Cosmic Queries – Understanding Infinity with Stephon Alexander

Hey, StarTalkians, Neil here. You're about to listen to an episode specially drawn from our archives to serve your cosmic curiosities. The archives run deep. If you enjoy this, take a peek at the full catalog on your favorite podcast platform. There's a lot there to tickle your geek underbelly. Check it out. Welcome to StarTalk, your place in the universe where science and pop culture collide. StarTalk begins right now. This is StarTalk. Neil deGrasse Tyson here, your personal astrophysicist. We're doing another Cosmic Queries. These have become fan favorites. I guess I understand why, because you get to participate. Well, actually, if you're a Patreon member, you get to participate in asking those questions at the entry level of Patreon. Today's topic, infinity, with my friend and fellow physicist, Stefan Alexander. We'll get to him in a moment. Let me introduce my co-host, Nagin Fassad. Nagin, it's been so long. Hello. Yes, I'm your honorary astrophysicist comedian friend. Yes. Everybody needs one of those, right? Minus any of the astrophysics, just to be clear. I have none of that. You are a host of the show Fake the Nation. That's right. Very cool. And in addition to Fake the Nation, you've got some side gig where you've got a succession recap? That's right. What's up with that? I'm doing a succession recap pod on the Fake the Nation feed. And in addition to talking about space, I love talking about billionaires. So those are my two main interests right now. So, yeah, definitely subscribe to hear all the succession chatter. Succession from HBO, right? I saw the whole first season, and it's, like, really weird for me to continue. Yeah. It's like, I don't want this to be true, you know? I don't want that. Please, you know? I know. It's pretty gross, but so hilarious at the same time. Well, help me welcome my friend and colleague, Stefan Alexander. Stefan, your returning guest. You first appeared with us when we were on the Nat Geo channel, and it was a Nat Geo TV episode. You're a theoretical physicist, a cosmologist, a musician, and an author, and professor of physics at Brown University up in Providence, Rhode Island. And among those books, the one I remember most is from now six years ago, seven years ago, The Jazz of Physics. Let me get the right subtitle here. The secret link between music and the structure of the universe. And then you follow that up with fear of a black universe, an outsider's guide to the future of physics. So you're still at it. But you're also a jazz saxophonist. So you're out of control here, it seems. You also appeared in the 2022 Netflix documentary, A Trip to Infinity. And that is the subject of today. Infinity, which boggles everybody's mind who's ever thought about it. And so could you just tell us what Infinity... Can I tell you my first encounter with Infinity? I'll tell you. I'm old enough to remember this, okay? So I am five when Kennedy is assassinated. Okay, that's how old I am. And there's the burial. and they put him in Arlington Cemetery. And there's a flame there at the burial spot. And they called it the Eternal Flame. And I said, what? Does this flame never go out? How could it never go out? What? And at age five, this f***ed with me. Okay, sorry. This was like, how? At night, do they secretly put more oil in the flame? You know, but the camera doesn't show it. I was, and then I would later learn, yes, that was figurative, that it's eternal, but there is a formal mathematical concept called infinity. Nagin, did you have any existential angst over infinity at any time in your life? Just to put that on, put it on the table right now because we got the man who's going to straighten us out. God, I feel, I mean, I had just an existential angst as a teenager in general and started reading all of the works of Jean-Paul Sarch as like a 16 year old and not fully understanding them. Oh, that'll mess you up. That'll mess you up. That messed me up big time. And it led to a lot of brooding and a lot of eye rolls on my part, but it didn't, it didn't freak me out the way infinity freaked you out. Okay. Okay. All right. So Stefan, tell me about infinity. What's up with that? Let me admit something to you. And again, I don't know what infinity is. Okay, we're done here. Okay. Bye, everybody. Nikki, you got any jokes to take us out? Okay. Wow, who booked this guy? I know, right? I think my first encounter with infinity was just as a kid. Like, you know, you get taught how to count. And it's okay. One, two, three. And you realize that you could just go on counting for eternity. And, you know, at some point, I think it was a friend or a teacher, I forget, I was in third grade, who said, actually, there's this number, it's called infinity. And so basically, once you get to the largest possible number, you can count it. And infinity is that number that goes on, basically, and it falls to what? To infinity. And plus, the old geek contest is, what's the biggest number you can name? Then you name it and say, is that plus one? You know, and that's how you win. You win the geek counting contest. exactly and so what i'm going to do is give a couple of like you know examples of like where infinity comes up in everyday common sense stories let's look at um fractions right i have one over two well you if you tell a kid hey i'm going to give you half of a pie of pizza or one quarter of a pie of pizza right the kid will know i want half of the pie of pizza they know that the larger you make that fraction of the slice, they get a smaller slice of pizza. If I say, you get one over one of the pizza. Well, a smart kid will say, I get the whole pie. One over one. If I go smaller than one, which is smaller than one is something that looks like zero, one over zero, then that number goes, that's what infinity is. and that we call that a division by zero and so computers crash actually because you know you want to avoid these kind of things when you wrote code these divisions by zero because what would happen right the yeah the program crashes yeah crashes exactly computer doesn't know what to do with it by the way in star trek smoke would come out of the computer if they did are you trying to say the computer was the computer was doing things that you didn't want to do yeah Yeah, Captain Kirk would outreason the computer, and then the smoke would come out. But in modern times, no, the computer just crashes. Wait, can I? This is actually giving me flashbacks of when I first had to graph an asymptote, which is this is essentially right asymptotic, this situation. And I remember just being like, oh, let them touch. Let the thing touch the line. You cared for them. You wanted them. I wanted them to touch. It felt, you know, it just felt like a missed connection forever, you know? And it felt so frustrating. They do touch at infinity. So get your ass to infinity and you'll see them touch. Oh, that's good. But right, so Stefan, asymptote is another one of these concepts, right? Yeah. It's a great word. It's a great word, too. Right. It's a fun word. You almost get there, but never quite. until you go out to infinity. And that's a very good, that's another, in fact, that's very relevant to physics. And by the way, the ideas of the asymptote and this division by zero, all of these things, you know, does, you know, touch, you know, have, you know, a deep relationship with physics and astrophysics and cosmology. So you say it shows up in a lot of different ways. It shows up in a lot of different ways. And we physicists, you know, there's, of course, philosophers pay a lot of attention to infinity. These mathematicians actually make a living from it, and we physicists try to run away from it. How do you do that? We try to avoid it. I'm trying to see a mathematician busker on the street, you know, trying to make a living off of infinity, you know. I can't. I'm trying to picture that. I'm sorry. Someone makes a living off infinity. But, Nagin, do you have questions from our Patreon members? I absolutely do. Let me dive in with a question from Captain James Riley. They rate, it always drives me crazy when I hear that a singularity has infinite density or that the universe is infinite. Is this just something we label things that we don't fully understand? I hate the concept of infinity. It seems like a cop-out. I love that. Which is how I felt about asymptotes. So I'm totally with you, Captain Riley. Yeah, so Stefan, you know the captain's got a point here. You know, are we just invoking infinity because we can't otherwise solve the problem? Yes or no. Can we evoke one of your favorite astrophysical objects, Neil, the black hole? What's that? Because I think this is a very good example of where you kind of get to have your cake and eat it, too. Because here is an interesting thing. When Einstein came up with his theory of general relativity, which describes, you know, how matter and energy can warp the space-time fabric and create the effect that we call gravity. A mathematical prediction, a mathematical solution came out of that theory. This theory spat out a very extreme sort of extreme warp in space-time from a very, you know, from basically a collapse, a star that has collapsed into a very dense region. And this thing is called a black hole. and Neil, you've done some excellent reports on that in the past. But just to be clear, Nagin, he said that Einstein's theory just spat out the equations for a black hole, but with the help of really brilliant people who understood the theory. Mm-hmm. Right. It did just poop it out like... Yeah, yeah. Although I like the imagery of just a bunch of numbers coming out of someone butt It just poops it out En route to whatever it was doing No no some brilliant people applied Brilliant people Applied Einstein general relativity now that they had that framework to arrive at a black hole as a new object, a new prediction, yeah. Right. Yeah. And it was literally, you know, the Einstein's theory was 10, what we call 10 couple nonlinear partial differential equations. Very, very difficult and still difficult to solve. So you're lucky when you get one solution and the black hole solution or Schwarzschild's solution. But at that time, like people, some people, and one of my mentors, David Finkelstein, of the Eddington Finkelstein coordinate system, which was based on Schwarzschild's solution about the event horizon, right? The point of no return once you fall into this black hole after it gobbles you up. You know, this was seen by many to just be some mathematical trickery, some mathematical solution that has no element of reality until, of course, we found one. Right. Okay. We found many, right? Now there are black hole laboratories out there. Yeah, yeah, yeah, yeah. and so the thing I find interesting about that was people already knew that the black hole the reason why they thought it was a mathematical artifact or mathematical gobbledygook of Einstein's theory some physicists thought was because it actually had a singularity it actually had an infinity what do I mean by that this is the example we used before if you look at the if I fall into a black hole if I describe going in as the radius, like a ball, think of the black hole as a gigantic ball in outer space, a gigantic invisible dark ball. And as I go in to the center of the black hole, this radius will eventually go to zero. But if I divide, and it turns out that the density and the force really falls off, it actually decreases as 1 over r, sometimes one of our r squared one of r so what happens when r goes to zero you get an infinity you get an infinity in the density the mass density infinite density you also get an infinite density thank you you get an infinity in the forces right and you get an infinity in the curvature because the curvature becomes infinite so so i okay so i think the person who asked the question knew that that's what you would say the question is is that real is it is it yes no good good no this is interesting i'm pretending i'm the dude who asked i'm i'm the captain no you're just making this just how can you have anything that's infinite anything that's that's a physical thing how is that even possible we we agree you can do that mathematically no one's arguing right now How are you going to tell me an actual physical thing hits the infinity that your math delivered? And that's what... Cause like, yeah, cause like at the end of the day, if we're looking at like, if the black hole is in a Tupperware container. Yes, very good. Okay, where are you going with this? Can it then... I'll stay with you, go. You're going to bake the black hole. I'm just saying like, if it's infinitely dense, the Tupperware container is going to break, right? Or whatever. Does that make any sense? No, that's actually, so that's right. So what, it's interesting that you had a theory that put out a sick solution. So many people thought that's not real, but then you find this thing in reality. So what do you do with the fact that this infinity is there in the prediction? So then this is where you get disagreements amongst physicists and astrophysicists. Some people say, well, there's something that replaces that theory, meaning general relativity. There's some new physics that we yet we do not know. Some people say you have to accept the infinity. And, you know, there's something that's censoring that infinity from actually realizing itself and coming out and doing bad things. I like that idea that nature might be censoring our infinities. I like that. And so it could be that the infinity is the limit of the applicability of this theory of the universe. That's a take I take, actually. Okay, all right. That's fine. I land on, that's why. Okay, now, where does the Tupperware go? I don't know. Exactly. I know. I feel like you have some really, yeah, some really expansive Tupperware. Leftovers forever in your Tupperware. Leftovers forever because it's infinitely dense. it could feed everyone forever. We got to take a quick break, but when we come back, more with Stefan Alexander, who's taken us to infinity and beyond with, of course, my co-host, Nagin Fassad. We'll be right back. I'm Brian Futterman, and I support StarTalk on Patreon. This is StarTalk with Neil deGrasse Tyson. We're back. StarTalk Cosmic Queries. We're talking about infinity. Oh, yeah. And we got one of the world's experts who thinks about this subject, Stefan Alexander, a friend and colleague, professor of physics at Brown University, Rhode Island. And I got Nagin Farsad. Nagin! You wrote a book. I did. A few years ago. Yeah. Just, it was, and I'm trying to remember the title. Is it How to Make White People Laugh or something like that? Yes, How to Make White People Laugh. Neil, it wasn't for you. Oh, it wasn't for me. That's why I never, I heard about the book, but I said, nope, this is not addressed to me. That's right. It's How to Make White People Laugh. So I remembered the title correctly. That's the title, yeah. Okay, very cool. Okay, so Stefan, you were going to add to the point about the black hole singularity being an infinite density point and possibly others stepping in to save the day. Yes. So there are other types of singularities that show up in physics that can maybe, I think, that where we were able to, what we call tame or cure the singularity. And the beast. The beast, yes. Tame the beast. One was the electric charge and the electric force. So if you look at a charged particle. An electron, okay. Or a magnet, right? The magnetic force also between two magnets, actually, as I bring the magnets closer together and closer together, actually turns out that that force, when you go to zero distance, according to the equations, that work really well for all of our motors and all of our, you know, electricity and all that wind energy and all that stuff. It uses the same physics that we trust. But according to this physics, when you go here, all that good stuff goes out the window because you will get, according to the theory, an infinite force and an infinite amount of energy. And we do not measure that because the magnets touch and nothing blows up. And you're strong enough to make the magnets touch if they're resisting each other, for example. That's right. You're strong enough to do that. But according to this thing, the magnets should never touch. You can never be strong enough because you require infinite force to make them touch. All right. Okay, so what solved that problem? It turns out Richard Feynman and his colleagues figured out, actually, there's quantum physics going on. So what happens is that quantum physics fuzzifies and softens in a sense. You just made up that word, fuzzify. I'm pretty sure you just made it. I'm pretty sure. But okay, we know what you mean. Let the record show. He's making up words as he goes along. which by the way which is what infinity sometimes sound like sounds like just throw in the word infinity and that's exactly the point of the question that sounds like a cop-out like it falsifies but continue falsifying infinity all right so so this is this so weird things happen so in the quantum world now if you say okay you know the force between the magnets you know is really what we call a non-quantum or classical theory doesn't require quantum things. What do you mean by quantum now? Well, it means that there are things called quanta. And in this case, the thing that becomes the quanta is light, because light is actually the thing that's mediating, communicating the force, actually. And so what Feynman taught us is that you can't no longer think about the magnetic field as a magnetic field, but actually as a particle called a photon that gets transmitted, bouncing back and forth. And as a photon, and gold is communicating this force and the magnet gets closer and closer, the photon can actually, you know, do weird things. It can do weird quantum. Okay, but the point is, you are saving the magnetic field problem invoking quantum physics. Yes, yes. Is quantum physics going to save you from the center of the black hole, from the singularity? Very good. So there are now people, not people, but great physicists that argue, like Stephen Hawking being one, and Gerard of Tuft and Lenny Suskind and others, that said, ah, what if what happened with, you know, with real magnets, by analogy, there's something quantum, what quantum? Quantum gravity. There's something to do with gravity being a quantum, having a quantum effect. What if that would like jump in and save the day? And as I go into the singularity of a black hole, you don't get infinity, but you get new quantum effects. Right. What would that look like? You'd have to marry quantum physics with Einstein relativity for that. You have to do that. And it's some kind of shotgun wedding right at that. Some kind of shotgun wedding. I'm just saying. But here's the problem. None of the in-laws are happy in that. None of the in-laws. Here's a funny thing. If gravity and quantum mechanics were to be a couple, they're very incompatible with each other. Every reconcilable difference is that this allowed them from actually making a bond. Yeah. All right. It's like when I tried to date a Pisces. It never works out. You know, I could have told you that. Why didn't you call me? That's right. So we replied to the captain whether or not we fully satisfied his question. So what are the questions you got, Nagin? All right. Let's move on to David. He's actually happy to submit his very first question after years of being a Patreon subscriber. Oh, excellent. David, does he have a last name or is it just David? It's just David. He's like Madonna. He just goes by the one. I once heard Alex Filippenko explain infinity and our universe is operationally infinite to us because we can never achieve the edges of it, not even at the speed of light, because space is expanding faster than the speed of light, almost like going up an escalator that is going faster than you can walk up it. You'll never reach the top. Is my small mind grasping this concept of an infinite universe? And if so, or if not, how do multiple universes fit into our infinite universe? Ooh I love those questions But I love that escalator metaphor because if that right that puts things into making sense for me Right, right, right. The way I look at it is, and I can contribute a little bit to this answer, all right? So I'll contribute two parts. You take care of the rest. So yes, if the universe is expanding, and Alex Filippenko is a colleague of mine. We came up together, actually, in graduate school. and so if you have an infinite universe that's expanding, right, you'll never reach the edge. And I'd love, like you said, we all agree that escalator analogy is excellent. However, you don't need an infinite universe to never reach the edge. For example, the surface of the earth is not infinite, Yet you could just keep walking and never reach the edge. So don't equate reaching an edge with something having to be infinite. Because the space can turn back on itself. And you can end up just making loops. And never stop walking and always walk in the same direction. Whichever direction you choose and you'll never get to the edge. That's my first point to that. And the second point is, if you embed, so I can have a sheet of paper that's infinite. Infinite. Okay? Now, but a sheet of paper is two dimensions. I can have another sheet of paper that's infinite. And put them one centimeter apart from each other, and they will never intersect. Even though they're both infinite. Because I pulled one into a third dimension. and so when you embed infinities in higher dimensions you got no problems at all you can put them in to cram as many as you want in there there's plenty of room so you take it from there you took all the good examples oh no and of course you know there's um infinite time oh You can have a finite world, but the clock can continue ticking for an infinity, meaning that the universe could be finite and extent, but just continue expanding for an infinity. So the universe is like a vampire that never dies in that scenario. Nagin, it's exactly like that. Great, got it. Just wanted to explain for the listeners. Minus the blood, minus the blood. And just to follow up on what you just said, Stefan, so if the spherical universe were expanding, you would still have a finite universe, but you could walk in it forever, even though it's expanding. So there's a lot of variations on this geometry that make for fascinating thought in all this. Absolutely, absolutely. And in fact, one of the great mathematicians, you know, somebody that you know, Neil, he went off and made a lot of money. But he literally, you know, he put a lot of money towards the satellite so that he can, you know, know about the Big Bang, called a Simons Observatory. Oh, yes. Yes. Jim Simons. Jim Simons. He's a geometrist. So he came up with some important mathematics all about this topic. He believes that the universe actually is finite. It's a sphere. It has a spherical geometry. And if you play with the assumptions and the data and the statistics enough, you might be able to still accommodate that the universe actually might be finite in terms of the data. So that's an interesting side note. And just for, in case people don't know, Jim Simons made his billions trading in the stock market, bringing high-level mathematics to his predictive models that no one knew was even possible at the time. And now he's put his money back to further research. There's the Simons Foundation, the Simons Center for Research in Physics, Biology, and Computing, which is right here in downtown Manhattan. Oh, I thought you were going to say, which is on a yacht, because that's what he gets to afford now. He does have a yacht, and I've been on his yacht, and it's called the Archimedes. Of course. Yes, yes. So thank you for that, for queuing. That was your cue. Time for another question? Yeah, please, please. So from Gavin Bamber, he says, hello from North Vancouver. Please visit. Can string theory be represented by music? if so would it be more of a monophony classical or jazz would it be a complete composition or would it continue on into infinity what is that a word monophony is that is that like does that mean a one note concert is that what he's saying there that's what it sounds like to me yeah it's something else oh my god we have two of the smartest people on the planet and and none of us know if that's like a word well this is actually actually a good point to actually talk about um you know going back to the Feynman so and and his colleagues that they use quantum mechanics to smoothen out for lack of better words de-infinitize the infinity that I'm going up a new word um get rid of the infinity we're up to six new words this episode right keep going there is now a you know an uber quantum theory and that theory is called string theory um and it turns out that just when you thought that quantum mechanics actually would help with infinities it turned out that quantum mechanics itself had infinities okay and we call these things divergences or you know instabilities these are all words that just basically mean that things in your theory go to infinity okay okay um so anyway so in a long it turns out that there is you're saying quantum physics was brought on to possibly help with the classical infinities but then it introduces finities infinities of its own that's correct okay that ain't right that ain't right that ain't right right right right and um these things are called like ultraviolet or infrared divergences for the audience member who want to get fancy um now um so it turns out that string theory actually one of the reasons why many people got behind string theory including a younger version of myself um uh when i was a young researcher younger researcher um was that it actually was an infinity free theory quantum theory actually that contained gravity in it as well contain you know aspects of all the forces but you have to live in 10 dimensions okay um um there's a there's some give there's a catch and going back to what neil exactly said is that now that you have all these other dimensions you can go and stuff infinities on those and those other dimensions now right um but anyway shrink theory is such a such a theory that does that. It's a theory that does not have in its mathematical structures and the solution it spits out, it does not have infinities. So we all love that. It's elegant and beautiful. And it's also a musical theory. That's correct. I do want to hear what you have to say about string theory and music because that is a part of the questioner's content. But we got to take a quick break. When we come back, the third and final segment of Infinity. Does Infinity have three segments? Can it have three segments? I don't know. Come back and find out on StarTalk Cosmic Query. We're back. The Infinity Edition with Stefan Alexander, a physicist who's thought a lot about cosmology and infinities. And, of course, Nagin Persad. Nagin. Hello. Love having you here. It's been too long. Come back more often, okay? Absolutely. Yeah, yeah. All right. But I'm on nearly every show in other dimensions. Oh! So, you have to go to the other dimensions, I think, is what's going on. And if you don't tell me that dimension, I will never find you. You'll be found only when you allow yourself to be found. I've also got hot dog fingers in those other dimensions, but don't worry about it. Oh, yes. Oh, okay. Everything, everywhere, all at once. I think that was. So, Stefan, why would string theory have to do with music at all? Just because it has the word string in it and just because music has string instruments. I don't, you know. It's a weak connection. Yes, yes. Yeah, that feels like really weak. They should have just called it maybe something like guitar string theory. But yeah, so string theory, one good way to be able to solve these infinities had to do with an assumption that we made about even our physics pre-string theory, which is that things fundamentally are made up of point particles. And the minute you talk about a particle, then you're forced to go to zero. And that's when things blew up on you. the infinity revealed itself. And the idea of string theory is that nothing is ever made up of a point particle anymore. Even when you take a magnifying glass and you try to resolve that point, instead of what looks like a point from really, really far away, you zoom in and you realize it's a string. But it's not just any old string. The string, because it's quantum, has to be vibrating. We know very well the physics of any kind of vibrating string. The vibrating string generates a spectrum or, you know, generates characteristics, types of waves. And these waves are called standing waves. What is a standing wave? It's basically what you know as a note, a tone. A particular type of vibration that can be represented as a sound or a note on the piano. So when I play a note on a piano, what's really going on is that there's a piano string hidden, and that piano string is vibrating. And because it vibrates, it undulates at a given rate. That rate of vibration, called a frequency, denotes what we call a tone or a sound. and so string theory, the physics of strings really does match on very nicely to the physics of how notes are generated in instruments so sorry to badmouth you at the front of that I'm sorry, Nagin needs to apologize too I'm so sorry it's an analogy but it's a really good analogy I get it, I get it, it feels right Nagin, keep going, it's the last segment Okay, so rapid fire section. Here we go. From Anthropocosmic Dillon in San Diego writes, Question for Dr. Alexander. Neal says, quote, the universe is under no obligation to make sense to us. So how do the concepts of infinity and quantum mechanics get distorted due to our human condition And how do you reconcile this gap with your research and your artistic expression through jazz music Whoa. Whoa, whoa, whoa. That's a very good question. Let me tighten up the beginning of that. So he's asking, if I say the universe is under no obligation to make sense to you, do these infinities make sense to you and does it bother you? Or do you keep going? Do you just accept it? or because it doesn't make sense, you have to do something about it and then violate the Neal principle. Very good. I like the Neal principle. I adhere to it, actually, because it doesn't make sense to me a lot of times, but I have to pay my bills. You have to continue. Yeah, pay into fun. No, no, I write and publish papers in respect to journals. But having said that, so yes, I think there is a sense in which we have to, My take on it is that I actually embraced the infinities. I embraced it. I said, let's live with the infinities. And wherever we can, try to sidestep it and make progress. And I see. OK. So you kind of, even if they're difficult, it doesn't, shouldn't prevent you from making other kinds of discoveries in the terrain that surrounds them. I get it. OK. And how about the, Nagin, the second part was about jazz. What was the, read that again? Yeah. Yeah. They wrote, how do you reconcile this gap with your research and your artistic expression through jazz music? Yeah. I mean, you know, one of the things that's great about jazz music is that, you know, you, you know, it's a dual thing. You're always striving to master your craft and, you know, and build on the foundations of others. but you also must try to break the rules and stumble and fall to make something new based on that foundation so really embracing the mistakes that you made and not being afraid of that that's kind of what jazz improvisation is also about while at the same time building on the foundation and getting your chops together and practicing and all that good stuff and there's surely some people who would say would would invoke the new the nihilism on jazz jazz is under no obligation to make sense to you. I'm pretty sure some people out there feel that way. Well, there's a funny story about that. I mean, I want to hear your thoughts about it very quickly. When I first heard Ornette Coleman, I was like, what kind of? It made no sense. It didn't make any musical sense. And then much later on in life, as I thought I became more advanced musically, it started making sense to me. Oh, okay. All right. So it doesn't have to make sense up front. That's right. Also, just for when jazz doesn't make sense, I usually go to the bar, get another drink, and then jazz starts to make a lot of sense. That's why jazz is in bars. That's why. And also why all physicists and astrophysicists should be drinking when they talk about infinity. Well, I learned something very cool about it. I'm very proud of this. I always feel like I was the outside of physicists that played music. It turned out that the hero, the guy that won the Nobel Prize, for figuring out how to actually deal with infinities and our quantum field theory that led to the discovery of the Higgs boson, his name was Ken Wilson. I just found out that he played the oboe when he was a postdoc. Except I don't know that the oboe shows up much in jazz concerts. I'm pretty sure. Well, now it should. I'm pretty sure that that was not a first choice. I know. The oboe feels like something you just get saddled with in middle school. Exactly. You don't choose it. What? In elementary school, you would have last in line. Exactly, exactly. You get the oboe. Here it is. Now he's saddled with a Nobel. Ugh. Well, let's take a question from Bruce Ryan. Bruce writes, I saw that Stefan's specialty includes quantum loop gravity, and I've always wanted to ask, what the heck is quantum loop gravity? Yeah, me too. Me too. Count me in that question as well. It's a beautiful, it is, it's a very tantalizing idea. And it actually does deal with gravitational infinities in some respects. And the idea is really interesting. You know, like how, let's go back to our picture of the magnet. You know, if you actually can see a magnetic field line with these iron filings, you see that it's like, some of it is concentrated in like a tube, like a magnetic tube. Well, what looped quantum gravity is saying is that, imagine that you can make tubes of gravitational fields and sort of loop them around like chains, like a chain. A link in a chain. A link in a chain. And I can link a fabric of space sign with those loops. But what's linking is a gravitational field. And you can think of them as atoms of space. Oh, I see. Not atoms, pixels of space. Even better. Yeah, pixels of space. The smallest unit of space. Yeah, okay. All right, Nagin, we might have time for one, maybe one and a half more questions. Okay, so let's see. Abhinav Yadov from Philly asks, I struggle to think about space-time as a concept that exists in our daily lives. As a medium, though, which light wave travels? As a fabric that gets shaped by mass and as a vacuum out of which virtual particles pop in and out of? What's an easier way to think about space-time? Well, silence. Wait, wait, what was that question? Wait, space-time is all those things, so what is the question? I guess, yeah, there's a grammatical something missing that's making it hard to understand this question. Yeah, we need some semicolons, but all those things are true, right, Stefan? They're all going on in space-time, right? And what's the easiest way of thinking about the concept of space-time? Okay, so if all that's going on in space-time, what's the first way you teach it? you don't dump the bucket onto people before they know what's going on. What's your first step to say what space time is? To like a kid. Yeah. Yeah. So I would say that, yeah, I, I, I think it's, I think it's a good analogy to think of space time as some sort of very, very faint and invisible fabric that, But it's a special kind of fabric because that fabric can also support space-time itself to move along, like gravitational waves, right? So space-time itself can actually support motion of ripples up itself. And that is different than any other types of medium that we know, right? Normally, something like an electric field or particles need space-time to move through. but they can't move through their own medium. Space time has a very special type of medium in that sense. But it's a very weird medium, for lack of a better word. It's what we call a relational medium. And nor is it under any obligation to make sense to us. Yes, okay. What you described as kind of like... It still makes no sense to me. So the answer to this person's question is basically there's no way of really thinking about it in your daily life. No, I mean, again, this is what Neil just said. It makes no sense. But I know I could write down this object called a space-time metric, and we'd describe it as a field of, you know, space-time as some kind of a field. But again, these are just words that we attach to the equations that we write down. But they make predictions and they work. They make very good predictions and they work very well. So that's why, however fantastical they sound, they still are connected to reality in that important way. So it's very. I mean, the detection of gravitational waves with LIGO and Virgo. Yep. Yeah, yeah, yeah. And then some. Again, I think we got one more question. So, I mean, this is sort of like related. Everyone seems to be having a crisis in understanding. But Malcolm Marfan from Trinidad and Tobago says, infinity is often described as a mathematical abstraction. How can we know that the concept of infinity exists in the physical world and not just in our minds? They are really testing you today. Yeah, they are, Stefano. They want hard answers. And I tell you, I remembered learning infinity mathematically, and they said one divided by zero is undefined. I remember being taught that in my math class. Well, I have a math friend who we actually had as a guest, John Allen Paulos, professor of math at Temple University outside of Philly. And I tweeted, I called him out in Twitter. And I said, John, if one divided by zero is undefined, why don't you guys define it? What are you waiting for? Okay. I've been waiting my whole life. And all you have to do is define it. And we're cool. what's up with that? So apparently to him infinity is undefined because one divided by zero is infinity. So wait so this thing is just totally up for grab I could just do a journal article right now and just be like one divided by infinity is a bowl of jello and like that's if this is up for grabs I'd like to take a stab. We have to put closure on your theory and one divided by zero is an acetote captured in Tupperware. I mean, that's beautiful. And that's a beautiful theorem right there, right there. We got to call it quits there. Stefan, great to have you back on the show. Thanks for having me again, Neil. All right, Nagin, it's been a delight. And by the way, Nagin, just quickly, weren't you on TV with Hillary Clinton? I'm channel surfing. I say, that's McGee. Wait, that's Hillary Clinton. What are you doing? What was that? Briefly, tell me real quick. I'm on the show Gutsy on Apple TV. Hillary Clinton is just basically doing a series about gutsy women. And crazily, I'm one of them. So check it out. It's a really great series. You're one of the gutsy women. Okay, it's just called Gutsy. Yeah, it's called Gutsy on Apple TV. Gutsy. Very cool. I don't mean to brag but Hillary Clinton said I'm her favorite astrophysicist oh yeah I'm pretty sure she knows only one astrophysicist that's the problem the best is when I meet my favorite musician and he goes hey by the way can you get me introduced to Neil deGrasse Tyson please no no alright guys we're done here land this plane This has been StarTalk Cosmic Queries, the Infinity Edition. It's a delight to have an old friend and colleague, Stefan Alexander and Nagin Farsad. Always good to have you back. Neil deGrasse Tyson here, as always, bidding you to keep looking up.