Is the Universe a Math Problem? With Terence Tao

Do we need new math to explain dark matter? Neil deGrasse Tyson and comedian Paul Mecurio explore unsolved problems in math, simulation theory, base systems and more with mathematician Terence Tao.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Neil deGrasse Tyson?

  Paul, we have revisited the universe of math.

• 0:02Paul Mecurio?

  Yeah, but really drilled down and really applied ourselves.

• 0:06Neil deGrasse Tyson?

  Cause that's how we roll.

• 0:08Paul Mecurio?

  Yeah.

• 0:08Neil deGrasse Tyson?

  Coming up on StarTalk.

• 0:12Neil deGrasse Tyson?

  Welcome to StarTalk, your place in the universe where science and pop culture collide. StarTalk begins right now.

• 0:27Neil deGrasse Tyson?

  This is StarTalk. Neil deGrasse Tyson, your personal astrophysicist, and we're gonna have a Cosmic Queries edition on the subject of mathematics.

• 0:40Neil deGrasse Tyson?

  Why you laughing at me like that?

• 0:42Paul Mecurio?

  Paul, you're gonna scare people with this?

• 0:45Paul Mecurio?

  Everybody thinks it's a math quiz coming up.

• 0:46Neil deGrasse Tyson?

  That was a Halloween laugh, wasn't it?

• 0:48Paul Mecurio?

  It was.

• 0:49Neil deGrasse Tyson?

  I got Paul Mecurio here. How you doing, man?

• 0:51Paul Mecurio?

  I'm good, man. Good to see you.

• 0:52Neil deGrasse Tyson?

  Yeah, you got your podcast. What was it called again?

• 0:54Paul Mecurio?

  Inside Out with Paul Mecurio.

• 0:55Neil deGrasse Tyson?

  Inside Out. Did you get Disney permission for that?

• 0:57Paul Mecurio?

  I did not. Well, thanks for bringing that up. I'm gonna be getting sued right after this.

• 1:03Neil deGrasse Tyson?

  And you are out of a job after May.

• 1:05Paul Mecurio?

  Yes, thanks for bringing that up as well. Anybody have any deadly diseases they wanna talk about? Yes, The Late Show gets gut canceled, so I work on The Late Show. You've been on The Late Show a bunch. We love you there.

• 1:17Neil deGrasse Tyson?

  Yeah.

• 1:18Paul Mecurio?

  Well, not everybody. No, and yeah.

• 1:21Neil deGrasse Tyson?

  You've been with Stephen Colbert since The Colbert Report.

• 1:27Paul Mecurio?

  Since The Daily Show.

• 1:28Neil deGrasse Tyson?

  The Daily Show, yeah.

• 1:29Paul Mecurio?

  Yeah, I started at The Daily Show as one of the original writers performers there. He came in as a performer. We actually-

• 1:35Neil deGrasse Tyson?

  You predate him on The Daily Show?

• 1:37Paul Mecurio?

  I'm old school. I'm OG. And we actually shared an office together, would write a lot together, and then he had The Colbert Report. I worked on that. So he and I have been together a long time.

• 1:47Neil deGrasse Tyson?

  Okay.

• 1:47Paul Mecurio?

  And it's weird and sad, you know, because it's like, it's not a lot of change over in the 10 years that we've been on The Late Show, so it's like a family breaking up, you know, it's really kinda, yeah.

• 1:58Neil deGrasse Tyson?

  Okay.

• 1:58Paul Mecurio?

  So I'll be at your house cutting your lawn for two bucks. I hope our guest needs some help. I'll go to California. It doesn't snow out there, but I'll shovel anyway.

• 2:08Neil deGrasse Tyson?

  All right.

• 2:09Paul Mecurio?

  And by the way, Baron?

• 2:12Neil deGrasse Tyson?

  You did get the title.

• 2:14Paul Mecurio?

  United Me Baron.

• 2:15Neil deGrasse Tyson?

  Only if the people asking questions remember that. That's where that comes from. You'll find out. So who do we have today? I love me some mathematics.

• 2:22Paul Mecurio?

  Yeah.

• 2:22Neil deGrasse Tyson?

  Ever since high school.

• 2:23Paul Mecurio?

  Brilliant.

• 2:24Neil deGrasse Tyson?

  I've been a big fan of mathematics. Even the obscure math that doesn't relate to anything ever. But it's still fun.

• 2:31Paul Mecurio?

  Yeah.

• 2:31Neil deGrasse Tyson?

  But of course.

• 2:32Paul Mecurio?

  Well, initially you like math because there's a finality to it. But then when you really get into it, you realize there's a whole bunch of non non finality to it. It can take you everywhere, right?

• 2:41Neil deGrasse Tyson?

  Yeah, yeah, everywhere and anywhere and everywhere.

• 2:43Paul Mecurio?

  Yes, exactly.

• 2:44Neil deGrasse Tyson?

  Yeah, so you know what we found? We found like a badass mathematician.

• 2:48Paul Mecurio?

  Ooh.

• 2:49Neil deGrasse Tyson?

  Yeah.

• 2:49Paul Mecurio?

  That sounds like a good movie title. Is he also an assassin?

• 2:54Neil deGrasse Tyson?

  We cannot divulge that publicly. We have Terence Tao. Terence, did I pronounce your name correctly?

• 3:02Speaker 02

  That's correct. Yes, please, please be here.

• 3:04Paul Mecurio?

  No, that's wrong. That's not how you pronounce your name.

• 3:08Neil deGrasse Tyson?

  You are professor of mathematics at UCLA. UCLA?

• 3:14Paul Mecurio?

  Okay, that is not a community college in Oxnard.

• 3:18Neil deGrasse Tyson?

  Yeah, UCLA Community College. You're professor of mathematics at UCLA. That's officially University of California, Los Angeles. Yes, it is. And here's the, here's the best part. Director of Special Projects.

• 3:31Paul Mecurio?

  Ooh.

• 3:31Neil deGrasse Tyson?

  At I-PAM Institute for Pure and Applied Mathematics.

• 3:36Paul Mecurio?

  Can I just ask, Terence? Did they give you the title of the Director of Projects? And you insisted the word special be put in there? That's what people are saying on social media. I'm just relaying information right now.

• 3:48Speaker 02

  No, it, it foredates me, but certainly that title helped me accept the position.

• 3:54Neil deGrasse Tyson?

  So we can say, we can say he has a special set of skills.

• 3:58Paul Mecurio?

  Oh, there you go. This guy is definitely badass.

• 4:02Neil deGrasse Tyson?

  He's got a special set of skills.

• 4:04Paul Mecurio?

  In a weird way, you could be like the accountant, right? That's that movie.

• 4:08Neil deGrasse Tyson?

  Yes.

• 4:08Paul Mecurio?

  Where he's mathematically brilliant, but then also could just kill you with two fingers.

• 4:12Neil deGrasse Tyson?

  Yes, yes, but that is not our guest today.

• 4:15Paul Mecurio?

  Okay.

• 4:17Neil deGrasse Tyson?

  I love with the superhero.

• 4:19Paul Mecurio?

  Right, okay.

• 4:20Neil deGrasse Tyson?

  So tell us about this center that you direct.

• 4:23Speaker 02

  Yeah, so I'm not the main director, but I'm the director of what's called special projects. Yeah, so IPAM is an institute that brings together pure mathematicians and applied mathematicians and scientists and people from industry to work on topics where it's time for mathematics to get involved. So, for example, we hold very early workshops and conferences on AI, deep fakes, self-driving cars, many years before they became a reality. And often industry people were working on these problems, but they came up, they were blocked by various mathematical obstacles and they needed mathematicians to talk to. So we create these programs where we just have lots of experts in different fields

• 5:05Speaker 02

  in the same room, listening to talks and just socializing, and good things happen. I once talked with an engineering engineer and statistician 20 years ago in one of these programs, and we ended up finding a new way to do MRI scans that's actually 10 times faster than traditional scans. In fact, now all the modern MRI machines use our algorithms.

• 5:29Paul Mecurio?

  Can I just say, I recently had an MRI. Still took a long time. Maybe you could have done a little better.

• 5:35Speaker 02

  Yeah.

• 5:41Paul Mecurio?

  I mean, I don't have all day, Terence. I have stuff to do. I want in and I want out. I want it to be as fast as when I microwave soup.

• 5:48Speaker 02

  Right. I think when they make them faster, they trade it off for more detail. So they can get a more detailed image of you. The cutting edge now is they can get videos of like your heart, whatever, in real time. So since you're there anyway, I think they will keep you for the same amount of time, but they can extract more data out of you.

• 6:06Neil deGrasse Tyson?

  At the risk of stating the obvious, one of the great things when you establish institutes or these umbrella gatherings of people from different professions that wouldn't otherwise ever talk to one another. I mean, think about it. You have departments of, you know, mechanical engineering, electrical engineering, biology, chemistry, physics, ba-da-da-da-da-da. And they have lunch together, you know, they have coffee together, and they don't know what anybody else is thinking or what anybody else is doing. And now you put this umbrella over an institute, and you bring them all together, and oh my gosh.

• 6:41Paul Mecurio?

  And I would think one of the benefits is that, you know, you look at something yourself or with your group, a new set of eyes comes in and brings a different perspective and sees things that you didn't see.

• 6:52Speaker 02

  Yeah, exactly. I mean, science is just way too broad now. You know, maybe 100 years ago, it was possible to have a pretty decent understanding of every corner of science, but that's basically impossible now. So you have to specialize.

• 7:04Neil deGrasse Tyson?

  The universe doesn't compartmentalize science.

• 7:10Paul Mecurio?

  As much as we wanted to.

• 7:11Neil deGrasse Tyson?

  Yeah, it's all mixed together at all times.

• 7:14Paul Mecurio?

  You guys figure this out.

• 7:16Speaker 02

  Yeah, all the modern problems in the world are really interdisciplinary. I think the specialist problems we've kind of solved in the 20th century, and the 21st century is all about collaboration.

• 7:26Neil deGrasse Tyson?

  This should be obvious, but let's just so we're all on the same page. Tell us the difference between pure and applied math.

• 7:31Speaker 02

  Pure math is curiosity-driven math. You know, we see patterns in very abstract things like numbers or shapes, and we just ask, you know, does this pattern keep continuing? And it doesn't necessarily, it's not necessarily motivated by any practical application. Or maybe it started out that way, but people just sort of just kept asking questions.

• 7:50Neil deGrasse Tyson?

  Well, would that include people who are obsessed with what's going on in the sequence of digits of pi?

• 7:56Speaker 02

  In principle, yes, that is part of pure mathematics. It turns out not to lead very far because there basically aren't any interesting patterns there.

• 8:04Neil deGrasse Tyson?

  But did you prove that there are no interesting patterns?

• 8:07Speaker 02

  This is actually still an open question.

• 8:09Neil deGrasse Tyson?

  So it could be that the fact that there's not an interesting pattern is itself an interesting fact.

• 8:16Speaker 02

  Right, except that we know that like 99% of all the numbers in the world have no interesting patterns, and it's like only a very small fraction of numbers that actually have something detectable going on. So the fact that pi is part of the 99% is, in retrospect, not exceptionally interesting.

• 8:33Paul Mecurio?

  Do we have a theory why 99% don't have a pattern?

• 8:36Speaker 02

  Yeah, no, it's, it comes from the law of probability, from the law of large numbers. Like, if you pick a number randomly, just for every digit, you roll a die, a 10-sided die, and you select digits at random, the law of large numbers says that 99% or 99.99% of the time, you never see any patterns. You get as many zeros as ones, as many ones as twos. There's only a very small fraction of numbers that exhibit bias.

• 9:02Speaker 02

  It's a very useful law. This is why, for example, we can do statistics polling. Like if you want to poll 300 million Americans and see what they're thinking, you can't poll 300 million Americans, but you can poll 1,000, 2,000. And the law of large numbers actually tells you that as long as you poll a very representative set of people, the outcome of a poll is actually pretty close 99% of the time to the general population.

• 9:29Neil deGrasse Tyson?

  So I could ask a question that you might be able to answer. How many digits of pi would I have to roll out before I got 10 nines in a row?

• 9:39Speaker 02

  That would be about 10 to the 10, so I guess 10 billion.

• 9:42Neil deGrasse Tyson?

  Okay, all right. We got an answer to that.

• 9:44Paul Mecurio?

  You're both wrong. It's 11 billion. I'm the guy that knows nothing and you're both wrong. Why are we doing it now?

• 9:51Neil deGrasse Tyson?

  Okay, so now, applied math, the world, other than mathematicians, care about the answer in applied math?

• 9:57Speaker 02

  Right, yeah. So, applied math, it's still not quite directly applied to the real world. That's what scientists and engineers do. But it's about the mathematics that is of practical value to those scientists. So, for example, atmospheric scientists might care about predicting climate or the weather. And applied mathematicians might develop the software or the equations to actually model the atmosphere or oceans. They may not actually work directly with real data. They may only work with sort of test data or something. And it still has a lot of theory to it. But it's still intermediate between the pure mathematicians and scientists and engineers.

• 10:38Neil deGrasse Tyson?

  We face that a lot in astrophysics, where you can generate data that you can then apply your ideas to, to see if that works. And then you check later to see if the data you generate matches what you actually end up observing. So just the methods, tools, and tactics.

• 10:53Paul Mecurio?

  So when does applied mathematics sort of do? A cheat, if you will, right? Sort of simplify things intentionally, drawing on pure mathematics. And where's that line where it's too much of a cheat? Or it's just enough of a tweet cheat that it's still?

• 11:09Neil deGrasse Tyson?

  Do you mean approximation?

• 11:10Paul Mecurio?

  Yeah, well, you know, the term is intentional simplified reality, right?

• 11:16Speaker 02

  Yeah, yeah, so there's a spectrum. So the world is messy. And if you try to incorporate every single aspect of it, it's just too much to model. And you can't see the flowers for the trees. So yeah, so mathematicians intentionally simplify reality. They work with what's called toy models. Physicists call them spherical cow type assumptions, where you want to model a cow. It's actually easier for the physics of the cow is a complete sphere and fictionless. That's not realistic, but it's a good starting point. And then, and then over time, you decide to add some friction, add some legs to the cow. But you start with the easiest cases to get some, to get some initial idea. I guess the difference between math and the other science and basically anything else

• 12:00Speaker 02

  is that we can change all our hypotheses and work with these toy cases. Like, you know, if you want to build a bridge and you're an engineer, you can't just sort of build a toy bridge over a creek first and then float your way up to a real bridge. If you're a heart surgeon, you can't do some experimental surgery on rats or something first. And then, well, I guess in training, maybe you do, but.

• 12:20Paul Mecurio?

  Mine has, that's why I have a bad ticker.

• 12:24Speaker 02

  Okay, well, my condolences. But in most professions, you don't get to play your toy models because you're not allowed to fail. But in math, math failure is very, very cheap. You know, you try a problem, you don't solve it, fine, you just toss the paper away and you try again. No, no, no one gets hurt, no one dies.

• 12:43Neil deGrasse Tyson?

  Yeah, the patient doesn't die.

• 12:44Paul Mecurio?

  Exactly.

• 12:45Neil deGrasse Tyson?

  Yeah, and let me add something because you just blew by the spherical cow. But it's worthy of another comment. Okay, so in physics, everything is about simplification. Because often the details, while they may be interesting, don't actually influence the outcome.

• 13:03Neil deGrasse Tyson?

  In any important way, okay? And if they do, you would have solved the case then to see how it influences the outcome. So here's the point. You're tasked with, I want to design a cow that can maximize milk production.

• 13:17Paul Mecurio?

  Mm hmm.

• 13:17Neil deGrasse Tyson?

  Okay? So then you say, consider a spherical cow. Okay? So a sphere holds the maximum amount of milk for it, for the, for the area.

• 13:28Paul Mecurio?

  Okay.

• 13:29Neil deGrasse Tyson?

  The surface area.

• 13:29Paul Mecurio?

  Okay, where are the legs?

• 13:30Neil deGrasse Tyson?

  So now, if you add legs and a head and a tail and, okay, that reduces the number, but it means I have calculated the upper limit to how much milk the cow is gonna make.

• 13:44Paul Mecurio?

  Because what does that sphere?

• 13:45Neil deGrasse Tyson?

  The sphere, exactly. So you can't come in later and say, here, have the cow produce five times as much.

• 13:50Paul Mecurio?

  Having those details of legs, tail and head.

• 13:52Neil deGrasse Tyson?

  It subtracts from the total, yes.

• 13:54Paul Mecurio?

  That's the detail that you said doesn't matter, matters.

• 13:56Neil deGrasse Tyson?

  Well, what I'm saying is, it caps how much you can think about that problem. It keeps everybody in the same room.

• 14:03Paul Mecurio?

  Got it.

• 14:04Neil deGrasse Tyson?

  Yeah. It's not, it's not an unlimited place to guess outcomes.

• 14:08Paul Mecurio?

  Have you found that applied mathematics can change a settled pure math theory? Has that ever gone back and sort of?

• 14:17Neil deGrasse Tyson?

  Well, let's lead into that by asking, tell us about unsolved problems in mathematics. And when they're solved, who solves them? Is it the computer person? Is it the pure math person? Is it something else?

• 14:29Paul Mecurio?

  Is it Matt Damon writing on a board when he's a janitor?

• 14:31Neil deGrasse Tyson?

  Exactly.

• 14:32Paul Mecurio?

  Come on.

• 14:33Speaker 02

  Well, increasingly, there's a conversation going in all directions. Um, so traditionally, pure mathematicians just, um, experiment with patterns and, and they, they, based on analogies and intuition they built up, they propose that some, uh, phenomenon that they see, um, for one type of pattern also extends to some other setting.

• 14:55Speaker 02

  But sometimes it goes, it comes from the physical world. Physicists notice that something keeps happening. So for example, there are these laws in physics that are seemingly universal. That there are certain distributions, like the bulk of distribution is an example of a universal distribution. Many, if you plot, say, the heights of people or, you know, or the size of cows, if you wish.

• 15:22Paul Mecurio?

  Can I just tell you something right now? I want a milkshake in the worst way.

• 15:27Paul Mecurio?

  I am so craving one, anyway.

• 15:29Speaker 02

  Yeah, but lots of distributions in nature have the same shape. In this case, a bell curve. There's even a meme about it on the internet.

• 15:37Neil deGrasse Tyson?

  And we would, in physics, and I think in pure math, it's a Gaussian curve.

• 15:41Speaker 02

  Yes, that's the name, right? Yes.

• 15:43Neil deGrasse Tyson?

  Named after Gauss, brilliant mathematician, one of the most brilliant there ever was, I think.

• 15:48Speaker 02

  Yeah, so mathematicians did actually find an explanation for why this curve appears all the time. Something called the central limit theorem in probability. But there are some other distributions that physicists have discovered that we haven't yet fully explained why they show up so often. Like gaps between spectral lines, and it's more technical to explain.

• 16:08Speaker 02

  But yeah, there are laws that physicists and other scientists have found are universal. And mathematicians, and they're good sources of conjectures for mathematicians to work out. Yeah, well, mathematicians are in some ways exploring other universes, but just very abstract numerical universes, not as interesting as the sci fi alternative universes.

• 16:27Paul Mecurio?

  I mean, to put this in sort of practical terms, pure math versus applied. It's like you're painting a room and you exactly calculate the number of gallons of paint. And then two days later, you made three trips to Home Depot because you need three more gallons and you're gonna have a nervous breakdown because you couldn't, that's the applied part, right? Once you get into it, you sort of go, oh, wait a minute, I didn't factor this in. And that's sort of what happens with applied math. And it would then correct some of your pure math calculations, right? So it's sort of this, it's this symbiotic relationship between the two, right?

• 17:01Speaker 02

  Yeah, so Vladimir Arnold, who is a famous mathematician, he once wrote that mathematics is the part of science where experiments are cheap.

• 17:09Neil deGrasse Tyson?

  Oh, I like that.

• 17:10Speaker 02

  Before you invest billions of dollars in a new telescope or a collider or something, you do the math. And you see what is theoretically possible, maybe assuming spherical cows.

• 17:20Speaker 02

  But it tells you in theory what you can and what can't do, and it sets good targets. And then it allows you to allocate the more expensive resources more intelligently.

• 17:43Speaker 03

  Hey, this is Kevin the Sommelier, and I support StarTalk on Patreon. You're listening to StarTalk with Neil deGrasse Tyson.

• 18:01Neil deGrasse Tyson?

  So I got here something called the Kolatz conjecture. What is that?

• 18:05Speaker 02

  Yeah, so this is a dangerous conjecture. It's it's it has trapped many mathematicians and amateurs because it feels like something so simple that we should be able to solve it. But it's been around for at least 100 years, and we haven't solved it.

• 18:18Paul Mecurio?

  Well, maybe if you tried a little harder.

• 18:21Speaker 02

  When you try, I've worked on this too.

• 18:23Neil deGrasse Tyson?

  If you were just a little smarter.

• 18:25Paul Mecurio?

  Playing with spherical cows all day.

• 18:29Speaker 02

  I could describe it. I'm just worried, as I said, it could trap some some audience members to work on it obsessively.

• 18:35Neil deGrasse Tyson?

  That's good. We like trapping our people. So tell me, tell me about it. So these are the best of the unsolved problems are the ones that can be described simply.

• 18:43Speaker 02

  So the Kolatz conjecture, it's also called the hailstone conjecture for a reason I'll explain later. So it says something. So you could be a number, your favorite number 37 or 69 or whatever. Okay. And then we do the following. So if your number is even, we divide by two, we make it smaller. So 16 becomes eight. But if it's odd, you multiply by three and you add one. So if you can be five, I multiply by five, it goes to 15, add one to 16. So odd numbers become bigger, even numbers become smaller. So now just repeat this process. So five becomes 16, but then 16 becomes eight because it's even, eight becomes four, four becomes two, two becomes one, one is odd, you multiply by three and add one, it becomes four again, and you end up in a loop, one, four, two, one, four, two, one.

• 19:28Neil deGrasse Tyson?

  It always takes you back down to there.

• 19:31Speaker 02

  Well, that's the conjecture. So we've used computers. If you take any number up to, say, a trillion, every single number that we've tested ends up going down to 142, 142, 142. But we don't know if all of them do. So it's called the hailstone conjecture because there's this oversimplified model of hailstones. Again, a spherical cow, that model of hailstones. Where hail forms because little ice crystals forms in the clouds. Sometimes currents bring it up where it's colder and then more ice

• 20:01Speaker 02

  forms and then it goes down a little bit and maybe it melts. And the hailstone bounces up and down in the cloud, but eventually it lands to Earth. All the hailstones eventually hit the ground.

• 20:11Neil deGrasse Tyson?

  But just to be clear, they hit the ground because they reach a mass that the upward currents can no longer sustain them. And then they drop out.

• 20:19Paul Mecurio?

  They're too heavy.

• 20:19Neil deGrasse Tyson?

  And the bigger the hailstone, the bigger the uplifting air was that kept them there for that long.

• 20:25Paul Mecurio?

  And the bigger insurance claims for your car.

• 20:29Speaker 02

  In principle, there could be some really unusually lucky hailstone that somehow always hit the currents that go up and don't hit the ones that go down. And just keep bouncing up and up forever. I mean, occasionally you could sort of defy the statistical laws of physics. And so in principle, there could be this very lucky number that just sort of always keeps hitting the odd numbers and going up rather than hitting the even numbers to go down. It would be like someone who's consistently winning at a casino at a game that's rigged. It's theoretically possible, but we don't know if you can actually do it with any given, with an actual number. And that's the collapse conjecture.

• 21:07Paul Mecurio?

  But this is so basic. It's sort of a yes, it's a yes no moment, right? It's even odd. It should seem like, why does it devolve into chaos? Because it starts with such a basic premise. That's the part that's confounding me and I guess obviously others, but.

• 21:23Neil deGrasse Tyson?

  You are now confounded.

• 21:24Paul Mecurio?

  Thank you very much. Can I have my official spherical cow, please? Yeah, but what is that about?

• 21:31Speaker 02

  So it's part of a general phenomenon called chaos. So you can have very simple operations like halving a number which is even or 1391 if it was odd. As you say, if you just do it once or twice, it's a very easy operation. You know, a kid in third grade can implement it. But when you iterate. Even very simple operations over and over again, you can get vast, vast complexity. And so sometimes you don't. Sometimes you get like these universal laws, like these bell curves and things settle down. But but sometimes you just get this this enormous complexity. The act of reproduction and splitting DNA is is fairly simple. But you know, it leads to, you know, immense biodiversity.

• 22:12Neil deGrasse Tyson?

  We have computers, we have AI. Why hasn't the Colet's conjecture been affirmed?

• 22:18Speaker 02

  Well, because we have to check an infinite number of cases.

• 22:20Neil deGrasse Tyson?

  We'll get to work on that.

• 22:21Paul Mecurio?

  I was gonna say, there's a there's a thing called a computer. Look at my finger, just go like that.

• 22:27Neil deGrasse Tyson?

  Why don't we crowdsource it? All right, it's still not an infinite number of people, but there's quite a bit of of computing power out there. You know, the SETI Institute did it where they that you would upload software and they'd give you data. And while your while your computer was what you were not using your computer on screensaver, it was using your CPUs to to calculate.

• 22:51Speaker 02

  Yeah, so there was a project, I think it was called Collapsed Grid, which was exactly that. Like SETI at home, but for collapse. And it did extend the numbers. So a couple of quadrillion, I think, or 10 to the 18, 10 to the 19, we could do from this crowdsourcing. But no matter how much you do, there's still an infinite number of numbers left to go.

• 23:12Speaker 02

  So if you want to roll out all the numbers, you need you need proofs. You need mathematical, you need to use mathematical laws that work for all numbers.

• 23:19Neil deGrasse Tyson?

  Otherwise, it's not elegant and it's not even interesting.

• 23:22Paul Mecurio?

  It's not elegant. It's like you're putting a bunch of crazy ingredients in a blender. You always get and it always outputs oatmeal like every time.

• 23:30Speaker 02

  Some some problems you can only solve by brute force.

• 23:32Paul Mecurio?

  Are we any closer to solving this conjecture? I mean, how close?

• 23:36Speaker 02

  So I I worked on this a couple of years ago. I proved a result that if you take a really large number, like 10 to the 15, to 10 to the 20, whatever, I could I could show statistically that 99% of all numbers that are very, very big would would become very, very small and become much smaller than than where they started. I couldn't show they hit one, but I could show that that 99% of all numbers become as small as, say, the logarithm of the number. So like 10 to the 20, I could show drops down to 20, 10 to the 100 drops down to 100.

• 24:06Paul Mecurio?

  You know what? I'm going to use a term from your world. Why don't you apply yourself?

• 24:12Speaker 02

  Yeah, so in mathematics, we've made much value partial progress.

• 24:16Neil deGrasse Tyson?

  They're very good.

• 24:17Speaker 02

  Yeah, we can't stop completely, but we are happy with half a loaf or 99% of a loaf. Because someone else can build upon that.

• 24:23Neil deGrasse Tyson?

  Do you like those math movies like The Beautiful Mind and the Matt Damon movie?

• 24:30Paul Mecurio?

  Good Will Hunting. Do you sit there and yell at the screen, "That's not the way you do it"? Are you one of those guys?

• 24:37Speaker 02

  I enjoy those movies mostly for the non-math part of it. Now, maybe if there's an expert in schizophrenia, they would be complaining about that, but saying that the math was very, was very cool. I think this is, this is common. I have a brother who is, who did some CGI back in the day. And like every time it's animated movie, he cannot enjoy the special effects because he knows how they were made. So I remember watching one of these movies, it was a movie called Gifted, stars Chris Evans and this amazing young character. Who is supposed to be this math genius and her mother was a math genius. And she was working on a non-soft math problem. And it actually was a problem that I worked on. And at some point, they were going to review some of her notes on how she was making progress was the problem.

• 25:21Speaker 02

  And I was actually quite interested to see what, what, what they would do. And they actually showed a little snippet of her notebook. And there was actually some equations from one of my papers. Wow, okay. Two years before the movie was, was made, I actually got an email from the directors saying, "We're making a movie about, about a gift to get in math. Could you supply some, some samples of some math computations that would be, look, look good?" And, and I actually supplied some, some, some from my own work, some from others. And they said, "Thank you very much." And I didn't hear of them for two, for two years. And then this movie came out. So I was, I was caught unawares, but it, it did actually come for me.

• 26:02Neil deGrasse Tyson?

  So before we go to our, our question base, there's one more. Just tell me, tell me about the ESDO's problems.

• 26:07Speaker 02

  Uh, right. So Paul Erdes was this Hungarian mathematician. He was a rather extreme, like so mathematicians have a reputation for being a little idiosyncratic, but but he was rather extreme even among mathematicians. He didn't own a home. He would travel the world constantly and and crash on other mathematicians' couches, basically, for his whole life. But while doing so, he would talk math to them and they would often write papers. He has like two or three thousand papers. He's one of the most prolific mathematicians in history. And he was famous for posing problems that he would attach little cash prizes to often. Like, here's a little problem I just came up with. You you get twenty five dollars or something if you can solve this problem.

• 26:46Speaker 02

  And in fact, many of his problems did get solved and Erdes would send them a check with that amount of money. But these checks were almost never cashed because they they were they were more valuable framed on the wall as someone who had solved an Erdes problem.

• 26:57Neil deGrasse Tyson?

  I wouldn't be that famous. I could pay people and they don't cash the check.

• 27:00Paul Mecurio?

  Well, maybe if Mr. Smarty Pants cashed the checks, he could buy himself a house and not have to sleep in other people's bed.

• 27:08Paul Mecurio?

  That's all I'm saying.

• 27:09Speaker 02

  There's a biography of of Paul Erdes called The Man Who Loved Only Numbers. And that that was that is a pretty good description of it. I I met him once and he basically basically all the entire conversation was about math. He was not one for small talk or or anything.

• 27:22Neil deGrasse Tyson?

  From my notes here, we have problem ten twenty six. Is that is that the correct way to say that? And was that an Erdes problem?

• 27:31Speaker 02

  Right. So, yeah, so so recently, there's been a systematic effort to actually so. There's there's a website which has collected over a thousand Erdes problems.

• 27:41Neil deGrasse Tyson?

  Oh, so this is just a number. It's a rank. It's one thousand and twenty six. Right. That's all that is.

• 27:45Speaker 02

  Yeah. So, yeah, we just gave each Erdes problem a number. And this is the and this is the ticket that this number got. This problem got one thousand twenty six. And there's been a systematic effort in recent years to to solve these problems by any means possible. So some people use pen and paper. Some people use computers old school with with also computations. And some people are are using AI tools. And, yeah, there was a recent problem, ten twenty six, that that got solved by a combination of all of these. Lots of people threw out ideas on in in there. So there was a discussion forum and people used the latest AIs to gather some numerical evidence. I was involved a little bit.

• 28:24Paul Mecurio?

  And I can ask a question and it's relevant and not off track. So when you're collaborating that extensively, who is sort of? Who is curating all of that? Who is in charge of that? You need someone to sort of kind of manage that process, right?

• 28:38Speaker 02

  Yeah, so surprisingly, it's very decentralized. I mean, it's what, there was about five, six people involved and there was just a chat room. And we just all spoke, we contributed ideas. It was a very respectful environment. If we had to write it, we haven't written a paper. The problem was solved. We haven't decided to actually formally make an official paper. If we did, then we'd have to organize it a bit better. But a lot of these crowdsourced solutions, they're just like very spontaneous and very organic. I actually like this, this more to collaboration than than sort of a more directed top down thing where there's some principal investigator that sort of assigns tasks. We can do that too, but sometimes we get it from the crowd, which is great.

• 29:21Neil deGrasse Tyson?

  Yeah, and the P I won't necessarily always be the cleverest person. Someone can come in from somewhere else and jump right in on it. I will, I just want to show off a little bit of my childhood math wizardry. So 1026, that number is divisible by both 3 and 9.

• 29:40Speaker 02

  Okay.

• 29:41Neil deGrasse Tyson?

  Evenly divisible.

• 29:42Paul Mecurio?

  Leave it to you.

• 29:43Neil deGrasse Tyson?

  No, no, we just add up the digits and what do you get?

• 29:45Paul Mecurio?

  Okay, you get, you get 9.

• 29:48Neil deGrasse Tyson?

  9, so it's divisible by 9.

• 29:49Paul Mecurio?

  There you go.

• 29:50Neil deGrasse Tyson?

  And 9 itself is divisible by 3, so it's divided by 9. Did I get that right?

• 29:54Speaker 02

  Yes, yes, that is a classic test for divisibility by 5.

• 29:59Neil deGrasse Tyson?

  Exactly.

• 30:00Paul Mecurio?

  So, but a meaningful chunk of its value is forced to line up in some order, right? Isn't that what this problem says on some level?

• 30:07Neil deGrasse Tyson?

  Oh yeah, what was, we didn't say what the problem was.

• 30:09Speaker 02

  Ah, okay, yeah, so the part that you can play, you can phrase it as a game. Like suppose, suppose you have a pile of coins, like 100 coins. And you arrange them in stacks, like maybe you put 30 coins here and then 50 coins here and then 20 coins here. So you arrange them in stacks and some stacks are taller than others. And then I get to pick some of the stacks and claim those coins for myself. But I can only pick a sequence of stacks that's in increasing order or in decreasing order. I can't pick a sequence of stacks that goes up and down. So your aim is to lose as little money as possible. My aim is to get as much money from you as possible. So you want to arrange your stacks to sort of bounce up and down in such a way.

• 30:50Speaker 02

  It's hard for me to find a sequence of coins that go up or a sequence of coins that go down.

• 30:55Paul Mecurio?

  And it's no matter how scrambled the list is, you can pick this up decreasing and increasing order, no matter how scrambled it is, right?

• 31:02Speaker 02

  Right, yeah. So like, for example, if you're only allowed to divide your coins into three piles, I can always pick the two biggest ones, because the two biggest ones will either be an increasing or decreasing sequence. So I can always grab at these two thirds of your coins. But the more columns, the more stacks that you're allowed to make, the less and less I can win from you. And the question was exactly how much, what is the maximum loss you can have from this game? So what is the fair price to charge from me to play this game?

• 31:37Paul Mecurio?

  So it's like there's chaos in this order in this chaos, right? It's like a crazy group chat, but there's always one guy making sense a little bit?

• 31:46Speaker 02

  Yeah, yeah, yeah, yeah. So it comes actually from this theorem of Erdos and another mathematician, Zakeresh, that given any sequence of numbers that goes up and down, you can find within it some sequence that goes up for a long time or some sequence that goes down for a long time. Yeah, there is order and chaos, actually. That's almost exactly how it's described.

• 32:04Neil deGrasse Tyson?

  That's beautiful. That's a beautiful concept.

• 32:06Paul Mecurio?

  Well, I have a beautiful mind.

• 32:08Neil deGrasse Tyson?

  We should make a movie with that title. All right, so you got questions?

• 32:11Paul Mecurio?

  I have questions, great questions as always.

• 32:14Neil deGrasse Tyson?

  Patreon membership.

• 32:15Paul Mecurio?

  Yes, and they're always terrific. And let me jump right in here. This is JKW. Greetings, Professor Tao and Dr. Tyson. James from Norfolk, England here. My question is rather simple. How often are discoveries made in pure mathematics, which would appear to have no practical application, all the time, outside the realm of pure mathematics, but consequently, subsequently rather, find very useful applications in other fields? What is one of the most surprising examples of this?

• 32:44Neil deGrasse Tyson?

  I love that.

• 32:46Speaker 02

  Yeah, I know this happens all the time. Eugene Wigner, a physicist, once called this the unreasonable effectiveness of mathematics in the physical sciences. That there are lots of concepts that mathematicians played with for their own sake, and only later did, often decades later, did scientists realize they were valuable for other things. The most famous example is that non-Euclidean geometries.

• 33:11Neil deGrasse Tyson?

  There you go.

• 33:12Speaker 02

  People played with notions of curved space, not because they thought that the actual world was not Euclidean, but...

• 33:19Neil deGrasse Tyson?

  Wait, wait, back up for a sec. There used to be just regular Euclidean geometry, okay? Where everything is flat. Boring. That's where you have squares with 90-degree angles and triangles have, that the angles add to 180. That, there's that. And that has direct application, that, you know, geometry stands for earth measurement. Oh. Think about that. You're measuring surfaces. Oh, I didn't know that. Yeah, yeah, but, all right. So anyhow, so now...

• 33:45Speaker 02

  Yeah, so Euclidean geometry has all these amazing theorems, like some of the angles of triangles are always 180 degrees, it's a classic theorem. But they were very, very hard to prove, very complicated to prove. And mathematicians have tried for a long time to see if there was any simpler way to prove these, to prove these theorems. Like, if you take away some of the axioms of geometry, could you still, could you still prove these theorems are right angles and whatever? And then, by doing so, they discovered these non-Euclidean geometries, like where you're on a sphere or some hyperboloid instead of flat space, and now the sum of angles of triangles is not 180 degrees. The area of a circle is not pi r squared. And these are very weird geometries.

• 34:30Neil deGrasse Tyson?

  And parallel lines converge or diverge?

• 34:34Speaker 02

  Right, right.

• 34:35Neil deGrasse Tyson?

  Either or, yeah. Yeah, yeah, depending on the curvature of the space. Yeah, completely wacky stuff. And what were they thinking at the time? Were they thinking, oh, this is just pure math, no one will ever care, but I'm going to do it anyway?

• 34:46Paul Mecurio?

  I mean, it's really like, it's like you're, it's like you're creating, discovering things that you don't think you'll ever use. It's like either you're a genius or super anal retentive.

• 34:57Paul Mecurio?

  It's like you keep throwing stuff in your garage for 40 years, then you clean it out and you're like, "That's why I kept that hatbox. See, I knew," right? Isn't it like that on some level? Just say yes, Darren.

• 35:09Speaker 02

  Well, fiction and art is like that too. You explore worlds that aren't real, and there's value to that. So, yeah, so these were kind of geometries that weren't real in some sense, until Einstein, when he was developing general relativity, realized he needed a theory of curved space, and he asked a mathematician friend, Marcel Grossman, "Hey, do you know of any mathematics that deals with curved space?" He's, "Oh yeah, this non-including geometry stuff, this British bright guy Riemann who developed this wonderful Riemannian geometry," and he took a look and it was almost exactly what he needed, almost word for word, the language he needed to express the theory of relativity.

• 35:49Paul Mecurio?

  So it's almost like when you're doing pure mathematics, somewhere in your gut, there's an instinct that this, there's something this can be used for or will be used for, right? I would imagine?

• 35:59Neil deGrasse Tyson?

  But it's not what motivates, they're not motivated by that.

• 36:01Paul Mecurio?

  No, but I mean, once you get in it, you start to go, "This, I know this doesn't apply now, but there's something, this, isn't it as intuitive at some point?"

• 36:09Speaker 02

  Yeah, so my theory is that both pure math and science are motivated by compressing the world around them. So they have all this data, in the case of pure mathematicians, it's mathematical data, in the case of scientists, it's physical data, and they want some nice theory or explanation to compress all that data into something that they can understand. And somehow, when you compress, when you compress either theoretical data or experimental data, it often tends to compress to similar-looking theories, even if they come from completely different origins.

• 36:40Neil deGrasse Tyson?

  Next question.

• 36:41Paul Mecurio?

  Let's move on.

• 36:41Neil deGrasse Tyson?

  That's a good, that's a good one. Thank you. From Norfolk, England.

• 36:45Paul Mecurio?

  England. This is actually from the Turkish Republic of North Cyprus.

• 36:49Neil deGrasse Tyson?

  Wow, nice.

• 36:50Paul Mecurio?

  Absolutely, yeah, they have a great Home Depot there. Greetings, Gem here from Turkish Republic of North Asia. I hope you're all having a great day. Here's my question. If due to some reason, we were to adopt another base system instead of 10 and spent all these years doing math in that system instead of base 10, do you think there would be theories that we would fail to develop? Alternatively, do you think we would have maybe developed even better or more successful theories if humanity had been using another base number system all these years?

• 37:22Neil deGrasse Tyson?

  I love that. In fact, let's start out by asking you, when did the concept of base as a counting system reach maturity? That can have been from ancient times, was it?

• 37:36Speaker 02

  Well, I think like the Babylonians. I mean, every time you have to do either very big numbers or very small numbers, you know, there's a limit to... You can give every single number a different name, but that's really doesn't scale.

• 37:49Neil deGrasse Tyson?

  Yeah, every single numeral, a different name. Right, right, right, right.

• 37:52Speaker 02

  So the Babylonians had a base 60 system, for example. You know, the reason why an hour is 60 minutes and a minute is 60 seconds comes from the Babylonians.

• 38:00Neil deGrasse Tyson?

  So you get to 60 and then you start counting again.

• 38:03Paul Mecurio?

  Right, you say back a zero.

• 38:04Neil deGrasse Tyson?

  Yeah, so in base 10, when you run out of digits, you come back again, you start stapling the digits together to keep counting.

• 38:11Paul Mecurio?

  But why do you just say, Terry, that you either have to start with a big number or a small number? Can you elaborate on that a little bit?

• 38:17Speaker 02

  The way base systems work is that if you have a really, really big number, you try to break it up into tens or in the case of Babylonians, 60s. You know, so if you had 1,000 minutes, you want to describe 1,000 minutes, you break it up into hours and it would be like what, 16 hours or something, plus some change. So actually, humans have used multiple base systems. The Babylonians had base 60. Base 12, there's still remnants of base 12. We talk about dozens and gross, although gross is very archaic now. We used base 20, score, four score and seven years ago. It's a base 20 system. The French still use base 20 in the number system. Yeah, and computers use base 2. So, you know, binary is 0 and 1.

• 39:01Neil deGrasse Tyson?

  But does using one base or another hide certain access to discovery? Or reveal access to discovery? Because that's really what the question is getting at.

• 39:13Speaker 02

  I think it can slow it down or speed up a little bit. But you're still accessing the same numbers. So, you know, like, it's always true that a plus b is b plus a regardless of whether you use base 10 or base 20 or whatever. So, once computers came along, people did experiment with like, there was a base 3 system that the Soviets tried, didn't work very well. We found that binary works really, really well for computers. And so, yeah, once we had to do computation at massive scale, we found the best base was base 2. But base 10 is completely fine for everyday purposes.

• 40:14Paul Mecurio?

  Hello, Dr. Tyson. This is Raul. Hello, Dr. Tyson, Professor Tao. I am Raul. I have a few steps on the C train from the Natural History Museum. Oh, nice. My question is to all of you, if you could, which means I'll handle this, guys. If you could, how would you change the pedagogical landscape for mathematics education? I recall reading an old math text where a question at the end of the chapter had me write a short essay on the behavior of a function rather than do something more mechanical. This exercise was really quite beautiful and left me with far more intuition than if I had been asked to do something else.

• 40:51Neil deGrasse Tyson?

  Yeah, so what is the state of math education? Because there's this whole set, there's a whole demographic of the mathematically walking wounded. In their math class, they got bad grades, the teacher sucked, and now they have no appreciation for math the rest of their lives.

• 41:06Speaker 02

  Right, it is, it is a tough problem, especially since there's a shortage of really qualified math teachers. It's not a profession that is very appealing, often, that don't often get enough respect or salary for what they do. My theory is that different people have a different kind of math language. So, some people are very visual learners, and they like to see awesome pictures. Some people are very narrative driven, and they want to see a story. Some actually like working with symbols and solving puzzles, some like playing games, some like being competitive. So, there's many, many different ways to access math. But when you teach a class of thirty, forty kids, you can only teach one way.

• 41:46Speaker 02

  And inevitably, many of the students in that class will not, will not click with them, the style. So, if there's some way to have multiple pathways to learn the same material, maybe outside the classroom, some enrichment activities, I think that would help.

• 42:03Paul Mecurio?

  Well, you can, you can get into the mechanics of what you need to do to make it more interesting, but at the core of it, and I mean this seriously, and I've said this about Neil, it really is about the emotionality of the person delivering the information, right? If that person is in, I had a terrible science teacher in middle school. He smoked cigarettes, and he'd be like, "All right, we're gonna make a battery today." And he'd be, and I always say, if I had Neil as a science teacher, it's the only compliment I can give him, is I would probably be in science today. Because he emanates passion, and enthusiasm, and love, and fun. And at that point, you can come up with all the sort of mechanical mechanisms through which you teach math, but if it's being delivered in a dry way by someone who's indifferent

• 42:46Paul Mecurio?

  or disconnected, it is never gonna land on the student.

• 42:49Neil deGrasse Tyson?

  You're saying mathematicians are generally unfun people?

• 42:51Paul Mecurio?

  They're, they're all dead to me, I gotta be honest with you. No, no, I don't mean that about, I mean about, if any, any, any presentation to human beings comes through best, when the person delivering the information-

• 43:03Neil deGrasse Tyson?

  Whether or not it's math, whether or not it's math.

• 43:04Paul Mecurio?

  Whether it's math, science, if you're talking about English, if you're watching somebody interview somebody on TV, you're only compelled in that interview because, by that interview, because you're seeing a real relationship between two people, which emanates initially from the host. It's all about emotionality and then the information comes and is absorbed.

• 43:24Speaker 02

  Yeah. So yeah, if the teacher doesn't care, the students won't either. But yeah, but good teachers are so precious and so rare, hard to find.

• 43:32Neil deGrasse Tyson?

  So are you a good teacher?

• 43:35Speaker 02

  I try, yeah.

• 43:37Neil deGrasse Tyson?

  Like time for a couple more questions?

• 43:38Paul Mecurio?

  Sure, absolutely. This is William Warren, William from Abingdon, yeah, Abingdon, Maryland. Abingdon, Maryland. When you're working on a very difficult proof, how do you decide whether you're missing a key idea versus simply not pushing far enough with the tools you already have?

• 43:55Neil deGrasse Tyson?

  I love that.

• 43:56Paul Mecurio?

  Yeah.

• 43:57Neil deGrasse Tyson?

  Good, yeah, do you, because in physics, when we approach a problem, you first lay down all the parameters. And if you're missing a parameter and don't know it, you're not solving the problem.

• 44:07Paul Mecurio?

  Right.

• 44:07Neil deGrasse Tyson?

  So if you're solving a problem that's never been solved before, how do you gain the confidence that you have everything necessary at your disposal to actually solve it?

• 44:17Speaker 02

  So it's really important in math to not just prove positive results, but negative results. So results where you know you cannot prove the thing you want with the hypothesis you have because you can find some counter examples which satisfy all your hypotheses, but don't satisfy your conclusion. Now, these hypotheses may not be, correspond to the reward problem that you were working with, but by comparing that counter example with the reward problem, you can see what you're missing. So actually, a lot of math is actually exploring the negative space of what doesn't work and what you know doesn't work. And it's only after you sort of map out the negative space, can you see kind of the very narrow path, which dodges all the pitfalls and gets you to your goal.

• 45:01Paul Mecurio?

  Did you ever just like say, I'm going to write it out cleaner and neater and then the answer will appear? Did you ever just like kind of clarify it a little bit?

• 45:10Speaker 02

  Sometimes, yeah, you can just, what's the modern term, like raw dog it or something? Yeah.

• 45:15Neil deGrasse Tyson?

  Raw dog, oh.

• 45:16Speaker 02

  Yeah. That's what the young kids say. Okay, but.

• 45:20Neil deGrasse Tyson?

  The young, but what you did describe was very Sherlock Holmesian, because Sherlock Holmes is once you've removed all. Everything that's not possible, then all that's left is what is possible. Yeah, I mangled it, but that's the idea.

• 45:33Paul Mecurio?

  Yeah.

• 45:34Neil deGrasse Tyson?

  Yeah.

• 45:34Speaker 02

  Right. Yeah, so it's good to not be emotionally invested in one outcome that this has to be true or this has to be false, but to actually actively work to prove both the one conclusion or the opposite. And sometimes you get surprised, sometimes your initial guess is wrong, and actually, the answer is the opposite of what you thought it is.

• 45:51Paul Mecurio?

  It sounds like at some point, you're not doing math, you're just seeing if the universe respects effort.

• 45:57Speaker 02

  Yeah, yeah.

• 45:59Paul Mecurio?

  Come on, man, give it to me. I've tried so hard here.

• 46:01Neil deGrasse Tyson?

  I'll throw your bone on this one.

• 46:03Paul Mecurio?

  Come on. I got a headache. I'm supposed to take my wife to the ballet. I'm not going.

• 46:09Speaker 02

  Yeah, you can sometimes feel that these problems have agency and sometimes some malice in some cases.

• 46:18Paul Mecurio?

  We have another one?

• 46:19Neil deGrasse Tyson?

  Yeah, yeah, one more.

• 46:20Paul Mecurio?

  Joel, hello, Dr. Tyson, Professor Tao. Joel here from Chambersburg, Pennsylvania. Will a new math system have to be invented the more we explore space? It seems as if there are a lot of places in the universe where our math simply just breaks down.

• 46:37Neil deGrasse Tyson?

  Wow. Okay, so let me give a lead in, and I want to.

• 46:41Paul Mecurio?

  Nice intersection.

• 46:42Neil deGrasse Tyson?

  Yeah, let me tee him up here. So it's not where our math breaks down, which in fact it does, but you don't blame the math for that. The math is just a representation of the physical model that we have created for the universe. Right? So I have a physical model, and I say, I want to represent it using math. And then I do that, and I calculate with it, hey, I'm getting some good answers here. And like, as Einstein did, you get some good answers. And then you reach the center of a black hole, and you end up dividing by zero, and that's no-no. And so the math blows up. But I'm not blaming the math, because that was just the math I used to represent

• 47:24Neil deGrasse Tyson?

  my idea, and I had to modify my idea. Don't blame this gentleman here, just because your equation of your idea failed.

• 47:31Paul Mecurio?

  No, no, I'd blame him.

• 47:32Neil deGrasse Tyson?

  So in the broader context, could there be simply missing mathematics?

• 47:39Neil deGrasse Tyson?

  That in the same way, the non-uklidian geometry, we're scratching our heads over dark matter, dark energy, singularities, and the limits of our physical theories. Is there a new kind of math that we're just waiting for you guys to invent that can help us out?

• 47:57Speaker 02

  That I believe so. Yeah, so the math we have has become extremely good at explaining most of the universe. So as long as you're not at extremely very tiny scales and extremely high temperatures or like a black hole, like the rest of the universe, the math checks out. You know, we can make measurements of galaxies, you know, a billion light years away and all the measurements line up with what our current cosmological models give the math works. But yeah, there are some, the early universe and the center black holes. The current math is not giving us answers that make sense. And yeah, in physics, I think the biggest problem is that we don't have a theory of quantum gravity,

• 48:41Speaker 02

  which is the theory that would govern extremely strong gravitational fields at extremely small scales. And I think the current theory is that we have to abandon our notions of space and time. Even non-uklidian geometry will not be enough to understand what quantum spacetime looks like. And Zippin proposed, string theory is the most famous, but nothing has really stuck as being convincingly the answer.

• 49:07Neil deGrasse Tyson?

  One of your own people was right in the middle of this, Ed Witten, right? He's a mathematician who lent his efforts to string theorists.

• 49:15Speaker 02

  Yeah, he's had a lot of ideas. Unfortunately, there was some, string theory has very pretty math, but it doesn't seem to be fitting reality as much as the string theorists had hoped. So sometimes even if the math is pretty, it's not the right answer.

• 49:28Neil deGrasse Tyson?

  So we can type one more question.

• 49:29Paul Mecurio?

  One more question. This is a good one. This is Hayden from Hawaii. Like Dr. Tyson, my favorite movie is The Matrix. Is there a mathematical way to prove or disprove we are not in a simulation? Is anyone working on this? Now, if you answer no, that's exactly what the simulation would want you to say, which means we're in a simulation. Ah ha! I got you. Come on.

• 49:54Neil deGrasse Tyson?

  You gotta help us out because a lot of people have existential angst over that question.

• 50:00Speaker 02

  Right, right. It's a great question. We may not have enough. The bottleneck is not math. So there is a science, like if there's competing hypotheses explaining the world. So you're in a simulation, or the universe was created by a deity, or whatever. There's a branch of statistics called Bayesian probability, which can help you guide which of these outcomes is more possible. You have to lay out all the possible scenarios that could be true. Assign some prior probability to each being true. And then take all the data that you have, and there's a formula that allows you to take, for every observation that you have, update.

• 50:44Speaker 02

  So some data confirms some theories and makes their probability go up. And some data makes some theories less likely, and their probability goes down. And in principle, if you could compute everything, you could end up and say, oh, now I'm 20% confident I'm in simulation, or 80% that the universe is real, or whatever. But the problem is that we don't know all the possible different types of universes that could happen. And we don't know what their prior probabilities are. And there are just so many of them. We can't compute how many of them would replicate a world that looks like ours. So while people attempt to do these calculations, there's just so many gaps, and there's all the implicit biases in how you choose which universes. You know, maybe some hypotheses you have implicitly set would fail,

• 51:29Speaker 02

  or something you're biased to make succeed.

• 51:32Paul Mecurio?

  You can't do it, because if you're trying to prove that this is, that it's fake, the proof that you have is fake. So you're caught in this loop, so you have... But why would the proof be fake? Because you're within a simulation that's fake, so the proof within the simulation is fake, right? Isn't that the argument? I mean, it's got the same credibility as like, as an email from a Nigerian prince at this point, right? That's very dated. Thank you. How about Amazon support? How about that? You're still getting Nigerian prince emails? I am. That was like from 1994. He doesn't have any friends. Like, two years after email. If this were fake, the proof would be fake, which means that reality's not reality. So we don't even know if we're in reality.

• 52:12Speaker 02

  Right. So you could never rule out hypotheses with 100% certainty, because whatever data you have collected could itself be faked, as you said. But it just may take enormous effort. Like, if you collect more and more data, and it keeps pointing to a different hypothesis that the universe is real... You know, whoever's doing the simulation will have to keep faking more and more data to consistently do a complete, a complete different outcome. And at some point, it's why would they go through so much effort?

• 52:40Neil deGrasse Tyson?

  So there's, there's another pathway into this, which is when you program a world, there's a, there's a part of the program where you set up the basic parameters for it. You know, how big is it? How old is it? What's the passage of time?

• 52:57Paul Mecurio?

  Population.

• 52:58Neil deGrasse Tyson?

  Population. You just set it up and you'd take it from there. Well, in our world, there are, we can measure, for example, the energy of cosmic rays. Just take that as a thing. Very, very high energies. You can imagine, suppose the energy distribution has an abrupt cutoff for no obvious reason. Maybe that's the programmers' limit because they didn't think we'd ever get there. It's like, it's like a Truman Show.

• 53:25Paul Mecurio?

  Oh.

• 53:26Neil deGrasse Tyson?

  He's not gonna get to the, to the edge. So let's just put, so you get to the edge and oh my gosh.

• 53:32Paul Mecurio?

  We didn't think.

• 53:33Neil deGrasse Tyson?

  This is the edges of the programmers' parameters.

• 53:36Paul Mecurio?

  So you see the flaw in the program and then you know you're in a program.

• 53:38Neil deGrasse Tyson?

  The limits of the program. What do you think of that possibility? Because you can't program infinity, right?

• 53:43Speaker 02

  Yeah. So it seems like if the universe was a simulation, whoever designed it has great attention to detail.

• 53:49Paul Mecurio?

  Yes.

• 53:50Speaker 02

  At really fine scales or something, you still see the same laws of physics that you see, you know, it's not like a cheaply made movie where, where once, once you're out of, out of shot or something, everything's all made of cardboard. It wasn't made by a lazy simulator. It was made by a very obsessive simulator, if it was.

• 54:08Neil deGrasse Tyson?

  This is the first time I've ever heard the simulator complimented.

• 54:11Paul Mecurio?

  There you go. Well, maybe we are in a simulator, maybe you are in a program. I mean, I'm getting endless spam calls about a loan that I supposedly asked about and took out or whatever.

• 54:22Neil deGrasse Tyson?

  That's a parallel universe. Where the Paul McCurry who is in that universe owes money.

• 54:27Paul Mecurio?

  It's three times a day.

• 54:30Paul Mecurio?

  I'm telling you, we're in a simulation controlled by the banks.

• 54:35Speaker 02

  The world is feeling less real these days, I think, just because there's so much simulated everything, unfortunately.

• 54:40Neil deGrasse Tyson?

  Yes, it is. And thank you and good luck. I think sometimes you need a little bit of that as you explore that moving frontier.

• 54:48Speaker 02

  Thank you.

• 54:49Neil deGrasse Tyson?

  And Paul, always good to have you, man.

• 54:51Paul Mecurio?

  Good to have you.

• 54:52Neil deGrasse Tyson?

  Is your show still on the road?

• 54:53Paul Mecurio?

  Permission to speak. Yeah, my Broadway show, directed by Frank Oz, we're touring with that. I'm doing my podcast, Inside Out with Cosmic Queries.

• 55:00Neil deGrasse Tyson?

  And I'd love that. And Permission to Speak, you engage the audience.

• 55:02Paul Mecurio?

  I do. I basically...

• 55:04Neil deGrasse Tyson?

  Which is a very important bit of improv.

• 55:06Paul Mecurio?

  Yeah. So we basically found that, you know, everybody's got a story and we're in a world where people want and need to tell their stories and people share and at the end of the show...

• 55:14Neil deGrasse Tyson?

  And you can add some math to your...

• 55:15Paul Mecurio?

  Yeah, we'd love to have Terry come on stage. Ladies and gentlemen, welcome the T-Man!

• 55:23Speaker 02

  Anything's possible in this simulation.

• 55:26Paul Mecurio?

  Ah, there you go.

• 55:28Neil deGrasse Tyson?

  That's the right answer to everything.

• 55:30Paul Mecurio?

  Great.

• 55:31Neil deGrasse Tyson?

  All right. This has been StarTalk, Cosmic Queries edition on mathematics of all things. Until next time, Neil deGrasse Tyson bidding you to keep looking up.