Is the Universe a Math Problem? With Terence Tao

26:24I 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 an actual number. And that's the Collapse conjecture. 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?

26:59Because it starts with such a basic premise. That's the part that's confounding me and I guess obviously others. You are now confounded. Thank you very much. Can I have my official spherical cow, please? Yeah, but what is that about? So it's part of a general phenomenon called chaos. So you can have very simple operations, like halving a number of its even or three and adding one if it's 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 amounts of complexity.

27:40And so sometimes you don't. Sometimes you get these universal laws like these bell curves and things settle down. But sometimes you just get this enormous complexity. The act of reproduction and splitting DNA is fairly simple, but it leads to immense biodiversity. We have computers. We have AI. Why hasn't the Collatz conjecture been affirmed? Well, because we have to check an infinite number of cases. We'll get to work on that. I was going to say, there's a thing called a computer. Look at my finger. Just go like that. Why don't we crowdsource it? All right. It's still not an infinite number of people, but there's quite a bit of computing power out there.

28:19You know, the SETI Institute did it where you would upload software and they'd give you data. And while you were not using your computer on screensaver, it was using your CPUs to calculate. Yeah, so there was a project, I think it was called Collapse Grid, which was exactly that. Like Citi at home, but for Collapse. And it did extend the numbers. So a couple 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. So if you want to roll out all the numbers, you need proofs. You need to use mathematical laws and work for all numbers.

29:03Otherwise, it's not elegant and it's not even interesting. Well, it's not elegant. It's like you're putting a bunch of crazy ingredients in a blender and it always outputs oatmeal every time. Some problems you can only solve by brute force. Are we any closer to solving this conjecture? I mean, how close? So I worked on this a couple of years ago. I proved a result that if you take a really large number, like 10 to 15, 10 to 20, whatever, I could show statistically that 99 % of all numbers that are very, very big would become very, very small, become much smaller than where they started. I couldn't show they hit one, but I could show that 99 % of all numbers become as small as, say, the logarithm of their number.

29:45So like 10 to the 20, I could show it drops down to 20. 10 to the 100 drops down to 100. You know what? I'm going to use a term from your world. Why don't you apply yourself? Yeah. So in mathematics, we very much value partial progress. They're very good. Yeah. We can't solve completely, but we are happy with half a loaf or 99 % of a loaf because someone else can build upon that. Do you like those math movies like The Beautiful Mind and the math movie? Good Will Hunting. 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? I enjoy those movies mostly for the non-math part of it.

30:24Now, maybe if there's an expert in schizophrenia, they would be complaining about that, but saying that the math was very cool. I think this is common. I have a brother who did some CGI back in the day, and every time it's animated a movie, he cannot enjoy the special effects because he knows how they were made. So I remember watching one of these movies, and it's a movie called Gifted. It stars Chris Evans and this amazing young character. who was supposed to be this math genius, and her mother was a math genius, and she was working on an unsolved math problem. And it actually was a problem that I worked on.

31:01And at some point, they were going to review some of her notes on how she was making progress was the problem. And I was actually quite interested to see what they would do. And they actually showed a little snippet of her notebook. And it was actually some equations from one of my papers. Oh, wow. Two years before the movie was made, I actually got an email from a director saying we're making a movie about a gift to get in math. Could you supply some samples of some math computations that would look good? And I actually supplied some from my own work, some from others. And they said, thank you very much.

31:37And 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 Methodician. He was rather extreme. So Methodicians have a reputation for being a little idiosyncratic, but he was rather extreme even among Methodicians. He didn't own a home. He would travel the world constantly and crash on other Methodicians' couches, basically, for his whole life. But while doing so, he would talk math with them, and they would often write papers.

32:13He has like 2 ,000 or 3 ,000 papers. He's one of the most prolific Methodicians 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 than they were framed on the wall as someone who had solved an Erdős problem. I wouldn't be that famous. I could pay people and they don't cash the checks.

32:44Maybe if Mr. Smarty Pants cashed the checks, he could buy himself a house and not have to sleep in other people's living. That's all I'm saying. There's a biography of a poet called The Man Who Loved Only Numbers. And that was a pretty good description of it. I met him once and basically the entire conversation was about math. He 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. So, yeah, so recently there's been a systematic effort to actually, so there's a website which has collected over 1 ,000 Erdos problems.

33:24Oh, so this is just a number. It's 1 ,026. Right, that's all that is. Yeah, so, yeah, we just gave each Erdos problem a number. And this is the ticket that this number got. This problem got 1 ,026. And there's been a systematic effort in recent years to solve these problems by any means possible. So some people use pen and paper. Some people use computers old school with lots of computations. And some people are using AI tools. And, yeah, there was a recent problem, 1026, that got solved by a combination of all of these. Lots of people threw out ideas. There was a discussion forum and people used the latest AIs to gather some numerical evidence.

34:06I was involved a little bit. 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. 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 contribute 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 it official paper.

34:44If we did, then we'd have to organize it a bit better. But a lot of these crowdsourced solutions, they're just actually very spontaneous and very organic. I actually like this more collaboration 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. Yeah, and the PI won't necessarily always be the cleverest person. someone can come in from somewhere else and jump right in on it i i will i just want to show off a little bit of my childhood math wizardry so 1026 that number is divisible by both three and nine okay evenly divisible leave it to you no no we just add up the digits and what do you get okay you get uh you get nine nine so it's divisible by nine there you go and nine itself is divisible by three so it's divided by nine did i get that right yes yes that is a classic classic test for divisibility exactly so but like 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 yeah what was we didn't say what the problem was ah okay yeah so the part you can play it you can phrase in terms of a game like suppose suppose you have a pile of coins um like 100 coins um and you arrange them in stacks like maybe you put 30 coins here and then 50 coins here and then 20 coins here.

36:06So 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 that it's hard for me to find a sequence of coins that go up or a sequence of coins that go down. 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?

36:46Right. Yeah. So, 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 least two thirds of your coins. But 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? So it's like this chaos in this order, in this chaos, right? It's like a crazy group chat, but there's only one, always one guy making sense a little bit.

37:30Yeah, yeah, yeah, yeah. So it comes actually from this, this, this theme of Erdős and other Methodist-Sekhavish, yeah, 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. That's beautiful. That's a beautiful concept. Well, I have a beautiful mind. We should make a movie with that title. So you got questions. I have questions. Great questions as always. From our Patreon membership. Yes, and they're always terrific.

38:00And we'll 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, not 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? I love that. 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, often decades later, did scientists realize they were valuable for other things.

38:51The most famous example is that non-Euclidean geometries. There you go. People play with notions of curved space, not because they thought that the actual world was not Euclidean. Wait, wait, back up for a sec. There used to be just regular Euclidean geometry, where everything is flat. Boring. That's where you have squares with 90 degree angles and triangles that the angles add to 180. There's that. And that has direct application that, you know, geometry stands for earth measurement. Oh. Think about that. You're measuring surfaces. All right. So anyhow, so now. Yeah. So Euclidean geometry has all these amazing theorems, like the sum of the angles of triangles, always 100, 100 degrees.

39:35It's a classic theorem. But they were very, very hard to prove, very complicated to prove. and mathematicians are trying for a long time to see if there was any simple 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 that space. And now the sum of angles of triangle is not 180 degrees. The A of a circle is not pi r squared. And these are very weird geometries.

40:14And parallel lines converge or diverge. Right, right. Either or, 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? I mean, it's really like, 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. 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 hat box. See, I knew, right?

40:49Isn't it like that on some level? Just say yes, Darren. 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, I think Marcel Grossman, hey, do you know of any mathematics that deals with curved space? He said, oh, yeah, there's this non-Euclidean geometry stuff. This is a British bright guy, Riemann, who developed this wonderful Riemannian geometry.

41:24and he took a look and it was almost exactly what he did almost word for word the theory the language he needed to uh to to express the theory of relativity 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 but it's not what motivates they're not motivated by that no but i mean once you get in it you start to go with this i know this doesn't apply now but there's something this isn't it as intuitive at some point yeah so My theory is that both pure math and science are motivated by compressing the world around them.

42:00They have all this data. In the case of pure mathematicians, it's mathematical data. In the case of scientists, it's physical data. They want some nice theory or explanation to compress all that data into something that they can understand. Somehow, 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 knowledge. Next question. Let's move on. These are good. That's a good one. Yeah. That was from Norfolk, England. England. This is actually from the Turkish Republic of North Cyprus. Whoa.

42:33Yeah. Nice. Absolutely. Yeah. They have a great Home Depot there. Greetings. Jem here from Turkish Republic of North Cyprus. 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? I love that. In fact, let's start out by asking you, when did the concept of base as accounting system reach maturity?

43:17That can't have been from ancient times, was it? 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 really doesn't scale. Every single numeral a different name. Right, right, right, right. 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. So you get to 60 and then you start counting again. Right. So you're back at zero. Yeah. So in base 10, when you run out of digits, you come back again, you start stapling the digits together to keep counting.

43:55But 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? 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. So if you have a thousand minutes, you want to describe a thousand minutes, you break it up into hours and it would be like 16 hours or something plus some change. so actually humans have used multiple base systems the babylonians had base 60 um base 12 we still there's still remnants of base 12 you know we talk about dozens and gross although gross is very archaic now um we use base 20 uh score in four score and seven years ago it's a base 20 system um the french still use base 20 in their number system um yeah and and computers use base two um so um you know binary zero and one 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 i think it can slow it down or speed up a little bit um but you're still accessing the same numbers so um 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.

45:12So once computers came along, people did experiment with, like there was a base three system that the Soviets tried. It 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 two. But base 10 is completely fine for everyday purposes.

45:46You may have heard the best voice in show business, Morgan Freeman, talking about a serious and underdiagnosed heart condition that's often missed, a TTR cardiac amyloidosis or a TTRC-M. It's a condition that can greatly disrupt your life with symptoms like severe fatigue, shortness of breath and carpal tunnel. If left untreated, a TTRCM may become serious, leading to a shorter lifespan. A Truby helps adults with a TTRCM live longer and have fewer hospitalisations due to heart issues, so you can focus more on living for what you love. Tell your doctor if you're pregnant, plan to become pregnant or are breastfeeding, and about the medications you take.

46:32The most common side effects were mild and included diarrhoea and abdominal pain. If you have a TTRCM, talk to your cardiologist about Atruby and visit atruby.com slash podcast. That's A-T-T-R-U-B-Y dot com slash podcast to learn more. It's time to get busy living. Brought to you by Bridge Bio. These days, we're used to getting things delivered on demand. groceries, a new gadget, or the latest book, expanding your view of the universe. And now you can add T-Mobile 5G home internet to that list. Just order from T-Mobile and enjoy same-day delivery with DoorDash. And you can set it up yourself in about 15 minutes, no advanced engineering degree required.

47:21That means more time doing the things you actually enjoy, like streaming a space documentary or going down a rabbit hole about exoplanets, asteroids, or whatever's pulling your curiosity. And those online explorations are a lot easier with the fastest 5G home internet. So if you're moving into a new place or just ready to upgrade your connection to something a little more advanced, visit t-mobile.com slash home internet to check availability and get your home internet delivered today. Same-day delivery for most internet-eligible customers. See if it's an option during checkout. Fastest according to Ookla Speedtest Intelligence Data, second half 2025.

48:08All rights reserved. Summer always changes how you get dressed. You want pieces that feel lighter and more breathable, things that are easy but still put together. That's where Quince comes in. They focus on high-quality essentials that feel and look amazing. Think breathable linen and soft organic cotton. And Quince goes way beyond clothing. They have customer-pollstered sofas, ceramic cookware, premium bedding, and even more for your home. It's the kind of brand you end up recommending to everyone for everything, which is what I'm about to do right now. Because speaking of breathable, easy summer clothing, without even knowing I was going to do this ad, I just picked up four linen pants from Quince.

48:51Why? Because I've been shopping with Quince for years and I was delighted to see that they are now supporting StarTalk. So if you want to look good like me, if you want to elevate your summer wardrobe, even though let's be for real, you're not going to look as good as me. Go to Quince.com slash StarTalk for free shipping on your order and 365 day returns. Now available in Canada, too. That's Q-U-I-N-C-E dot com slash StarTalk for free shipping and 365 day returns. Quince.com slash StarTalk. And guess what? You're going to look even better than me.

49:35Hello, 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 is really quite beautiful and left me with far more intuition than if I had been asked to do something else.

50:12Yeah. 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. Right, 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, they 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.

50:50Some 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 30, 40 kids, you can only teach one way. And inevitably, many of the students in that class will not it 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. Well, you can get into the mechanics of what you need to do to make it more interesting.

51:29But 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 engaged, I had a terrible science teacher in middle school. he smoked cigarettes and he'd be like, all right, we're going to make a battery today. 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.

52:04But if it's being delivered in a dry way by someone who's indifferent or disconnected, it is never going to land on the student. You're saying mathematicians are generally unfun people. They're all dead to me. I gotta be honest. No, no, I don't mean that about, I mean about if any presentation to human beings comes through best when the person delivering the information. Whether or not it's math. 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 by that interview because you're seeing a real relationship between two people which emanates initially from the host.

52:39it's all about emotionality and then the information comes and is absorbed yeah so yeah if the teacher doesn't care the students won't either but yeah good teachers are so precious and so rare uh hard to find so are you a good teacher i try yeah time for a couple more questions sure absolutely this is william warren uh william from uh abby abbingdon yeah abbingdon 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 i'd love that yeah 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 right 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.

53:38So 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 hypotheses you have because you can find some counterexamples which satisfy all your hypotheses but don't satisfy your conclusion. Now, these hypotheses may not correspond to the real-world problem that you were working with. But by comparing that counterexample 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.

54:13And it's only after you sort of map out all the negative space can you see kind of the very narrow path, which dodges all the pitfalls and gets you to your goal. Do you ever just like say, I'm going to write it out cleaner and neater, and then the answer will appear do you ever just like kind of clarify it a little bit sometimes yeah you can just uh what's what's the modern to like raw dog it or something yeah um that's what the young kids say okay but 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.

54:55Right. 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're surprised. Sometimes your initial guess is wrong, and actually the answer is the opposite of what you thought it is. It sounds like at some point you're not doing math. You're just seeing if the universe respects effort. Yeah, yeah. Come on, man, give it to me. I've tried so hard here. I'll cut you out. I'll throw your bone on this one. Come on. I got a headache. I'm supposed to take my wife to the ballet.

55:28I'm not going. Yeah, yeah. You can sometimes feel that these problems have agency and sometimes some malice in some cases. Malice. We have another one? Yeah, yeah. Good. One more. 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. Wow, okay, so let me give a lead in, and I want to... Nice intersection. 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.

56:14The math is just a representation of the physical model that we have created for the universe right so so i have a physical model 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 up 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 the math i used to represent my idea and I need to modify my idea. Don't blame this gentleman here just because your equation of your idea failed.

56:52No, no, no, I'd blame him. So in the broader context, could there be simply missing mathematics that in the same way the non-Euclidean geometry, we're scratching our heads over dark matter, dark energy, singularities, and they're 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? 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 or extremely high temperatures or like a black hole, like the rest of the universe, the math checks out.

57:36We can make measurements of galaxies 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 of 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, 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-euclidean geometry will not be enough to understand what what quantum space-time looks like and the proposed string theory is the most famous but nothing has really stuck as being convincingly the answer one of your own people was right in the middle of this Ed Witten right he's a mathematician who lent his his efforts to string theorists yeah he's had a lot of ideas unfortunately there was some string theory has a very pretty math but it doesn't seem to be fitting reality as much as as a string theorist had hoped so sometimes even if the math is pretty it's not the right answer so we get time for one more question one more question this is this is a good one this is Hayden from Hawaii like Dr.

58:55Tyson 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. Aha! I got you! Come on! You've got to help us out on this because a lot of people have existential angst over that question. 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.

59:48You have to lay out all the possible scenarios that could be true, assign some prior probability to each being true. Then take all the data that you have. There's a formula that allows you to take for every observation that you have, update some data confirms some theories and makes their probability go up. Some data makes some theories less likely and it probably goes down. 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.

1:00:30And we don't know what their prior probabilities are. And there's 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 sort of implicit biases in how you choose which universes. Maybe some hypotheses you have implicitly set up to fail. or something 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?

1:01:09Isn'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. 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.

1:01:42But 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 different outcome. And at some point, it's 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.

1:02:22Well, 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 programmer's limit because they didn't think we'd ever get there it's like it's like a truman show oh he's not going to get to the to the edge yeah so let's just so yeah you get to the edge and oh my gosh we didn't think the edges of the programmer's parameters so you see the flaw in the program and then you know you're in a program the limits of the program what do you think of that possibility because you can't program infinity right yeah so it seems like if the universe was a simulation, whoever designed it has great attention to detail.

1:03:10Yes. 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 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, this is the first time I've ever heard the simulator complimented. 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 a parallel universe with a paul mercurio in that oh my god it's three times a day i'm telling you we're in a simulation controlled by the banks the world is feeling less real these days i think just because there's so much simulated everything unfortunately yes it is and thank you and uh good luck i think sometimes you need a little bit of that as you explore that moving frontier.

1:04:10Thank you. And Paul, always good to have you, man. Good to have you. Is your show still on the road? Permission to Speak. Permission to Speak. Yeah, my show directed by Frank Oz. We're touring with that. I'm doing my podcast, Inside Out with Paul McCurrey. And I love that. And Permission to Speak, you engage the audience. I do. I basically - Which is a very important bit of improv. Yeah. And so we basically found that everybody's got a story and we're in a world where people want and need to tell their stories and people share. And you can add some math to your... Yeah, we'd love to have Terry come on stage.

1:04:40Ladies and gentlemen, welcome to T-Man! Anything's possible in this simulation. There you go. That's the right answer to everything. Great. 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.

1:05:16This episode of StarTalk is brought to you by six all-new McCafe drinks at McDonald's. We're talking crafted sodas made with your favorite sodas and topped with velvety cold foam, like a Spriteberry Blast made from Sprite and blueberry raspberry syrup. Don't miss the Dirty Dr. Pepper or Orange Dream, too. And there are refreshers made from fruit flavors and add-ins like Popping Boba and Freeze-Dried Dragon Fruit. Try the Blackberry Pass and Fruit Refresher, Mango Pineapple Refresher, or Strawberry Watermelon Refresher with Freeze-Dried Strawberries. Try all new McCafe drinks now at McDonald's.

1:05:54Prime Day is June 23rd through the 26th. These deals are so appealing. like portable steamers for steaming. Whoa, did I just sing soprano? I think I'm breaking into song. Epic deals on air fryers, vacuums, and skincare. I can't stop singing. Shop Epic Deals this Prime Day, June 23rd through the 26th. I think that's it. Nope, there's more. Luggage, smart glasses.