Cosmic Queries – Understanding Infinity with Stephon Alexander

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.

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

• 0:00Neil deGrasse Tyson?

  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.

• 0:24Neil deGrasse Tyson?

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

• 0:37Neil deGrasse Tyson?

  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, Stephane Alexander. We'll get to him in a moment. Let me introduce my co-host, Nagin Fassad. Nagin, it's been so long.

• 1:12Negin Farsad?

  Hello. Yes, I'm your honorary astrophysicist comedian friend.

• 1:21Neil deGrasse Tyson?

  Everybody needs one of those, right?

• 1:22Negin Farsad?

  Mine, right. Minus any of the astrophysics, just to be clear. I have none of that.

• 1:28Neil deGrasse Tyson?

  You are a host of the show Fake the Nation?

• 1:33Negin Farsad?

  That's right.

• 1:33Neil deGrasse Tyson?

  And very cool. And wait, and in addition to Fake the Nation, you've got some side gig where you've got a succession recap?

• 1:40Negin Farsad?

  That's right.

• 1:41Neil deGrasse Tyson?

  What's up with that?

• 1:41Negin Farsad?

  I'm doing a succession recap pod on the Fake the Nation feed, and I, 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.

• 1:58Neil deGrasse Tyson?

  Succession from HBO, right? I saw the whole first season, and it was too, it's like really weird for me to continue.

• 2:05Negin Farsad?

  Yeah.

• 2:06Neil deGrasse Tyson?

  It's like, I don't want this to be true. You know, I don't want that. Please.

• 2:11Negin Farsad?

  I know. It's pretty gross, but so hilarious at the same time.

• 2:17Neil deGrasse Tyson?

  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 you had, 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 followed that up with Fear of a Black Universe,

• 3:01Neil deGrasse Tyson?

  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.

• 3:44Neil deGrasse Tyson?

  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-

• 4:10Neil deGrasse Tyson?

  with me, okay? Sorry. This was like, how, at night, do they secretly put more oil in the flame? You know, but there's 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?

• 4:34Negin Farsad?

  Um.

• 4:34Neil deGrasse Tyson?

  Just to put that on, put it on the table right now, because we got the man who's going to straighten us out.

• 4:39Negin Farsad?

  God, I feel, 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.

• 4:52Neil deGrasse Tyson?

  Oh, that'll mess you up. That'll mess you up.

• 4:54Negin Farsad?

  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, it didn't freak me out the way infinity freaked you out.

• 5:06Neil deGrasse Tyson?

  Okay, okay. All right. So Stefan, tell me about infinity. What's up with that?

• 5:10Speaker 02

  Let me admit something to you and again. I don't know what infinity is. Okay.

• 5:15Neil deGrasse Tyson?

  Okay, we're done here. Okay.

• 5:18Negin Farsad?

  Bye, everybody.

• 5:20Neil deGrasse Tyson?

  Nagin, you got any jokes to take us out? Okay.

• 5:25Negin Farsad?

  Wow, who booked this guy?

• 5:27Neil deGrasse Tyson?

  I know, right? Right?

• 5:29Speaker 02

  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, that 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 in, and infinity is that number that goes on basically, and it's cause to what? To infinity.

• 6:00Neil 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.

• 6:10Speaker 02

  Exactly. And so what I'm gonna 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 gonna 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 of the slice, right? 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 I get the whole pie, one over one. If I make if I go smaller than one,

• 6:55Speaker 02

  which is smaller than one is something that looks like zero, one over zero, then that number goes. That's what infinity is. Um, 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?

• 7:18Neil deGrasse Tyson?

  Yeah, the the program crashes.

• 7:20Speaker 02

  It crashes. Exactly. Computer doesn't know what to do with it.

• 7:22Neil deGrasse Tyson?

  By the way, in Star Trek, smoke would come out of the computer if they did that.

• 7:28Speaker 02

  Are you trying to say the computer was the computer was doing things that you didn't want to do?

• 7:32Neil deGrasse Tyson?

  Yeah, yeah, a computer would Captain Kirk would out reason the computer and then the smoke would come out. But in modern times, no, they're just the computer. It just crashes.

• 7:42Negin Farsad?

  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.

• 7:52Speaker 02

  Yes, yes, yes.

• 7:53Negin Farsad?

  And I remember just being like, oh, let them touch. Let the thing touch the line.

• 7:59Neil deGrasse Tyson?

  You you cared for them. You wanted them.

• 8:02Negin Farsad?

  I wanted them to touch. It felt, you know, it just felt like a missed connection forever, you know?

• 8:10Neil deGrasse Tyson?

  Well, they do they do touch. At infinity.

• 8:17Neil deGrasse Tyson?

  So get your ass to infinity and you'll see them touch.

• 8:20Speaker 02

  That's good.

• 8:22Neil deGrasse Tyson?

  But right. So Stefan, asymptote is another one of these concepts, right?

• 8:26Speaker 02

  Yeah.

• 8:26Neil deGrasse Tyson?

  It's a great word. It's a great word, too.

• 8:29Speaker 02

  Right. You kind of you almost get there, but never quite until you go out to infinity. Um, and that's a very good, that's another, in fact, that's very relevant um to physics. And by the way, the ideas of the asymptote and this division by zero, all of these things, you know, um does, you know, touch, you know, have, you know, a deep relationship with with physics and astrophysics and cosmology.

• 8:52Neil deGrasse Tyson?

  So you're saying it shows up in a lot of different ways?

• 8:54Speaker 02

  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 infinities. Mathematicians actually make a lot, a lot, a living from it. And we physicists try to run away from it and try to avoid it.

• 9:11Neil 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 don't, I can't, I'm trying to picture that. I don't, I'm sorry. Someone makes a living off infinity. But, but Nagie, do you have, you have questions from our Patreon members?

• 9:26Negin Farsad?

  I, I absolutely do. Let me dive in with a ca- a question from Captain James Riley. Um, 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.

• 9:47Neil deGrasse Tyson?

  I love that.

• 9:48Negin Farsad?

  Which is how I felt about asymptotes. So I to- I'm totally with you, Captain Riley.

• 9:55Neil deGrasse Tyson?

  Yeah, so, so Stefan, it's, you know, the captain's got a point here, you know. Are, are we ju- are we just invoking infinity because we can't otherwise solve the problem?

• 10:05Speaker 02

  Uh, yes and no. Um, I can, can we, can we evoke one of your favorite astrophysical objects, Neil? The black hole, the black hole.

• 10:12Neil deGrasse Tyson?

  What's that?

• 10:13Speaker 02

  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 spacetime fabric and create the effect that we call gravity. A mathematical prediction, a mathematical solution came out of that, that theory. This theory spat out on a very extreme, sort of extreme walk in a space-time from a very, you know, from a basically a collapse, a star that has collapsed into a very dense region. And this thing is called a black hole.

• 10:55Speaker 02

  And Neil, you've done some excellent reports on that in the past.

• 11:00Neil 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.

• 11:12Speaker 02

  Right.

• 11:14Neil deGrasse Tyson?

  It didn't just poop it out like, like.

• 11:17Negin Farsad?

  Yeah, yeah. Although I like the imagery of just a bunch of numbers coming out of someone's butt.

• 11:24Neil deGrasse Tyson?

  Poop it out on route to whatever it was doing. No, no, some brilliant people applied.

• 11:29Speaker 02

  Brilliant people.

• 11:30Neil deGrasse Tyson?

  Applied Einstein's general relativity. Now that they had that framework to arrive at a black hole as a new, a new object, a new prediction, yeah.

• 11:38Speaker 02

  Right.

• 11:39Neil deGrasse Tyson?

  Yeah.

• 11:39Speaker 02

  And it was a ma-, it was literally, you know, the Einstein's theory was 10, what we call 10 coupled nonlinear partial differential equations. Very comp-, very, 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 Edington-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

• 12:21Speaker 02

  solution that has not, no element of reality, until of course we found one.

• 12:26Neil deGrasse Tyson?

  Right.

• 12:27Speaker 02

  Okay. We found many, right? Now there are black hole laboratories out there.

• 12:31Neil deGrasse Tyson?

  Yeah, yeah, yeah, yeah.

• 12:33Speaker 02

  And so the thing that I find interesting about that was people already knew. That the black hole, this, the reason why they thought it was a mathematical artifact or mathematical gobbledygook of this, of, of, of Einstein's theory. Some, some physicist thought was because it actually had a singularity. It actually had an infinity. What do I mean by that? If you actually, this is the, the example we used before. If you look at the, you know, if I fall into a black hole, if I, um, you know, describe going in as some, the radius, you know, like a ball, think of the black hole as a gigantic ball in outer space. A, a gigantic invisible dark ball.

• 13:14Speaker 02

  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 one over R, sometimes one over 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.

• 13:39Neil deGrasse Tyson?

  Infinite density.

• 13:39Speaker 02

  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.

• 13:49Neil deGrasse Tyson?

  So, 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?

• 13:59Speaker 02

  Yes.

• 14:00Neil deGrasse Tyson?

  No.

• 14:01Speaker 02

  Good. Good. No, this is interesting.

• 14:04Neil deGrasse Tyson?

  I'm pretending I'm the dude who has, I'm, I'm the captain. No, you're just making this.

• 14:11Neil deGrasse Tyson?

  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.

• 14:20Speaker 02

  Right.

• 14:20Neil deGrasse Tyson?

  Now you're gonna tell me an actual physical thing hits the infinity that your math delivered. And that's what.

• 14:29Negin Farsad?

  Yeah, cuz like at the end of the day, if we're looking at like a top, if the black hole is in a Tupperware container.

• 14:35Speaker 02

  Yes.

• 14:36Negin Farsad?

  Right?

• 14:36Neil deGrasse Tyson?

  Okay, where you going with this? I'll stay with you, go.

• 14:41Speaker 02

  You're gonna bake the black hole?

• 14:42Negin Farsad?

  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?

• 14:53Speaker 02

  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 amongst physicists and astrophysicists. Some people say, well, there's something that replaces that theory. Um, meaning in general relativity, there's some new physics that we yet we do not know. Some people say you have to accept the infinity, um, and you know, there's something is censoring that infinity from actually realizing itself and coming out and doing bad things.

• 15:35Neil deGrasse Tyson?

  I like that idea that nature might be censoring our infinities. I like that.

• 15:40Speaker 02

  Yes.

• 15:40Neil deGrasse Tyson?

  And so it could, it could be that the infinity is the limit of the applicability of this theory of the universe.

• 15:48Speaker 02

  That's, that's, that's a take I take, actually.

• 15:50Neil deGrasse Tyson?

  Okay, alright.

• 15:51Speaker 02

  That's why I land on, that's why.

• 15:52Neil deGrasse Tyson?

  Okay, now, where, where's the Tupperware go? We got enough.

• 15:56Negin Farsad?

  Exactly. I know. I feel like.

• 15:59Neil deGrasse Tyson?

  Back to the Tupperware.

• 16:00Negin Farsad?

  You, you have some really, yeah, some really expansive Tupperware. Leftovers forever in your Tupperware.

• 16:07Neil deGrasse Tyson?

  Leftovers for, cuz it's infinitely dense, it could feed everyone forever. We gotta 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.

• 16:34Speaker 03

  I'm Brian Futterman and I support StarTalk on Patreon. This is StarTalk with Neil deGrasse Tyson.

• 16:48Neil 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, Stephane Alexander, a friend and colleague, professor of physics at Brown University, Rhode Island. And I got Nagin Fassad. Nagin, you wrote a book.

• 17:09Negin Farsad?

  I did.

• 17:10Neil deGrasse Tyson?

  A few years ago.

• 17:12Negin Farsad?

  Yeah.

• 17:12Neil deGrasse Tyson?

  Just, it was, and I'm trying to remember the title. Is it How to Make White People Laugh? Or something like that?

• 17:18Negin Farsad?

  Yes, How to Make White People Laugh. Neil, it wasn't for you.

• 17:21Neil deGrasse Tyson?

  Oh, it wasn't for me. That's why I never, I heard about the book, but I said, nope, this is not, no, not addressed to me.

• 17:30Negin Farsad?

  That's right. It's How to Make White People Laugh.

• 17:32Neil deGrasse Tyson?

  So I remembered the title correctly?

• 17:34Negin Farsad?

  That's the title. Yeah, that's the one.

• 17:37Neil deGrasse Tyson?

  Okay, so Stephane, you were gonna add to the point about the black hole singularity being an infinite density point and possibly others stepping in to save the day.

• 17:47Speaker 02

  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.

• 17:58Neil deGrasse Tyson?

  The beast.

• 18:00Speaker 02

  The beast, yes.

• 18:01Neil deGrasse Tyson?

  Tame the beast.

• 18:02Speaker 02

  One was the electric charge and the electric force. So if you look at a charged particle.

• 18:07Neil deGrasse Tyson?

  An electron, okay.

• 18:08Speaker 02

  Or a magnet, 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.

• 18:23Speaker 02

  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's used as 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 infinite amount of energy. And we do not measure that because the magnets touch and nothing blows up.

• 18:49Neil deGrasse Tyson?

  And you're strong enough to make the magnets touch if they're resisting each other, for example.

• 18:52Speaker 02

  That's right. You're strong enough to do that. But according to this thing, the magnets should never touch you. You can never be strong enough because you require infinite force to make them touch.

• 19:00Neil deGrasse Tyson?

  All right.

• 19:00Speaker 02

  Okay, so what solved that problem? It turns out Richard Feynman and, you know, 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.

• 19:18Neil deGrasse Tyson?

  You just made up that word fuzzify. I'm pretty sure you just made up. I'm pretty sure, but okay, we know what you mean. But let the record show, he's making up words as he goes along.

• 19:29Negin Farsad?

  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. It sounds like a cop out, like it fuzzifies, but continue.

• 19:40Neil deGrasse Tyson?

  Fuzzifying infinity.

• 19:42Speaker 02

  Okay, so, so this is, 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. 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. And as a photon goes, it's communicating this force and the magnet gets closer and closer.

• 20:27Speaker 02

  The photon can actually, you know, do weird things. It can do weird quantum.

• 20:31Neil deGrasse Tyson?

  Okay, but the point is you are saving the magnetic field problem invoking quantum physics. Is quantum physics going to save you from the center of the black hole, from the singularity?

• 20:42Speaker 02

  Very good. So there are now people, not people, there are great physicists um um that argue like Stephen Hawking being one and Gerard Tofte and Lenny Susskind and others that said, ah, what if what happened with, you know, with ma- real magnets um by analogy, there's something quantum. What 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?

• 21:20Neil deGrasse Tyson?

  You'd have to marry quantum physics with Einstein relativity for that.

• 21:24Speaker 02

  You have to do that.

• 21:25Neil deGrasse Tyson?

  And it's some kind of shotgun wedding right at that last moment.

• 21:28Speaker 02

  Some kind of shotgun wedding.

• 21:29Neil deGrasse Tyson?

  I'm just saying.

• 21:30Speaker 02

  But here's the problem.

• 21:31Negin Farsad?

  None of the in-laws are happy in that scenario.

• 21:34Neil deGrasse Tyson?

  None of the in-law.

• 21:37Speaker 02

  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.

• 21:48Neil deGrasse Tyson?

  All right.

• 21:48Negin Farsad?

  It's like when I've tried to date a Pisces, it never works out.

• 21:52Neil deGrasse Tyson?

  You know, I could have told you that. Why didn't you call me? That's right.

• 21:57Neil deGrasse Tyson?

  So that's the, so that's the, we replied to the captain whether or not we fully satisfied his question. So what are the questions you got, Nagin?

• 22:04Negin Farsad?

  All right, let's move on to David. Um, he's actually happy to submit his very first question after years of of being a Patreon subscriber.

• 22:11Neil deGrasse Tyson?

  Oh, excellent. Oh, David, does he have a last name or is it just David?

• 22:14Negin Farsad?

  Um, he just, it's just David. He's like Madonna. He just goes by the one. Um, I once heard Alex Filippenko explain infinity in our universe as operationally infinite, 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?

• 22:48Neil deGrasse Tyson?

  Ooh, I love those questions.

• 22:50Negin Farsad?

  But I love that escalator metaphor because if that, if that's right, that puts things into making sense for me.

• 23:00Neil deGrasse Tyson?

  Right, right.

• 23:02Neil deGrasse Tyson?

  Right. The way I look at it is, and I can, I can contribute a little bit to this answer.

• 23:06Speaker 02

  Mm-hmm.

• 23:07Neil deGrasse Tyson?

  All right. So I'll contribute two parts. You take care of the rest. So, yes, if the universe is expand, and Alex Filippenko is a colleague of mine, we came up together, actually, in graduate school. Uh, and so if you, 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.

• 23:38Neil deGrasse Tyson?

  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, and never stop walking and always walk in the same direction. Whichever direction you choose, and you'll never get to the edge. Just 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.

• 24:23Neil deGrasse Tyson?

  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 cram, put them in, cram as many as you want in there, there's plenty of room. So, you take it from there, Stefan.

• 24:52Speaker 02

  You, you, you took all the good examples.

• 24:54Neil deGrasse Tyson?

  Oh, no!

• 24:57Speaker 02

  And of course, you know, there's, um, infinite time.

• 25:01Neil deGrasse Tyson?

  Ooh!

• 25:02Speaker 02

  You can have a finite world, but the clock can continue ticking for, you know, for an infinity. You know, meaning that the universe could be finite in extent, but just continue expanding for infinity.

• 25:15Negin Farsad?

  So the universe is like a, is like a vampire that never dies in that scenario.

• 25:21Neil deGrasse Tyson?

  Nagin, it's exactly like that.

• 25:25Negin Farsad?

  Great, got it. Just wanted to explain for the listeners.

• 25:28Neil deGrasse Tyson?

  Minus the blood, minus the blood.

• 25:30Negin Farsad?

  Okay.

• 25:30Neil deGrasse Tyson?

  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 of this.

• 25:50Speaker 02

  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 this satellite so that he can, you know, know about the Big Bang, call it Simon's Observatory.

• 26:08Neil deGrasse Tyson?

  Oh, yes, yes, Jim Simons.

• 26:09Speaker 02

  Jim Simons, he's a geometern, 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, you know, 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.

• 26:39Neil 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 a Simons Foundation, the Simons Center for Research in Physics, Biology, and Computing, which is right here in downtown Manhattan.

• 27:08Negin Farsad?

  Oh, I thought you were gonna say, which is on a yacht, because that's what he gets to afford now.

• 27:14Neil deGrasse Tyson?

  He does have a yacht, and I've been on his yacht, and it's called the Archimedes. And it's called the Archimedes.

• 27:19Negin Farsad?

  Of course, of course.

• 27:21Neil deGrasse Tyson?

  Yes, yes. So thank you for that, for queuing. That was your cue.

• 27:26Negin Farsad?

  Time for another question?

• 27:27Neil deGrasse Tyson?

  Yeah, please, please.

• 27:28Negin Farsad?

  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?

• 27:46Neil deGrasse Tyson?

  Wait, is that a word, monophony? Is that, is that like, does that mean a one-note concert? What are you saying there?

• 27:53Speaker 02

  That's what it sounds like to me.

• 27:54Neil deGrasse Tyson?

  Yeah.

• 27:55Speaker 02

  Something else.

• 27:56Negin Farsad?

  Oh my god, we have two of the smartest people on the planet and, and none of us know if that's like a, a word.

• 28:04Speaker 02

  Well, this is actually, actually a good point to actually talk about, um, you know, going back to Feynman. So, and, and his colleagues that they use quantum mechanics to smoothen out, for lack of a better words. De-infiniteize the infinity, that, I'm gonna up a new word. Get rid of the infinity.

• 28:20Neil deGrasse Tyson?

  We've got up to six new words this episode, right? Keep going.

• 28:23Speaker 02

  There is now a, you know, uber quantum theory and that theory is called string theory.

• 28:30Speaker 02

  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?

• 28:50Neil deGrasse Tyson?

  Okay.

• 28:50Speaker 02

  And so anyway, so in a long, it turns out that there is.

• 28:54Neil deGrasse Tyson?

  You're saying, you're saying quantum physics was brought on to possibly help with the classical infinities, but then it introduces infinity, infinities of its own?

• 29:03Speaker 02

  That's correct.

• 29:03Neil deGrasse Tyson?

  Okay, that ain't right, that ain't right.

• 29:05Speaker 02

  That ain't right, right.

• 29:05Neil deGrasse Tyson?

  Right, right.

• 29:06Speaker 02

  And, um, these things are called like ultraviolet or infrared divergences for the audience member who wanna get fancy. 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 research, younger researcher, 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 had to live in 10 dimensions, okay?

• 29:39Speaker 02

  There's, there's some gift.

• 29:41Neil deGrasse Tyson?

  There's a catch.

• 29:43Speaker 02

  There's a catch. And, and no, and going back to what Neil exactly said is that now that you have the, all these other dimensions, you can go and stuff infinities on those, in those other dimensions now, right? Um, but anyway, string theory is such a, such a theory that does that. Um, it, it does, it's a, 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, um, it's also a musical theory. That's correct.

• 30:12Neil 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, the questioner's, uh, 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 StarTalk Cosmic Queries.

• 30:53Neil deGrasse Tyson?

  We're back, the Infinity Edition with Stephane Alexander, physicist who's thought a lot about cosmology and infinities. And of course, Nagin Persad. Nagin.

• 31:05Negin Farsad?

  Hello.

• 31:06Neil deGrasse Tyson?

  Love having you here. It's been too long. Come back more often, okay?

• 31:09Negin Farsad?

  Absolutely.

• 31:10Neil deGrasse Tyson?

  Yeah, yeah, all right.

• 31:11Negin Farsad?

  But I'm, I'm, I'm on nearly every show in other dimensions.

• 31:15Neil deGrasse Tyson?

  Oh.

• 31:16Negin Farsad?

  So you have to go to the other dimensions, I think is what's going on.

• 31:22Neil deGrasse Tyson?

  And if you don't tell me that dimension, I will never find you. Right. You'll be, I'll be found only when you allow yourself to be found.

• 31:30Negin Farsad?

  I've also got hot dog fingers in those other dimensions, but don't worry about it.

• 31:34Neil deGrasse Tyson?

  Oh, yes. Oh, okay. Everything, everywhere, all at once, I think that was. So, so Stephane, 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?

• 31:49Negin Farsad?

  It's a weak connection.

• 31:50Speaker 02

  Yes, yes.

• 31:50Neil deGrasse Tyson?

  Yeah, that's it feels like really weak.

• 31:53Speaker 02

  They they should have just called it maybe something like guitar string theory.

• 31:59Speaker 02

  But yeah, the you know, so string theory, the 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 with and that's when things blew up on you. The infinity revealed itself. But if and the idea of string theory is that replace nothing is ever made up of a point particle anymore. When you even when you take a magnifying glass and you you try to resolve that point. And so what looks like a point from really, really far away, you zoom in and you realize it's a string.

• 32:40Speaker 02

  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'd know as a note, a tone.

• 33:06Neil deGrasse Tyson?

  Okay.

• 33:06Speaker 02

  Particular type of vibration that can be represented as a sound or, you know, a note on the piano. So like when I play a note on a piano, what's really going on is that there's a piano string hit him and that piano string is vibrating. And because it vibrates, it undulates at a very at a given rate. That rate of vibration, called a frequency, denotes what we call a tone or a sound. And so so string theory, the physics of strings really does match on very nicely.

• 33:38Neil deGrasse Tyson?

  Okay.

• 33:38Speaker 02

  For the physics of how notes are generated in instruments.

• 33:42Neil deGrasse Tyson?

  All right. So sorry to badmouth you at the front of that. I'm sorry. Nagin needs to apologize, too.

• 33:48Negin Farsad?

  So sorry.

• 33:53Negin Farsad?

  But

• 33:54Speaker 02

  It's an analogy, it's an analogy, but it's a really good analogy.

• 33:56Neil deGrasse Tyson?

  I get it, I get it. It feels right, it feels right. Alright. Again, keep going, we have, it's the last segment.

• 34:02Negin Farsad?

  Okay, so rapid fire section, here we go. From Anthropoc cosmic Dylan in San Diego writes, "Question for Dr. Alexander. Neil 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?"

• 34:26Neil deGrasse Tyson?

  Whoa.

• 34:28Speaker 02

  Whoa, whoa, whoa. That's a very tight question.

• 34:30Neil deGrasse Tyson?

  Let me tighten up the beginning of that. So, 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? Do you keep going? Do you just accept it? Or because it doesn't make sense, you have to do something about it? And that violates the Neil Principle?

• 34:50Speaker 02

  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 you know, but I have to pay my bills.

• 35:02Speaker 02

  Yeah. Paying the fun. No, no, I write and publish papers and respect the 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. I embrace it. I said, "Let's live with the infinities and wherever we can, try to sidestep it and make progress." And, um, yeah.

• 35:25Neil deGrasse Tyson?

  I see, okay. 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, okay. And how about, again, the second part was about jazz. What was, read that again?

• 35:42Negin Farsad?

  Yeah, they wrote, "How do you reconcile this gap with your research and your artistic expression through jazz music?"

• 35:52Speaker 02

  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 traps together and practicing and all that good stuff.

• 36:27Neil deGrasse Tyson?

  And there's surely some people who would say would would invoke the nihilism on jazz. Jazz is under no obligation to make sense.

• 36:38Neil deGrasse Tyson?

  I'm pretty sure some people out there feel that way.

• 36:41Speaker 02

  Well, there's a funny story about that. I mean, I want to hear your thoughts about very quickly. Um, when I first heard On it Coleman, I was like, what kind of I I made no sense. It didn't make any musical sense. And then much later on in life, as I thought I became more um advanced musically, it started making sense to me.

• 36:58Neil deGrasse Tyson?

  Oh, okay. All right. So it doesn't have to make sense upfront. That's right.

• 37:03Negin Farsad?

  Also, in in I would just for 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.

• 37:13Neil deGrasse Tyson?

  Right. That's why jazz is in bars. That's why.

• 37:17Negin Farsad?

  And also why all physicists and astrophysicists should be drinking when they talk about infinity.

• 37:25Speaker 02

  Well, I learned something very cool about it. I'm very proud of this. I always feel like I was the outsider physicist that played music. It turned out that the hero, the guy that won a 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.

• 37:44Neil deGrasse Tyson?

  Okay.

• 37:45Speaker 02

  Played when he was a postdoc, yeah.

• 37:47Neil deGrasse Tyson?

  Except I don't know that the oboe shows up much in jazz concerts. I'm pretty sure.

• 37:50Speaker 02

  Well, now it should.

• 37:51Neil deGrasse Tyson?

  I'm pretty sure that that was not a first choice.

• 37:56Negin Farsad?

  I know. The oboe feels like something you just get saddled with in middle school. You don't choose it.

• 38:02Neil deGrasse Tyson?

  You're in in elementary school. That was you would have last in line.

• 38:05Negin Farsad?

  Exactly, exactly.

• 38:07Neil deGrasse Tyson?

  You get the oboe.

• 38:08Negin Farsad?

  Now he's now he's saddled with a Nobel. Ugh.

• 38:13Negin Farsad?

  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?"

• 38:25Neil deGrasse Tyson?

  Yeah, me too, me too. Count me in that question as well.

• 38:28Speaker 02

  It's a beautiful, it is, it's a very tantalizing idea, and it actually does deal with gravitational affinities 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 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.

• 39:02Neil deGrasse Tyson?

  A link in a chain, like a link in a chain.

• 39:04Speaker 02

  A link in a chain, and I can link, I can link a fabric of spacetime with those loops. But what's linking is a gravitational field, and they're kind of, you can think of them as atoms of space.

• 39:14Neil deGrasse Tyson?

  Oh, actually, not atoms, pixels of space.

• 39:16Speaker 02

  Even better.

• 39:17Neil deGrasse Tyson?

  Yeah, pixels of space.

• 39:18Speaker 02

  Pixels of space, yes.

• 39:19Neil deGrasse Tyson?

  The smallest unit of space, yeah, okay. All right, again, we might have time for one, maybe one and a half more questions.

• 39:24Negin Farsad?

  Okay, so let's see. Abinav Yadav from Philly asks, "I struggle to think about spacetime 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 spacetime?"

• 39:45Speaker 02

  Well...

• 39:47Neil deGrasse Tyson?

  Silence. Wait, wait, what? Wait, what was that, what was that question?

• 39:53Neil deGrasse Tyson?

  Wait, spacetime is all those things, so what is the question?

• 39:56Negin Farsad?

  I guess, yeah, there's like, there's a grammatical something missing that's making it hard to understand this question.

• 40:04Neil deGrasse Tyson?

  Yeah, we need some semicolons, but, we need some semicolons, but all those things are true, right, Stefan? They're all going on in spacetime, right?

• 40:10Negin Farsad?

  And what's the easiest way of thinking about the concept of spacetime?

• 40:16Neil deGrasse Tyson?

  Okay, so if all that's going on in spacetime,

• 40:19Negin Farsad?

  Yeah.

• 40:19Neil deGrasse Tyson?

  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 spacetime is?

• 40:29Negin Farsad?

  To like a kid?

• 40:30Speaker 02

  Yeah.

• 40:32Speaker 02

  Um, yeah, so I would say that, yeah, I, I, I think it's, I think it's a good analogy to think of spacetime 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 spacetime itself to move along like gravitational waves. Right? So spacetime itself can actually support motion of, of ripples up itself. And, and that is different than any other types of medium that we know, right? Normally, something like, like electric field or particles need spacetime to move through.

• 41:17Speaker 02

  But they can't move through their own, their own medium. Spacetime has a, it's a very special type of medium in that sense. But, um, it's a very weird medium, for lack of a better word.

• 41:28Neil deGrasse Tyson?

  And nor is it under-

• 41:29Speaker 02

  It's a, it's a relational medium, okay?

• 41:32Neil deGrasse Tyson?

  And nor is it under any obligation to make sense to us. Yes, okay.

• 41:36Negin Farsad?

  But it just sounds like what, what you described is kind of like-

• 41:39Speaker 02

  It still makes no sense to me.

• 41:40Negin Farsad?

  Yeah.

• 41:42Negin Farsad?

  So the, the answer to this person's question is basically there's no way of really thinking about it in your daily life.

• 41:49Speaker 02

  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 spacetime metric and we describe it as a field of, you know, spacetime as some kind of a field. But again, these are just words that we attach to the equations that we, we, we write down, yeah.

• 42:07Neil deGrasse Tyson?

  But they make predictions and they work, so.

• 42:08Speaker 02

  They make very good predictions and they work very well, yeah.

• 42:11Neil deGrasse Tyson?

  That's why, however fantastical they sound, they still are connected to reality in that important way. So it's very, very good.

• 42:19Speaker 02

  I mean, the detection of gravitational waves with Lygo and Virgo, yep.

• 42:23Neil deGrasse Tyson?

  Yeah, yeah, yeah.

• 42:24Speaker 02

  And that's some-

• 42:25Neil deGrasse Tyson?

  Again, I think we got one more question.

• 42:27Negin Farsad?

  So, I mean, this is sort of like related. Everyone seems to be having a crisis in understanding. But Mal- Malcolm Marfan, um, 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.

• 42:49Neil deGrasse Tyson?

  Yeah, they are, Stefan.

• 42:51Negin Farsad?

  They want hard answers.

• 42:52Neil deGrasse Tyson?

  And I tell you, I, I remembered learning infinity mathematically and they said one divided by zero is undefined. Okay, I remember being taught that in my math class. Well, I have a math friend who we actually had as a guest. Um, John Allen Paulus, professor of math at Temple University outside of Philly. And I tweeted, I called him out in Twitter. And I said, John,

• 43:16Neil deGrasse Tyson?

  if one, one divided by zero is undefined, why don't you guys define it?

• 43:23Neil deGrasse Tyson?

  What are you waiting for? Okay.

• 43:26Neil deGrasse Tyson?

  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, so apparently to him, infinity is undefined because one divided by zero was infinity.

• 43:38Speaker 02

  Mm-hmm, mm-hmm.

• 43:39Negin Farsad?

  So, wait, so this thing is just totally up for grabs. Like, I could just do a, a journal, like 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.

• 43:54Neil deGrasse Tyson?

  We have to put closure on your theory. And one divided by zero is an acetate captured in Tupperware.

• 44:08Negin Farsad?

  That's, I mean, that's beautiful.

• 44:10Neil deGrasse Tyson?

  And that, that, that's a, that's a beautiful theorem right there, right there. We gotta call it quits there. Stefan, great to have you back on the show.

• 44:17Speaker 02

  Thanks for having me again, Neil.

• 44:18Neil deGrasse Tyson?

  All right, Nagin, it's been a delight. And, and by the way, Nagin, just quickly, weren't you on TV with Hillary Clinton? I did, I'm channel surfing. They say, that's Nagin. Wait, that's Hillary Clinton. What's he doing? What was that? Briefly tell me real quick.

• 44:36Negin Farsad?

  I'm on the show Gutsy on Apple TV. Um, Hillary Clinton is just basically, um, doing a series about gutsy women. And I, and crazily, I, um, I'm one of them. So, check it out. It's a really great series.

• 44:49Neil deGrasse Tyson?

  You're one of the gutsy women. Okay, it's just called gutsy.

• 44:51Negin Farsad?

  Yeah, it's called Gutsy on Apple TV.

• 44:53Neil deGrasse Tyson?

  Gutsy, very cool. I don't mean to, I don't mean to brag, but Hillary Clinton said I'm her favorite astrophysicist.

• 44:59Negin Farsad?

  Oh, uh.

• 45:01Neil deGrasse Tyson?

  Yeah, I'm sure, I'm pretty sure she knows only one astrophysicist. That's the problem.

• 45:05Speaker 02

  Oh, the best is when I meet my favorite musician and, and, and he goes, hey, by the way, can you, can you, can you get me introduced to Neil deGrasse Tyson, please?

• 45:20Neil deGrasse Tyson?

  All right, 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 Fersad. Always good to have you back. Neil deGrasse Tyson here, as always, bidding you to keep looking up.