Chapter 1: What is the main topic discussed in this episode?
Paul, we have revisited the universe of math. Yeah, but really drilled down and really applied ourselves. Because that's how we roll. Yeah. Coming up on StarTalk. Welcome to StarTalk. Your place in the universe where science and pop culture collide. StarTalk begins right now. This is StarTalk. Neil deGrasse Tyson, your personal astrophysicist.
And we're going to have a Cosmic Queries edition on the subject of mathematics. Why are you laughing at me like that?
Apparently you're going to scare people with this.
Everybody thinks there's a math quiz coming up.
That was a Halloween laugh, wasn't it? It was. I got Paul Mercurio here. How are you doing, man? I'm good, man. Good to see you. Yeah, you got your podcast. What was it called again?
Inside Out with Paul Mercurio.
Inside Out.
Did you get Disney permission for that? I did not. Well, thanks for bringing that up. I'm going to be getting sued right after this.
And you are out of a job after May.
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Chapter 2: How does mathematics relate to dark matter?
Yes, the Late Show got canceled. So I work on the Late Show. You've been on the Late Show a bunch. We love you there. Yeah. Well, not everybody. No, and yeah.
You've been with... With Stephen Colbert since the Colbert Report. Since the Daily Show. The Daily Show, yes.
I started at the Daily Show as one of the original writers, performers there. He came in as a performer. You predate him on the Daily Show. I'm old school. I'm OG. And we actually shared an office together. We'd 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. 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 kind of, yeah. Okay. So I'll be at your house cutting your lawn for two bucks. Okay. I hope our guests need some help. I'll go to California. It doesn't snow out there, but I'll shovel anyway. All right. And by the way, Barron.
Oh, you did get the title of Baron. You knighted me, Baron. 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. Yeah, this is fascinating. Ever since high school. Brilliant. I've been a big fan of mathematics. Even the obscure math that doesn't relate to anything ever, but it's still fun.
Yeah. But, of course... 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-finality to it. It can take you everywhere, right?
Yeah, yeah, everywhere and anywhere and everywhere. Yes, exactly. Yeah, yeah. So, you know what we found? We found like a badass mathematician. Ooh. Yeah. That sounds like a good movie title. Is he also an assassin? We cannot divulge that publicly. We have Terence Tao. Terence, did I pronounce your name correctly? That's correct. Yes, please speak up. No, that's wrong.
That's not how you pronounce your name.
You are professor of mathematics at UCLA. That is not a community college in Oxnard. Yeah, UCLA Community College. You're professor of mathematics at... UCL, that's officially University of California, Los Angeles. Yes, it is. And here's the best part. Director of Special Projects at IPAM, Institute for Pure and Applied Mathematics.
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Chapter 3: What are the differences between pure and applied mathematics?
And they said, thank you very much. And I didn't hear from them for two years. And then this movie came out. So I was caught unawares. But it did actually come from me.
So before we go to our question base, there's one more. Just tell me about the Erdos problems.
Right. So Paul Erdős was this Hungarian mathematician. He was rather extreme. So mathematicians have a reputation for being a little idiosyncratic, but he was rather extreme even among mathematicians. He didn't own a home. He would travel the world constantly and crash on other mathematicians' couches basically for his whole life.
But while doing so, he would talk math with them, and they would often write papers. He has like 2,000 or 3,000 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 get $25 or something if you can solve this problem.
And in fact, many of these problems did get solved and Erdős would send them a check with that amount of money. But these checks were almost never cashed because they were more valuable framed on the wall as someone who had solved an Erdős problem.
I want to be that famous.
I can pay people and they don't cash the check. Well, maybe if Mr. Smarty Pants cashed the checks, he could buy himself a house and not have to sleep in other people's bedrooms. No.
That's all I'm saying. There's a biography of Paul Erdos called The Man Who Loved Only Numbers. And that is a pretty good description of it. I met him once and basically the entire conversation was about math. It was not one for small talk or anything.
From my notes here, we have problem 1026. Is that the correct way to say that? And was that an Erdos problem? Right.
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Chapter 4: How do mathematicians approach unsolved problems?
So while people attempt to do these calculations, there's just so many gaps and sort of implicit biases in how you choose which universes, you know, maybe some hypotheses you have implicitly set up to fail, or some that you're biased to make succeed.
You can't do it because if you're trying to prove that it's fake, the proof that you have is fake. So you're caught in this loop. 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 an email from a Nigerian prince at this point, right? That's very dated. Yeah. Thank you.
That's like from 10 years ago. 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 is not reality. So we don't even know if we're in reality.
Right. So you could never rule out a hypothesis 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 completely different outcome. And at some point, it's just why would they go through so much effort?
So there's another pathway into this, which is when you program a world, 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? Population. You just set it up and you take it from there. Well, in our world, we can measure, for example, the energy of cosmic rays. Just take that as a thing.
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