Cosmic Queries – Understanding Infinity with Stephon Alexander

Summary

StarTalk Radio: Cosmic Queries – Understanding Infinity with Stephon Alexander

Original Air Date: February 6, 2026
Host: Neil deGrasse Tyson
Guest: Dr. Stephon Alexander, Professor of Physics at Brown University
Co-host: Negin Farsad (Comedian and host of Fake the Nation)

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Episode Overview

In this highly engaging and frequently comedic episode of StarTalk Radio, Neil deGrasse Tyson teams up with comedian Negin Farsad and theoretical physicist Dr. Stephon Alexander to tackle one of the biggest head-scratchers in all of science: infinity. Through a series of “cosmic queries” submitted by Patreon fans, the trio explores where infinity appears in mathematics, physics, and cosmology—diving into black holes, the expanding universe, string theory, the limits of our understanding, and the power (and peril) of mathematical abstraction. Expect playful banter, deep insights, and an unflinching look at the limits of science, sprinkled with metaphors about Tupperware, escalators, and jazz.

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1. What Is Infinity? Childhood Encounters and Existential Angst

[03:02 – 09:39]

• Neil shares his first encounter with “infinity” at age five, grappling with the idea of JFK’s “eternal flame.”

  • “At age five, I was like, ‘What? Does this flame never go out? How could it never go out?’” — Neil deGrasse Tyson [04:04]

• Stephon Alexander confesses up front:

  • “Let me admit something to you and Negin—I don't know what infinity is.” — Stephon Alexander [05:55]

• Stephon explains the childlike realization that counting never ends and introduces the idea of infinity as “the number that goes on forever.”

  • “You realize you can just go on counting for eternity…there’s this number, it’s called infinity.” — Stephon Alexander [06:13]

Infinity in Math and Physics

• Using fractions, Stephon connects division by zero to infinity, explaining computer crashes:

  • “If I go smaller than one, which is…one over zero, that number goes…that’s what infinity is. We call that division by zero.” — Stephon Alexander [06:56]
  • “Computers crash, actually, because…these divisions by zero…what would happen?” [08:02]

• Negin brings up the emotional trauma of graphing asymptotes, which Neil describes as “they do touch at infinity.”

  • “I wanted them to touch—it just felt like a missed connection forever!” — Negin Farsad [08:45]
  • “They do touch at infinity. So get your ass to infinity and you’ll see them touch.” — Neil deGrasse Tyson [08:54]

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2. Where Infinity Shows Up in the Universe

[09:39 – 20:48]

Physicists vs. Mathematicians vs. Philosophers

• Stephon notes that mathematicians “make a living from infinity,” philosophers obsess over it, but “we physicists try to run away from it.”
  • “We physicists try to run away from it, try to avoid it.” — Stephon Alexander [09:39]

Infinity as a Placeholder for Ignorance? (Fan Question: Captain James Riley)

[10:12 – 16:38]

• Does “infinity” just mean “we don’t know”?

  • Negin reads a fan’s question: Is infinity a cop-out? Is it real, or just a label for what we don’t understand? [10:12]

• Stephon uses black holes as a case study.

  • He describes how Einstein’s equations led to the prediction of black holes, which eventually were observed:
    • “A mathematical prediction…spat out…a black hole.” — Stephon Alexander [11:45]
    • The singularity at a black hole’s center produces “infinite density, an infinity in the forces, right, and an infinity in the curvature.” [14:24]

• Neil and Negin challenge: Is this physical, or a mathematical artifact?

  • Stephon explains, “Some people say…there’s some new physics we do not know. Some people say you have to accept the infinity, and…nature might be censoring our infinities.” [16:21]
  • “It could be that the infinity is the limit of the applicability of this theory.” — Neil deGrasse Tyson [16:26]

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3. Can We “Tame” Infinities? Lessons from Quantum Physics

[20:48 – 32:42]

How Quantum Physics Fuzzifies the Infinite

• Stephon recounts how electromagnetism once predicted impossible infinite forces, but quantum mechanics “fuzzifies and softens” the problem.

  • “Quantum physics fuzzifies and softens…you just made up that word!” — Neil deGrasse Tyson [22:20]

• Explanation: Photon exchange (quanta of light) prevents infinite forces as particles get super close, showing quantum effects resolve some classical infinities.

Will Quantum Gravity Save Us from Black Hole Infinities?

• Stephon: Some physicists (e.g., Stephen Hawking, Lenny Susskind) hope a quantum theory of gravity, by analogy, “jumps in and saves the day” as we approach black hole singularities.

  • “What if…quantum gravity…as I go into the singularity of a black hole, you don’t get infinity, but you get new quantum effects.” — Stephon Alexander [24:20]

• But quantum mechanics and gravity are “very incompatible with each other…never reconciled their differences.” — Stephon Alexander [24:37]

  • Neil: “It’s like when I’ve tried to date a Pisces. It never works out.” [24:49]

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4. Is the Universe Actually Infinite? (Fan Question: David)

[25:05 – 30:26]

• Patreon listener asks if the universe is “operationally infinite” (escalator metaphor)—and how multiverses fit in.

• Neil’s take: The universe can be finite but “you could just keep walking and never reach the edge,” just like on Earth—a sphere (surface) without a boundary.

  • “Don’t equate reaching an edge with something having to be infinite.” — Neil deGrasse Tyson [26:00]

• Embedding infinities: Two infinite sheets of paper in three dimensions can “both be infinite and never intersect,” so multiple infinite universes are no problem.

• Stephon adds: Even if the universe is finite, time (or expansion) can be infinite—think “a vampire that never dies.”

  • “You can have a finite world, but the clock can continue ticking for…infinity.” — Stephon Alexander [27:53]

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5. String Theory, Music, and Infinity (Fan Question: Gavin Bamber)

[30:26 – 38:14]

• Question: Can string theory be represented by music? Would it be a composition that continues into infinity?

The Music of String Theory

• Stephon discusses why string theory appeals: It eliminates some mathematical infinities.
• It replaces point particles (which lead to infinities) with tiny vibrating strings. The vibrations correspond to different particles, analogous to musical notes.
  • “It’s not just any old string—the string, because it’s quantum, has to be vibrating…that generates a spectrum…what we know as a note, a tone.”
  • “String theory really does match on very nicely to the physics of how notes are generated in instruments.” — Stephon Alexander [36:02–37:54]

But…Does It Still Have Infinities?

• Quantum theories themselves can develop new types of infinities (ultraviolet and infrared divergences). But in string theory, “it is an infinity-free theory” if you allow for extra (10) dimensions.
• Neil: “There’s a catch.” [32:42]
• Stephon: “You can go and stuff infinities in those other dimensions.” [32:42]

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6. The Human Mind, Infinity, and Jazz (Fan Question: anthropocosmic Dylan)

[38:14 – 41:32]

• Does infinity “make sense” to physicists, or do we force sense onto it? How does Stephon reconcile this gap in his research and through his jazz?

• Stephon: “I adhere to the Neil Principle—the universe is under no obligation to make sense to us…there is a sense in which we have to…embrace the infinities…try to sidestep it and make progress.” [39:02]

• In jazz, too, the process is messy, incomplete, and reliant on improvisation:

  • “You must try to break the rules and stumble and fall to make something new…embracing the mistakes…that’s what jazz improvisation is about.” — Stephon Alexander [40:04]

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7. Loop Quantum Gravity, Pixels of Space, and Space-Time Explained (Fan Questions: Bruce Ryan, Abhinav Yadav)

[42:19 – 46:23]

What Is Loop Quantum Gravity?

• Stephon: It’s a framework proposing that the fabric of space-time itself is woven from quantum “loops”—like links in a chain, or “pixels of space.” [43:16]
  • “I can link a fabric of space-time with those loops…pixels of space.”

How Should We Think of Space-Time?

• Stephon describes space-time as “a very faint and invisible fabric…that can support ripples of itself (gravitational waves)…a very special type of medium.” [44:22–45:39]
• Neil: “However fantastical [these ideas] sound, they are still connected to reality in that important way.” [46:23]

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8. Does Infinity Exist in the Physical World? (Fan Question: Malcolm Marfan)

[46:39 – 48:29]

• How do we know infinity isn’t just an abstraction? Neil recounts frustrations with the undefined status of “1 divided by 0” in math.

  • “If one divided by zero is undefined, why don’t you guys define it?” — Neil deGrasse Tyson [47:04]

• The episode closes with playful jokes:

  • Negin: “Can I just do a journal article right now and just be like, ‘1 divided by infinity is a bowl of jello’…?” [48:06]
  • Neil: “One divided by zero is an asymptote captured in Tupperware.” [48:16]

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9. Notable Quotes & Memorable Moments

• “Nature might be censoring our infinities.”—Neil deGrasse Tyson [16:21]
• “When you embed infinities in higher dimensions, you got no problems at all.”—Neil deGrasse Tyson [26:00]
• “You must try to break the rules and stumble and fall to make something new…that’s what jazz improvisation is about.” — Stephon Alexander [40:04]
• “[The universe] makes no sense, but…these are just words we attach to equations. They make very good predictions and they work very well.” — Stephon Alexander [46:18–46:23]
• “However fantastical [these ideas] sound, they are still connected to reality in that important way.”—Neil deGrasse Tyson [46:23]

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10. Engaging, Playful Banter

• Negin’s analogy of jazz and drinking:

  • “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.” [41:15]
  • “That’s why jazz is in bars. That’s why all physicists and astrophysicists should be drinking when they talk about infinity.” [41:25]

• Stephon: “I always feel like the outsider physicist that played music. Turned out…the guy that won the Nobel for figuring out infinities…Ken Wilson…played the oboe.” [41:37]
  Negin: “It feels like something you just get saddled with in middle school.” [42:08]

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11. Final Thoughts

• The episode ends with the acknowledgment that infinity remains both a mathematical tool and a source of deep philosophical confusion. Physicists often treat infinities as signals of unknown physics rather than “real” physical entities, preferring theories that “tame” or avoid infinities if possible. Whether existing in reality or merely in human minds, infinity—like jazz—might ultimately be “under no obligation to make sense to us.”

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For Listeners:
This episode is a great primer into the big questions of physics, framed in a relatable and entertaining way—even if (as the hosts repeatedly admit) “it still makes no sense!” You'll come away with new metaphors, a few laughs, and a deeper (if perpetually incomplete) appreciation of infinity in science.

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Key Segments & Timestamps:

• Introduction to Infinity: [03:02 – 09:39]
• Infinity & Black Holes: [10:12 – 16:38]
• Quantum Physics & Taming Infinity: [20:48 – 32:42]
• Is the Universe Infinite?: [25:05 – 30:26]
• String Theory & Music: [30:26 – 38:14]
• Infinity, Mind, and Jazz: [38:14 – 41:32]
• Loop Quantum Gravity & Space-Time: [42:19 – 46:23]
• Physical Reality of Infinity: [46:39 – 48:29]

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Summary by StarTalk Podcast Summarizer AI, episode released February 6, 2026.

Transcript

[A]

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[B]

Hello.

[C]

Yes, I'm your honorary astrophysicist comedian friend.

[A]

Yes. Everybody needs one of those, right?

[C]

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

[A]

You are a host of the show Fake the Nation. That's right. Very cool. And in addition to Fake the Nation, you got some side gig where you've got a succession recap.

[C]

That's right.

[A]

What's up with that?

[C]

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.

[A]

Succession up from hbo. Right. I saw the whole first season and it was too. It's like really weird for me to continue. Yeah, it's like, I don't want this to be true. You know, I don't want that. Please.

[C]

I know it's pretty gross, but so hilarious at the same Time.

[A]

Well, help me welcome my friend and colleague, Stefan Alexander Stephan, your returning guest. You first appeared with us when we were on the NatGeo 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 follow that up with Fear of a Black 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. 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 5 when Kennedy is assassinated. Okay? That's how old I am. And there's the burial. And they put him in Arlington Cemetery, and there's a flame there at the burial spot, and they called it the eternal flame. And I said, what? Does this flame never go out? How could it never go out? What? And at age five, this with me. Okay, sorry. This was like how at night do they secretly put more oil in the flame, you know, but the camera doesn't show it. I was. And then I would later learn, yes, that was figurative, that it's eternal. But there is a formal mathematical concept called infinity. Nagin, did you have any existential angst over infinity at any time in your life? Just to put that on. Put it on the table right now, because we got the man who's gonna straighten us out.

[C]

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.

[A]

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

[C]

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.

[A]

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

[B]

Let me admit something to Ewan again. I don't Know what infinity is? Okay. I mean, I can.

[A]

Okay, we're done here.

[C]

Okay, bye, everybody.

[A]

Nikki, you got any jokes to take us out?

[B]

Okay.

[A]

I mean, the first.

[C]

Who booked this guy.

[A]

I know, right?

[B]

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, 1, 2, 3. And you realize that you can 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? To infinity.

[A]

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. The geek counting contest.

[B]

Yeah, 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. If I say you get one over one of the pizza, well, a smart Joe will say, I get the whole piece 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 wanted to avoid these kind of things when you wrote code, these divisions by zero, because what would happen?

[A]

Right, yeah, the program crashes.

[B]

Yeah, crashes, exactly. Computer doesn't know what to do with it.

[A]

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

[B]

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

[A]

Yeah, yeah. Computer would. Captain Kirk would out reason the computer and then the smoke would come out. But in modern times, no, the computer, it just crashes. Yeah.

[C]

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

[A]

You cared for them, you wanted them.

[C]

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

[A]

You know, they do touch at infinity. So get your ass to infinity and you'll see them touch.

[B]

But.

[A]

Right, so Stefan, asymptote is another one of these concepts, right?

[B]

Yeah, it's a great word.

[A]

It's a great word too.

[B]

Right. You can kind of, 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, with physics and astrophysics and cosmology.

[A]

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

[B]

It 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, try to avoid it.

[A]

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 Nagin, do you have, you have questions from our Patreon members?

[C]

Yeah, I absolutely do. Let me dive in with a question from Captain James Riley. They rate. It always drives me crazy when I hear that a singularity has infinite density or that the universe is infinite. Is this just something we label things that we don't fully understand? I hate the concept of infinity. It seems like a cop out.

[A]

I love that.

[C]

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

[A]

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

[B]

Yes or no? Can we evoke one of your favorite astrophysical objects, Neil? The black hole. The black hole.

[A]

What's that?

[B]

Because I think this is the perfect, very good example of where you kind of get to have your cake and eat it too. Because here is an interesting thing. When Einstein came up with his theory of general relativity, which describes how matter and energy can warp the space time fabric and create the effect that we call gravity, a mathematical prediction A mathematical solution came out of that theory. This theory spat out a very extreme sort of extreme 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. And Neil, you've done some excellent reports on that in the past.

[A]

But just to be clear, Negin, 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. It didn't just poop it out like, like.

[C]

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

[A]

Someone'S butt en route to whatever it was doing. No, no, Some brilliant people applied. Brilliant people applied Einstein's general relativity, now that they have that framework to arrive at a black hole as a new. Under a new object, a new prediction. Yeah, right, yeah.

[B]

And it was a ma. It was literally, you know, the Einstein theory was 10, what we call 10 couple 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 Schwarzschild solution. But at that time, like people, some people and one of my mentors, David Finkelstein, I have the Edenton Finkelstein coordinate system, which was based on Schwarz solution about the event horizon. Right. The point of no return once you fall into this black hole, after it gobbles you up. You know, this was seen by many to just be some mathematical trickery, some mathematical solution that has not. No element of reality. Until, of course, we found one. Right, okay. We found many. Right. Now there are black hole laboratories out there.

[A]

Yeah, yeah, yeah, yeah.

[B]

And so the thing that I find interesting about that was people already knew that the black holes this the reason why they thought it was a mathematical artifact or mathematical gobbledygook of Einstein's theory. Some physicists thought was because it actually had a singularity, it actually had an infinity. What do I mean by that? If you actually, this is the idea 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, you know, like a ball. Think of the black hole as a gigantic ball in outer space, a gigantic invisible dark ball. And as I go in to the center of the black hole, this radius will eventually go to zero. But if I divide and it turns out that the density and the force really falls off, it actually decreases as 1 over r, sometimes 1 over r squared, 1 of r so what happens when r goes to zero? You get an infinity. You get an infinity in the density. The mass density.

[A]

Infinite density.

[B]

You also get in infinite density. Thank you. You get an infinity in the forces. Right. And you get an infinity in the curvature, because the curvature becomes infinity.

[A]

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?

[B]

Yes. No. Good, Good. This is interesting.

[A]

I'm pretending I'm the dude who has to. I'm the captain. No, you're just making this. How can you have anything that's infinite? Anything that's. That's a physical thing. How is that even possible?

[B]

We. We agree.

[A]

You can do that mathematically. No one's arguing right now. You're gonna tell me an actual physical thing hits the infinity that your math delivered, and that's what.

[C]

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

[B]

Yes. Very good.

[A]

Okay. Where you going with this? I'll stay with you. Go.

[B]

I'm gonna bake the black hole.

[C]

I'm just saying, like, it's infinitely dense. The Tupperware container is gonna break.

[B]

Right.

[C]

Or whatever. Does that make any sense?

[B]

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? So then this is where you get disagreements in. Amongst physicists and astrophysicists. Some people say, well, there's something that replaces that theory, meaning general relativity, there's some new physics that we. Yet we do not know. Some people say you have to accept the infinity. And, you know, there's something Is censoring that infinity from actually realizing itself and coming out and doing bad things.

[A]

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

[B]

Yes.

[A]

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

[B]

That's. That's. That's a take. I take, actually. Okay. All right. That's fine. I land on. That's why.

[A]

Okay, now where's the Tupperware go?

[B]

We gotta know exactly.

[C]

I know. I feel like.

[A]

Back to the Tupperware.

[C]

You have some really. Yeah. Some really expansive Tupperware leftovers forever in.

[A]

Your Tupperware leftovers forever. Because it's infinitely dense, it could feed everyone forever. We got to take a quick break, but when we come back, more with Stefan Alexander, who's taken us to infinity and beyond with, of course, my co host, Nadine Fassad. We'll be right back. T Mobile 5G Home Internet has some big news you should know about. They now have the fastest 5G home Internet, according to the experts at OOKLA Speed Test. All right, so let's unpack that. It means photo backups happen faster. Streaming a documentary does install halfway through. What's really notable is that the jump in speed doesn't come with added complexity. Setup is simple. Plug it in and you're online in less than 15 minutes. And the value side of the equation holds too, with a plan price that's backed by a five year price guarantee. So if you want the fastest 5G home Internet with a simple setup and savings that stick, get t mobile 5G home Internet. And if you don't want that, wait a minute, why wouldn't you want that? Just visit t mobile.com homeinternet to check availability today. Price guarantee exclusions like taxes and fees apply Fastest based on Ookla Speed test intelligence data. Second half 2025. All rights reserved.

[B]

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Formerly, he's Cooper Manning, the more intelligent and handsome of the Manning brothers.

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And he's Brian Baumgartner.

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But to me, he'll always be Kevin from the office. Yeah, you and everybody else together, we're.

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The hosts of the new comedy golf.

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[C]

Please welcome aboard the Johnson family.

[A]

The whole fam's here for the Disney cruise. So you know, we came to play. And listen, the adults are gonna have a ball. First we're chilling in the infinity pool, onto massages at Sense's Spa, then gliding into Star Wars Hyperspace lounge for a toast. We're even gonna kick back with Mickey on Disney's private island. That's how we get down. Cause Disney Cruise Line is where we came to play. I'm Brian Futterman and I support StarTalk on Patreon this is StarTalk with Neil DeGrasse Tyson. We're back. Star Talk 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 Negeen Frassad Nagin. You wrote a book. I did a few years ago.

[B]

Yeah.

[A]

Just. It was. And I'm trying to remember the title. Is it how to make white people laugh or something like that?

[C]

Yes, how to make White people Laugh. Neil, it wasn't for you?

[A]

No, 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.

[C]

That's right. Make white people laugh.

[A]

So I remembered the title correctly.

[C]

That's the title.

[A]

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.

[B]

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 beasts, yes. Tame the beast one was the electric charge and the electric force. So if you look at a charged particle, an electron. 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, according to the equations that work really well for all of our motors and all of our, you know, electricity and all that wind energy and all that stuff, it uses the same physics that we trust. But according to this physics, when you go here, all that good stuff goes out the window because you will get, according to the theory, an infinite force and an infinite amount of energy. And we do not measure that because the magnets touch and nothing blows up.

[A]

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

[B]

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

[A]

All right.

[B]

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, you just made up that word fuzzify.

[A]

I'm pretty sure you just Made up, I'm pretty sure. But okay, we know what you mean. Let the record show he's making up words as he goes along.

[C]

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 fuzzifies.

[A]

But continue fussifying infinity.

[B]

All right. 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, doesn't require quantum things. What do I 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. The photon can actually do weird things. It can do weird quantities.

[A]

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

[B]

Very good. So there are now people, not people, they're great physicists that argue, like Stephen Hawking being one and Gerardo Tuft and Lenny Susskind and others that said, ah, what if what happened with, you know, with real magnets, 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 today? And as I go into the singularity of a black hole, you don't get infinity, but you get new quantum effects. Right.

[A]

What would that look like? You'd have to marry quantum physics with Einstein relativity for that.

[B]

You have to do that and it's.

[A]

Some kind of shotgun wedding right at that.

[B]

Some kind of shotgun with it.

[A]

I'm just saying.

[B]

But here's the problem.

[C]

None of the in laws are happy in that.

[A]

None of the in laws.

[B]

Here's the funny thing. If gravity and quantum mechanics were to be a couple, they're very incompatible with each other. Every reconciled difference is that this allow them from actually making a bond. Yeah.

[A]

All right.

[C]

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

[A]

You know, I Could have told you that. Why didn't you call me? So that's. We replied to the captain whether or not we fully satisfied his question. So what are the questions? You got, Nagin.

[C]

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

[A]

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

[C]

He just. It's just David. He's like Madonna. He just goes by the one I once heard Alex Filipenko explain infinity. And our universe is operationally infinite, infinite to us because we could 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?

[A]

Ooh, I love those questions.

[C]

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

[A]

Right, right, right. The way I look at it is. And I can. 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 expand, and Alex Filipenko is a colleague of mine, we came up together actually, in graduate school. And so if you. If you have an infinite universe that's expanding right, you'll never reach the edge. And I'd love. Like you said, we all agree that escalator analogy is excellent. However, you don't need an infinite universe to never reach the edge. For example, the surface of the Earth is not infinite yet. You could just keep walking and never reach the edge. So don't equate reaching an edge with something having to be infinite, because the space can turn back on itself and you can end up just making loops and never stop walking and always walk in the same direction, whichever direction you choose. And you'll never get to the edge. Just that. My first point to that. And the second point is if you embed. So I can have a sheet of paper that's infinite. Infinite. Okay, now, but a sheet of paper is two dimensions. I can have another sheet of paper that's infinite and put them 1cm apart from each other, and they will never intersect, even though they're both infinite, because I pulled one into a third dimension. And so when you embed infinities in higher Dimensions, you got no problems at all. You can put them in, cram as many as you want in there. There's plenty of room. So you take it from there. Stuff.

[B]

You took all the good examples. Oh, no. And of course, you know, there's infinite time. Oh, 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 an infinity.

[C]

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

[A]

It's exactly like that.

[C]

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

[A]

Minus the blood. Minus the blood, yeah.

[B]

Okay.

[A]

And just to follow up on what you just said, Stephanie, 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.

[B]

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, he put a lot of money towards this satellite so that he can, you know, know about the Big bang called the Simons Observatory.

[A]

Oh, yes, yes. Jim Simon.

[B]

Jim Simons, he's, he's a geometer. So he came up with some, some important mathematics all about this topic. He believes that the universe actually is finite. It's a, what, you know, a sphere, it has a spherical geometry. And if you, you know, if you play with the, 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.

[A]

And, 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.

[C]

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

[B]

Now.

[A]

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

[C]

Of course.

[A]

Yes, yes. So thank you for that, for cueing. That was your cue? Yeah.

[C]

Time for another question?

[A]

Yeah, please, please.

[C]

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?

[A]

Wait, is that a word? Monophony? Is that, is that like, does that mean a one note concert? Is that what he's saying there?

[B]

That's what it sounds like to me.

[A]

But it's something else.

[C]

We have two of the smartest people on the planet and none of us know if that's like a word.

[B]

Well, 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 smoothing out, for lack of a better words, de. Infinitize the infinity that I made up a new word. Get rid of the infinity.

[A]

You have up to six new words this episode.

[B]

Right?

[A]

Keep going.

[B]

There is now a, you know, 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. So anyway, so in a long.

[A]

It turns out you're saying quantum physics was brought on to possibly help with the classical infinities, but then it introduces finities, infinities of its own.

[B]

That's correct.

[A]

That ain't right. That ain't right.

[B]

That ain't right. Right, 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 research, younger researcher, was that it actually was an infinity free theory, quantum theory electron that contained gravity in it as well contain, you know, aspects of all the forces. But you had to live in 10 dimensions. Okay. There's a, there's some, some give.

[A]

There's a catch.

[B]

Going back to what. There's a catch 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. But anyway, string theory is such a, such a theory that does that. It's a theory that does not have in its mathematical structures, and the solution it spits out, it does not have infinities. So we all love that. It's elegant and beautiful. And it's also a musical theory. That's correct.

[A]

I do want to hear what you have to say about string theory and music, because that is a part of the questioner's content. But we got to take a quick break. When we come back, the third and final segment. Infinity. Does infinity have three segments? Can it have three segments? I don't know. Come back and find out on StarTalk. Cosmic query. Step aboard a Disney cruise and Discovery. Discover where memories meet adventure. Where escape meets imagination. Where magic meets the sea. Disney Cruise Line. This is Rich Cannon from Sirius XM NFL Radio, reminding you that Sirius XM is the place to hear every NFL playoff game from the wild card round all the way through the Super Bowl. Plus, you get to decide how you want to listen to the game. We'll have the hometown announcers for each game and the national broadcasters on your radio and on the Sirius XM app. And if it's football talk that you want, just search for NFL Radio on the app or tune to Sirius XM channel 88 in your car. Hey, Sal. Hank. What's going on? We haven't worked a case in years. I just bought my car at Carvana and it was so easy. Too easy.

[B]

Think something's up?

[A]

You tell me.

[B]

They got thousands of options, found a.

[A]

Great car at a great price, and it got delivered the next day. It sounds like Carvana just makes it easy to buy your car, Hank. Yeah, you're right. Case closed.

[C]

Buy your car today on Carvana. Delivery fees may apply.

[A]

We're back. The Infinity edition with Stefan Alexander, a physicist who's a lot about cosmology and infinities. And, of course, Nagin Farsad. Nagin, hello. Love having you here. It's been too long. Come back more often. Okay.

[C]

Absolutely.

[A]

Yeah. Yeah.

[B]

All right.

[C]

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

[A]

Oh.

[C]

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

[A]

And if you don't tell me that dimension, I will never find you.

[B]

Right.

[A]

You'll be found only when you allow yourself to be found.

[C]

I've also got hot dog fingers in those other dimensions. But don't.

[B]

Yes.

[A]

Oh, okay. Everything everywhere, all at once. I think that was so. 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 they're. Music has string instruments. I don't.

[C]

You know, it's a weak connection.

[B]

Yes.

[A]

Yeah. That sound, it feels like really Weak.

[B]

They, they should have just call it maybe something like guitar string theory, maybe. But yeah, the, you know, so string theory, one of the 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 where 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 instead, what looks like a point from really, really far away, you zoom in and it. You realize it's a string, okay? 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 vibrant 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 standard wave? It's basically what you know as a note, a tone, okay, 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 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.

[A]

So sorry to badmouth you at the front of that. Sorry. Nagin needs to apologize.

[C]

So sorry.

[B]

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

[A]

I get it. I get it. It feels right. It feels right. All right, Nagin, keep going. We got. It's the last segment.

[C]

Okay, so rapid fire section.

[B]

Here we go.

[C]

From anthropocosmic. 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?

[B]

Whoa, whoa, whoa, whoa. So that's a very good question.

[A]

Let me tighten up the beginning of that. So he's asking if I say the universe is under no obligation to make sense to you, do These infinities make sense to you, and does it bother you or do you keep going? Do you just accept it or. Because it doesn't make sense, you have to do something about it. And that violate the Neil principle.

[B]

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. Yeah. Baking the fun. No, no. I write and publish papers and respect to journals. But having said that. So, yes, I think there is a sense in which we have to. My take on 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.

[A]

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 the Nagin, the second part was about jazz. What was the. Read that again.

[C]

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

[B]

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.

[A]

And there's surely some people who would say would. Would invoke the Neil, the nihilism on jazz. Jazz is under no obligation to make sense to you. I'm pretty sure some people out there feel that way.

[B]

Well, there's a funny story about that. I want to hear your thoughts about. 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.

[A]

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

[C]

Also, just for when jazz doesn't make sense, I usually go to the bar, get another drink, and then jazz starts to make a lot of sense.

[A]

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

[C]

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

[B]

Well, I learned something very cool, by the way. 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 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.

[A]

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

[B]

Well, now it should.

[A]

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

[C]

I know. It feels like something you just get saddled with in middle school.

[B]

Exactly.

[A]

You don't choose it in elementary school. You were the last in line.

[C]

Exactly, exactly.

[A]

You get the oboe.

[C]

Now he's saddled with a Nobel. 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?

[A]

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

[B]

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 ion 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. Like chains. Like, you know, like a chain.

[A]

But I can have a link in a chain. Like a link.

[B]

A link in a chain. And I can link. I can link a fabric of space time with those. With those loops. But what's. Lincoln is a gravitational field. And they're kind of. You can think of them as atoms of space.

[A]

Oh, I see. Not atoms. Pixels of space.

[B]

Even better.

[A]

Yeah, even better.

[B]

Pixels of space.

[A]

The smallest unit of space. Yeah. Okay. All right, Nagin, we might have time for one, maybe one and a half more questions.

[C]

Okay, so let's see. Abhinav Yadav 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 pull. Pop in and out of. What's an easier way to think about space time?

[B]

Well, the same silence.

[A]

Wait, wait, wait. What was that? What was that question? Wait. Space time is all those things. So what is the question?

[C]

I guess. Yeah, there's like. There's a. There's a grammatical. Something missing that's making it hard to understand.

[B]

Yeah.

[A]

We need some semicolons, but. Some semicolons, but all those things are true. Right, Stefan? They're all going on in space time.

[B]

Right.

[C]

And what's the easiest way of thinking about the concept of. Of space time?

[A]

Okay, so if all that's going on in space time.

[C]

Yeah.

[A]

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 to.

[C]

Like a kid.

[B]

Yeah. Yeah. So I would say that, yeah, I think it's a good analogy to think of space time as some sort of very, very faint and invisible fabric that. But it's a special kind of fabric because that fabric can also support space time itself to move along, like gravitational waves. Right. So space time itself can actually support motion of ripples of itself. And that is different than any other types of medium that we know. Right. Normally something like an electric field or particles need space time to move through, but they can't move through their own. Their own medium. Space time is a very special type of medium in that sense, but it's a very weird medium, for lack of a better word.

[A]

And nor is it what we call.

[B]

It's a relational medium. Okay.

[A]

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

[C]

But it just.

[B]

Right. It makes no.

[C]

What you described as.

[B]

It still makes no sense to me.

[C]

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

[B]

It's like, no, I mean, again, this is. What Neil just said makes no sense. But I know I could write down this object called a space time 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 write down. Yeah.

[A]

But they make predictions and they work.

[B]

So they make very good predictions and they work very well.

[A]

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

[B]

I mean, the detection of gravitational waves with LIGO and Virgo. Yep.

[A]

Yeah, yeah, yeah.

[B]

And then some again.

[A]

I think we got one more question.

[C]

So.

[A]

Last one.

[C]

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.

[A]

Yeah, they are, Stefan.

[C]

They want hard answers.

[A]

And I tell you, I remembered learning infinity Mathematic, 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. John Allen Paulos, professor of Math at Temple University outside of Philly. And I tweeted, I called him out in Twitter, and I said, john, if one divided by zero is undefined, why don't you guys define it? What are you waiting for? Okay. I've been waiting my whole life, and all you have to do is define it and we're cool. What's up with that? So. So apparently to him, infinity is undefined because 1 divided by 0 is infinity. Kind of.

[C]

So, 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. If this is not for grabs, I'd like to take a stab.

[A]

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

[C]

That's what they're kind of. That's beautiful. I mean, that's beautiful.

[A]

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

[B]

Thanks for having me again, Neil.

[A]

All right, Nagin, it's been a delight. And by the way, Nagin, just quickly, weren't you on TV with Hillary Clinton? Did I. I'm channel surfing.

[C]

They say that's Nagin.

[A]

Wait, that's Hillary Clinton.

[B]

What are you doing?

[A]

What was that briefly?

[C]

Tell me about that. I won the show Gutsy on Apple tv. Hillary Clinton is just basically doing a series about gutsy women. And I in crazily. I. I'm one of them. So check it out. It's.

[A]

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

[C]

It's called Gutsy on Apple tv.

[A]

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

[C]

Oh, yeah, I'm sure.

[A]

I'm pretty sure she knows only one astrophysicist.

[B]

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?

[A]

All right, guys, we're done here. Land this plane. This has been startalk Cosmic queries, the infinity edition. It's delight to have an old friend and colleague, Stefan Alexander and Nagin Fursad. Always good to have you back. Neil degrasse Tyson here as always, bidding you to keep looking up. Foreign Ted Danson here to tell you about my podcast with my longtime friend and sometimes co host Woody Harrelson. It's called where everybody knows your name. And we're back for another season. I'm so excited to be joined this season by friends like John Mulaney, David Spade, Sarah Silverman, Ed Helms, and many more. You don't want to miss it. Listen to where everybody knows your name with me, Ted Danson and Woody Harrelson sometimes, wherever you get your podcasts. Okay, ladies, when I said we came.

[B]

To play, didn't I mean it? This Disney cruise got me feeling like a queen. We can get massages at sense of.

[A]

Spa, have a meet and greet with black Panther.

[B]

Oh, I love him.

[A]

And I can't wait to sunbathe on the private island.

[B]

And the kids will be fine. Girl, they're good.

[A]

Exactly. While they hang in the kids club with Mickey Mouse, we can do our thing thing and do it well all day.

[B]

Disney cruise line is where we came to play.