WEBVTT - Why do scientists do simulations? 0:00:08.560 --> 0:00:11.360 Hey, am I speaking to the real Joorge today? 0:00:11.440 --> 0:00:12.280 Who else could it be? 0:00:12.480 --> 0:00:14.800 I don't know. It could be the simulated Jorge or 0:00:14.840 --> 0:00:18.120 an AI generated horheage GPT. 0:00:18.800 --> 0:00:21.960 Yes, chat Jorge. Would it make a difference. 0:00:22.040 --> 0:00:24.360 That sounds like something the simulated Jorge would say? 0:00:24.520 --> 0:00:27.360 Mmm. I kind of wish I had simulated Horges. Then 0:00:27.600 --> 0:00:30.280 I might avoid a lot of mistakes I make. Or 0:00:30.280 --> 0:00:31.960 they could do all the work while I sleep in. 0:00:32.040 --> 0:00:34.239 Why do you think simulated Hojoges are less likely to 0:00:34.240 --> 0:00:34.879 make mistakes? 0:00:35.000 --> 0:00:36.879 No? I mean they would do the mistakes, and then 0:00:36.920 --> 0:00:39.080 I would learn from them. That's the idea. 0:00:39.159 --> 0:00:39.319 Right. 0:00:39.520 --> 0:00:41.000 That does sound useful, But I think you have to 0:00:41.080 --> 0:00:44.000 be careful about the sim Jorges organizing and rising up 0:00:44.000 --> 0:00:44.479 against you. 0:00:44.680 --> 0:00:45.840 Oh do you think. 0:00:45.680 --> 0:00:48.560 They would form their own union or a revolt? 0:00:48.560 --> 0:00:51.800 Do you mean, yeah, either mutiny or fair wages. Either one. 0:00:52.040 --> 0:00:53.720 Well, I could just pay them in simulated money. 0:00:53.760 --> 0:00:55.440 I guess as long as they can use that to 0:00:55.440 --> 0:00:57.920 feed their simulated children, I bet they'd be happy. Oh. 0:00:57.960 --> 0:01:01.680 No, I definitely provide simulated benefits too. The whole simulated 0:01:01.680 --> 0:01:02.920 family gets a bonus. 0:01:03.000 --> 0:01:17.600 You're not a good employer, but you can simulate one. 0:01:20.640 --> 0:01:23.480 Hi, I'm Jory mccartoonists and the author of Oliver's Great 0:01:23.480 --> 0:01:24.560 Big Universe. Hi. 0:01:24.680 --> 0:01:25.240 I'm Daniel. 0:01:25.319 --> 0:01:28.520 I'm a particle physicist and a professor at UC Irvine, 0:01:28.640 --> 0:01:32.200 and I am constantly simulating crazy conditions. 0:01:32.400 --> 0:01:34.440 You mean in your life or in your work. 0:01:35.160 --> 0:01:37.160 Well, work is a big part of my life. But yeah, 0:01:37.200 --> 0:01:41.720 my job involves simulating collisions at very high energies all 0:01:41.760 --> 0:01:42.160 the time. 0:01:42.840 --> 0:01:45.240 And you also actually do them, right, You actually collide 0:01:45.240 --> 0:01:46.800 things at the Large Hadron Collider. 0:01:46.959 --> 0:01:49.880 That's right. We both collide particles together in real life, 0:01:50.040 --> 0:01:53.200 and we simulate what would happen if we collided particles 0:01:53.280 --> 0:01:56.919 under various different potential laws of the universe to see 0:01:56.920 --> 0:01:59.840 what might happen. Will the Earth get gobbled up with 0:02:00.120 --> 0:02:02.400 to create a black hole that destroys the Earth or not? 0:02:02.840 --> 0:02:03.600 Let's find out. 0:02:03.800 --> 0:02:07.000 Does that mean your whole career is a simulation or 0:02:07.040 --> 0:02:07.840 your whole life? 0:02:08.040 --> 0:02:10.519 You know, our computers are not fast enough to keep 0:02:10.600 --> 0:02:13.519 up with reality. So while we generate lots and lots 0:02:13.560 --> 0:02:17.240 of simulated collisions, the real collider has generated more collisions 0:02:17.280 --> 0:02:18.600 than we could ever simulate. 0:02:19.360 --> 0:02:21.120 But how do you know, Daniel, that we're not in 0:02:21.200 --> 0:02:24.160 a simulation right now, Like you might think you're doing experiments, 0:02:24.200 --> 0:02:26.720 but really you're just inside of a video game somewhere. 0:02:26.800 --> 0:02:28.440 Well, I want to find the cheap goods, then, well I. 0:02:28.440 --> 0:02:29.919 Think if you had found them by now, you probably 0:02:30.040 --> 0:02:31.280 would have a noble price. 0:02:31.400 --> 0:02:34.880 Right, I'm hoping smashing particles together gives me the cheek goods. 0:02:34.720 --> 0:02:37.080 And then that opens up the real boss level. 0:02:38.120 --> 0:02:40.079 Where I fight the simulated army of Jorges. 0:02:40.200 --> 0:02:44.519 No, you fight the real Jegeo. That's the real boss. 0:02:45.240 --> 0:02:47.760 But anyways, welcome to our podcast Daniel and Jorge Explain 0:02:47.840 --> 0:02:50.600 the Universe, a production of iHeartRadio. 0:02:50.040 --> 0:02:52.359 In which we use our tiny little minds to try 0:02:52.360 --> 0:02:55.639 to understand the vast universe. We hope to build in 0:02:55.720 --> 0:02:59.800 your head a simulation of sorts, one that describes the 0:02:59.800 --> 0:03:02.920 way the real universe works out there. We hope to 0:03:03.160 --> 0:03:06.079 encode into your brain some laws of physics that will 0:03:06.080 --> 0:03:09.120 help you understand how the real universe out there is 0:03:09.320 --> 0:03:12.760 smashing and bashing to create our Bonker's reality. 0:03:12.960 --> 0:03:15.399 That's right, the universe are doing all kinds of amazing 0:03:15.520 --> 0:03:18.480 and awe sometimes and saying things out there in reality. 0:03:18.800 --> 0:03:22.160 And so it's our job as humans and as scientists 0:03:22.200 --> 0:03:25.000 to understand what's going on and to ask questions, to 0:03:25.080 --> 0:03:27.519 probe into the true answers to why things are the 0:03:27.520 --> 0:03:27.880 way they are. 0:03:28.080 --> 0:03:30.520 And the classical way that science does this is with 0:03:30.760 --> 0:03:35.160 theories and experiments, hypotheses and tests. You have an idea, 0:03:35.240 --> 0:03:37.400 you go and see out there in the universe. If 0:03:37.440 --> 0:03:40.200 it works, you predict something happens, and you go and 0:03:40.280 --> 0:03:43.080 check to see if it does. But the modern scientific 0:03:43.120 --> 0:03:45.839 method has a third way, which lives sort of uncomfortably 0:03:45.880 --> 0:03:48.400 between theory and experiments. 0:03:48.560 --> 0:03:51.240 Oh, why is it uncomfortable? Is it like uncomfortable, awkward 0:03:51.320 --> 0:03:53.240 or uncomfortable, like physically uncomfortable. 0:03:53.280 --> 0:03:55.080 It's a little bit uncomfortable for those of us who 0:03:55.080 --> 0:03:57.320 specialize in not to know where we fit into the 0:03:57.360 --> 0:04:01.360 picture of science. Some people consider me experimental physicists. Some 0:04:01.400 --> 0:04:03.680 people are like, nah, he mostly runs simulation, so he's 0:04:03.720 --> 0:04:06.040 really a theorist. So you can be sort of like 0:04:06.120 --> 0:04:09.400 uncomfortably between two different communities. If you do a lot 0:04:09.440 --> 0:04:10.960 of simulations. 0:04:10.920 --> 0:04:13.640 You start your own simulated community. Can you be like 0:04:13.680 --> 0:04:16.120 a simulating physicist. 0:04:15.800 --> 0:04:20.120 A simulator a simulate trist. That sounds not safe for work. 0:04:20.120 --> 0:04:24.680 Actually, I don't know what you mean, but I'll take 0:04:24.680 --> 0:04:25.279 your word for it. 0:04:25.400 --> 0:04:28.560 You know, academic communities change pretty slowly, and for example, 0:04:28.720 --> 0:04:32.159 in departments of physics, people tend to hire people that 0:04:32.200 --> 0:04:35.039 are like them. The experimentalists get to hire somebody. They 0:04:35.080 --> 0:04:38.920 want to hire somebody who's a blue blooded experimentalist down 0:04:38.960 --> 0:04:41.440 to the core. So if you work at the intersection 0:04:41.600 --> 0:04:44.279 of fields, you do some experiments, you do some theory, 0:04:44.320 --> 0:04:47.040 maybe even do some computer science and machine learning, then 0:04:47.040 --> 0:04:48.760 you don't necessarily have a home, you don't have a 0:04:48.839 --> 0:04:50.440 tribe that's going to go to bat for you to 0:04:50.480 --> 0:04:52.839 get hired. So it's sort of about the sociology of 0:04:52.880 --> 0:04:54.479 science as a real practice. 0:04:54.920 --> 0:04:56.560 Well, I think that kind of makes sense, right, Like 0:04:56.640 --> 0:05:00.239 why hire a simulating physicist when you can just simulate one? 0:05:00.839 --> 0:05:02.000 Why go to all the trouble? 0:05:02.120 --> 0:05:04.520 You know, I think that's true. If we could simulate physicists, 0:05:04.560 --> 0:05:06.440 we could get a lot more done. But we're not 0:05:06.560 --> 0:05:09.720 quite there yet. Human physicists still have a little bit 0:05:09.720 --> 0:05:10.240 of an edge. 0:05:10.440 --> 0:05:14.600 Yeah, maybe till next week when chat GPT catches up 0:05:14.640 --> 0:05:15.960 and starts doing physics. 0:05:16.200 --> 0:05:18.640 I mean, have you ever asked chat GPT a physics question. 0:05:18.960 --> 0:05:21.120 You don't get physics out, that's for sure. 0:05:21.240 --> 0:05:23.680 But anyways, it is an interesting universe because I guess 0:05:23.720 --> 0:05:26.520 sometimes there are questions. You can't just go out there 0:05:26.560 --> 0:05:28.840 and try for yourself in the universe, right, that's right. 0:05:28.880 --> 0:05:31.719 Simulation has emerged in the past fifty years as an 0:05:31.800 --> 0:05:34.839 extraordinarily powerful tool as a little bit of experiment and 0:05:34.880 --> 0:05:37.160 a little bit of theory, and it lets us answer 0:05:37.240 --> 0:05:40.680 questions that we otherwise could not answer. It really is 0:05:40.720 --> 0:05:43.440 a completely new tool in the science tool. 0:05:43.240 --> 0:05:45.680 Belt, although I would argue it's maybe one of the 0:05:45.720 --> 0:05:48.599 oldest tools in science. And so today on the podcast, 0:05:48.600 --> 0:05:57.800 we'll be asking the question why do scientists do simulations? 0:05:58.080 --> 0:05:59.840 Why do scientists do anything. 0:06:00.480 --> 0:06:03.119 Other than the obvious that simulations are so much fun. 0:06:03.320 --> 0:06:05.600 You get to build your own little universe. You are 0:06:05.640 --> 0:06:08.279 the creator and god of that simulated universe. 0:06:08.520 --> 0:06:12.479 Oh boy, is that that the ultimate goal? There? To 0:06:12.560 --> 0:06:17.200 be gods? No, you know, you don't have to get 0:06:17.200 --> 0:06:19.440 a degree for that. You could just buy some legos. 0:06:20.800 --> 0:06:22.760 Oh, I've been doing that since I was a little kid. 0:06:22.800 --> 0:06:25.440 I just want more and more powerful simulations. 0:06:26.000 --> 0:06:28.840 You want more powerful legos, smaller legos. 0:06:28.960 --> 0:06:31.160 Jokes aside, There is a real sense of power when 0:06:31.200 --> 0:06:34.440 you create a simulated universe, because you are deciding what 0:06:34.520 --> 0:06:37.440 the laws of physics are in that universe, what particles 0:06:37.440 --> 0:06:39.680 do they have, how do they interact? And then you 0:06:39.720 --> 0:06:41.800 get to see how it all plays out. 0:06:42.080 --> 0:06:44.440 Mmmm yeah, I sort of get that. I mean I 0:06:44.480 --> 0:06:46.839 write a lot, I create characters, and I sort of 0:06:46.839 --> 0:06:49.279 build my own world. What's the difference. 0:06:49.440 --> 0:06:52.960 Yeah, you could think of fiction as simulated human interaction 0:06:53.160 --> 0:06:55.839 and lives. Right, we're exploring what it would be like 0:06:55.920 --> 0:06:58.120 to be in those situations. 0:06:58.400 --> 0:07:00.080 Yeah. Wait, did you just say your work. 0:06:59.920 --> 0:07:04.840 Is simulations are definitely fiction. Sometimes they align with reality, 0:07:04.880 --> 0:07:07.400 and one deep question is how well they align? What 0:07:07.520 --> 0:07:11.360 lessons you can learn from your simulated fiction that carry 0:07:11.400 --> 0:07:13.160 over into the real world. 0:07:13.560 --> 0:07:17.880 Interesting, So your research is science fiction is what you're saying. 0:07:20.720 --> 0:07:23.160 You know, I've always argued that there's a strong connection 0:07:23.240 --> 0:07:24.680 between science and science fiction. 0:07:25.000 --> 0:07:25.240 Right. 0:07:25.440 --> 0:07:27.640 One aspect of science is like, well, what are the laws? 0:07:27.640 --> 0:07:28.080 Could they be? 0:07:28.120 --> 0:07:28.240 This? 0:07:28.400 --> 0:07:28.880 Could they be? 0:07:28.960 --> 0:07:29.120 That? 0:07:29.120 --> 0:07:33.400 There's an element of creativity and exploration there, absolutely so. Yeah, 0:07:33.440 --> 0:07:36.880 I'm constantly creating science fiction universes and trying to see 0:07:36.960 --> 0:07:38.400 if they line up with ours. 0:07:39.240 --> 0:07:40.960 And then you wonder why the other physicis don't want 0:07:40.960 --> 0:07:41.440 to play with you. 0:07:43.520 --> 0:07:46.320 Fortunately I got tenured before I revealed all of these 0:07:46.360 --> 0:07:48.120 crazy instincts. That's the game. 0:07:50.120 --> 0:07:52.240 Well, this is an interesting question, and so as usual, 0:07:52.320 --> 0:07:55.040 we were wondering how many people out there had thought 0:07:55.080 --> 0:07:58.000 about why scientists do the things they do, and in particular, 0:07:58.160 --> 0:08:00.560 why they do simulations in their work. 0:08:00.840 --> 0:08:03.480 So thanks very much to everybody who answers these questions 0:08:03.480 --> 0:08:06.400 for this fun segment of the podcast, one of my favorites. 0:08:06.680 --> 0:08:09.280 If you like to join the team or just answer 0:08:09.280 --> 0:08:12.120 one or two questions right to us to questions at 0:08:12.240 --> 0:08:14.000 Danielandhorge dot com. 0:08:14.200 --> 0:08:16.400 So think about it for a second. If someone asks 0:08:16.400 --> 0:08:19.760 you why scientists do simulations, what would you say. 0:08:19.800 --> 0:08:26.360 Well, using simulations, we can observe scenarios in our models 0:08:26.880 --> 0:08:32.120 that we can't necessarily observe in real life, and see 0:08:32.480 --> 0:08:36.079 what can happen in certain situations like in a black 0:08:36.080 --> 0:08:38.520 hole or when galaxies collide or something like that. 0:08:38.840 --> 0:08:44.319 Scientists do simulations because the universe is really old, really big, 0:08:45.040 --> 0:08:49.160 sometimes really destructive. Frankly, I'm happy they do a lot 0:08:49.200 --> 0:08:52.760 of that modeling and simulations and don't necessarily try to 0:08:52.800 --> 0:08:57.520 create big bang conditions on a big scale, or the 0:08:57.679 --> 0:08:59.240 explosion of stars or something. 0:09:00.760 --> 0:09:03.439 Couple of interesting answers did anyone look at you funny 0:09:03.440 --> 0:09:04.480 when you ask them the question. 0:09:05.720 --> 0:09:07.839 I don't know. These were all on the internet, so 0:09:08.000 --> 0:09:11.239 I couldn't capture their facial expressions. Did they send an emoji? 0:09:12.600 --> 0:09:15.800 But I do sense some relief in there that, for example, 0:09:15.800 --> 0:09:18.560 we are trying to simulate galaxy collisions rather than trying 0:09:18.559 --> 0:09:20.400 to arrange galaxy collisions. 0:09:20.559 --> 0:09:22.360 Well, if we could do that, that'd be pretty cool. 0:09:23.160 --> 0:09:25.560 I mean, not for those galaxies, but just to have 0:09:25.640 --> 0:09:26.120 that power. 0:09:26.320 --> 0:09:28.679 Yeah, you'd have to have like sign offs from every 0:09:28.720 --> 0:09:32.520 alien civilization in both galaxies before you could even begin. 0:09:32.760 --> 0:09:34.800 I guess that would be the polite thing to do. Yes. 0:09:35.240 --> 0:09:36.960 But anyways, as you were saying, this is a big 0:09:37.000 --> 0:09:40.680 part of how science is done these days, and so Daniel, 0:09:40.679 --> 0:09:42.960 I guess let's start from the basics. What is a 0:09:43.000 --> 0:09:45.960 simulation in your view as a physicists. 0:09:45.480 --> 0:09:48.840 So, a simulation, or more specifically, a computer simulation, is 0:09:48.880 --> 0:09:53.200 a specific program that involves a scientific model. A model 0:09:53.320 --> 0:09:56.079 is like our picture of how the world might work. 0:09:56.360 --> 0:10:00.280 It's like a simplified version of the real universe. Let's 0:10:00.320 --> 0:10:04.160 us explore a specific question, and a simulation is usually 0:10:04.240 --> 0:10:07.240 a program on a computer that uses like step by 0:10:07.240 --> 0:10:10.960 step methods to explore the behavior of that model. 0:10:11.800 --> 0:10:15.440 And usually this model has the form of an equation, right, Like, 0:10:15.480 --> 0:10:18.400 for example, F equalsma is a model of the world, right, 0:10:18.440 --> 0:10:19.839 and how things move in the world. 0:10:20.000 --> 0:10:22.560 Yeah, the science we do is mathematical, and the way 0:10:22.559 --> 0:10:26.599 we describe things is mathematical, and so usually that involves equations, 0:10:26.880 --> 0:10:29.640 equations that represent constraints on the model, like the way 0:10:29.720 --> 0:10:32.120 things have to happen. And as you say, F equals 0:10:32.200 --> 0:10:34.000 ma is a model. If I want to toss a 0:10:34.040 --> 0:10:36.640 baseball across my backyard, I want to answer the question 0:10:37.040 --> 0:10:39.560 where is it going to land? Then I have lots 0:10:39.559 --> 0:10:42.320 of possible ways to answer that question, but the most 0:10:42.320 --> 0:10:46.720 appropriate ways to make the simplest model possible that still 0:10:46.760 --> 0:10:50.640 captures everything that I'm interested in, and so often in 0:10:50.679 --> 0:10:53.240 our world, like when we're tossing baseballs, we can do 0:10:53.280 --> 0:10:56.680 something pretty simple just F equals ma, which ignores all 0:10:56.720 --> 0:11:00.160 sorts of swarming quantum details about what's happening inside at 0:11:00.160 --> 0:11:03.959 the baseball and just describes simple motion of a parabole. 0:11:04.400 --> 0:11:07.000 Yeah, it's almost like you. I mean, as a scientist, 0:11:07.000 --> 0:11:09.120 you're trying to come up with the rules of the universe, right, 0:11:09.120 --> 0:11:11.640 that's sort of the goal of science, right, And what 0:11:11.880 --> 0:11:15.520 sometimes that rule looks like is in a question that says, 0:11:15.559 --> 0:11:17.880 you know, if you have a mass and you apply 0:11:17.920 --> 0:11:19.679 a force to it, then it's going to start moving 0:11:19.679 --> 0:11:20.839 with a certain acceleration. 0:11:21.000 --> 0:11:23.880 Exactly in your words, these are all science fictions. We're 0:11:23.880 --> 0:11:26.120 living in this world and we're wondering what are the rules, 0:11:26.200 --> 0:11:28.040 and so we're trying a bunch of different rules, saying 0:11:28.080 --> 0:11:30.560 does this rule describe our universe? Does that rule describe 0:11:30.600 --> 0:11:34.000 our universe? So every sort of theoretical exploration of the 0:11:34.080 --> 0:11:37.400 universe involves building a model and then asking the question 0:11:37.760 --> 0:11:40.960 does that model align with the reality that we see. 0:11:41.120 --> 0:11:43.920 Computer simulations are a special kind of model or a 0:11:43.920 --> 0:11:47.120 special what a test? Really complicated models that we can't 0:11:47.160 --> 0:11:50.560 otherwise test, Like the model F equals M a pretty simple. 0:11:50.600 --> 0:11:53.120 I can use pencil and paper to make predictions, and 0:11:53.160 --> 0:11:54.960 then I can throw a ball in my backyard to 0:11:55.000 --> 0:11:56.720 confirm those predictions. 0:11:56.440 --> 0:11:58.720 Right, because I guess F equals A has like a 0:11:58.800 --> 0:12:01.480 mathematical But I think the idea is that you take 0:12:01.520 --> 0:12:03.240 in a question like F equals in May and you 0:12:03.440 --> 0:12:06.000 basically program that into a computer and say, you know, 0:12:06.280 --> 0:12:09.640 any masses in this program, they have to move according 0:12:09.679 --> 0:12:10.440 to this law. 0:12:10.679 --> 0:12:12.960 That's right. If, for example, I don't just want to 0:12:13.000 --> 0:12:15.400 describe one ball, but I want to describe like ten 0:12:15.440 --> 0:12:19.400 to the twenty five balls, right, some huge number of balls. 0:12:19.640 --> 0:12:22.559 Maybe I'm modeling an ideal gas, or like a swimming 0:12:22.600 --> 0:12:25.120 pool full of ping pong balls or something, and I 0:12:25.160 --> 0:12:27.000 want to describe that. Then I can no longer use 0:12:27.040 --> 0:12:28.959 pencil and paper. But you're in. I can take those 0:12:29.000 --> 0:12:31.240 equations and put them into a computer and ask the 0:12:31.240 --> 0:12:34.120 computer to force those balls to follow that equation, and 0:12:34.160 --> 0:12:36.720 then I could see what happens. It's sort of like 0:12:36.800 --> 0:12:38.559 a virtual experiment. 0:12:38.960 --> 0:12:41.559 Yeah, it's like you're creating your own little universe. 0:12:41.200 --> 0:12:44.720 Right exactly. And this becomes super essential when we don't 0:12:44.720 --> 0:12:48.080 have like a single equation that describes everything, Like we 0:12:48.120 --> 0:12:51.280 don't have a solution to what happens when you put 0:12:51.320 --> 0:12:53.800 ten to the twenty five ping pong balls into a 0:12:53.800 --> 0:12:55.920 swimming pool. We just don't know how to do that 0:12:56.000 --> 0:12:59.440 calculation to come up with some nice summary of the results. 0:13:00.120 --> 0:13:01.840 What we can do is put it into a computer 0:13:01.920 --> 0:13:04.959 and have the computer step it forward in time very carefully, 0:13:05.120 --> 0:13:07.880 and we can see what happens without ever actually having 0:13:07.880 --> 0:13:09.800 to buy that number of ping bomb balls. 0:13:09.960 --> 0:13:12.720 Right. That's sort of the power of the computer, right, 0:13:12.800 --> 0:13:16.440 Like you can simulate one ball, which is a calculator, right, 0:13:16.520 --> 0:13:18.400 Like you can say after one second, it's going to 0:13:18.400 --> 0:13:19.839 be here, after two seconds, it is going to be 0:13:19.880 --> 0:13:22.880 here by following these rules. But if you have, like 0:13:22.920 --> 0:13:26.120 you said, a whole bunch of balls, or a more 0:13:26.160 --> 0:13:28.960 complicated system, then a computer can sort of do all 0:13:29.000 --> 0:13:31.480 those calculations for you faster, exactly. 0:13:31.600 --> 0:13:34.960 One huge advantage is tackling a very large number of objects, 0:13:35.120 --> 0:13:38.040 and the other is when we don't have the equations, 0:13:38.040 --> 0:13:40.480 we don't know how to solve them, Like for f equals, 0:13:40.480 --> 0:13:42.720 I may we know how to solve that. Technically, that 0:13:42.920 --> 0:13:46.880 is a differential equation because A is a second derivative 0:13:46.920 --> 0:13:50.200 of position, right, there's derivatives on both sides. And in 0:13:50.240 --> 0:13:53.400 general and mathematics, differential equations are very very hard to solve. 0:13:53.400 --> 0:13:56.040 This a small number that we actually know how to solve. 0:13:56.520 --> 0:13:58.880 So sometimes you have a system that's described by a 0:13:58.880 --> 0:14:02.480 differential equation you don't know how to solve, Like fluid flow, 0:14:02.520 --> 0:14:05.440 for example, described by the Navier Stokes equation. We don't 0:14:05.440 --> 0:14:07.760 know how to solve that. In general. But what we 0:14:07.800 --> 0:14:10.400 can do on a computer is approximated. You can say, 0:14:10.520 --> 0:14:12.600 you know, let's just move it forward in time, not 0:14:12.840 --> 0:14:15.640 a year or a minute or some long period of time, 0:14:15.640 --> 0:14:18.760 but just like a microsecond, and across a microsecond, we 0:14:18.760 --> 0:14:21.360 can make some approximations. We can say, let's not use 0:14:21.360 --> 0:14:23.560 the full equation, let's simplify it and take some like 0:14:23.720 --> 0:14:25.880 linear approximation of it, and then if we take a 0:14:25.880 --> 0:14:28.320 lot of tiny little steps, we hope that we roughly 0:14:28.320 --> 0:14:29.520 get the right answer. 0:14:29.280 --> 0:14:31.240 Right, because I think, as you were saying, like something 0:14:31.280 --> 0:14:34.240 like f EQUOSM has the solution, meaning that you can 0:14:34.480 --> 0:14:37.200 derive a formula for like the precision of your ball 0:14:37.240 --> 0:14:40.240 at all times, where you can just like after three 0:14:40.280 --> 0:14:41.960 seconds you just put the time in and it gives 0:14:42.000 --> 0:14:44.000 you the position of the ball, right, because you can 0:14:44.080 --> 0:14:46.880 integrate that equation and find the solution. But some equations 0:14:46.880 --> 0:14:49.480 you can, like they're so complex you can get a 0:14:49.560 --> 0:14:51.400 formally that will tell you what's going to happen ten 0:14:51.480 --> 0:14:53.360 years from now or twenty years from now. Right, those 0:14:53.400 --> 0:14:56.040 you need to do little steps by little steps exactly. 0:14:56.080 --> 0:14:58.240 And the crucial idea there is that you're making a 0:14:58.280 --> 0:15:00.880 linear approximation you're taking the full equation which you don't 0:15:00.880 --> 0:15:02.840 know how to solve, and you're saying, well, let's replace 0:15:02.880 --> 0:15:05.480 it with an approximate version of it, which is not 0:15:05.520 --> 0:15:07.520 going to be correct, but it might be correct for 0:15:07.720 --> 0:15:11.040 like a microsecond. And so we'll use the approximate linear 0:15:11.160 --> 0:15:12.840 version of that that we do know how to solve 0:15:12.960 --> 0:15:15.120 from a tiny little step, and then we'll start again, 0:15:15.160 --> 0:15:17.240 and we'll make another tiny little step, and we hope 0:15:17.240 --> 0:15:19.760 them little mistakes cancel out and don't build up into 0:15:19.800 --> 0:15:21.240 some big overall mistake. 0:15:21.680 --> 0:15:24.400 Right Yeah. It's almost like if you take small enough steps, 0:15:24.440 --> 0:15:28.000 then you're less likely to deviate from the reality of. 0:15:27.960 --> 0:15:30.560 It, right, Yeah, exactly. And people who do approximations know 0:15:30.640 --> 0:15:32.560 that there's lots of times this is useful. Like you 0:15:32.560 --> 0:15:35.360 want to calculate Trigg function like sign sign is really 0:15:35.400 --> 0:15:38.480 hard to calculate like sort of from scratch, but for 0:15:38.640 --> 0:15:41.720 very small values of the angle, sign of x is 0:15:41.760 --> 0:15:44.640 just equal to x, you can like approximate this complicated 0:15:44.680 --> 0:15:47.280 function with a simple one. It mostly gets the right answer. 0:15:47.440 --> 0:15:48.480 That's just one example. 0:15:48.560 --> 0:15:51.320 I'm not sure you're going to Trigonometry usually makes things 0:15:51.520 --> 0:15:55.360 you understand, but I think I think we get the idea, 0:15:55.400 --> 0:15:57.120 which is that you know, if you take small enough 0:15:57.160 --> 0:16:00.360 steps and you you sort of a simplified version of 0:16:00.400 --> 0:16:04.560 your model, then you're less likely to make mistakes. 0:16:04.720 --> 0:16:07.800 Exactly. You can't trust those approximations forward a second or 0:16:07.840 --> 0:16:09.800 a minute or a year, but you could trust them 0:16:09.800 --> 0:16:13.120 like a microsecond. And so you have the simulated universe 0:16:13.240 --> 0:16:16.320 in your computer. You feed in the initial conditions, and 0:16:16.360 --> 0:16:18.320 then you ask it to take a step forward in time, 0:16:18.600 --> 0:16:20.720 and you ask it to take another step forward, and 0:16:20.720 --> 0:16:22.680 if you have enough computing power, you can run it 0:16:22.720 --> 0:16:25.040 for a while and you can see what happens to 0:16:25.080 --> 0:16:27.680 all my ping pong balls in my simulated swimming pool, 0:16:28.000 --> 0:16:30.600 or what happens to my galaxy as the stars all 0:16:30.640 --> 0:16:31.840 swirl around each other. 0:16:32.000 --> 0:16:35.160 Right, Like you were saying, like fluids are notoriously really 0:16:35.240 --> 0:16:38.600 hard to solve as an equation, right, These are really 0:16:38.640 --> 0:16:41.880 complex equations that govern what's going on because they sort 0:16:41.880 --> 0:16:43.640 of like depend on a lot of things. Like there's 0:16:43.640 --> 0:16:46.040 a lot going on, right, there's time, and then there's 0:16:46.080 --> 0:16:49.080 distance and the velocity of things and all those factor 0:16:49.160 --> 0:16:52.480 in that's hard or impossible to like predict exactly what's 0:16:52.480 --> 0:16:53.960 going to happen in the future exactly. 0:16:54.040 --> 0:16:57.240 And the big complication there is the interactions. Like back 0:16:57.280 --> 0:16:58.880 to the ping pong balls. If you just had a 0:16:58.880 --> 0:17:01.000 lot of ping pong balls and they're all flying around 0:17:01.040 --> 0:17:03.320 but not touching each other, it wouldn't be that hard 0:17:03.360 --> 0:17:05.960 to calculate what's going to happen to each one, But 0:17:06.000 --> 0:17:08.160 as soon as they start banging against each other, becomes 0:17:08.240 --> 0:17:11.040 much much more complicated because the solution of ping pong 0:17:11.080 --> 0:17:13.879 ball number six hundred and forty two now depends on 0:17:13.960 --> 0:17:17.040 ping pong ball number one, one hundred and eleven and 0:17:17.160 --> 0:17:20.240 every other ping pong ball, so becomes much more complicated. 0:17:20.320 --> 0:17:23.520 And that's why fluids are so complicated, because every sheet 0:17:23.600 --> 0:17:25.680 of the fluid depends on the friction with the other 0:17:25.760 --> 0:17:27.959 sheet of the fluid. And that's what makes the Navier 0:17:28.000 --> 0:17:30.440 Stokes equation, for example, so intractable. 0:17:30.800 --> 0:17:32.679 Right, And so you take it little by little, and 0:17:32.720 --> 0:17:34.760 so you say, okay, this time, I'm going to ignore 0:17:34.840 --> 0:17:37.520 some of these effects and just take one small step 0:17:37.600 --> 0:17:40.680 to see where all those little molecules go. And then 0:17:40.920 --> 0:17:43.960 you keep repeating that and hopefully it sort of looks 0:17:44.080 --> 0:17:45.080 like the real thing. 0:17:45.080 --> 0:17:48.119 Exactly, and it gives you this incredible power that you 0:17:48.160 --> 0:17:52.240 can hopefully identify emergent behavior. The way we do science 0:17:52.280 --> 0:17:54.560 in our universe is that we like focus on one 0:17:54.680 --> 0:17:57.399 level where we understand things we can describe, like the 0:17:57.440 --> 0:18:00.840 microphysics of how particles being against each other. But sometimes 0:18:00.880 --> 0:18:03.520 we're interested in things at another level, Like you understand 0:18:03.520 --> 0:18:05.640 how rain drops move through the wind, but your real 0:18:05.720 --> 0:18:08.400 question is like is this hurricane going to hit Florida 0:18:08.520 --> 0:18:10.879 or Alabama? And so even if you don't have like 0:18:10.920 --> 0:18:13.600 an equation that describes hurricanes, if you have an equation 0:18:13.680 --> 0:18:16.359 that describes the rain drops, you can feed that all 0:18:16.400 --> 0:18:19.439 into your computer, run simulations, and then get answers to 0:18:19.520 --> 0:18:22.600 your higher level question. You can see like the emergent 0:18:22.640 --> 0:18:25.160 phenomena of the hurricane in simulation. 0:18:25.480 --> 0:18:28.280 Well, it's dig a little bit deeper into how simulation 0:18:28.400 --> 0:18:32.439 works and the things like weather and why scientists use 0:18:32.480 --> 0:18:36.000