In short
Infinity—how it appears in everyday reasoning, mathematics, and physics; whether “infinite” quantities in theories (e.g., black holes) are real or artifacts; and how modern physics (quantum effects, quantum gravity, string theory) “tames” infinities. It also covers whether the universe must be infinite, and how spacetime and infinity relate to human understanding, plus a music/jazz analogy.
Guests
Stefan Alexander, theoretical physicist and cosmologist; professor of physics at Brown University; author of The Jazz of Physics and Fear of a Black Universe; also a jazz saxophonist; appeared in the 2022 Netflix documentary A Trip to Infinity. Nagin Farsad, co-host/comedian; host of Fake the Nation; does a Succession recap podcast.
Key claims
Division by zero and asymptotes illustrate mathematical “approach” to infinity; black hole singularities imply infinite density/curvature in GR but may be limited by unknown new physics or “censorship” by nature; quantum effects can soften classical infinities (analogy: magnets/electric forces); string theory replaces point particles with vibrating strings to avoid infinities; infinities can be embraced while still making progress.
Notable examples
eternal flame as a childhood “infinity” encounter; division by zero causing computer crashes; black hole (Schwarzschild) singularity; magnet force becoming infinite classically but softened by quantum photons; universe expansion “escalator” metaphor; infinite sheets embedded in higher dimensions; LIGO/Virgo gravitational-wave detection; jazz improvisation as rule-breaking within a foundation.
Written by AI. May contain mistakes. Listen to the episode to check what was said.
Chapters
Tap a time to open that second in VOMeet the Guests
0:28 to 1:09
Introduction of guest Stefan Alexander and discussions about his background.
“TikTok is where wonder is shared, where curiosity turns into discovery, and where millions learn something new every day.”
Meet the Guests
1:55 to 4:49
Introduction of guest Stefan Alexander and discussions about his background.
“Welcome to StarTalk, your place in the universe where science and pop culture collide.”
Personal Encounters with Infinity
4:49 to 6:10
Neil and Nagin share personal stories about their first experiences with the concept of infinity.
“This was like, how, at night do they secretly put more oil in the flame?”
Understanding Infinity
6:10 to 10:55
The conversation dives into mathematical concepts of infinity and related physics.
“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 Sartre as like a 16-year-old and not fully understanding them.”
Infinity and Black Holes
10:55 to 14:01
Discussion about black holes and how infinity relates to their properties.
“Let me dive in with a question from Captain James Riley.”
Exploring Black Holes and Infinity
14:01 to 17:43
Learn about the implications of black holes and the concept of infinity in physics.
“If you actually, this is the example we used before.”
Exploring Black Holes and Infinity
19:13 to 21:26
Learn about the implications of black holes and the concept of infinity in physics.
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Exploring Black Holes and Infinity
21:31 to 21:42
Learn about the implications of black holes and the concept of infinity in physics.
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The Nature of an Infinite Universe
21:42 to 28:00
Discussion on the concept of an infinite universe and the escalator analogy.
“This is StarTalk with Neil deGrasse Tyson.”
Exploring the Nature of Infinity
28:00 to 32:30
Discussion about the nature of infinity and its implications in cosmology.
“that puts things into making sense for me.”
Show all 19 chapters
Jim Simons and the Geometry of the Universe
32:30 to 36:49
Insights into Jim Simons’ contributions to cosmology and his beliefs about the universe's shape.
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Jim Simons and the Geometry of the Universe
37:50 to 39:09
Insights into Jim Simons’ contributions to cosmology and his beliefs about the universe's shape.
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String Theory and Music
39:21 to 42:00
Exploration of the connections between string theory and musical concepts.
“We're back, the Infinity Edition, with Stefan Alexander, a physicist who's thought a lot about cosmology and infinities.”
String Theory and Sound Frequencies
42:00 to 44:08
Explore the relationship between string theory and sound frequencies.
“And because it vibrates, it undulates at a given rate.”
Infinity, Quantum Mechanics, and Jazz
44:08 to 47:20
Discuss the concepts of infinity and quantum mechanics through the lens of jazz music.
“And how about the second part was about jazz?”
Understanding Space-Time
47:20 to 50:53
Delve into the complexities of space-time as a fundamental concept.
“Well, what loop quantum gravity is saying is that imagine that you can make tubes of gravitational fields and sort of loop them around like chains, like, you know, like a chain.”
The Concept of Infinity in the Physical World
50:53 to 54:03
Examine how the concept of infinity manifests in our understanding of the physical world.
“I mean, the detection of gravitational waves with LIGO and Virgo.”
The Concept of Infinity in the Physical World
54:27 to 55:21
Examine how the concept of infinity manifests in our understanding of the physical world.
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The Concept of Infinity in the Physical World
55:24 to 55:56
Examine how the concept of infinity manifests in our understanding of the physical world.
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Transcript
Automatic transcript. May contain errors.0:00Our listeners love puzzles, paradoxes and hidden patterns almost as much as we do. On TikTok, those fascinations come to life. People are breaking down physics, exploring geology and explaining why the world works the way it does. You'll see impressive experiments, explanations that finally make sense and connections you didn't expect. It's like having a lab, a lecture hall and science museum in your pocket. TikTok is where wonder is shared, where curiosity turns into discovery, and where millions learn something new every day. Rosetta Stone Sapphire is designed for personal learning, helping you go beyond generic lessons and focus on the topics that matter most to you.
0:45You've heard me talk about Rosetta Stone before. You know that I love the fact that I can learn on the go, anytime, anywhere, easily integrate it into my schedule. And more importantly, it helps me learn the language like a native. And that's why I love it, because I can secretly sit at the table and listen to my mother-in-law talk about me in Spanish, and she doesn't even know that I know what she's saying. Go ahead, be a stealth bilingual spy like me. Visit rosettastone.com slash startalk to get 20 % off your Rosetta Stone Sapphire subscription when you sign up today. You'll get unlimited access to all 25 Rosetta Stone languages plus all new Sapphire learning tools.
1:26Just la order, amigos.
1:28Neil deGrasse Tyson:They are Rosetta Stoneway mismo. 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.
2:21Neil deGrasse Tyson: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 Fasad. 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?
3:11That'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.
3:29Neil deGrasse Tyson:Succession from HBO, right? I saw the whole first season, and it's really weird for me to continue. Yeah. It's like, I don't want this to be true. I don't want that. Please. I know. It's pretty gross, but so hilarious at the same time. Well, help me welcome my friend and colleague, Stefan Alexander. Stefan, you're a 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.
4:20Neil deGrasse Tyson: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 I 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 go wait can I tell you my first encounter with infinity i'll tell you i 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 in arlington cemetery and there's a flame there at the burial spot and they called it the eternal flame And I said, what?
5:33Neil deGrasse Tyson:Does this flame never go out? How could it never go out? What? And at age five, this 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, it's 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 Sartre as like a 16-year-old and not fully understanding them.
6:23Neil deGrasse Tyson:Oh, that'll mess you up. That'll mess you up big time. So 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 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, Nigan. I don't know what Infinity is. Okay, we're done here. Okay. Bye, everybody. Nigan, you got any jokes to take us out? Okay. okay i mean the first book this guy i know right right i think my first encounter with infinity was just as a kid like you know you get taught how to count and you say 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 of course to what?
7:30To infinity.
7:31Neil deGrasse Tyson: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 fractions, right? I have one over two. Well, 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, right, they get a smaller slice of pizza.
8:15If 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 make, 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 want to avoid these kind of things when you wrote code, these divisions by zero, because what would happen, right? Yeah, the program crashes. Yeah, crashes, exactly.
8:52Neil deGrasse Tyson: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 that. Are you trying to say the computer was doing things that you didn't want to do? Yeah, yeah, computer would... 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.
9:30Neil deGrasse Tyson: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? Wow. And it felt so frustrating. They do touch at infinity.
9:47Neil deGrasse Tyson: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? 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're saying it shows up in a lot of different ways.
10:25It shows up in a lot of different ways. And we physicists, you know, there's, of course, philosophers that pay a lot of attention to infinities. 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.
10:42Neil deGrasse Tyson: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 don't. I'm sorry. That film 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 read, 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.
11:19Which is how I felt about asymptotes. So I'm totally with you, Captain Riley.
11:26Neil deGrasse Tyson:Yeah, so Stefan, you know the captain's got a point here. Are we just invoking infinity because we can't otherwise solve the problem? Yes and no. Can we evoke one of your favorite astrophysical objects, Neil? The black hole? The black hole. What's that? Because I think this is a perfect, very good example of where you kind of get to have your cake and eat it too because here is um interesting thing um 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 um a mathematical prediction a mathematical solution came out of that um that theory this theory spat out on a very extreme um sort of extreme in a space time from a very, you know, from a basically collapse, a star that has collapsed into a very dense region.
12:24And this thing is called a black hole. And Neil, you've done some excellent reports on that in the past.
12:31Neil deGrasse Tyson: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's butt it just pooped it out on route to whatever it was doing some brilliant people applied applied Einstein's general relativity now that they had that framework to arrive at a black hole as a new object a new prediction yeah and it was literally you know, the Einstein's theory is 10, what we call 10 couple nonlinear partial differential equations.
13:17Very, very difficult and still difficult to solve. So you're lucky when you get one solution and the black hole solution or the Schwarzschild 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 solution about the event horizon, the point of no return once you fall into this black hole after it gobbles you up 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 we found many now there are black hole laboratories 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.
14:23It actually had an infinity. What do I mean by that? If you actually, this is the example we used before. If you look at the, you know, if I fall into a black hole, if I, you know, describe going in as some, the radius, 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 1 over r squared, 1 over r. So what happens when r goes to zero? You get an infinity.
15:06you 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 as well so I okay
15:22Neil deGrasse Tyson: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 yes no good good no this is interesting I'm pretending I'm the dude who asked I'm the captain. No, you're just making this up. How can you have anything that's infinite anything? That's a physical thing. How is that even possible? We agree you can do that mathematically. No one's arguing. Now you're going to tell me an actual physical thing. It's the infinity that your math delivered. And that's what. Because like, yeah, because like at the end of the day, if we're looking at like a top if the black hole is in a tupperware container yes right okay where you going with this i'll stay with you go i'm gonna bake the black hole i'm just saying like it can't if it's infinitely dense the tupperware container is gonna break right or whatever does that make any sense no that's actually so that's right so what it's interesting that you 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 and so then this is where you get disagreements in amongst physicists and astrophysicists some people say well there's something that replaces that theory um 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 yes and so it could 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 that's my that's why I land on that's why okay now where does the Tupperware go?
17:26Neil deGrasse Tyson:we gotta 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 can 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.
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21:38Neil deGrasse Tyson:I'm Brian Futterman, and I support StarTalk on Patreon. This is StarTalk with Neil deGrasse Tyson.
21:52We're back.
21:53Neil deGrasse Tyson: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, no, this is not addressed to me. That's right.
22:35It's not to make white people laugh.
22:36Neil deGrasse Tyson: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 charge particle. An electron, okay. Or a magnet, right? The magnetic force also between two magnets, actually, as I bring the magnets closer together and close 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.
23:49And we do not measure that because the magnets touch and nothing blows up. And you're strong enough to make the magnets touch
23:55Neil deGrasse Tyson: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 need quite 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 like you know 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 okay 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 But continue.
24:45Flusifying infinity. So weird things happen. So in the quantum world now, if you say, okay, the force between the magnets is really what we call a non-quantum or classical theory. It 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.
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25:25And as a photon is communicating this force and the magnet gets closer and closer, the photon can actually do weird things. It can do weird quantum things.
25:35Neil deGrasse Tyson: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, there are great physicists that argue, like Stephen Hawking being one, and Gerard Tuft and Lenny Susskind and others, that said, ah, what if what happened 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 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 Some kind of child been wedded.
26:33Neil deGrasse Tyson:I'm just saying. But here's the problem. None of the in-laws are happy in that scenario. 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've 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, Nagina? All right, let's move on to David.
27:10He's actually happy to submit his very first question after years of being a Patreon subscriber. Oh, excellent.
27:16Neil deGrasse Tyson: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.
27:55Neil deGrasse Tyson:But I love that escalator metaphor, because if that's 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 like 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.
28:52Neil deGrasse Tyson: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. So 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, 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.
29:42Neil deGrasse Tyson:And so when you embed infinities in higher dimensions, you got no problems at all. You can put them in cram as many as you want in there and there's plenty of room. So you take it from there, Stefan. You took all the good examples. Oh no! And of course there's infinite time. You can have a finite world but the clock can continue ticking for an infinity. You know, meaning that the universe could be finite in an extent, but just continue expanding for 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.
30:32Neil deGrasse Tyson: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, 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 know about the Big Bang, called the Simons Observatory.
31:12Oh, 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.
31:43Neil deGrasse Tyson: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.
32:26Neil deGrasse Tyson: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? Wait, is that a word, monophony? Does that mean a one-note concert? Is that what he's saying there? That's what it sounds like to me. Yeah. Maybe it's something else. Oh, my God. We have two of the smartest people on the planet, and none of us know if that's like a word.
33:07Well, this is actually a good point to actually talk about, you know, going back to Feynman and his colleagues, that they use quantum mechanics to smoothen out, for lack of better words, de-infinitize the infinity. I'm going to put up a new word. Get rid of the infinity. You're up to six new words this episode. Keep going. There is now an uber quantum theory, and that theory is called string theory. 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 and so anyway so in a long it turns out that there
33:58Neil deGrasse Tyson:So you're saying quantum physics was brought on to possibly help with the classical infinities, but then it introduces infinities of its own. That's correct. That ain't right. That ain't right. That ain't right. Right. And these things are called like ultraviolet or infrared divergences for the audience member who want to get fancy. now 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 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 contained you know aspects of all the forces but you had to live in 10 dimensions, okay?
34:43There's some give. There's a catch. 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 other dimensions now, right? But anyway, string theory is 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 infinity. so we all love that it's elegant and beautiful and um it's also a musical theory that's correct
35:16Neil deGrasse Tyson:i do want to hear what you have to say about string theory and music because that is a part of the the questioner's uh 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 star talk cosmic query
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39:20And by that, I mean StarTalk.
39:32We're back, the Infinity Edition, with Stefan Alexander,
39:37Neil deGrasse Tyson: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.
40:18Neil deGrasse Tyson: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 their music has string instruments i don't you know it's a weak connection yes yes yeah that's it feels like really weak they they should have just called it maybe something like um guitar string theory um but yeah the you know so string theory one good reason ways was 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.
40:59The 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 generates characteristics types of waves, and these waves are called standing waves. What is a standing wave?
41:42It's basically what you know as a note, a tone. Okay. 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 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.
42:22Neil deGrasse Tyson:So sorry to badmouth you at the front of that. I'm sorry. Nagin needs to apologize too. I'm so sorry.
42:33Neil deGrasse Tyson:It's an analogy, but it's a really good analogy. I get it. I get it. It feels right. It feels right. All right. McGeean, keep going. It's the last segment. Okay, so rapid fire section. Here we go. From Anthropocosmic Dylan 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.
43:09Neil deGrasse Tyson: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, are 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 Neil principle? Very good. I like the Neil 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, making the 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 embrace the infinities.
43:56I embrace it. I said, let's live with the infinities and wherever we can, try to sidestep it and make progress.
44:04Neil deGrasse Tyson:And I say, 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 second part was about jazz? What was the read that again? 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've you know it's a dual thing you you're always struggling 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.
44:57That's kind of what jazz improvisation is also about, while at the same time building on a foundation and getting your chops together and practicing and all that good stuff.
45:07Neil deGrasse Tyson:And there's surely some people who would say, would invoke the nihilism on jazz. Jazz is under no obligation to make sense to you. Very good. I'm pretty sure some people out there feel that way. Well, there's a funny story about that, and I want to hear your thoughts about it very quickly. When I first heard On It Coleman, I was like, what kind of, I 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, 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.
45:53Neil deGrasse Tyson: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 is Ken Wilson. I just found out that he played the oboe. Okay. When he was a postdoc, yeah. Except I don't know that the oboe shows up much in jazz concerts.
46:29Neil deGrasse Tyson: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. In elementary school, you would have lasted 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 um 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 and 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 concentrated in like a tube, like a magnetic tube.
47:29Well, what loop quantum gravity is saying is that imagine that you can make tubes of gravitational fields and sort of loop them around like chains, like, you know, 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 linked in is the 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.
47:59Neil deGrasse Tyson: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.
48:43Yeah, we need some semicolons, but...
48:45Neil deGrasse Tyson:We did 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. um yeah so i would say that yeah i i think it's i think it's a good analogy to think of space-time as some sort of very very faint um and invisible um fabric um that but it's a special kind of fact because that fabric can also support space-time itself to move along like gravitational waves right so space time itself can actually support motion uh uh ripples up itself and and that is different than any other types of medium that we know right normally something like like an electric field or particles need space time to move through but they can't move through their own their own medium space time has a it's a very special type of medium in that sense but um it's It's a very weird medium, for lack of a better word.
50:07It's what we call, it's a relational medium, okay?
50:12Neil deGrasse Tyson:And nor is it under any obligation to make sense to us. Yes, okay. But it just sounds like 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, makes no sense. But 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.
50:48They make very good predictions and they work very well.
50:51Neil deGrasse Tyson:So that's why, however fantastical they sound, they still are connected to reality in that important way. I mean, the detection of gravitational waves with LIGO and Virgo. Yep. Yeah, yeah, yeah. 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.
51:30They want hard answers.
51:32Neil deGrasse Tyson: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? 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.
52:19so wait so this thing is just totally up for grab like i could just do a journal right like a journal article right now and just be like one divided by infinity is a bowl of jello and like that's
52:29Neil deGrasse Tyson: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. That's beautiful. 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 Nadine. Wait, that's Hillary Clinton? What are you doing? What was that? Briefly, tell me real quick.
53:16I'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.
53:30Neil deGrasse Tyson: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
53:59Neil deGrasse Tyson: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.
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55:27Neil deGrasse Tyson:With a Capital One Saver Card, You'll earn unlimited 3 % cash back on dining, entertainment, and at grocery stores. And for a limited time, new card members can earn a$250 cash bonus after spending$500 on purchases within the first three months. So grab a bite, grab a seat, and earn unlimited 3 % cash back with the Saver Card. Capital One. What's in your wallet? Terms apply. See CapitalOne.com slash Saver for details.
From the publisher
What is infinity? Neil deGrasse Tyson and comedian Negin Farsad explore whether we are in a finite universe, the issues with infinity, string theory, and more with theoretical physicist Stephon Alexander.
Originally aired April 11, 2023.
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