.560 and I've never solved an outstanding math problem. Not yet, 0:01:20.600 --> 0:01:22.640 do you mean? Right? Like if you had solved it, it 0:01:22.520 --> 0:01:25.959 it wouldn't be an an outstanding math problem. That's true. Yeah, 0:01:26.120 --> 0:01:28.880 there are these famous, outstanding problems, and it's cool when 0:01:28.880 --> 0:01:31.320 they stand for hundreds of years and then somebody comes 0:01:31.319 --> 0:01:33.880 along and figures them out. What do you think happens? 0:01:33.920 --> 0:01:35.560 Like somebody just comes up with the right way to 0:01:35.640 --> 0:01:38.800 look at it, or like they see something nobody else 0:01:38.840 --> 0:01:41.120 has seen before, or the history was just waiting for 0:01:41.160 --> 0:01:44.640 the right intellect. Yeah, sometimes it's a slow construction of 0:01:44.760 --> 0:01:47.280 ideas over hundreds of years. When you look at the 0:01:47.360 --> 0:01:50.280 history of it and be like, problem proposed in sixteen nineteen, 0:01:50.440 --> 0:01:55.440 progress has made in eighteen fourteen, and then Samantha figures 0:01:55.440 --> 0:01:58.280 it out, and it's pretty awesome to see the stretch 0:01:58.320 --> 0:02:00.840 of history there. I'm waiting for people to solve some 0:02:00.960 --> 0:02:05.480 pretty intractable parenting problems. Didn't sometimes they had Those are eternal, man, 0:02:05.680 --> 0:02:07.920 they will never be solved. They will never be solved. 0:02:09.280 --> 0:02:11.840 It's part of being human, I guess. Welcome to our 0:02:11.840 --> 0:02:14.680 podcast Daniel and Jorge Explain the Universe, a production of 0:02:14.720 --> 0:02:17.800 our Heart Radio in which we tackle the hardest problem, 0:02:17.800 --> 0:02:21.360 which is understanding the nature of this universe we find 0:02:21.360 --> 0:02:24.120 ourselves in. How does it work, where did it come from, 0:02:24.240 --> 0:02:26.720 why is it the way that it is, and is 0:02:26.720 --> 0:02:30.200 it even possible to understand it. We dive right into 0:02:30.240 --> 0:02:33.960 the biggest, hardest, deepest questions. We explain the answers and 0:02:34.080 --> 0:02:36.919 our ignorance to you. What if that's the harder problem, 0:02:36.960 --> 0:02:40.320 Daniel explaining something to other people. We do our best here, 0:02:40.400 --> 0:02:43.240 but um, it's pretty hard to wrap your head around 0:02:43.320 --> 0:02:46.000 all the amazing and incredible stuff that is happening in 0:02:46.080 --> 0:02:48.440 the universe. And one of my favorite things about doing 0:02:48.440 --> 0:02:51.400 this podcast is exercising that part of my brain that 0:02:51.520 --> 0:02:54.440 translates these ideas from like the cutting edge of physics, 0:02:54.600 --> 0:02:57.000 two things everybody can understand, because to do that you 0:02:57.040 --> 0:03:00.240 have to have a really good grasp on what's going on. See, 0:03:00.320 --> 0:03:03.080 you actually have to understand it first before explaining into people. 0:03:03.280 --> 0:03:05.839 So what am I doing here? Then? Well, sometimes when 0:03:05.840 --> 0:03:08.000 you try to explain something, you realize whole lot of second, 0:03:08.080 --> 0:03:10.080 I don't really understand how this works as well as 0:03:10.120 --> 0:03:13.079 I thought it did sometimes only sometimes, though that never 0:03:13.120 --> 0:03:15.480 happens on our podcast. It happens to me all the 0:03:15.520 --> 0:03:17.800 time when I'm teaching and also on this podcast, And 0:03:17.840 --> 0:03:19.799 that's one reason why it's so fun, because not only 0:03:19.840 --> 0:03:22.359 are we explaining stuff, we're also learning as we go. 0:03:22.680 --> 0:03:25.160 But that is a pretty good parenting lesson. Also, it's 0:03:25.200 --> 0:03:26.960 good to share what you know when you learn what 0:03:27.040 --> 0:03:30.320 you love about this crazy beautiful costmas. Yeah, how does 0:03:30.360 --> 0:03:32.040 that help you with your parenting? Well, it's just good 0:03:32.080 --> 0:03:33.959 to share. I think it's good. Well, you have to 0:03:33.960 --> 0:03:35.840 share with your children. I think it's a law, that 0:03:35.960 --> 0:03:37.880 is a rule. But it's also good to teach it 0:03:37.960 --> 0:03:40.440 to share, you know. It's just everyone's more generous with 0:03:40.480 --> 0:03:42.680 their what they have in their knowledge. We're all happy. 0:03:42.880 --> 0:03:44.800 I thought you were going to use the wondering glamor 0:03:44.840 --> 0:03:47.080 of the universe to convince your kids to do their chores, 0:03:47.120 --> 0:03:51.280 like take out the trash because stars are amazing? Are 0:03:51.320 --> 0:03:54.120 you are insignificant in this universe? You're a tiny speck 0:03:54.200 --> 0:03:57.000 of dust in the floating and vast vacuum of perhaps 0:03:57.040 --> 0:04:00.440 infinite space, and therefore you should do your homework. I 0:04:00.480 --> 0:04:02.320 think that will work against you. So then why should 0:04:02.360 --> 0:04:06.640 I bother taking out the trash if nothing matters? Because 0:04:06.640 --> 0:04:11.160 if nothing matters children, everything matters. Like that that trended 0:04:11.200 --> 0:04:14.520 philosophical use that PhD for something. But anyways, we do 0:04:14.600 --> 0:04:17.800 like to talk about not only what scientists know about 0:04:17.839 --> 0:04:20.400 this universe and all of the wonderful stuff in it, 0:04:20.480 --> 0:04:24.160 but also what scientists are struggling with understanding about how 0:04:24.200 --> 0:04:27.760 things work. That's right, because we have this amazing mental 0:04:27.839 --> 0:04:31.200 machinery of science that lets us build up a body 0:04:31.200 --> 0:04:34.240 of knowledge. Things we do understand about the universe has 0:04:34.240 --> 0:04:37.440 a machinery to it, and that machinery is mathematical. It's 0:04:37.440 --> 0:04:41.160 incredible in me sometimes that mathematics can describe the way 0:04:41.200 --> 0:04:43.359 the world works at all. You know, you throw a 0:04:43.400 --> 0:04:46.080 baseball and it follows a parabola, which is a very 0:04:46.120 --> 0:04:49.800 simple mathematical relationship. So it's incredible when you can use 0:04:49.880 --> 0:04:54.119 mathematics to describe what's really very complex behavior, all sorts 0:04:54.120 --> 0:04:57.200 of zillions of particles moving through the air altogether. But 0:04:57.440 --> 0:05:00.840 sometimes it's easier than other times. And the cool thing 0:05:00.839 --> 0:05:02.680 about sciences is that it's always at the sort of 0:05:02.720 --> 0:05:05.080 the leading edge of human knowledge, right, Like that's what 0:05:05.279 --> 0:05:08.320 science is. It's sort of like asking the questions nobody's 0:05:08.360 --> 0:05:11.279 ever asked, or finding the answers nobody that has so far. 0:05:11.480 --> 0:05:13.760 And so sometimes you run into things that are just 0:05:14.200 --> 0:05:17.760 really really extra hard or maybe even impossible. Yeah, and 0:05:17.839 --> 0:05:20.960 sometimes they are impossible because the physics is really hard, 0:05:21.000 --> 0:05:23.359 and sometimes they're impossible because we just don't have the 0:05:23.400 --> 0:05:26.400 mathematics yet. Like, there's been lots of times in history 0:05:26.600 --> 0:05:29.600 when mathematicians have developed tools, not because they thought they 0:05:29.600 --> 0:05:31.480 were gonna be useful for physics, but just because they 0:05:31.480 --> 0:05:34.240 thought it was fun, and then later on physicists were 0:05:34.320 --> 0:05:36.640 like a whold on a second. That totally helps me 0:05:36.720 --> 0:05:39.159 solve this problem I've been struggling with for twenty years. 0:05:39.400 --> 0:05:43.440 A great example is general relativity, which is built on geometry, 0:05:43.480 --> 0:05:46.200 which was developed just ten years before. Without all that 0:05:46.279 --> 0:05:50.680 work developing geometry, there's no way Einstein could have developed relativity. 0:05:50.880 --> 0:05:54.760 Is this really fascinating dance between mathematics and physics? Yeah? 0:05:54.960 --> 0:05:56.880 What kind of dance? How would you describe that dance? 0:05:56.920 --> 0:05:59.480 Is it like a Charleston or more like a waltz? 0:05:59.800 --> 0:06:03.440 Or like hip hop breakdancing competition? What would you call it? 0:06:03.520 --> 0:06:06.040 The mathematicians carefully build their tools and we just sneak 0:06:06.080 --> 0:06:08.400 in and steal them, So maybe it's more like a 0:06:08.440 --> 0:06:14.200 cat Burglar dance. Oh man, I can't wait for that, 0:06:14.320 --> 0:06:18.240 you know, interpretive dance History of Science Broadway play that 0:06:18.240 --> 0:06:19.800 you're working on. Yeah, you know, I wish it was 0:06:19.880 --> 0:06:22.719 more back and forth. Sometimes I feel like, shouldn't the 0:06:22.760 --> 0:06:26.080 mathematicians be excited when their tools actually get used to 0:06:26.120 --> 0:06:28.400 describe the real universe? But a lot of times they 0:06:28.440 --> 0:06:30.839 don't seem to care at all, and they're like, whatever, 0:06:31.040 --> 0:06:34.000 who cares about the real universe? I'm walking the halls 0:06:34.080 --> 0:06:38.080 of truth. You're selling their halls with like reality and 0:06:38.120 --> 0:06:41.320 like red and dirt, Like that's just dirt. Adams are 0:06:41.400 --> 0:06:43.800 just dirt. If they cared about getting dirty, they would 0:06:43.800 --> 0:06:47.880 have been physicists instead of mathematicians. I see, physicis are 0:06:48.000 --> 0:06:50.320 are the down and dirty of of scientists. I think 0:06:50.320 --> 0:06:53.880 physicists are to mathematicians what engineers are to physicists. Oh, 0:06:53.920 --> 0:06:57.680 I see the better the better people, right, the true 0:06:57.720 --> 0:07:02.520 heroes on the hierarchy of useless pure the hierarchy of usefulness. 0:07:02.520 --> 0:07:06.320 You mean, depending on what you put in the top? Yes, 0:07:06.360 --> 0:07:09.960 exactly right. Yes, if you turn upside down, we're actually 0:07:10.000 --> 0:07:13.360 at the top. Yes, it's all about your perspective, that's right. 0:07:13.360 --> 0:07:15.680 There is no up in space anyway. Well, there are 0:07:15.800 --> 0:07:19.680 interesting problems in physics, some of them which are even intractable, 0:07:19.680 --> 0:07:21.800 and so in this episode we'll be talking about one 0:07:21.880 --> 0:07:25.560 such problem that maybe affects are very movement through space, 0:07:25.560 --> 0:07:28.600 and it affects how planets revolve around their suns, and 0:07:28.640 --> 0:07:31.160 which we may never find the answer for. So to 0:07:31.240 --> 0:07:38.400 be on the podcast, we'll be asking the question, what's 0:07:38.400 --> 0:07:43.560 so hard about the three body problem? Now, Daniel, this 0:07:43.680 --> 0:07:45.600 is not something that's not safe for work, is it? 0:07:47.040 --> 0:07:49.600 I mean, I see something here at three bodies? Is 0:07:49.640 --> 0:07:52.280 this about? You know? No, this is not about being 0:07:52.320 --> 0:07:56.280 exploratory in your relationships at all. It's what's so mathematically 0:07:56.360 --> 0:08:01.840 difficult about three gravitationally attracting objects? Is the safe preparatory 0:08:02.160 --> 0:08:06.280 in the heavenly bodies relationships? You know, some bodies here 0:08:06.320 --> 0:08:08.280 on Earth are quite heavenly as well, but we're talking 0:08:08.280 --> 0:08:12.360 about celestial bodies, that's right, the real stars. Alright, So 0:08:12.560 --> 0:08:14.960 the three button. More specifically, this is kind of about 0:08:15.000 --> 0:08:17.480 what is the three body problem at all? Because I 0:08:17.520 --> 0:08:19.480 imagine that a lot of people have heard of him, 0:08:19.720 --> 0:08:21.840 although it is the title of sort of a well 0:08:21.960 --> 0:08:25.600 known science fiction novel out there, right, that's fairly recent, 0:08:26.080 --> 0:08:28.080 that's right. Yeah, it's like one of the biggest novels 0:08:28.120 --> 0:08:30.559 in the last few years. It's a whole trilogy written 0:08:30.640 --> 0:08:32.920 by a fantastic Chinese author. A lot of people are 0:08:32.920 --> 0:08:34.600 really into this book, and a lot of our listeners 0:08:34.640 --> 0:08:37.160 have written in asking us to talk about this book. 0:08:37.640 --> 0:08:40.200 But I thought, first maybe be more fun to talk 0:08:40.200 --> 0:08:42.559 about like the physics problem that's at the heart of 0:08:42.679 --> 0:08:45.520 the novel, that we can talk about the actual problem itself. Yeah, 0:08:45.559 --> 0:08:47.440 I think. I try to read the novel. It's it's 0:08:47.480 --> 0:08:49.880 pretty dense, it's kind of thick. Yeah, there's a lot 0:08:50.000 --> 0:08:52.199 of physics in that book, which is pretty fun for 0:08:52.280 --> 0:08:55.959 people who like really well thought out physics novels. And 0:08:56.160 --> 0:08:57.520 so it's a good idea to try to get an 0:08:57.600 --> 0:09:00.679 understanding for like what is the underlying problem at the 0:09:00.840 --> 0:09:03.400 core of the story? Right? And it was like a 0:09:03.480 --> 0:09:05.920 bestseller and want all the awards right in science fiction. 0:09:06.120 --> 0:09:08.040 M So you can check that out if you like. 0:09:08.200 --> 0:09:10.200 But the title of it refers to kind of an 0:09:10.240 --> 0:09:14.880 old and famous problem in physics about I imagine three bodies. 0:09:15.040 --> 0:09:18.000 That's right, it's really old problem, and old problems are 0:09:18.040 --> 0:09:20.360 the funniest problems because it means that like a lot 0:09:20.520 --> 0:09:22.959 of smart people have been butting their heads against this 0:09:23.040 --> 0:09:27.320 problem for decades or even centuries, and nobody has figured 0:09:27.360 --> 0:09:29.320 it out. And doesn't mean it's impossible. There are other 0:09:29.440 --> 0:09:32.319 mathematical problems that have existed for hundreds of years and 0:09:32.320 --> 0:09:34.200 then all of a sudden, some dude in a cabin 0:09:34.280 --> 0:09:36.600 in Russia comes out with like a hundred page proof 0:09:36.640 --> 0:09:38.679 of it. So it might be possible to be solved, 0:09:38.720 --> 0:09:41.720 but nobody's cracked this one. Yeah, just a book on Airbnb, 0:09:41.880 --> 0:09:44.599 that cabin in Russia, and you know, book it for 0:09:45.160 --> 0:09:46.960 for a couple of years, and that you might solve 0:09:47.120 --> 0:09:51.640 a famous problem. That's the real answer. That wasn't a metaphor. 0:09:51.720 --> 0:09:54.480 That was that really happened to you, not to me. No, 0:09:55.080 --> 0:09:57.679 there really is a Russian mathematician who worked all by 0:09:57.800 --> 0:10:01.400 himself for a decade and saw the famous problem in math, 0:10:01.600 --> 0:10:04.400 the remon conjecture. Wow. And he was in a cabin, 0:10:04.679 --> 0:10:06.400 using a cabin. He worked all by himself, and he 0:10:06.520 --> 0:10:08.800 just sent in the solution and they tried to give 0:10:08.880 --> 0:10:10.959 him the Fields Medal for it and he wouldn't even 0:10:10.960 --> 0:10:14.120 show up. Wow. That feels like such a fine line 0:10:14.200 --> 0:10:19.560 between like, you know, genius and you know, socially unacceptable behavior. 0:10:21.840 --> 0:10:25.440 He's well on one side of that line. But anyways, 0:10:25.559 --> 0:10:28.280 let's talk about this problem, the three body problem. And so, 0:10:28.360 --> 0:10:30.440 as usually we were wondering how many people out there 0:10:30.800 --> 0:10:32.679 we knew what this was, if they had heard of 0:10:32.760 --> 0:10:36.160 it before beyond the novel, or how important it is 0:10:36.200 --> 0:10:39.920 to sort of predicting the movement of our planets in 0:10:40.080 --> 0:10:42.679 our solar system. So Daniel as usually went out there 0:10:42.720 --> 0:10:45.040 into the wilds of the internet to ask people what 0:10:45.360 --> 0:10:48.240 is the three body problem? So, while we are still 0:10:48.360 --> 0:10:51.480 pandemically shut down, I am very grateful to all of 0:10:51.559 --> 0:10:54.319 you who are willing to participate via email on the 0:10:54.520 --> 0:10:58.000 person on the virtual street interviews. So if you would 0:10:58.040 --> 0:11:00.640 like to participate and hear your speculation on the podcast, 0:11:00.720 --> 0:11:03.760 please don't be shy. Send us a message to questions 0:11:03.880 --> 0:11:06.319 at Daniel and Jorge dot com. Think about it for 0:11:06.320 --> 0:11:08.719 a second. Do you know what the three body problem is? 0:11:09.240 --> 0:11:11.280 Here's what people have to say. I don't know what 0:11:11.400 --> 0:11:14.600 the three body problem is, I'm afraid so I'm barely 0:11:14.720 --> 0:11:18.320 aware of what the three body problem is. I did 0:11:18.480 --> 0:11:22.760 read as you should use three body problem trilogy. My 0:11:22.960 --> 0:11:27.160 understanding is that it's a problem with how three bodies 0:11:27.480 --> 0:11:30.559 orbit one another and how it could continue to do 0:11:30.720 --> 0:11:34.120 that and be stable without cuestion into one another. A 0:11:34.200 --> 0:11:38.520 lot of people spend a fair amount of time calculating 0:11:38.720 --> 0:11:42.760 how two massive bodies interacts due to the gravitational field 0:11:42.880 --> 0:11:45.640 surrounding them. But actually, if you add a third body, 0:11:45.960 --> 0:11:51.040 the system becomes unstable, it becomes chaotic, so you can't 0:11:51.120 --> 0:11:56.120 determine an exact solution. And also if you make a 0:11:56.240 --> 0:12:01.480 small change let's say in the initial positions of the bodies, um, 0:12:01.720 --> 0:12:06.400 you can't actually determine how let's say the forces between 0:12:06.440 --> 0:12:09.040 the three bodies will be affected. I think that's to 0:12:09.120 --> 0:12:12.600 do when you've got three bodies that rotatue interacts, usually 0:12:12.760 --> 0:12:16.840 like the Sun, the Earth and the Moon, for example, 0:12:16.880 --> 0:12:19.679 would be that would be three bodies, and I think 0:12:19.760 --> 0:12:22.040 you can solve two bodies. Any more than a few 0:12:22.120 --> 0:12:23.800 more and you can't solve it. I think is it 0:12:23.840 --> 0:12:27.439 is one of the issues. Wow, that is something I 0:12:27.600 --> 0:12:31.760 am not sure where it is. I don't know what 0:12:31.920 --> 0:12:36.439 the three body problem is m unless it's relating to 0:12:36.559 --> 0:12:41.720 a previous question where if you have three bodies acting 0:12:42.280 --> 0:12:47.439 on each other gravitationally, um, you haven't got sort of 0:12:47.520 --> 0:12:50.599 one orbiting another or one with a joint orbit with 0:12:50.679 --> 0:12:56.840 another that that will be probably quite at random implication 0:12:56.960 --> 0:13:00.439 to their orbits. I have never heard of the three 0:13:00.480 --> 0:13:04.760 body problem before. But if I were to guess, I 0:13:04.880 --> 0:13:07.760 think it is three bodies interacting with each other, and 0:13:08.000 --> 0:13:11.880 something unusual happens, like something that doesn't happen between two 0:13:12.000 --> 0:13:15.960 bodies of four bodies. It just happens between these three 0:13:16.320 --> 0:13:20.199 bodies for some reason, and for some reason the number 0:13:20.320 --> 0:13:23.040 is three. Actually, I've studied physics before, so I know 0:13:23.240 --> 0:13:26.199 that the three body problem is this problem where if 0:13:26.280 --> 0:13:30.960 you have two objects pulling on each other, then those 0:13:31.000 --> 0:13:33.480 equations can be solved pretty easily. But if you add 0:13:33.520 --> 0:13:36.440 in a third body, now you have three different interactions 0:13:36.520 --> 0:13:40.600 between A B, A C and C B. And when 0:13:40.640 --> 0:13:44.880 you have interactions of that order that that many interactions, 0:13:45.400 --> 0:13:48.480 it becomes sort of an unsolvable math problem. And so 0:13:48.640 --> 0:13:51.600 we don't have like good solutions for those sort of situations. 0:13:51.679 --> 0:13:54.959 We have to essentially come up with approximations and simulate it. 0:13:55.400 --> 0:13:58.679 All right, There not a lot of knowledge about this, 0:13:58.880 --> 0:14:02.120 But someone did read the True Gene. Yeah, exactly three 0:14:02.200 --> 0:14:04.640 books in the three Body Problem trilogy. It's nice. It 0:14:04.679 --> 0:14:06.199 must have been good because he read all three or 0:14:06.679 --> 0:14:09.480 I wonder if your completest, you know, tendencies would kick 0:14:09.520 --> 0:14:11.520 in after you rerund well, I can't just read one 0:14:11.679 --> 0:14:14.160 three body problem book. I gotta read all three depends 0:14:14.160 --> 0:14:15.679 if they leave a cliffhanger at the end of the 0:14:15.720 --> 0:14:18.439 first novel. You should title all your trilogies with the 0:14:18.600 --> 0:14:20.920 number three in it. But it seems like most people 0:14:20.960 --> 0:14:22.600 here are guessing it has to do with bodies in 0:14:22.720 --> 0:14:26.160 space and then specifically three bodies of course, But a 0:14:26.240 --> 0:14:28.880 lot of people are saying maybe it's about it becoming 0:14:29.040 --> 0:14:32.440 unsolvable or chaotic or unstable. Are they sort of in 0:14:32.480 --> 0:14:34.720 the right track. They are exactly on the right track. 0:14:35.160 --> 0:14:38.120 It's really interesting. There's a problem which is easy if 0:14:38.160 --> 0:14:41.600 there's only two objects involved, and then becomes basically unsolvable 0:14:41.800 --> 0:14:45.640 if you have three objects involved, right, like real human relationships, 0:14:47.800 --> 0:14:50.880 which can be tricky even when there are two bodies involved, 0:14:51.560 --> 0:14:54.920 even if everyone is open minded, it gets tricky. Al Right, Well, 0:14:55.000 --> 0:14:57.760 let's dig into Daniel, how would you describe the three 0:14:57.880 --> 0:15:00.040 body problems? I think the best way to describe it 0:15:00.240 --> 0:15:02.800 is to first talk about what we can do and 0:15:03.040 --> 0:15:06.280 simply said, if you have two objects in space, and 0:15:06.360 --> 0:15:09.080 you know where they are, how heavy they are, and 0:15:09.240 --> 0:15:12.480 the direction they're going in, then you can predict their motion. 0:15:12.800 --> 0:15:15.280 You can say at some time in the future, I 0:15:15.400 --> 0:15:17.720 know where they are going to be. So, for example, 0:15:18.000 --> 0:15:20.640 imagine just the Sun and the Earth. These are two 0:15:20.680 --> 0:15:23.360 objects that pull on each other. There are forces involved. 0:15:23.800 --> 0:15:25.560 And if you know where the Sun and the Earth 0:15:25.640 --> 0:15:28.120 are at some moment in time, in which direction they're heading, 0:15:28.160 --> 0:15:30.320 and their masses, you can write down a very simple 0:15:30.400 --> 0:15:33.040 formula that will tell you where they will be in 0:15:33.120 --> 0:15:35.040 the future. Like you say, where will the sun be 0:15:35.360 --> 0:15:37.480 in a year, or in a thousand years or in 0:15:37.520 --> 0:15:40.760 a million years. It's like a very simple mathematical expression. 0:15:40.920 --> 0:15:42.800 You plug in the time, it tells you where the 0:15:42.880 --> 0:15:45.760 Sun will be. So that's the two body problem, and 0:15:45.840 --> 0:15:48.080 we have a solution for that. We can crank through 0:15:48.080 --> 0:15:50.480 the mathematics and get a very nice simple formula that 0:15:50.560 --> 0:15:52.640 tells us where they will be at any moment in 0:15:52.720 --> 0:15:54.640 the future. Right, But you have to kind of assume 0:15:54.680 --> 0:15:56.840 that they're alone in the in the whole universe, like 0:15:56.880 --> 0:15:59.120 there's nothing else in the universe pulling on them. Right, 0:15:59.160 --> 0:16:01.880 that's right, only two bodies. And as usual, you know, 0:16:02.000 --> 0:16:05.359 physics is telling a story, and that story is always approximate. 0:16:05.720 --> 0:16:08.720 The reality never matches the approximate stories we try to 0:16:08.840 --> 0:16:11.440 use when we tell physics stories because in reality, there's 0:16:11.440 --> 0:16:13.520 an infinite number of bodies out there in space, and 0:16:13.760 --> 0:16:16.840 gravity works for over infinite distances, and so everything in 0:16:16.880 --> 0:16:19.800 the universe is hugging on things all the time. But 0:16:20.120 --> 0:16:23.120 usually you can get away with disregarding that. You don't 0:16:23.160 --> 0:16:25.360 have to care about what's happening in Andromeda when you're 0:16:25.360 --> 0:16:27.680 doing in the calculation of whether your satellite is going 0:16:27.720 --> 0:16:30.680 to go around the Earth, because it's basically zero contribution. 0:16:30.920 --> 0:16:32.960 So here we're talking about the scenario where you have 0:16:33.080 --> 0:16:36.000 two bodies and everything else can be ignored without changing 0:16:36.040 --> 0:16:38.280 anything down to like, you know, the tenth decimal place 0:16:38.400 --> 0:16:41.160 or something. Yes, so in the sort of simplified universe 0:16:41.240 --> 0:16:44.120 of exactly two things in your universe, you can predict 0:16:44.200 --> 0:16:46.800 the motion of two objects, all right, So then I'm 0:16:46.880 --> 0:16:49.120 guessing when you get to three bodies, it gets a 0:16:49.200 --> 0:16:51.600 little harder. When you get to three bodies, it doesn't 0:16:51.640 --> 0:16:54.440 just get a little harder, it becomes impossible. If you 0:16:54.480 --> 0:16:56.360 know where three objects are. You know, so you have, 0:16:56.480 --> 0:16:59.720 for example, the Sun, the Earth, and then another object. 0:17:00.040 --> 0:17:02.000 Now you just have three objects and you know exactly 0:17:02.040 --> 0:17:04.440 where they are, what direction they're going in, and you 0:17:04.520 --> 0:17:07.520 know their masses. You cannot write down a simple formula 0:17:07.840 --> 0:17:10.200 that tells you where they're going to be in a week, 0:17:10.520 --> 0:17:13.200 or in a year or in a thousand years. Well, 0:17:13.320 --> 0:17:16.840 it gets really complicated. Suddenly, it gets really complicated. We 0:17:16.920 --> 0:17:19.399 don't have a solution. Now, we have an understanding for 0:17:19.520 --> 0:17:22.320 what's going on, Like we know the forces involved, We 0:17:22.440 --> 0:17:26.479 know what the gravity is between two objects given their distance. Right, 0:17:26.520 --> 0:17:28.840 that's a pretty simple formula. Newton told us how to 0:17:28.880 --> 0:17:30.879 do that. But that doesn't mean we know how to 0:17:30.960 --> 0:17:33.479 find the solution. Doesn't mean we can take those forces 0:17:33.520 --> 0:17:35.800 and predict the motion. Right. Well, I think this might 0:17:35.880 --> 0:17:37.639 be kind of a subtle subject for a lot of 0:17:37.680 --> 0:17:39.680 people out there, which is like what you mean in 0:17:39.840 --> 0:17:43.000 physics as a solution, because it doesn't mean that you 0:17:43.040 --> 0:17:44.720 can't predict where they're going to be. You just don't 0:17:44.720 --> 0:17:48.000 have an easy solution to the equations to predict this. Right. 0:17:48.160 --> 0:17:50.399 It means that we know what the constraints are. Like 0:17:50.520 --> 0:17:52.639 physics tells you what the rules are, tells you like, 0:17:52.720 --> 0:17:55.760 for example, how two objects pull on each other. It 0:17:55.880 --> 0:17:58.320 doesn't tell you how those objects are going to move. 0:17:58.600 --> 0:18:00.720 To figure out how the objects are to move, which 0:18:00.800 --> 0:18:03.040 is what you need to predict their emotion. You need 0:18:03.080 --> 0:18:05.200 to be able to solve all of those equations and 0:18:05.320 --> 0:18:08.000 get the answer out. So physics gives you, like all 0:18:08.040 --> 0:18:10.359 the equations you need to solve. It doesn't mean you 0:18:10.480 --> 0:18:13.360 know how to solve the equations, Like not every equation 0:18:13.480 --> 0:18:16.680 you get is solvable, or we don't necessarily have the 0:18:16.760 --> 0:18:20.399 mathematical tools to solve an arbitrary equation. Turns out, in 0:18:20.480 --> 0:18:23.000 physics there are only like five problems we do know 0:18:23.200 --> 0:18:27.200 how to solve and everything else is intractable. Well, that 0:18:27.560 --> 0:18:30.760 probably makes for a short workday there free. But I 0:18:30.840 --> 0:18:32.640 think what you mean is, like, for example, like a ball, 0:18:32.760 --> 0:18:35.080 if I throw a ball here at my son in 0:18:35.440 --> 0:18:39.159 our backyard here, like I know that that ball, I 0:18:39.240 --> 0:18:41.120 know the constraints on it, like I know the forces 0:18:41.160 --> 0:18:43.399 pulling on it, the force of gravity, and I know 0:18:43.520 --> 0:18:45.840 that F equals m A for example. So I can solve, 0:18:45.920 --> 0:18:50.600 for example, for its exceloration very easily. But maybe getting 0:18:50.640 --> 0:18:53.200 like a formula for what its position is going to 0:18:53.280 --> 0:18:55.960 be is a little tricky. It's different than knowing what 0:18:56.080 --> 0:18:58.600 it's acceleration is going to be exactly. The acceleration just 0:18:58.760 --> 0:19:01.680 tells you how is momentums and change in a given moment. 0:19:02.080 --> 0:19:04.679 Right to know where it's going to be, you need 0:19:04.720 --> 0:19:07.439 to then solve the equations of motion, which incorporate all 0:19:07.480 --> 0:19:10.280 these forces and is affected by that acceleration. But it 0:19:10.359 --> 0:19:13.760 requires actually solving the equation. You know. It's like if 0:19:13.840 --> 0:19:17.439 I have an equation that says X plus five equals ten. Right, 0:19:17.600 --> 0:19:20.520 that's an equation that constrains X. It limits what X 0:19:20.680 --> 0:19:23.360 can be, but it's not actually the solution. The solution 0:19:23.480 --> 0:19:26.159 is X equals five. That's a very simple one, right. 0:19:26.200 --> 0:19:28.960 You know exactly how to go from the equation X 0:19:29.000 --> 0:19:31.760 plus five equals tend to the solution, But you don't 0:19:31.760 --> 0:19:34.120 necessarily know how to do that for an arbitrary equation. 0:19:34.200 --> 0:19:37.720 Take another simple example, like X squared equals forty nine. 0:19:38.280 --> 0:19:40.040 How do you find the solution to that? You know 0:19:40.200 --> 0:19:43.280 off the top of your head that x equals seven works, 0:19:43.400 --> 0:19:45.119 You can plug it in and check it. But how 0:19:45.160 --> 0:19:47.800 do you find the solution? If I tell you X 0:19:47.800 --> 0:19:51.000 square equals an arbitrary number? How do you find the 0:19:51.040 --> 0:19:53.720 square root of an arbitrary number? There actually is no 0:19:53.960 --> 0:19:56.639 way to do that. There is no mechanism for solving 0:19:56.760 --> 0:20:00.359 that equation other than guessing and checking us like my 0:20:00.480 --> 0:20:04.119 parenting strategy right there. And I think what you mean is, like, 0:20:04.280 --> 0:20:06.639 you know, in physics, you have equations to tell you, 0:20:06.720 --> 0:20:09.600 for example, like the acceleration of x, which is like 0:20:09.680 --> 0:20:12.680 how the velocity changes, which is like how the position 0:20:12.800 --> 0:20:14.680 is changing. Like you have equations for that. But to 0:20:14.760 --> 0:20:17.160 actually get the pocsisition, you have to kind of backtrack 0:20:17.200 --> 0:20:20.840 from acceleration to velocity to position. And that's where the 0:20:20.960 --> 0:20:24.960 trickiness comes from, right yeah, because the acceleration changes through time, 0:20:25.040 --> 0:20:27.760 and so to figure out how all those accelerations add 0:20:27.840 --> 0:20:30.280 up to describe the motion of the object is not 0:20:30.440 --> 0:20:33.200 always easy. And then what you want is a simple 0:20:33.320 --> 0:20:37.159 formula that describes it, and that doesn't necessarily exist, right 0:20:37.200 --> 0:20:39.159 because I guess when you go from two bodies to 0:20:39.280 --> 0:20:42.840 three bodies, then the formula just get too complicated. The 0:20:42.920 --> 0:20:47.080 formula gets too complicated. Exactly, the system gets really complicated 0:20:47.160 --> 0:20:50.080 because now you have these three different objects pulling on 0:20:50.160 --> 0:20:53.280 each other, and it actually becomes chaotic. All right, Well, 0:20:53.359 --> 0:20:56.040 let's dig into why exactly it is so hard and 0:20:56.160 --> 0:20:59.520 how it becomes pure chaos when you add a third 0:20:59.760 --> 0:21:03.000 cell steel body into the mix, and what consequences it 0:21:03.160 --> 0:21:06.760 has for our ability to predict the universe. But first, 0:21:06.800 --> 0:21:21.520 let's take a quick break. All right, Daniel, we're talking 0:21:21.560 --> 0:21:24.080 about the three body problem, and I guess we're not 0:21:24.200 --> 0:21:26.320 just talking about like what happens if your spouse moves 0:21:26.359 --> 0:21:29.040 to another city, right, this is more cosmic. I can't 0:21:29.080 --> 0:21:31.080 solve that problem for you. There is no equation that 0:21:31.200 --> 0:21:35.120 tells you how to live your life. That's the one 0:21:35.200 --> 0:21:37.960 body problem is already pretty hard. Now we're talking about 0:21:38.000 --> 0:21:40.520 the three body problem. One is the loneliest number. But 0:21:40.720 --> 0:21:42.960 this is not a relationship helpline, and this is not 0:21:43.119 --> 0:21:46.000 a podcast about human emotions. We are trying to solve 0:21:46.040 --> 0:21:49.480 the much easier problem of motion of objects through space. 0:21:49.680 --> 0:21:52.040 And so you're saying that when I have two objects 0:21:52.080 --> 0:21:54.760 in space, it's easy enough to sort of predict where 0:21:54.760 --> 0:21:56.920 they're going to be once you have three. It because 0:21:56.960 --> 0:21:59.680 there's no easy solution to that problem. Yeah, there's no 0:21:59.840 --> 0:22:03.399 easy solution. There's no like short mathematical answer when you 0:22:03.520 --> 0:22:05.840 like is something like x f T or x is 0:22:05.880 --> 0:22:08.280 the position of the object, and then a simple formula 0:22:08.480 --> 0:22:10.400 where you can plug in the time and it will 0:22:10.440 --> 0:22:13.280 tell you exactly the position of the object. That's what 0:22:13.359 --> 0:22:15.639 you're looking for because you'd like to be able to 0:22:15.800 --> 0:22:18.080 take that system and say, I want to know where 0:22:18.119 --> 0:22:19.399 the moon is going to be, where I want to 0:22:19.480 --> 0:22:20.920 know where the sun is going to be in a 0:22:21.000 --> 0:22:23.360 thousand years. The problem is that there is no such 0:22:23.440 --> 0:22:25.879 simple formula. We haven't found one at least, and we 0:22:25.960 --> 0:22:28.800 suspect that it might not exist because the system of 0:22:28.920 --> 0:22:32.240 three objects is much much more complicated than a system 0:22:32.280 --> 0:22:35.120 of just two objects, right, And it gets really complicated 0:22:35.119 --> 0:22:38.240 because now you have three objects in three D? Is 0:22:38.280 --> 0:22:40.200 it kind of about going to the third dimension? That 0:22:40.280 --> 0:22:42.080 makes it hard because I imagine if you have two 0:22:42.119 --> 0:22:44.440 bodies in space, you can just treat him as like 0:22:44.480 --> 0:22:46.920 a two D problem, right, like you just imagine the 0:22:47.000 --> 0:22:48.879 plane where these two bodies are. But once you have 0:22:49.000 --> 0:22:51.240 three and then it's like, now it's a three D problem. 0:22:51.359 --> 0:22:53.359 It's true that two objects in space you can always 0:22:53.359 --> 0:22:55.480 define a plane between them. You can also put three 0:22:55.560 --> 0:22:58.320 objects on a plane though, right, three points define a plane, 0:22:58.440 --> 0:23:00.679 so there's always a plane for three jects. I think 0:23:00.720 --> 0:23:03.040 the problem is that when you have three objects, a 0:23:03.200 --> 0:23:07.320 small change in their location leads to a big change 0:23:07.640 --> 0:23:09.320 in where they're going to be in the future. At 0:23:09.400 --> 0:23:12.760 least for gravitational interactions, whereas if you have two objects, 0:23:13.040 --> 0:23:15.000 a small change and where the Earth is going to be, 0:23:15.280 --> 0:23:17.879 it will mostly settle back into the same answer. And 0:23:18.000 --> 0:23:20.879 so in terms of like finding an equation that describes it, 0:23:21.080 --> 0:23:24.240 there's a whole family of equations that can describe stable solutions. 0:23:24.640 --> 0:23:27.400 We don't really have functions that are very good describing 0:23:27.640 --> 0:23:31.399 chaotic situations, whereas very small change in the angle or 0:23:31.440 --> 0:23:34.440 the velocity of the moon means it's now suddenly over here, 0:23:34.560 --> 0:23:36.120 or it's suddenly on the other side of the sun, 0:23:36.240 --> 0:23:39.040 or it flies off in a completely different direction. Our 0:23:39.040 --> 0:23:42.359 equations are not good at describing chaotic mathematics. But I 0:23:42.359 --> 0:23:44.399 guess maybe the question is, like, what is it that 0:23:44.480 --> 0:23:47.480 about going from two to three that actually makes the 0:23:47.600 --> 0:23:51.760 equations unsolvable? Like before, with two, I can solve the equations, 0:23:51.840 --> 0:23:54.480 but with three, there's no solution for them. Does it 0:23:54.560 --> 0:23:57.480 become nonlinear? Is that what it is? It's already nonlinear, 0:23:57.600 --> 0:24:00.119 right that even with an equals to it's nonlinear as 0:24:00.160 --> 0:24:03.400 these distances go like one over radius squared, so there's 0:24:03.400 --> 0:24:06.480 an inverse are squared there, So it's already nonlinear. I 0:24:06.560 --> 0:24:08.880 think something you said earlier is really the right way 0:24:08.920 --> 0:24:11.200 to think about it. We know the forces F and 0:24:11.240 --> 0:24:13.760 the mass M, and we have F equals m A, 0:24:14.080 --> 0:24:16.960 so we can get the acceleration. That's a very simple formula. 0:24:17.160 --> 0:24:19.680 But how do you go from knowing the acceleration, which 0:24:19.720 --> 0:24:22.639 is how much the speed is changing, to knowing the 0:24:22.760 --> 0:24:25.439 actual location. What you have to do is add up 0:24:25.480 --> 0:24:29.000 the effects of lots of little accelerations over time, which 0:24:29.080 --> 0:24:32.280 means you have to integrate. You have to use calculus. 0:24:32.600 --> 0:24:35.040 But just like there aren't that many physics problems that 0:24:35.080 --> 0:24:38.920 are solvable, not every function can be integrated, at least 0:24:39.200 --> 0:24:41.720 not into a simple formula you can write down. So 0:24:41.920 --> 0:24:44.560 just because you know the force and the acceleration doesn't 0:24:44.640 --> 0:24:47.760 mean you know how to integrate it into getting the location. 0:24:48.119 --> 0:24:49.960 And we can go a little bit further if you 0:24:50.040 --> 0:24:52.719 look at the structure of the problem. Mathematicians call these 0:24:52.760 --> 0:24:56.560 problems non integrable, which just means that, like the possible 0:24:56.600 --> 0:25:00.240 trajectories for these objects in this three D space don't 0:25:00.240 --> 0:25:04.240 follow simple paths right like, they diverge very quickly. It's 0:25:04.240 --> 0:25:06.320 not like it can be easily simplified from a whole 0:25:06.359 --> 0:25:08.920 big set of possible solutions down to just a few, 0:25:09.119 --> 0:25:11.080 and with any equals too. With the two body problem, 0:25:11.359 --> 0:25:13.480 there are a bunch of simplifications you can make that 0:25:13.640 --> 0:25:17.000 separate the problem so that, for example, the distance between 0:25:17.040 --> 0:25:20.480 the objects is independent of their relative angle, because for 0:25:20.600 --> 0:25:23.240 two objects, you know, the angle doesn't really matter. What 0:25:23.440 --> 0:25:26.120 only matters is really just the distance. But for three 0:25:26.200 --> 0:25:28.840 objects you have not just the relative distances, but you 0:25:28.960 --> 0:25:31.720 also have the relative angles. And so now all the 0:25:31.800 --> 0:25:34.320 problems are still tied together. You know, when you try 0:25:34.359 --> 0:25:36.600 to solve a set of equations, sometimes it's helpful to 0:25:36.640 --> 0:25:39.440 try to separate them and solve them independently, but that's 0:25:39.480 --> 0:25:42.080 not always possible, and when they're all entangled up with 0:25:42.160 --> 0:25:44.960 each other, you can't always find a solution. Now, I see, 0:25:45.000 --> 0:25:47.280 there's something sort of magical about the number two that 0:25:47.480 --> 0:25:49.520 then you lose once you get more than two, right, 0:25:49.560 --> 0:25:51.720 because it's not just three bodies that are hard, it's 0:25:51.720 --> 0:25:54.200 also four and five and six and infinite. Right. Yes, 0:25:54.320 --> 0:25:56.360 you might have thought, oh, well, two bodies are solvable, 0:25:56.440 --> 0:25:59.080 so then why not three? It's actually the other direction. 0:25:59.200 --> 0:26:02.360 Two is the the one that is solvable. Right. All 0:26:02.440 --> 0:26:05.560 the problems are unsolvable except for this one magic special 0:26:05.720 --> 0:26:08.680 case of two bodies which we have been able to 0:26:08.760 --> 0:26:12.240 separate using this special trick and solve. So it's sort 0:26:12.240 --> 0:26:14.639 of lucky that any of them are solvable. Well, the 0:26:15.000 --> 0:26:18.480 zero body problem is solvable too, and the one body problem, 0:26:18.560 --> 0:26:21.280 I imagine is solvable. It's just that it's just gets 0:26:21.320 --> 0:26:24.840 more complicate. Real equations start to like interact with each other, 0:26:24.920 --> 0:26:27.719 and then you can't like fit a simple formula as 0:26:27.760 --> 0:26:31.080 a solution, right, yeah, exactly. And in addition, there's something 0:26:31.160 --> 0:26:34.880 about chaos here, right, that's right, The results become chaotic. 0:26:35.080 --> 0:26:37.359 As we said before, if you change a little bit 0:26:37.400 --> 0:26:39.680 the initial conditions, if Earth is a little bit further 0:26:39.800 --> 0:26:43.119 away or pointing in a slightly different direction, you can 0:26:43.160 --> 0:26:46.959 get completely different outcomes. So Earth can be like tossed 0:26:46.960 --> 0:26:49.400 out of the Solar System, or it can fall into 0:26:49.440 --> 0:26:52.040 another orbit or something like that. Whereas if you just 0:26:52.160 --> 0:26:54.879 have two bodies, things tend to be pretty stable. That 0:26:55.000 --> 0:26:57.520 means that if you perturb it, something comes along, gives 0:26:57.560 --> 0:26:59.840 the Earth a little push, will probably roll back into 0:26:59.880 --> 0:27:03.040 a initial orbit, whereas in a three body system, things 0:27:03.119 --> 0:27:05.600 get out of hand very quickly. And that's you know, 0:27:05.720 --> 0:27:08.639 not just like is it complicated motion. That's one of 0:27:08.680 --> 0:27:11.760 the reasons why we don't have a simple formula because 0:27:11.760 --> 0:27:15.040 we don't have functions that describe that, like sign and 0:27:15.200 --> 0:27:18.560 co sign and logarithm. These things are mostly well behaved, 0:27:18.640 --> 0:27:22.399 and so it's very difficult to describe chaotic motion using 0:27:22.440 --> 0:27:25.119 the sort of mathematical language that we have developed. Oh, 0:27:25.280 --> 0:27:28.800 I see, because there's no function that is chaotic kind 0:27:28.840 --> 0:27:31.639 of is that what you're saying, like, chaotic motion is 0:27:31.760 --> 0:27:35.480 not easily kind of captured in a formula. Yeah, it's 0:27:35.480 --> 0:27:38.359 not easily captured in a formula. It's possible to describe 0:27:38.440 --> 0:27:42.760 chaotic motion, but usually our solutions there are numerical, they're approximate, 0:27:43.000 --> 0:27:46.879 use simulations. You know, we can describe chaotic systems like 0:27:47.280 --> 0:27:50.080 you build a computer system, you put three objects in it, 0:27:50.440 --> 0:27:52.280 and then what you do is you say, all right, 0:27:52.359 --> 0:27:54.960 what happens in the first second, and you say, well, 0:27:55.000 --> 0:27:56.760 the Earth's gonna move this way, the Sun is gonna 0:27:56.760 --> 0:27:58.119 move that way, and the moon is going to move 0:27:58.200 --> 0:28:00.399 this other direction, and then you update everything and then 0:28:00.440 --> 0:28:02.639 you do it again. So you slice the problem in 0:28:02.720 --> 0:28:04.680 time and you say, what if I only want to 0:28:04.760 --> 0:28:07.720 predict a half second from now or a milli second 0:28:07.800 --> 0:28:10.600 from now, then you can really simplify and say I 0:28:10.720 --> 0:28:12.399 know what to do for a half second. Then you 0:28:12.480 --> 0:28:14.320 just do that over and over and over again. That's 0:28:14.359 --> 0:28:16.520 the way we can describe a chaotic system is like 0:28:16.800 --> 0:28:19.440 slicing it in time and then try to move our 0:28:19.520 --> 0:28:23.359 stimulation forward, just one time slice at a time. But 0:28:23.480 --> 0:28:25.359 that doesn't mean that we can then look at that 0:28:25.440 --> 0:28:27.600 motion and say, oh, look it follows a sign wave, 0:28:27.720 --> 0:28:30.040 or oh look it follows a logarithm of a sign wave. 0:28:30.400 --> 0:28:33.160 We can't find a solution. We can't find a mathematical 0:28:33.240 --> 0:28:35.840 description of the motion, even if we can describe it 0:28:35.920 --> 0:28:39.400 in the simulation I see. So like we can maybe 0:28:39.520 --> 0:28:41.560 predict what the system is going to do, what these 0:28:41.880 --> 0:28:43.520 three bodies are going to do, but we have to 0:28:43.560 --> 0:28:45.960 do it step by step. We can't just say, like, hey, 0:28:46.040 --> 0:28:47.560 twenty years from now, this is what it's going to be. 0:28:47.960 --> 0:28:50.080 There's no formula that will tell you that. You have 0:28:50.200 --> 0:28:52.240 to like simulate it a little by little until you 0:28:52.320 --> 0:28:54.520 get to ten years from now. Yeah, and even those 0:28:54.600 --> 0:28:58.480 simulations are difficult because it's chaotic. Like if you don't 0:28:58.560 --> 0:29:02.040 make those calculations very very very precise, then your simulation 0:29:02.160 --> 0:29:03.880 is going to be wrong. As you try to predict 0:29:03.960 --> 0:29:07.960 further and further into the future, because small mistakes really 0:29:08.000 --> 0:29:11.080 add up the snowball into big mistakes. It's just like 0:29:11.200 --> 0:29:14.240 you know, the butterfly problem. Butterfly flaps its wings in 0:29:14.360 --> 0:29:17.720 China and that has cascading effects on the weather, which 0:29:17.800 --> 0:29:21.000 causes eventually a storm in Central Park in New York. 0:29:21.120 --> 0:29:23.720 And these things are real. They're real physical systems that 0:29:23.880 --> 0:29:26.080 behave this way where if you give them a very 0:29:26.200 --> 0:29:29.080 small nudge, it can have a very big effect downstream. 0:29:29.280 --> 0:29:32.000 And that makes them very very challenging even to simulate, 0:29:32.080 --> 0:29:34.320 as we talked about, because if you get something wrong 0:29:34.800 --> 0:29:38.080 very early on, your results in ten years are nonsense. 0:29:38.440 --> 0:29:40.719 We much prefer to have like a simple we call 0:29:40.760 --> 0:29:43.840 it an analytical formula, like a very short math expression 0:29:44.080 --> 0:29:45.920 that we can just plug numbers into, because it can 0:29:45.960 --> 0:29:47.800 be exact and it can tell us exactly what's going 0:29:47.840 --> 0:29:50.000 to happen in ten years or in a hundred years. 0:29:50.160 --> 0:29:52.600 I think what you're saying is that these numerical approaches 0:29:52.760 --> 0:29:56.440 or simulations, they're just an approximation basically, right Like you're 0:29:56.640 --> 0:29:58.960 looking at the equations like the f equals amaze or 0:29:59.040 --> 0:30:01.920 the you know, the horses between the three bodies, and 0:30:02.000 --> 0:30:04.280 you're saying, well, let's not try to get the exact solution. 0:30:04.360 --> 0:30:07.600 Let's just pretend that for the next millisecond everyone has 0:30:07.640 --> 0:30:10.560 the same acceleration or something like that. Exactly. You make 0:30:10.600 --> 0:30:12.600 a bunch of simplications and you say, well, I only 0:30:12.640 --> 0:30:14.920 want to predict a millisecond in the future, so can 0:30:14.960 --> 0:30:17.080 I do that? And then you just keep doing that 0:30:17.240 --> 0:30:19.600 over and over again. You're saying that if I'm wrong 0:30:19.640 --> 0:30:21.960 a little bit because of that implication, then in a 0:30:22.040 --> 0:30:25.400 chaotic system, I could be really wrong. Yeah, and that's 0:30:25.400 --> 0:30:27.680 a big deal. If you're doing something like planning a 0:30:27.800 --> 0:30:31.560 trip to the stars or sending your probe to Jupiter 0:30:31.800 --> 0:30:34.520 or whatever, you definitely want to get that right right, Yeah. 0:30:34.560 --> 0:30:37.000 You don't want to be off by a few light years. Yeah. 0:30:37.080 --> 0:30:39.120 Or even if you're just flying through the Solar System, 0:30:39.520 --> 0:30:41.360 if you get it wrong, you could end up crashing 0:30:41.400 --> 0:30:44.120 into the Sun or getting tossed out of the Solar 0:30:44.160 --> 0:30:46.080 System in the wrong direction. You're trying to make it 0:30:46.160 --> 0:30:49.040 to Pluto from here, right, Pluto is very far away 0:30:49.040 --> 0:30:52.000 in a very very small target. Imagine firing a gun 0:30:52.560 --> 0:30:54.920 from l A to New York and trying to hit 0:30:55.040 --> 0:30:57.400 a tiny and the tiny target, it's very difficult. They're 0:30:57.480 --> 0:31:00.640 very small. If you're off by a tiny little angle 0:31:00.960 --> 0:31:02.640 in l A, you're definitely not going to hit that 0:31:02.720 --> 0:31:04.480 target in New York. But I guess that. You know, 0:31:04.640 --> 0:31:07.320 we are pretty good these days with you know, supercomputers, 0:31:07.360 --> 0:31:10.600 we are pretty good at simulating things and kind of predicting. 0:31:10.720 --> 0:31:12.720 You know, maybe not the storm that comes from the 0:31:12.800 --> 0:31:14.920 butterfly wings, but you know, the weather is you know, 0:31:15.040 --> 0:31:17.520 predictable sort of up to like a week, right or 0:31:18.000 --> 0:31:20.760 a couple of weeks, which is super impressive because they 0:31:20.800 --> 0:31:23.960 have to simulate all of those you know, air molecules 0:31:24.000 --> 0:31:25.920 and pockets of hot air that are out there in 0:31:25.960 --> 0:31:28.920 the atmosphere. It's not that it makes the problem impossible, 0:31:29.040 --> 0:31:32.120 it's just makes it harder. Or you know kind of storms, 0:31:32.120 --> 0:31:33.880 how much we can predict it. Yeah, if you had 0:31:33.880 --> 0:31:36.960 an infinitely powerful computer, then we could solve these problems 0:31:37.200 --> 0:31:39.840 because we could simulate them with really high resolution. We 0:31:39.880 --> 0:31:43.200 could take like really really short time steps in our simulation. 0:31:43.400 --> 0:31:45.760 Instead of stepping forward a millisecond, we could step forward 0:31:45.800 --> 0:31:48.680 in nanosecond and then correct. And so if you had 0:31:48.840 --> 0:31:51.920 infinite computing resources, you could do these things very effectively. 0:31:52.080 --> 0:31:54.320 And some of the reasons why these problems which seem 0:31:54.400 --> 0:31:56.840 to be impossible for a long time, like predicting the weather, 0:31:57.400 --> 0:31:59.680 seem to be getting easier, and not because humans are 0:31:59.680 --> 0:32:02.840 getting smarter, but because our computers are getting more powerful, 0:32:03.160 --> 0:32:05.360 and so now we have a lot more computing power 0:32:05.400 --> 0:32:08.320 available to do things like predicting the weather and trying 0:32:08.320 --> 0:32:11.560 to predict earthquakes and all these really really hard problems 0:32:11.600 --> 0:32:14.719 that are really important. Like today we can predict how 0:32:14.800 --> 0:32:16.960 the whole Solar system works, right, We mostly can, And 0:32:17.000 --> 0:32:19.320 a lot of that is because mostly the Solar system 0:32:19.400 --> 0:32:21.880 is a bunch of two body problems, like the Earth 0:32:22.000 --> 0:32:24.800 moving around the Sun. Technically it's you know, it's an 0:32:24.840 --> 0:32:27.120 eight body problem because the Earth is pulled on by 0:32:27.160 --> 0:32:29.840 the Moon and Jupiter and Neptune and whatever. But mostly 0:32:29.880 --> 0:32:32.840 it's just the Sun. You can ignore everything else when 0:32:32.880 --> 0:32:35.480 you're calculating the Earth to some degree. If you want 0:32:35.480 --> 0:32:37.720 to get it exactly right, then yes, you need to 0:32:37.800 --> 0:32:40.600 include effects from Mars and Venus, and then you can't 0:32:40.680 --> 0:32:43.320 use Kepler's laws. You can't use the simple formulas that 0:32:43.400 --> 0:32:45.520 we have for a two body problem. You have to 0:32:45.560 --> 0:32:48.600 get down and dirty and do the simulations using very 0:32:48.680 --> 0:32:50.920 powerful computers. But then I guess, would you say that 0:32:51.000 --> 0:32:53.840 our Solar system is chaotic as well? Like is our 0:32:53.960 --> 0:32:56.560 Solar system a chaotic system? Because it seems sort of 0:32:56.600 --> 0:32:59.880 stable right now, but are you saying maybe, like if 0:33:00.040 --> 0:33:01.520 you give it enough time, it is kind of a 0:33:01.560 --> 0:33:04.960 little unpredictable. Yeah, definitely, the Solar System is chaotic, but 0:33:05.240 --> 0:33:08.400 on the cosmological time scales, not on like a year 0:33:08.840 --> 0:33:11.920 or ten years, but unlike millions and billions of years, 0:33:12.360 --> 0:33:14.480 and it was more chaotic in the beginning. We sort 0:33:14.520 --> 0:33:17.640 of settled into something that's more stable. But when the 0:33:17.720 --> 0:33:19.880 Solar System began, it was a big hot mess and 0:33:19.920 --> 0:33:23.280 things were flying everywhere. Planets were colliding into each other 0:33:23.400 --> 0:33:26.040 and making new planets and throwing things out of the 0:33:26.080 --> 0:33:29.080 Solar System. We probably had a different number of planets 0:33:29.240 --> 0:33:32.320 a billion or two billion years ago. People suspect there 0:33:32.400 --> 0:33:35.600 might have been like another giant planet which was tossed 0:33:35.640 --> 0:33:38.680 out of the Solar System by Jupiter and Saturn. So, yeah, 0:33:38.720 --> 0:33:41.280 that sounds pretty chaotic to me. Solar system was like, 0:33:41.600 --> 0:33:43.280 you know, I have enough to deal with with the 0:33:43.880 --> 0:33:46.920 nine bodies, possibly eight, let's get someone out. But you 0:33:47.040 --> 0:33:49.480 can take a very complicated system like the Solar system 0:33:49.760 --> 0:33:53.400 and find approximately stable solutions things which will last for 0:33:53.480 --> 0:33:56.160 a long long time. But how stable are they? Something 0:33:56.240 --> 0:33:58.480 which flies through the Solar system can perturb it a 0:33:58.560 --> 0:34:00.880 little bit, and then things can very quickly go out 0:34:00.960 --> 0:34:03.360 of whack. So if you have like another star and 0:34:03.440 --> 0:34:06.040 that gets a little close to our Solar system, it 0:34:06.080 --> 0:34:08.399 could change the orbit of Jupiter, which could have knock 0:34:08.440 --> 0:34:10.680 on effects about changing the orbit of Saturn, and then 0:34:10.760 --> 0:34:13.359 the asteroid belt and Mars, and pretty soon we could 0:34:13.400 --> 0:34:16.960 have craziness. All right, Well, let's get into that craziness 0:34:17.120 --> 0:34:19.719 of our Solar system and what the consequences are of 0:34:19.800 --> 0:34:24.040 this three body problem and our ability to understand the 0:34:24.760 --> 0:34:27.799 rest of the cosmos. But first let's take another quick break. 0:34:40.640 --> 0:34:44.080 All right, we're talking about the three body problem, and 0:34:44.320 --> 0:34:48.239 it's hard to find an analytical solution to it, as 0:34:48.280 --> 0:34:50.279 opposed to the two body problem, which you can find 0:34:50.320 --> 0:34:52.759 a nice, neat formula for it. But I wonder then 0:34:52.760 --> 0:34:55.000 if this is sort of like a physicist frustration, because 0:34:55.040 --> 0:34:57.640 as an engineer, I'm pretty much used to like things 0:34:57.680 --> 0:35:00.719 not having an analytical solution, like from day one, like 0:35:00.880 --> 0:35:02.960 nothing only like throwing a ball up in the air 0:35:03.000 --> 0:35:05.080 has an analytical solution. Everything else you have to do 0:35:05.200 --> 0:35:08.920 with numerical simulations or approximating, you know, the Navy, your 0:35:08.920 --> 0:35:12.040 Stokes equations and having non linear stuff that you can't solve, 0:35:12.560 --> 0:35:14.600 and so you know like it. As an engineer you 0:35:14.640 --> 0:35:17.560 always rely on simulations, but maybe in physics you get 0:35:17.640 --> 0:35:20.560 more frustrated for not having like a neat, you know, 0:35:21.320 --> 0:35:23.839 clean formula to predict the future. Well, the thing that's 0:35:23.880 --> 0:35:26.520 tantalizing is that there are a few cases when you 0:35:26.719 --> 0:35:29.000 can find a neat formula where you can start with 0:35:29.200 --> 0:35:32.640 just pencil and paper, describe the pushing and the pulling 0:35:32.680 --> 0:35:35.279 of your system, and then get out a formula that 0:35:35.360 --> 0:35:37.719 tells you where everything is going to be basically for 0:35:37.960 --> 0:35:41.520 all time. That's amazing, it's beautiful, and it's tempting. It 0:35:41.600 --> 0:35:43.840 makes you think, Wow, why can't I do this for 0:35:44.000 --> 0:35:47.080 other systems? Why can't I do this for every system? Right? 0:35:47.120 --> 0:35:49.560 Because if they exist for some systems, it gives you 0:35:49.640 --> 0:35:51.960 the sense that, like, if we had the right mathematics, 0:35:52.040 --> 0:35:55.080 if we knew the right language to talk about this stuff, 0:35:55.360 --> 0:35:58.920 maybe even really complicated problems would be simpler. So it's 0:35:58.960 --> 0:36:01.600 sort of aspirational yeah, I can imagine that frustration. You're 0:36:01.640 --> 0:36:04.600 in your cabin in the middle of Russia, in Siberia, 0:36:04.640 --> 0:36:06.240 in the middle of nowhere, and you're like, oh, shoot, 0:36:06.800 --> 0:36:09.480 I need a computer I didn't bring one, or oh shoot, 0:36:09.520 --> 0:36:11.640 I need to talk to somebody else, I don't have 0:36:11.719 --> 0:36:15.279 a phone. That's frustrating, right, It is frustrating. And you know, 0:36:15.400 --> 0:36:18.760 it's something funny about teaching freshman physics. I teach mechanics 0:36:18.920 --> 0:36:21.839 often here you see irvine, and you know there are 0:36:21.960 --> 0:36:24.680 not a lot of problems that really are solvable, like 0:36:24.960 --> 0:36:27.400 very few problems can you actually sit down with pencil 0:36:27.440 --> 0:36:30.480 and paper and say, here's the situation, here's the solution. 0:36:30.640 --> 0:36:32.720 And so, in teaching this class for like almost twenty 0:36:32.800 --> 0:36:36.000 years now, I've noticed that basically every physics Hormemork problem 0:36:36.080 --> 0:36:39.160 in every textbook is one variation on like one of 0:36:39.239 --> 0:36:41.960 these five solvable problems. And so as soon as you 0:36:42.000 --> 0:36:44.200 look at when you're like, oh, this is that one problem, 0:36:44.360 --> 0:36:46.359 or this is a problem number four, except they're using 0:36:46.400 --> 0:36:48.759 a squirrel instead of a ball of rolling down a 0:36:48.840 --> 0:36:51.120 plane or something, and so it all boils down to 0:36:51.239 --> 0:36:54.080 like a few solvable problems because there are only a 0:36:54.160 --> 0:36:56.799 few that can actually be solved. I mean, there's an 0:36:56.840 --> 0:36:59.920 analytical simple solutions to what Professor Whitesen is gonna have. 0:37:00.120 --> 0:37:02.879 But on the final test, I hope students are taking notes. 0:37:03.520 --> 0:37:05.439 I say, if you take my class for twenty years, 0:37:05.480 --> 0:37:09.640 it becomes pretty easy. I guess even physics professors are predictable. 0:37:09.680 --> 0:37:13.160 Is that what you're saying they're going to do. It's 0:37:13.200 --> 0:37:16.600 hard to invent new solvable problems in physics. And you 0:37:16.680 --> 0:37:20.120 know it's not just like motion of two objects. There 0:37:20.160 --> 0:37:22.200 are lots of places in physics where the problems are 0:37:22.239 --> 0:37:25.440 not solvable. Einstein developed general relativity, right, which means he 0:37:25.520 --> 0:37:29.880 wrote down the equations for how space curves when masses around. 0:37:30.239 --> 0:37:32.560 He wrote down the equations, which means those are the 0:37:32.600 --> 0:37:35.759 constraints that space has to follow. It doesn't mean he 0:37:35.880 --> 0:37:39.399 can tell you how space behaves when masses around. Those 0:37:39.440 --> 0:37:42.920 are the solutions to the Einstein equation. And he couldn't 0:37:42.960 --> 0:37:45.680 solve his own equations. Like he developed general relativity and 0:37:45.719 --> 0:37:47.759 he's like, here the equations, I don't know how to 0:37:47.800 --> 0:37:50.280 solve this. He wasn't even the first person to solve 0:37:50.360 --> 0:37:53.520 the Einstein equation that was short styled. Because these equations 0:37:53.560 --> 0:37:56.640 are like famously impossible to solve. Now, if you have 0:37:56.760 --> 0:37:59.120 a solution, you can check it. You can say I 0:37:59.239 --> 0:38:02.200 think space ends in this way when there's massed around. 0:38:02.400 --> 0:38:04.279 You can plug it into the equations, and if it works, 0:38:04.320 --> 0:38:06.560 you're like, cool, I found it. But again, just because 0:38:06.600 --> 0:38:08.600 you have the equations doesn't mean you know how to 0:38:08.680 --> 0:38:12.759 find the solution. Anybody who's done differential equations knows that's true. 0:38:12.800 --> 0:38:15.920 We have like no general mechanism for saying, here's a 0:38:15.920 --> 0:38:18.520 differential equation, I can go from the equation to finding 0:38:18.600 --> 0:38:21.480 the solution. And so there's lots of places in physics 0:38:21.800 --> 0:38:23.640 where we just don't know how to solve these things. 0:38:23.760 --> 0:38:26.200 Even still for general relativity, we only know how to 0:38:26.239 --> 0:38:29.680 solve it for a few cases, like an empty universe, 0:38:29.920 --> 0:38:33.560 a universe that's smoothly filled with matter like no lumps 0:38:33.600 --> 0:38:37.520 at all, or a black hole. Basically everything else is unsolvable. 0:38:37.719 --> 0:38:40.080 Then that's why before Sheeld found right like Evan found 0:38:40.120 --> 0:38:43.200 the solution for general relativity in the case of a 0:38:43.280 --> 0:38:45.759 simple black hole. Yeah, exactly. He was the first person 0:38:45.840 --> 0:38:48.400 to ever solve these equations, and he actually did it 0:38:48.719 --> 0:38:51.120 while he was a soldier in World War One. What 0:38:51.760 --> 0:38:54.239 was he like fighting in a cabin in Russia. Also, 0:38:55.200 --> 0:38:57.719 never fight a land war in Russian man, especially while 0:38:57.719 --> 0:39:02.360 you're trying to solve question. Extra difficulty points. Unless he 0:39:02.480 --> 0:39:04.759 was fighting for the Russians. Maybe I don't know, maybe 0:39:04.760 --> 0:39:06.799 he's Russian, and then he had a lot of time 0:39:06.840 --> 0:39:10.000 because the other team was doomed. No, but it's a 0:39:10.040 --> 0:39:12.040 great story. You should look up how short Starts solved 0:39:12.080 --> 0:39:14.680 this problem. I see. So it's not he solved general 0:39:14.680 --> 0:39:17.360 relativity for all time in all cases. He just found 0:39:17.400 --> 0:39:20.440 a solution for general relativity in this special case of 0:39:20.520 --> 0:39:22.560 a simple black hole. Yeah, of a universe that has 0:39:22.680 --> 0:39:25.480 nothing but a black hole in it. He figured out 0:39:25.560 --> 0:39:28.719 the solution how space bends in that scenario. And then 0:39:28.840 --> 0:39:31.279 later people figured out, Okay, well, if I assume that 0:39:31.360 --> 0:39:34.239 the universe is totally empty, can I solve the equations? Oh, 0:39:34.400 --> 0:39:36.240 I can do that? Or if I assume the universe 0:39:36.360 --> 0:39:39.000 is like filled smoothly with matter, can I do that? 0:39:39.160 --> 0:39:42.480 But like, nobody has solved general relativity for like our 0:39:42.600 --> 0:39:45.200 solar system, or even just for like the Sun and 0:39:45.280 --> 0:39:48.480 the Earth together. It's too complicated. Nobody has figured out 0:39:48.640 --> 0:39:51.359 how to go from those equations to say, here's how 0:39:51.520 --> 0:39:55.200 space has to bend in this situation. Oh wait, so 0:39:55.440 --> 0:39:57.920 not even like the two body problem has a solution 0:39:58.000 --> 0:40:01.000 in general relativity. Yeah, that's right. General auctivity much much 0:40:01.080 --> 0:40:05.480 harder than Newtonian mechanics. We can do things like numerical relativity, 0:40:05.520 --> 0:40:07.960 like we can describe how black holes orbit each other 0:40:08.040 --> 0:40:11.120 and collide and generally gravitational waves. Because we can do 0:40:11.200 --> 0:40:15.040 it numerically, we can use computers to do approximate solutions 0:40:15.080 --> 0:40:17.680 to these things. But nobody can like write down simple 0:40:17.760 --> 0:40:20.279 formulas to tell you like how black holes orbit each 0:40:20.280 --> 0:40:23.120 other and collapse. Oh, I see. All this time we've 0:40:23.120 --> 0:40:25.879 been talking about the two body probably being solvable. It's 0:40:25.920 --> 0:40:28.800 only solvable in the Newtonian case, right, Like if you 0:40:28.840 --> 0:40:33.319 assume the simplest or the simple physics of Newton, then 0:40:33.480 --> 0:40:35.840 you can find a solution, but not for three. But 0:40:35.920 --> 0:40:38.200 if you assume, like what we actually know what's going 0:40:38.239 --> 0:40:40.920 on general relativity, then it's we can't even start, Like 0:40:41.400 --> 0:40:44.319 there's no solution, Yeah exactly. You know, Einstein lays out 0:40:44.360 --> 0:40:46.800 the equations the constraints, but he doesn't tell you, and 0:40:46.880 --> 0:40:49.520 he doesn't know how to go from the constraints to 0:40:49.719 --> 0:40:52.080 a solution. You know, it's sort of like if you're 0:40:52.400 --> 0:40:54.319 driving down the highway with your family and you ask 0:40:54.320 --> 0:40:56.440 somebody what they want for dinner, and everybody says, I 0:40:56.520 --> 0:40:58.319 want a salad, or I want pizza, or I want 0:40:58.360 --> 0:41:01.280 hot dogs, Like those are the con straints. Doesn't necessarily 0:41:01.320 --> 0:41:03.759 mean you know how to find a restaurant that satisfies 0:41:03.880 --> 0:41:07.080 those constraints, right, Having the constraints doesn't tell you how 0:41:07.160 --> 0:41:10.000 to find a solution. Wow, it sounds like something from 0:41:10.080 --> 0:41:13.600 personal experience with data. You're trying to events, Yes, I'm 0:41:13.640 --> 0:41:17.160 looking for a restaurant the search salads and hotdogs and pizza. 0:41:18.120 --> 0:41:21.000 Let me know if you find one that's not even 0:41:21.040 --> 0:41:23.719 the general relativity solution. Like if you add relatives to 0:41:23.880 --> 0:41:27.279 this card, right, then it gets impossible, right, because then 0:41:27.360 --> 0:41:31.880 you have all these relative dynamics exactly, very chaotic, very quickly. Well, 0:41:31.920 --> 0:41:34.160 I think what's interesting is that this is not just 0:41:34.680 --> 0:41:38.240 difficult for us as physicists to like predict these things 0:41:39.080 --> 0:41:41.120 and kind of like know what's going to happen, but 0:41:41.200 --> 0:41:42.880 it's also kind of hard for the universe to know 0:41:42.920 --> 0:41:45.000 what's going to happen. Right, Like, if something is chaotic, 0:41:45.120 --> 0:41:48.600 it also means that things are kind of unpredictable in general, 0:41:48.719 --> 0:41:51.319 like crazy things can happen in our solar system. Yes, 0:41:51.480 --> 0:41:54.759 systems with three objects don't last very long because they 0:41:54.840 --> 0:41:57.880 are chaotic. They don't tend to fall into stable patterns 0:41:58.000 --> 0:42:00.560 and survive for very long. So if you have like 0:42:01.040 --> 0:42:04.960 three stars orbiting each other, then pretty quickly two of 0:42:05.040 --> 0:42:08.080 them will eject the third one out into the universe. 0:42:08.320 --> 0:42:11.279 Because there are not very many stable solutions to the 0:42:11.400 --> 0:42:13.839 three body problem. And this is different from like can 0:42:14.040 --> 0:42:17.560 human mathematicians write down a simple formula to predict what 0:42:17.680 --> 0:42:20.680 will happen? That's one question. Another question is like how 0:42:20.840 --> 0:42:23.560 long can three stars orbit each other before two of 0:42:23.600 --> 0:42:25.640 them kick out the other one. I guess you mean 0:42:25.719 --> 0:42:28.680 like three stars of about the same size, right, Yeah, 0:42:28.920 --> 0:42:30.960 three stars about the same size and about the same 0:42:31.040 --> 0:42:33.720 distance from each other at a real like three body system. 0:42:33.960 --> 0:42:36.400 Because the only way for that to really happen, for 0:42:36.480 --> 0:42:38.759 it to become stable is to sort of turn it 0:42:38.920 --> 0:42:42.840 into a double two body system. Take your three stars, 0:42:43.320 --> 0:42:46.000 group two of them together, make them really close, and 0:42:46.080 --> 0:42:48.440 put them far away from the third star, and then 0:42:48.480 --> 0:42:50.520 what you have is like a little two body system 0:42:50.520 --> 0:42:53.520 of two stars. And then you have that two body system. 0:42:53.560 --> 0:42:55.440 You can treat it sort of like as a single 0:42:55.560 --> 0:42:58.320 object when you're talking about the third star which is 0:42:58.360 --> 0:43:01.000 now orbiting that pair. And so when we do find 0:43:01.160 --> 0:43:04.400 trinary systems out there in the universe, they're typically this 0:43:04.600 --> 0:43:07.040 like two body system. In a hierarchy, we have a 0:43:07.120 --> 0:43:09.640 two body system, and then one of those bodies turns 0:43:09.680 --> 0:43:11.920 out to have two things inside of it, right, And 0:43:12.160 --> 0:43:14.040 I think this hierarchy we sort of talked about it 0:43:14.160 --> 0:43:17.400 in the last podcast, but it's acidly with distance, right, Like, 0:43:17.640 --> 0:43:20.760 if two of them are out here, you know, interacting 0:43:20.800 --> 0:43:23.919 and orbiting around each other, then to another body that's 0:43:24.320 --> 0:43:27.840 fairly far away, our two little bodies here, I feel 0:43:27.880 --> 0:43:30.600 like one. And so then that makes it more stable. Exactly, if, 0:43:30.640 --> 0:43:32.800 for example, we had two sons at the center of 0:43:32.840 --> 0:43:35.359 our solar system, if they were really close to each other, 0:43:35.640 --> 0:43:37.800 and they were much closer to each other than we 0:43:38.000 --> 0:43:40.400 were to them, we could treat it like it was 0:43:40.520 --> 0:43:42.800 just one object. It wouldn't matter to us that it 0:43:42.920 --> 0:43:45.359 was two objects. But if we got closer to them, 0:43:45.440 --> 0:43:47.560 or if we even like trying to get between them, 0:43:47.640 --> 0:43:50.160 then it would make a big difference on our trajectory 0:43:50.480 --> 0:43:52.520 that there were two objects instead of one, and so, 0:43:52.640 --> 0:43:54.960 for example, in that novel we talked about at the 0:43:55.040 --> 0:43:57.520 top of the episode, that's exactly what's going on. There's 0:43:57.520 --> 0:44:00.440 a solar system with two stars and a plan that's 0:44:00.480 --> 0:44:03.040 whizzing all around right through them in a very crazy, 0:44:03.200 --> 0:44:05.759 unstable orbit. And so not only does it have like 0:44:05.960 --> 0:44:08.120 really weird night and day patterns, but it has a 0:44:08.280 --> 0:44:12.800 very chaotic trajectory, and so you can't necessarily predict exactly 0:44:12.880 --> 0:44:14.480 where it's going to be. It's kind of like a 0:44:14.560 --> 0:44:17.840 real couples, I guess, you know, like from a distance, 0:44:18.000 --> 0:44:20.200 you can sort of assume they think and act as one, 0:44:20.440 --> 0:44:22.520 but once you get go up close to them easily, 0:44:22.520 --> 0:44:24.839 there's a lot of disagreement there. But you never want 0:44:24.880 --> 0:44:27.839 to get between them exactly. That's right. It soundstable. Yeah, 0:44:27.840 --> 0:44:29.880 you don't want to be the third body there, you 0:44:30.000 --> 0:44:31.919 definitely don't. You can get tossed out of your solar 0:44:32.000 --> 0:44:37.960 system or maybe eject the one of the others. But then, yes, 0:44:38.160 --> 0:44:40.480 it sounds like we're writing a romcom now involving a 0:44:40.560 --> 0:44:42.880 trip to the woods in Russia. All right, Well, this 0:44:43.040 --> 0:44:45.560 is kind of an interesting question here, and an interesting 0:44:45.640 --> 0:44:47.560 problem because it doesn't just tell you that some things 0:44:47.600 --> 0:44:50.319 are hard to solve in nature, but some things are 0:44:51.120 --> 0:44:55.160 hard and unpredictable themselves in nature, right, Like some of 0:44:55.239 --> 0:44:58.000 these things out in nature they just don't last long 0:44:58.080 --> 0:45:01.040 they been out of control, or they a settle into 0:45:01.120 --> 0:45:04.799 things that are more stable, like to body solar systems. Yeah, 0:45:04.920 --> 0:45:07.360 and it could be that in the future somebody events 0:45:07.440 --> 0:45:10.800 mathematics that makes it easier to describe that crazy chaotic 0:45:10.880 --> 0:45:13.120 motion and that you know, in twenty years or in 0:45:13.160 --> 0:45:15.560 fifty years, we have like a a new basic function, 0:45:15.800 --> 0:45:17.680 you know, like we have signed and coson. These were 0:45:17.760 --> 0:45:21.200 invented functions by human mathematicians. Somebody might come up with 0:45:21.280 --> 0:45:23.800 a new function which turns out to be really useful 0:45:23.880 --> 0:45:27.000 to describing three body motion and and allows us to 0:45:27.200 --> 0:45:31.120 find some expression. A lot of mathematicians are skeptical because 0:45:31.200 --> 0:45:33.880 they can sort of express these solutions is like an 0:45:33.920 --> 0:45:36.880 infinite series, and they showed that it's very complicated, and 0:45:37.000 --> 0:45:39.520 they suspect that there isn't a simple function. But you know, 0:45:39.760 --> 0:45:43.200 future mathematicians are usually smarter than today's mathematicians, and so 0:45:43.520 --> 0:45:45.760 I hold out hope or maybe like there are aliens 0:45:45.800 --> 0:45:48.239 who have figured this out, you know, like they'll come 0:45:48.280 --> 0:45:49.800 to us and be like, yes sign and cosap we 0:45:49.880 --> 0:45:53.360 don't have, you know, chaos sign or something that describes 0:45:53.440 --> 0:45:57.200 chaos motion. Yeah, exactly, And maybe somewhere some mathematicians is 0:45:57.280 --> 0:45:59.719 developing the tools and they don't even realize how it's 0:45:59.719 --> 0:46:02.800 going to useful. I love those stories of mathematicians developing 0:46:02.840 --> 0:46:06.640 these ideas and then them later being co opted by physicists. 0:46:06.680 --> 0:46:09.160 And so maybe those ideas exist right now and all 0:46:09.200 --> 0:46:10.560 you have to do is go out and read the 0:46:10.680 --> 0:46:13.280 right math paper and you're like, oh, this is exactly 0:46:13.360 --> 0:46:15.800 the hammer we need to hit this physics nail. Or 0:46:15.840 --> 0:46:18.279 maybe the answer is in some cabin in Russia, but 0:46:18.440 --> 0:46:20.600 the you know, the poor soul ran out of food 0:46:20.680 --> 0:46:24.560 or something and it's lost to us, but it's written 0:46:24.600 --> 0:46:26.800 down on a frozen sheet of paper in that cabin. 0:46:27.520 --> 0:46:31.000 It exists. But anyways, I guess the good news is 0:46:31.080 --> 0:46:33.240 that it's an open problem and there could be somebody 0:46:33.360 --> 0:46:35.759 listening to this podcast right now that might solve it 0:46:35.840 --> 0:46:38.120 in the future, maybe even you. Well we hope you 0:46:38.239 --> 0:46:41.239 enjoyed that. Thanks for joining us, see you next time. 0:46:49.120 --> 0:46:51.960 Thanks for listening, and remember that Daniel and Jorge explained 0:46:51.960 --> 0:46:54.840 the universe is a production of I heart Radio. For 0:46:55.000 --> 0:46:57.919 more podcast from My heart Radio, visit the I heart 0:46:58.000 --> 0:47:01.560 Radio app, Apple Podcasts, or wherever you listen to your 0:47:01.640 --> 0:47:02.360 favorite shows.