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Speaker 1: Hey, Katie, how many pets do you have living with

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Speaker 1: you at home? That depends on your definition. Does it

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Speaker 1: include all living creatures in my house? Does it include

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Speaker 1: the mites in my eyelashes? Maybe not, like all the

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Speaker 1: microobs and the tardy grades and all the bacteria in

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Speaker 1: your gut? What about my husband? That's your call. Depends

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Speaker 1: on your relationship, personal choice. Okay, then I've got a

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Speaker 1: dog named Cookie, I've got to fish. I'm going to

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Speaker 1: name them right now, called Bill and Head. So three

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Speaker 1: or four, depending on the definition of my husband. All right,

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Speaker 1: well that's more than I've got. And I got a

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Speaker 1: question for you about pets. At what point do you

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Speaker 1: say you have too many pets? I think that's the

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Speaker 1: wrong way to look at it. Once you have, you know,

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Speaker 1: two or three, like one more, there's no difference, right,

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Speaker 1: It's the cat principle, like once you have two cats,

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Speaker 1: there's no difference between two cats for cats tin cats.

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Speaker 1: I think that sounds dangerous. You're gonna mathematically induce yourself

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Speaker 1: to having an infinite number of cats. Exactly if you

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Speaker 1: already have infinite pets, you can add more and more

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Speaker 1: and still have infinite pets. Hi, I'm Daniel, I'm a

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Speaker 1: particle physicist, and I have an infinite number of questions

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Speaker 1: about the nature of our universe. And I am Katie Golden.

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Speaker 1: I like pets, but I am not a particle physicist,

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Speaker 1: and I still have infinite questions about the universe and

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Speaker 1: about how many cats I can have and get away with.

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Speaker 1: How many cats can there be in the universe? Could

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Speaker 1: we have an infinite universe field with infinite cats. I

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Speaker 1: think that if you replace the sort of building blocks

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Speaker 1: of the universe with cats, it would be a lot cuter.

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Speaker 1: But yeah, I come to the show with a little

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Speaker 1: bit of background in a psychology and evolutionary biology, and

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Speaker 1: that's why I like to talk about cats all the time.

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Speaker 1: And welcome then to the podcast Daniel and Jorge Explain

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Speaker 1: the Universe with its Infinite variety of Cats, a podcast

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Speaker 1: in which we talk about all the crazy, amazing things

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Speaker 1: that are out there in the universe. Not just the

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Speaker 1: things in the universe. We talk about the very nature

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Speaker 1: of the universe. We talk about the universe that's in

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Speaker 1: our minds, that mental model of what's going on outside,

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Speaker 1: and we talk about the real, actual universe, if it

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Speaker 1: actually exists, and what it means what's in it, how

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Speaker 1: it all works, and we try to explain all of

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Speaker 1: it to you. We tackled the biggest questions, the even

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Speaker 1: bigger questions, and the absolute biggest of big questions on

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Speaker 1: the podcast. I think we can do all of that

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Speaker 1: in an hour. I think we can. You know, I

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Speaker 1: was thinking as we were talking about this question of

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Speaker 1: an infinite universe is filled with infinite cats. And you know,

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Speaker 1: probably there was some like ancient Greek philosopher who first

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Speaker 1: raised this question. You know how the Greek philosophers had

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Speaker 1: like the craziest ideas about how the universe might work,

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Speaker 1: and basically every idea that is out there, some old

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Speaker 1: dude in a robe thought of his first thousands of

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Speaker 1: years ago. Yeah, just Plato surrounded by his cats thinking

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Speaker 1: about infinity as they're all me owing. The thing that

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Speaker 1: bugs me about the Greeks is that they had so

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Speaker 1: many ideas that even though only like one or two

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Speaker 1: of them turned out to be correct. Like Democratus, he's

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Speaker 1: the first one to name the adam and think about

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Speaker 1: the universe is made of tiny bits. People give him

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Speaker 1: credit for that because he had a right idea, but

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Speaker 1: he had like a million wrong totally idea. If you

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Speaker 1: just like spew ideas, eventually one of them is going

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Speaker 1: to be right. Statistically speaking, exactly, It's like Nostradamus, like

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Speaker 1: he predicted everything because he made a bunch of false

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Speaker 1: predictions as well, exactly. And so if I wrote down

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Speaker 1: literally every possible thing that could happen, if I made

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Speaker 1: an infinite number of predictions, then one of them would

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Speaker 1: be correct. I could predict the whole future of the

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Speaker 1: university if I had an infinite number predictions, and one

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Speaker 1: of those would be the actual theories of events of

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Speaker 1: the future, right exactly. If you think about, like if

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Speaker 1: you make a random noise in your head, like, the

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Speaker 1: chances are someone else is going to think that same

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Speaker 1: random noise in your head at some point in an

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Speaker 1: infinite universe. And that's what we're gonna talk about today

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Speaker 1: on the podcast. These big concepts, the concepts that are

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Speaker 1: bigger than big, the ones that are so hard that

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Speaker 1: we can only grapple with them in our minds. Today's

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Speaker 1: episode will be focused on this concept of infinity. Katie,

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Speaker 1: what do you think of when I say the word infinity?

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Speaker 1: Just real big, you know, really really big, actually, you know,

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Speaker 1: in a serious answer to that. When I was a

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Speaker 1: kid first learning about infinity, it was almost like the

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Speaker 1: concepts of infinity and nothing were very similar to me

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Speaker 1: because both kind of made my brain feel fuzzy. So

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Speaker 1: thinking about an infinite amount of stuff and thinking about

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Speaker 1: the absence of stuff, it's like a similar feeling to me,

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Speaker 1: where it's like my brain just gets this prickly static

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Speaker 1: feeling when I try to think too hard about it.

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Speaker 1: It's amazing that you can hold an idea in your

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Speaker 1: mind that also sort of confuses your mind. I also

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Speaker 1: remember learning about infinity as a kid, and you know,

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Speaker 1: my dad was really into math, and so this is

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Speaker 1: a very simple proof of like, all right, give me

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Speaker 1: a number. I can give you a bigger number, and

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Speaker 1: then I can give you a bigger number than that

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Speaker 1: shows you pretty quickly that there's like no biggest number.

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Speaker 1: And to me that was a crazy concept lying in

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Speaker 1: bed thinking about super big numbers and imagining, well, you know,

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Speaker 1: there's always one bigger than that. So it's super fun

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Speaker 1: to think about, like how your brain gets stretched by

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Speaker 1: the ideas that you stick inside of it. Yeah, it's like,

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Speaker 1: how do you fit a concept like infinity inside of

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Speaker 1: a finite brain with a finite number of neurons, so

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Speaker 1: you can't It's not something that you can really conceive

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Speaker 1: of without using some kind of shortcut, because our brains

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Speaker 1: aren't infinite, so you can't fit infinity in there. Well,

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Speaker 1: I haven't met you in person, so I don't know

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Speaker 1: if your brain is infinite or not, but I definitely

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Speaker 1: know that mine is finite in its capacity. But this

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Speaker 1: really goes to the heart of what we're trying to

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Speaker 1: do with the whole project of physics or of science,

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Speaker 1: which is to understand that external universe out there and

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Speaker 1: represent it in our minds. And so we do that

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Speaker 1: often using mathematics. Right, we have seen so many beautiful

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Speaker 1: moments when crazy things happening out there in the universe

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Speaker 1: can be represented with mathematical representations in our minds. Newton's

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Speaker 1: laws of motion, for example, tell us about the crazy

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Speaker 1: motions of all the planets and sort of lock them

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Speaker 1: into place to some mathematical rigor. So we know that

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Speaker 1: mathematics is very helpful in helping us understand what's going

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Speaker 1: on out there, that we can represent the craziness, the insanity,

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Speaker 1: the beauty, the complexity of the chaos of the universe

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Speaker 1: using simpler mathematical representations in our minds. But if we

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Speaker 1: know that everything that's physical has to be mathematical, do

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Speaker 1: we know that everything that's mathematical has to be physical? Like?

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Speaker 1: Is everything that you can imagine physically possible? Right? Right?

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Speaker 1: Because you can have something in math that's theoretical, but

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Speaker 1: it's not necessarily a tangible thing that you can like

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Speaker 1: observe or hold in your hands, Like can you pick

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Speaker 1: up a chunk of infinity and have that in your hand? Yeah,

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Speaker 1: And it seems like math is definitely sort of larger

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Speaker 1: than physics. A very simple example is I can come

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Speaker 1: up with a theory of particles that's wrong. It would

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Speaker 1: be mathematically correct, it could work, you know, it doesn't

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Speaker 1: generate nonsense or whatever. It just doesn't describe our universe.

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Speaker 1: So there are more theories. There are more mathematical theories

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Speaker 1: of the universe than actual physical laws that govern the universe. Right,

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Speaker 1: And so far we don't even think we found the one.

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Speaker 1: We have lots of really nice theories of the universe

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Speaker 1: that are beautiful but are probably not correct. So it

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Speaker 1: seems like not everything that's mathematical has to be physical, right.

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Speaker 1: I think for me. One of the simplest examples is,

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Speaker 1: just as you were saying before, things that are perfect,

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Speaker 1: like a circle, like a perfect circle. You can hold

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Speaker 1: that idea in your mind somehow there's a representation in

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Speaker 1: your brain to this concept of a perfect idealized circle.

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Speaker 1: But I've never seen a perfect circle in reality of you. Ah, well,

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Speaker 1: when I eat enough food, maybe, but no, I guess

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Speaker 1: that any kind of drawing or depiction of a circle,

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Speaker 1: even if it looks perfect, if you look at it

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Speaker 1: with like an electron microscope, you're gonna find imperfections. Yeah,

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Speaker 1: and everything is made out of particles, out of atoms

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Speaker 1: at a discrete chunks. Right, So you can't have a

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Speaker 1: perfectly continuous circle in reality. But of course you can

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Speaker 1: hold one in your mind, and you can write down

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Speaker 1: in just a few letters the equation for one right

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Speaker 1: x where it puss wise square, it equals four. That's

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Speaker 1: the equation that describes a perfect circle. But where is

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Speaker 1: that circle? Right? Have the equation? I have the idea

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Speaker 1: in my mind is this set of neurons in my

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Speaker 1: brain that's now representing that concept, But there is no

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Speaker 1: circle actually out there in the universe. It's sort of

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Speaker 1: hard to grapple with and even in our brains, like

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Speaker 1: that circle that you can kind of visualize is just

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Speaker 1: made up of the firing of your neurons, and so

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Speaker 1: is that circle in your brain even perfect? Who knows?

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Speaker 1: Who knows? And we'll dig into that in another episode.

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Speaker 1: But today I want to focus on this biggest concept

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Speaker 1: in mathematics, infinity, because it's something that pops up all

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Speaker 1: the time in physics. It's something that really tickles our

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Speaker 1: brain and makes us ask these really big questions. So

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Speaker 1: today on the podcast, we'll be asking is infinity real?

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Speaker 1: Is it physical? Or is it just mathematical? And people

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Speaker 1: have some answers to this question, which we're going to

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Speaker 1: listen to right now. That's right. Thank you very much

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Speaker 1: to those of you who answered my tough physics questions

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Speaker 1: with no preparation for the podcast. If you like to

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Speaker 1: participate for a future virtual Person on the Street interviews,

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Speaker 1: please write to me two questions at Daniel and Jorge

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Speaker 1: dot com. I promise it's fun. Here's what people have

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Speaker 1: to say. I think that infinity is definitely real. I

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Speaker 1: I believe that the universe is infinite in its size,

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Speaker 1: so that there is the real infinite in the universe

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Speaker 1: that we live in. And also if we believe in

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Speaker 1: the Einstein's theory about black holes, that also inside a

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Speaker 1: black hole we have a singularity that is a point

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Speaker 1: of infinite density. So there we go. We have another

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Speaker 1: very real infinite The only situation in which I can

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Speaker 1: think of um from a physics point of view, where

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Speaker 1: infinity might be real is if the universe has been internal,

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Speaker 1: if it's been around forever. Maybe if there is a

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Speaker 1: singularity in black holes and that might also be considered

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Speaker 1: a point of infinite density. I guess, well, that was

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Speaker 1: very interesting. I do like the idea of the universe

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Speaker 1: being eternal. I think that's kind of one of my

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Speaker 1: concepts of infinity, is that existence of something some you know, universe,

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Speaker 1: even if it's not our universe, but just the existence

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Speaker 1: of stuff has to be infinite, right, Like, there can't

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Speaker 1: be a start and an endpoint to stuff being around.

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Speaker 1: There can't be such an appeal to naturalism. Right, you're

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Speaker 1: just saying, like it's obvious that it must be this way.

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Speaker 1: You're basically a Greek philosopher. That's how they argued. Also, right,

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Speaker 1: I don't know whether to be insulted or not. But yeah,

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Speaker 1: I mean that's how I feel. This is not based

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Speaker 1: on science. It's just how I feel of like, well,

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Speaker 1: we can't just have stuff come out of nothing, go

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Speaker 1: do its thing for a while and then end and

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Speaker 1: then there'll be nothing again. But there's not any scientific

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Speaker 1: reason for that. That's coming from my human feelings of existence.

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Speaker 1: And maybe even that's what I want to believe, because

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Speaker 1: it's very comforting to think there's an infinite universe that

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Speaker 1: doesn't die, and I think it tells you something about

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Speaker 1: yourself and how your mind works and your understanding of

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Speaker 1: the universe to answer these questions that it feels natural

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Speaker 1: to you that the universe is infinite, or that it's

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Speaker 1: not that there are infinities or that there aren't. But remember,

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Speaker 1: of course, that the process of science is to question

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Speaker 1: all that intuition, is to go the opposite direction and

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Speaker 1: to start from the data and say, well, universe, tell

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Speaker 1: us what's out there, and then from that will build

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Speaker 1: our model of the universe, instead of saying like, well,

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Speaker 1: this just has to be this way. But it's hard

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Speaker 1: to sort of understand where those limits are. You can't

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Speaker 1: like question every single thing all the time. You can

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Speaker 1: do experiments every day about every tiny detail. So it's

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Speaker 1: hard to know sometimes when a question is this hard

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Speaker 1: to grapple with exactly how to figure it out. And

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Speaker 1: that's what I think we hear our listeners grappling with

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Speaker 1: whether it can be, whether it must be, whether it

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Speaker 1: can't be. Tricky stuff. Are you saying that I, Katie Golden,

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Speaker 1: could be wrong about one of the most difficult concepts

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Speaker 1: in the universe. I'm saying, basically, everybody is probably wrong

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Speaker 1: about almost everything you know. But those are the best

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Speaker 1: parts of science, right When your intuition is confronted with data,

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Speaker 1: that's when you learn something. That's when the universe is

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Speaker 1: telling you are n't I get why you think this

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Speaker 1: is true, but it turns out it's not. Works a

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Speaker 1: totally different way, And that's why we do science, right,

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Speaker 1: That's why we have this methodological approach to revealing the

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Speaker 1: truth about the universe, rather than just you know, eating

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Speaker 1: olives and lying around in robes and saying maybe it's

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Speaker 1: made of tiny cats, as fun as that is. So

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Speaker 1: say I'm Plato and I'm trying to conceive of infinity.

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Speaker 1: Am I just thinking of like a really really long

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Speaker 1: line of olives? What's going on with that. No, you're right,

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Speaker 1: the Greeks actually do have records of thinking about infinity.

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Speaker 1: And you know, probably people before that thought about infinity.

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Speaker 1: Who knows, But the earliest records we have about infinity

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Speaker 1: go back to about six hundred BC. And you know,

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Speaker 1: there are some examples there are people thinking about infinity,

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Speaker 1: not necessarily in terms of an infinite number of olives.

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Speaker 1: But for example Zeno's paradox. You know, when you say

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Speaker 1: I'm gonna walk first halfway home, and then how much

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Speaker 1: distance do I have to get to the rest of

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Speaker 1: my house, Well half the distance, and before I can

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Speaker 1: get home, I have to then walk half of that distance.

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Speaker 1: Then I have to walk half of that distance and

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Speaker 1: half of that distance, And there's no limit to the

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Speaker 1: number of times you can divide the rest of your

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Speaker 1: distance between yourself and your home. So in principle, there's

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Speaker 1: an infinite number of steps you need to take between

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Speaker 1: yourself and your house if every step is half as

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Speaker 1: long as the previous one. This is Zeno's famous paradox.

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Speaker 1: Of course, right, if there's an infinite number of steps

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Speaker 1: between you and your house, how do you ever get there?

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Speaker 1: You can't, But of course you do. This is how

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Speaker 1: I approach eating a cookie, because I think, well, I'm

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Speaker 1: not going to eat this whole cookie, so I'll just

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Speaker 1: eat half of this cookie. And I'm like, well, I

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Speaker 1: want a little more of this cookie, so we'll eat

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Speaker 1: half of the half of the cookie, and then half

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Speaker 1: of that half and so on and so that way

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Speaker 1: I get to say, like, well, I didn't eat the

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Speaker 1: whole cookie, even though there's only an infintestimally small chrome

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Speaker 1: left of the cookie. Yeah, that's a mathematical proof of

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Speaker 1: converging series. Right. You could have an infinite number of

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Speaker 1: terms and still have it converged to a finite number. Unfortunately,

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Speaker 1: my cookie eating strategy is a divergent series. I started

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Speaker 1: with great intentions. I'm like, I'm just gonna have one,

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Speaker 1: and then I'm like, well I had one, so mighty

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Speaker 1: will just have another one. And then I'm like, well

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Speaker 1: I've had two, so i can just grab a couple more.

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Speaker 1: And then I'm like, might it will just finished the box?

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Speaker 1: Because we all know where this is going, so let's

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Speaker 1: just get there right now. But the Greeks really struggled

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Speaker 1: with this idea. They didn't know if infinity was real,

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Speaker 1: and they had two different concepts. They talked about actual

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Speaker 1: infinity and potential infinity, and they separated these two concepts.

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Speaker 1: They're like, well, this potential infinity, we can think about

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Speaker 1: that for like proofs and geometry and stuff like that.

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Speaker 1: But you know, actual infinity, that's something they actually shied

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Speaker 1: away from. They didn't even want to talk about it.

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Speaker 1: They try to avoid it ever coming up in their

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Speaker 1: proofs and in their logic and in their thought. That

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Speaker 1: like saying sort of a naughty word, like what about

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Speaker 1: actual infinity? And then you get kicked out of class,

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Speaker 1: out of Greek class. Yeah, and they called it the

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Speaker 1: horror of the infinite. They did all these proofs where

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Speaker 1: you could have, you know, used infinity as a mathematical step,

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Speaker 1: but they took all these extra steps to make these

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Speaker 1: proofs happen without needing to resort infinity, without infinity appearing

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Speaker 1: anywhere in their math, because they thought, well, that must

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Speaker 1: be nonsense. That's so interesting. So they had a concept

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Speaker 1: of the potential for infinity, but actually discussing infinity itself

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Speaker 1: was taboo because it makes your brain feel bad. Because

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Speaker 1: I think they thought it wasn't real, you know. I

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Speaker 1: think they thought as a mathematical curiosity, and if you

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Speaker 1: invoked it, if you had to invoke it, then it's

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Speaker 1: somehow made your proofs invalid. And now, of course, you know,

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Speaker 1: we have the same sort of relationship with infinity, Like

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Speaker 1: it's a thing. We can think about it, we can

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Speaker 1: understand it, but it is difficult for us to wrap

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Speaker 1: our minds around, at least to all sorts of like

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Speaker 1: counterintuitive concepts, and infinity has many, many interesting layers. You know.

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Speaker 1: The basic notion of infinity is just the one we

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Speaker 1: talked about before, Like the number of numbers. Right, if

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Speaker 1: you start from zero and you keep going, you'll never

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Speaker 1: get to a point where you can't add another number.

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Speaker 1: Our number system just has that flexibility is no limit,

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Speaker 1: so that you can always make a bigger number. And

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Speaker 1: that's like a really powerful concept. It also makes me

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Speaker 1: wonder sometimes, like what's the biggest number any human has

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Speaker 1: ever thought of? Right? There isn't the biggest number in

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Speaker 1: principle that there might be a biggest number anybody has

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Speaker 1: ever like written down or held in their head. Yeah,

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Speaker 1: I mean, but then once you find that out, you

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Speaker 1: can just add one to it and then you've got

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Speaker 1: the record. Right, you're the human who's thought the biggest

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Speaker 1: number ever. That would be super cool. Yeah, like a googleplex,

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Speaker 1: a google plex plus one, that's it. You're the chain,

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Speaker 1: So that's super fun. And there's all these really interesting

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Speaker 1: exercises to get your brain used to the counterintuitive nature

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Speaker 1: of infinity, because the mathematics of infinity are quite slippery, right,

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Speaker 1: you can think about infinity plus one, but like infinity

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Speaker 1: plus one really is just infinity. One of my favorite

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Speaker 1: examples comes from David Hilbert. The guy invented Hilbert Space

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Speaker 1: like hundred years ago, and this is called Hilbert's Hotel.

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Speaker 1: And in Hilbert's Hotel, he's got a hotel with an

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Speaker 1: infinite number of rooms, right, but he's also got an

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Speaker 1: infinite number of guests. So every room in the hotel

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Speaker 1: has somebody in it. It's all occupied. And you might think, well,

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Speaker 1: if I had a thousand rooms and a thousand guests,

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Speaker 1: then I'm filled up, and if somebody shows up and

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Speaker 1: asked for a room, I would have to say no.

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Speaker 1: But Hilbert's Hotel is different because infinity is really different

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Speaker 1: from other numbers. If he's in the office, he's got

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Speaker 1: infinite rooms and infinite guests, and somebody shows up, he

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Speaker 1: can make room. What he has to do is this

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Speaker 1: special trick and sell everybody to pack up, leave your room,

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Speaker 1: and move over to the next room. So the person

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Speaker 1: in room number one goes to number two. Person room

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Speaker 1: number five hundred forty seven goes through room five hundred,

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Speaker 1: and in this way, room number one now becomes vacant.

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Speaker 1: What happens at the very very end, like in room infinity,

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Speaker 1: will room infinity goes through Room infinity plus one, right,

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Speaker 1: and I think, well that room didn't exist before. Well

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Speaker 1: it did because there were an infinite number of rooms.

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Speaker 1: And so in this weird way you can still make

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Speaker 1: room even if you had an infinite number of guests.

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Speaker 1: But you know, it sounds like this is going to

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Speaker 1: only get a two point five stars on Yell because

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Speaker 1: Albert's making you pack up and move your rooms all

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Speaker 1: the time. Terrible stay. Yeah, and he can even accommodate

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Speaker 1: an infinite number of guests, Like if an infinite number

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Speaker 1: of people show up and want rooms, he can just say,

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Speaker 1: all right, everybody, leave your room and go to twice

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Speaker 1: your room number right to then person in room four

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Speaker 1: goes to room eight for example, leaving three rooms open,

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Speaker 1: and so there's a lot of flexibility there left in infinity.

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Speaker 1: It's really fascinating, but of course it feels unfa of all,

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Speaker 1: this doesn't feel like something that could actually exist because

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Speaker 1: hotels have a certain number of rooms. Even if there

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Speaker 1: are very very large numbers, there is a number, and

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Speaker 1: so that shows you that, like infinity really not a

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Speaker 1: number in the same way that other big numbers are. Right,

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Speaker 1: when we try to apply something like infinity to something

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Speaker 1: that in our human minds is a finite thing, like

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Speaker 1: physical space of a hotel rooms, you know, those little

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Speaker 1: mints they put under your pillow, it's very difficult to

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Speaker 1: actually try to translate that concept into infinity, Like I

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Speaker 1: can't think of infinity mints. That's just not you know,

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Speaker 1: infinite meus. Like, although that would be a good brand

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Speaker 1: for those little hotel ments in the infinity, we are

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Speaker 1: copyrighting that right here. And you can play other fun

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Speaker 1: games to really blow your mind, because it turns out

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Speaker 1: that there are different sizes of infinity. Like you know,

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Speaker 1: I think a whole lot of infinity is everything is

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Speaker 1: the biggest thing. There can't be anything bigger than that.

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Speaker 1: But you can't actually take an infinite list and then

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Speaker 1: make something bigger than that infinite list. There's another really

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Speaker 1: clever example in mathematics, like say, for example, you write

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Speaker 1: down all of the numbers between one and two. How

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Speaker 1: many numbers are there between one and two? Well, is

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Speaker 1: an infinite number because you can always add another digit

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Speaker 1: to subdivice, like Zeno's paradox. If you have one point

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Speaker 1: seven and one point eight, you can always go one

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Speaker 1: point seven five, and then one point seven two five

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Speaker 1: and one point seven one seven five or whatever. So

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Speaker 1: there's an infinite number of numbers there because you can

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Speaker 1: always take half of a half exactly. So we have

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Speaker 1: an infinite number of numbers, and each of those numbers

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Speaker 1: can have an infinite number of digits. So between one

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Speaker 1: and two there's an infinite number of numbers, each of

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Speaker 1: which have an infinite number of digits, right, just like pie.

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Speaker 1: And so that's amazing just to think about. Now, if

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Speaker 1: you take that list, I can always find a number

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Speaker 1: that's not on that list. There's always one more number

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Speaker 1: between one and two that's not on that list. How

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Speaker 1: do you do that? Well, it's sort of just like

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Speaker 1: taking the biggest number and adding one which you need.

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Speaker 1: Is a recipe for generating a new number that's not

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Speaker 1: on that list, and that's not actually that hard. You

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Speaker 1: just take the first digit from the first number and

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Speaker 1: you add one to it, and you take the second

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Speaker 1: digit from the second number and you add one to it,

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Speaker 1: and the third digit from the third number, and you

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Speaker 1: add one to it, and then you're making a number

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Speaker 1: which disagrees with every number on your list in one

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Speaker 1: of the digits. So it wasn't on your list, which

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Speaker 1: means that you had an infinite number of numbers on

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Speaker 1: your list, but you can make it bigger. And so

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Speaker 1: that's an example of a kind of infinity we call

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Speaker 1: uncountable infinity, where you can't like associate all the things

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00:22:40,680 --> 00:22:44,359
Speaker 1: on your list with the natural numbers. With one, six, seven,

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Speaker 1: it's bigger than the infinity of all the numbers. So,

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Speaker 1: for those of us who are less numerically inclined, you're saying, basically,

430
00:22:53,560 --> 00:22:57,640
Speaker 1: you could have a pilot cats, but it's an infinite

431
00:22:57,680 --> 00:23:01,640
Speaker 1: pilot cat, like, well, this is infinity cats. But then

432
00:23:01,760 --> 00:23:04,600
Speaker 1: you find just one more cat and it looks so

433
00:23:05,040 --> 00:23:07,320
Speaker 1: cute that you have to add it to the pile

434
00:23:07,400 --> 00:23:10,240
Speaker 1: of infinity cats that you're hoarding, And now you have

435
00:23:10,760 --> 00:23:13,760
Speaker 1: an even bigger pile of cats, but they're both piles

436
00:23:13,800 --> 00:23:15,800
Speaker 1: of infinite cats, that's right. And you can have a

437
00:23:15,840 --> 00:23:18,920
Speaker 1: pile of cats that's so infinite that you can't even

438
00:23:19,000 --> 00:23:22,520
Speaker 1: assign them all numbers. You can't give them all unique numbers.

439
00:23:22,560 --> 00:23:25,800
Speaker 1: There's more cats on that list than there are numbers

440
00:23:25,920 --> 00:23:28,359
Speaker 1: in the infinite number line. At a certain point, you

441
00:23:28,440 --> 00:23:33,840
Speaker 1: just gotta start calling them all minute, mitten seventy two,

442
00:23:33,880 --> 00:23:36,960
Speaker 1: Come get your pill. That's a lot of being a

443
00:23:37,080 --> 00:23:40,600
Speaker 1: cat mom. So there's these crazy concept we have countable infinity,

444
00:23:40,600 --> 00:23:42,440
Speaker 1: which is like the natural numbers, and then we have

445
00:23:42,640 --> 00:23:46,480
Speaker 1: uncountable infinities, which are even bigger and hard to grapple with. Well,

446
00:23:46,800 --> 00:23:49,520
Speaker 1: I think one thing we can grapple with, though, is

447
00:23:49,520 --> 00:23:53,040
Speaker 1: a very finite break before we talk more about the

448
00:23:53,320 --> 00:23:57,480
Speaker 1: infinity of infinity after the break, which won't be infinity.

449
00:23:57,560 --> 00:24:13,080
Speaker 1: So don't worry, and we are back, And I hope

450
00:24:13,160 --> 00:24:16,440
Speaker 1: that break did not feel like an infinity being separated

451
00:24:16,600 --> 00:24:20,879
Speaker 1: from our lovely voices telling you about infinity. We are

452
00:24:20,920 --> 00:24:23,359
Speaker 1: having a lot of fun thinking and talking about infinities,

453
00:24:23,560 --> 00:24:26,080
Speaker 1: and so far we've been talking about infinity sort of

454
00:24:26,160 --> 00:24:29,920
Speaker 1: mathematically right in terms of like what the number means

455
00:24:30,080 --> 00:24:31,920
Speaker 1: and how big it is and how hard that is

456
00:24:31,960 --> 00:24:34,160
Speaker 1: to get your mind around. But now let's talk about

457
00:24:34,240 --> 00:24:40,280
Speaker 1: infinity in physics, because physics and theoretical physics specifically has

458
00:24:40,359 --> 00:24:44,000
Speaker 1: infinities all the time, right like their infinities all over

459
00:24:44,080 --> 00:24:48,240
Speaker 1: the place in theoretical physics. And so first let's talk

460
00:24:48,240 --> 00:24:50,800
Speaker 1: about infinities and theoretical physics, and then we'll figure out

461
00:24:50,840 --> 00:24:53,359
Speaker 1: whether any of those are actually real out there in

462
00:24:53,480 --> 00:24:57,000
Speaker 1: the universe. So when I think of physics, I think

463
00:24:57,240 --> 00:24:59,920
Speaker 1: of you know, you drop a ball off of a build,

464
00:25:00,200 --> 00:25:02,440
Speaker 1: and hey, you can figure out how fast that ball

465
00:25:02,560 --> 00:25:06,400
Speaker 1: is going, or even particle physics, you are looking at

466
00:25:06,560 --> 00:25:10,240
Speaker 1: the interaction of particles with each other. It's hard for

467
00:25:10,480 --> 00:25:14,119
Speaker 1: me to conceptualize what infinity looks like. How do you

468
00:25:14,280 --> 00:25:20,000
Speaker 1: have infinity tall building with the infinity balls dropping off

469
00:25:20,040 --> 00:25:23,000
Speaker 1: of it, or how do you have infinity particles interacting

470
00:25:23,040 --> 00:25:25,720
Speaker 1: with each other? Yeah, that's really as hard to think about,

471
00:25:25,880 --> 00:25:29,720
Speaker 1: but it entered into physics very very early with Newton. Like,

472
00:25:29,840 --> 00:25:31,720
Speaker 1: as you're saying, Newton is thinking of like an apple

473
00:25:31,840 --> 00:25:34,600
Speaker 1: falling off of the tree or the motion of something.

474
00:25:34,800 --> 00:25:37,240
Speaker 1: In order to solve those physics problems, he had to

475
00:25:37,359 --> 00:25:41,800
Speaker 1: invent a new kind of mathematics, calculus. Calculus is adding

476
00:25:41,880 --> 00:25:45,919
Speaker 1: up what we call infinitesimals, lots of tiny little contributions.

477
00:25:46,080 --> 00:25:48,399
Speaker 1: You know, for example, when the apple is falling from

478
00:25:48,440 --> 00:25:51,560
Speaker 1: the tree, it's not moving a constant velocity, is not

479
00:25:51,720 --> 00:25:54,639
Speaker 1: falling with the same speed all the time. It's falling

480
00:25:54,720 --> 00:25:57,639
Speaker 1: faster and then faster, and then faster. And so to

481
00:25:57,720 --> 00:25:59,919
Speaker 1: do those calculations to figure out like how long does

482
00:26:00,040 --> 00:26:02,840
Speaker 1: to take the apple to fall from the tree and

483
00:26:02,960 --> 00:26:06,640
Speaker 1: hit the ground means adding up lots of changing velocities.

484
00:26:06,920 --> 00:26:09,119
Speaker 1: So we have to invent a new kind of mathematics

485
00:26:09,240 --> 00:26:12,840
Speaker 1: called calculus, which allows you to add up an infinite

486
00:26:12,960 --> 00:26:16,600
Speaker 1: number of little slices of time to get the right answer.

487
00:26:17,119 --> 00:26:19,320
Speaker 1: And that's the way calculus works. It's like the limit

488
00:26:19,359 --> 00:26:22,080
Speaker 1: of taking a big sum when that limit becomes infinite,

489
00:26:22,119 --> 00:26:24,280
Speaker 1: when you have an infinite number of things you're adding up.

490
00:26:24,720 --> 00:26:28,439
Speaker 1: And so calculus is all about infinitesimals. It's everywhere around us.

491
00:26:28,640 --> 00:26:32,040
Speaker 1: So here's a potentially stupid question. If you had an

492
00:26:32,160 --> 00:26:36,640
Speaker 1: infinitely tall tree, and you had an apple fall from

493
00:26:36,680 --> 00:26:42,359
Speaker 1: an infinitely tall branch onto Newton, who was infinitely below

494
00:26:42,560 --> 00:26:47,440
Speaker 1: that apple, with that apple without when resistance become infinitely

495
00:26:47,560 --> 00:26:51,440
Speaker 1: fast and just pulverized Newton into infinitely nothing. Well, if

496
00:26:51,480 --> 00:26:54,480
Speaker 1: we're living in this universe, then there's a speed limit

497
00:26:54,640 --> 00:26:58,000
Speaker 1: and so it can't go infinitely fast. Right, that's a

498
00:26:58,080 --> 00:27:01,920
Speaker 1: really fascinating question about infinite because in theoretical physics, you

499
00:27:02,080 --> 00:27:05,680
Speaker 1: can't have infinite velocity. Right, there is a speed limit

500
00:27:06,200 --> 00:27:09,840
Speaker 1: to the universe. You can't go infinite velocity. So if

501
00:27:09,920 --> 00:27:12,400
Speaker 1: he's infinitely far away from the apple, then they would

502
00:27:12,440 --> 00:27:14,480
Speaker 1: never hit him. So is there some kind of like

503
00:27:14,600 --> 00:27:18,960
Speaker 1: space cops that are like space highway patrol enforcing this

504
00:27:19,400 --> 00:27:23,760
Speaker 1: space speed limit, because that seems like they're really harsh

505
00:27:23,800 --> 00:27:26,520
Speaker 1: and my mellow, No, it's just a fact of the universe.

506
00:27:26,760 --> 00:27:30,119
Speaker 1: But fascinatingly, there is no limit on the energy of

507
00:27:30,160 --> 00:27:32,920
Speaker 1: a particle, and so these particles can't go infinitely fast,

508
00:27:33,000 --> 00:27:36,440
Speaker 1: but they can have infinite energy. Like if you build

509
00:27:36,440 --> 00:27:39,360
Speaker 1: a particle accelerator, you can just keep pumping these particles

510
00:27:39,359 --> 00:27:42,360
Speaker 1: to have higher and higher energy even though they don't

511
00:27:42,400 --> 00:27:45,800
Speaker 1: go faster and faster. The relationship between energy and speed

512
00:27:46,000 --> 00:27:48,399
Speaker 1: changes as you approach the speed of light, and you

513
00:27:48,480 --> 00:27:50,800
Speaker 1: can like double the amount of energy a particle has

514
00:27:50,840 --> 00:27:53,480
Speaker 1: and it just goes a tiny little bit faster. So

515
00:27:53,680 --> 00:27:55,960
Speaker 1: there is no limit to the energy a particle can have,

516
00:27:56,119 --> 00:27:58,119
Speaker 1: but there is a limit to the speed it can have,

517
00:27:58,680 --> 00:28:02,040
Speaker 1: which is interesting sort of counterplay there between finite and infinite.

518
00:28:02,240 --> 00:28:05,119
Speaker 1: So what is the universal speed limit? Is it like

519
00:28:05,400 --> 00:28:09,159
Speaker 1: a hundred miles per hour or like KOs per hour?

520
00:28:09,320 --> 00:28:12,720
Speaker 1: I don't want to be too exclusive to our European listeners,

521
00:28:13,000 --> 00:28:16,399
Speaker 1: it's a three times ten the eight meters per second,

522
00:28:16,520 --> 00:28:19,960
Speaker 1: So three hundred million meters per second is the speed

523
00:28:20,040 --> 00:28:22,720
Speaker 1: limit for the speed of light in a vacuum, of course,

524
00:28:23,080 --> 00:28:25,600
Speaker 1: and that's the fastest that anything can move relative to

525
00:28:25,680 --> 00:28:28,600
Speaker 1: any other object in the universe. But again, no limit

526
00:28:28,800 --> 00:28:32,080
Speaker 1: on the energy, which is amazing. Wow. Well that's good

527
00:28:32,119 --> 00:28:33,840
Speaker 1: to know though, so we don't get a speeding ticket.

528
00:28:34,560 --> 00:28:38,000
Speaker 1: And theoretical physics also deals with infinity in terms of

529
00:28:38,120 --> 00:28:41,040
Speaker 1: the particles. As you were saying, you know what happens

530
00:28:41,120 --> 00:28:44,080
Speaker 1: when two particles bump against each other, Well, they're not

531
00:28:44,200 --> 00:28:47,800
Speaker 1: like physically actually touching each other. In our model, we

532
00:28:48,000 --> 00:28:51,400
Speaker 1: have them passing particles back and forth like two electrons

533
00:28:51,440 --> 00:28:54,360
Speaker 1: repel each other. How while they do it by emitting

534
00:28:54,480 --> 00:28:57,640
Speaker 1: a photon and passing that photon from one to the other,

535
00:28:57,760 --> 00:28:59,760
Speaker 1: which gives it a little push. It's a little momentum,

536
00:29:00,000 --> 00:29:02,760
Speaker 1: it's firm. But it's not just one photon. The electron

537
00:29:02,920 --> 00:29:07,000
Speaker 1: is constantly emitting photons. Most of the photons aren't like big,

538
00:29:07,080 --> 00:29:09,640
Speaker 1: heavy duty photons they're gonna do anything. Most of them

539
00:29:09,720 --> 00:29:14,160
Speaker 1: are very very very low energy, infinitesimally small energy. But

540
00:29:14,240 --> 00:29:17,280
Speaker 1: then there's an infinite number of them. So every photon

541
00:29:17,440 --> 00:29:21,680
Speaker 1: is constantly emitting an infinite number of tiny, tiny, tiny photons.

542
00:29:21,920 --> 00:29:26,120
Speaker 1: So that's like if you have a kitten who's got

543
00:29:26,200 --> 00:29:28,959
Speaker 1: a very weak little swipe of the paw, but if

544
00:29:29,000 --> 00:29:32,600
Speaker 1: you have infinity little kittens, it's gonna have an impact

545
00:29:32,680 --> 00:29:36,480
Speaker 1: on you exactly. And these infinite little photons or kittens

546
00:29:36,920 --> 00:29:39,160
Speaker 1: just add up to a normal number, and they don't

547
00:29:39,280 --> 00:29:41,040
Speaker 1: like give you a divergence. They don't give you an

548
00:29:41,120 --> 00:29:44,560
Speaker 1: infinite amount of force between the electrons. That's the key

549
00:29:44,680 --> 00:29:47,520
Speaker 1: that sometimes in these calculations you have an infinite number

550
00:29:47,520 --> 00:29:50,120
Speaker 1: of steps in the calculation, but you still get a

551
00:29:50,240 --> 00:29:53,760
Speaker 1: finite answer, right. The electron pushes against the other electron

552
00:29:54,040 --> 00:29:56,560
Speaker 1: with a certain finite number, and that's sort of like

553
00:29:56,680 --> 00:30:00,320
Speaker 1: Zeno's paradox, it tells you that the infinity isn't real.

554
00:30:00,640 --> 00:30:03,560
Speaker 1: It's just an artifact of how you're doing the calculation.

555
00:30:03,920 --> 00:30:05,959
Speaker 1: You can take any finite number and slice it up

556
00:30:06,000 --> 00:30:09,280
Speaker 1: into infinite pieces doesn't mean there's a real infinity there.

557
00:30:09,520 --> 00:30:11,440
Speaker 1: It just means that you've cut it into an infinite

558
00:30:11,520 --> 00:30:15,320
Speaker 1: number of pieces, because, like if you cut a single

559
00:30:15,480 --> 00:30:20,360
Speaker 1: cookie into infinitely small pieces, it's still just a single

560
00:30:20,440 --> 00:30:24,360
Speaker 1: cookie unfortunately exactly and now probably doesn't even taste as good,

561
00:30:24,360 --> 00:30:27,080
Speaker 1: because you've separated all the ingredients, right, And it's that

562
00:30:27,240 --> 00:30:30,040
Speaker 1: magical mixture of ingredients that makes a cookie what it is.

563
00:30:30,280 --> 00:30:32,840
Speaker 1: And often in theoretical physics, when you do get a

564
00:30:32,920 --> 00:30:35,880
Speaker 1: real infinity, when all the particles add up to give you,

565
00:30:36,040 --> 00:30:39,640
Speaker 1: like an infinite force between the two electrons, that's when

566
00:30:39,680 --> 00:30:42,920
Speaker 1: you know you've done something wrong that we call a divergence, right,

567
00:30:42,960 --> 00:30:46,320
Speaker 1: because you can have an infinite series that does diverge. Say,

568
00:30:46,360 --> 00:30:48,400
Speaker 1: for example, you just add up all the natural numbers

569
00:30:48,720 --> 00:30:52,000
Speaker 1: between one and infinity, that some if you add them

570
00:30:52,000 --> 00:30:54,160
Speaker 1: all up, is going to be infinity. If you add

571
00:30:54,240 --> 00:30:56,520
Speaker 1: up you know, one and then plus a half and

572
00:30:56,600 --> 00:30:58,560
Speaker 1: a fourth and an eighth, that's not going to be

573
00:30:58,600 --> 00:31:01,240
Speaker 1: an infinite number that's going to current verge. And so

574
00:31:01,480 --> 00:31:04,240
Speaker 1: in physics, when we do a calculation and it gives

575
00:31:04,360 --> 00:31:07,200
Speaker 1: us infinity, we usually think of that as a failure.

576
00:31:07,680 --> 00:31:11,160
Speaker 1: It's sort of like the Greeks, you know, like actual infinities,

577
00:31:11,200 --> 00:31:13,560
Speaker 1: like the horror of the infinite, because we don't think

578
00:31:13,600 --> 00:31:16,240
Speaker 1: that particles push against each other with infinite force. So

579
00:31:16,320 --> 00:31:19,760
Speaker 1: when buzz light year says to infinity and beyond, that's

580
00:31:19,840 --> 00:31:24,920
Speaker 1: like horrific. Physicists we're like, no, don't go there, fix

581
00:31:25,000 --> 00:31:27,520
Speaker 1: your calculation. You must have missed a minus sign or something.

582
00:31:29,360 --> 00:31:31,200
Speaker 1: And so it does pop up all the time, and

583
00:31:31,360 --> 00:31:33,520
Speaker 1: usually it's a sign that something is wrong. You've done

584
00:31:33,560 --> 00:31:36,360
Speaker 1: your calculation wrong, and so your series is like diverged

585
00:31:36,440 --> 00:31:39,160
Speaker 1: instead of converged. You know, you missed a minus sign maybe.

586
00:31:39,320 --> 00:31:40,880
Speaker 1: And this is how we know, for example, that a

587
00:31:41,000 --> 00:31:45,360
Speaker 1: theory isn't working, because we don't see these infinities in nature.

588
00:31:45,480 --> 00:31:49,479
Speaker 1: You don't see particles with infinite electric charge or pushing

589
00:31:49,520 --> 00:31:52,959
Speaker 1: against other particles with infinite forces. And so that's why

590
00:31:53,080 --> 00:31:55,640
Speaker 1: like the lack of seeing infinity in the physical universe

591
00:31:55,840 --> 00:31:57,840
Speaker 1: tells us that we can't have a cropping up in

592
00:31:57,960 --> 00:32:02,240
Speaker 1: our theoretical concepts as well. That also happens in biology.

593
00:32:02,400 --> 00:32:06,200
Speaker 1: You have like a Fibonacci sequence perhaps where you get

594
00:32:06,240 --> 00:32:10,280
Speaker 1: these fractals in nature, like you'll see them in plants

595
00:32:10,560 --> 00:32:13,520
Speaker 1: often where or like even if you see like a cauliflower,

596
00:32:13,640 --> 00:32:15,960
Speaker 1: or if you have ever had a romanesco it's this

597
00:32:16,360 --> 00:32:20,280
Speaker 1: very beautiful green plant that has tastes like cauliflower. It's

598
00:32:20,360 --> 00:32:23,760
Speaker 1: quite quite delicious when you fried up, and it has

599
00:32:24,000 --> 00:32:29,400
Speaker 1: a natural fractal that occurs with it. And with mathematical fractals,

600
00:32:29,640 --> 00:32:34,360
Speaker 1: they are theoretically infinite, but of course there's not infinite

601
00:32:34,400 --> 00:32:39,560
Speaker 1: amount of romanesco. So even though that fractal is repeating

602
00:32:39,720 --> 00:32:42,960
Speaker 1: and is you know, following the mathematical model of like

603
00:32:43,440 --> 00:32:47,440
Speaker 1: of an infinite pattern, at a certain point it tapers off.

604
00:32:47,560 --> 00:32:51,280
Speaker 1: There is a smallest, like little particle of romanesco that

605
00:32:51,480 --> 00:32:53,960
Speaker 1: we're not even getting to the particle physics. You're getting

606
00:32:54,000 --> 00:32:58,240
Speaker 1: to biology, which has a much larger cutoff for how

607
00:32:58,400 --> 00:33:01,320
Speaker 1: small an individual unit, because it can only be as

608
00:33:01,360 --> 00:33:04,800
Speaker 1: small as like a cell. Yeah, exactly, And so I

609
00:33:04,920 --> 00:33:07,480
Speaker 1: love that you just said the phrase particle of romanesquo.

610
00:33:08,240 --> 00:33:09,960
Speaker 1: You're right, we don't see those infinities and so we

611
00:33:10,000 --> 00:33:11,560
Speaker 1: have to sort of like try to cut them out

612
00:33:11,600 --> 00:33:13,480
Speaker 1: of our theory. But you know, in some cases we

613
00:33:13,600 --> 00:33:16,640
Speaker 1: don't know, And we have infinities in theories, we don't

614
00:33:16,680 --> 00:33:18,760
Speaker 1: know if they are real or they're just mathematical. I

615
00:33:18,840 --> 00:33:21,480
Speaker 1: think one of the most famous ones are infinities in

616
00:33:21,640 --> 00:33:26,560
Speaker 1: general relativity. Right, general relativity tells us that space is curved,

617
00:33:27,040 --> 00:33:29,240
Speaker 1: and that it gets curved when you're in the presence

618
00:33:29,320 --> 00:33:31,720
Speaker 1: of mass or energy, and if you have a huge

619
00:33:31,760 --> 00:33:36,360
Speaker 1: amount of mass, incredibly compact mass, then the curvature of space,

620
00:33:36,480 --> 00:33:40,320
Speaker 1: which determines how strong gravity feels, can get infinite. And

621
00:33:40,440 --> 00:33:43,960
Speaker 1: that's what we mean by, for example, a singularity. Singularity

622
00:33:44,080 --> 00:33:48,360
Speaker 1: is infinite curvature, essentially infinite gravitational force at that point.

623
00:33:48,680 --> 00:33:52,240
Speaker 1: So does that mean that a black hole is evidence

624
00:33:52,400 --> 00:33:56,920
Speaker 1: that there is actual tangible infinity. We just don't know,

625
00:33:57,120 --> 00:33:59,880
Speaker 1: because we don't know if there's a real singularity inside there.

626
00:34:00,200 --> 00:34:03,760
Speaker 1: There's a singularity in the theory, and that singularity predicts

627
00:34:03,800 --> 00:34:06,880
Speaker 1: black holes, and we see black holes. But also we

628
00:34:07,000 --> 00:34:09,840
Speaker 1: don't think those singularities are probably there because they're in

629
00:34:09,920 --> 00:34:12,839
Speaker 1: conflict with quantum mechanics, which says you can't have an

630
00:34:12,920 --> 00:34:16,759
Speaker 1: infinitely dense point at a certain location. So we're really

631
00:34:16,800 --> 00:34:19,840
Speaker 1: pretty confused about what's going on inside black holes, and

632
00:34:19,920 --> 00:34:21,560
Speaker 1: we'd love to see one because if an answer not

633
00:34:21,680 --> 00:34:24,200
Speaker 1: just the question of you know, our infinity is real,

634
00:34:24,640 --> 00:34:27,879
Speaker 1: but also tell us you know how general relativity works.

635
00:34:28,040 --> 00:34:30,040
Speaker 1: But if you talk to people who do general relativity,

636
00:34:30,320 --> 00:34:32,919
Speaker 1: they don't say this is a physical prediction. They don't

637
00:34:32,920 --> 00:34:37,719
Speaker 1: say general relativity predicts the existence of physical infinities and singularities.

638
00:34:37,920 --> 00:34:40,239
Speaker 1: They say this is a failure of the theory. This

639
00:34:40,400 --> 00:34:43,080
Speaker 1: is they say, we can't predict what happens there because

640
00:34:43,120 --> 00:34:46,839
Speaker 1: infinite curvature is like nonsense. It's like the theory breaks down.

641
00:34:47,000 --> 00:34:48,920
Speaker 1: It's like you have a hole in your fabric of

642
00:34:49,000 --> 00:34:51,800
Speaker 1: space where you don't know what to do. Instead of

643
00:34:51,880 --> 00:34:56,160
Speaker 1: like actually predicting an infinite singularity, I mean that seems

644
00:34:56,280 --> 00:34:58,840
Speaker 1: kind of like a bummer. And I guess until we

645
00:34:59,000 --> 00:35:01,840
Speaker 1: can get a big enough black hole where it's safe

646
00:35:01,840 --> 00:35:05,399
Speaker 1: to kind of float around on like a space inflatable

647
00:35:05,920 --> 00:35:09,279
Speaker 1: life jacket and then just kind of cruise right in, Like,

648
00:35:09,360 --> 00:35:12,320
Speaker 1: how would you even see, though, whether there's an infinite

649
00:35:12,360 --> 00:35:15,960
Speaker 1: singularity even if you could cruise around in a black

650
00:35:16,000 --> 00:35:18,680
Speaker 1: hole like how would you identify that. Yeah, we actually

651
00:35:18,719 --> 00:35:21,080
Speaker 1: need a fun podcast episode a few months ago about

652
00:35:21,239 --> 00:35:25,120
Speaker 1: seeing singularities. They're called naked singularities. And you could try

653
00:35:25,160 --> 00:35:27,560
Speaker 1: to take a black hole that's spinning and make it

654
00:35:27,640 --> 00:35:30,040
Speaker 1: spin faster and faster, so the event horizon sort of

655
00:35:30,160 --> 00:35:33,680
Speaker 1: shrinks and it might reveal the singularity, but nobody knows,

656
00:35:33,920 --> 00:35:36,839
Speaker 1: and that would take a crazy amount of energy. Until then, though,

657
00:35:36,880 --> 00:35:39,360
Speaker 1: we are trying to come up with a better theory,

658
00:35:39,800 --> 00:35:42,040
Speaker 1: one that can describe what's going on in the inside

659
00:35:42,040 --> 00:35:45,400
Speaker 1: of a black hole and be consistent with quantum mechanics,

660
00:35:45,600 --> 00:35:48,800
Speaker 1: and the category of theories are called quantum gravity. And

661
00:35:48,920 --> 00:35:50,880
Speaker 1: some of these theories are pretty good, but most of

662
00:35:50,960 --> 00:35:54,600
Speaker 1: them fail because they have infinities. Like you try to

663
00:35:54,640 --> 00:35:57,640
Speaker 1: calculate what happens when you have two big masses they

664
00:35:57,680 --> 00:36:00,759
Speaker 1: get close together, and they predict infinite horses and you're like, well,

665
00:36:00,800 --> 00:36:03,959
Speaker 1: we know that's not right, and so these theories break down,

666
00:36:04,160 --> 00:36:06,239
Speaker 1: like it doesn't agree with what we see, and so

667
00:36:06,640 --> 00:36:09,839
Speaker 1: their infinities are also a failure. So we have infinities

668
00:36:09,880 --> 00:36:12,200
Speaker 1: in these theories. But again it's the horror of the

669
00:36:12,280 --> 00:36:14,680
Speaker 1: infinite is the failure of the theory. We're trying to

670
00:36:14,760 --> 00:36:17,480
Speaker 1: remove those infinities so we can make predictions for what

671
00:36:17,600 --> 00:36:21,160
Speaker 1: happens in the actual physical world instead. Okay, so we

672
00:36:21,400 --> 00:36:26,440
Speaker 1: don't have a theory yet that doesn't have that mistake,

673
00:36:26,520 --> 00:36:29,560
Speaker 1: that oopsie of infinity. But we are going to take

674
00:36:29,600 --> 00:36:35,360
Speaker 1: a quick break about a minute, so everyone listening out there. Daniel,

675
00:36:35,680 --> 00:36:37,680
Speaker 1: I'll get out a calculator. Let's see if we can

676
00:36:37,719 --> 00:36:39,959
Speaker 1: get this before we get back from our quick break.

677
00:36:53,080 --> 00:36:55,840
Speaker 1: All right, we're back. Has anyone come up with the

678
00:36:56,080 --> 00:36:59,840
Speaker 1: theory without infinity as an answer? We should totally crowd

679
00:37:00,000 --> 00:37:02,880
Speaker 1: source the theory of quantum gravity. All our listeners, all

680
00:37:02,920 --> 00:37:07,239
Speaker 1: that brain power together approaches infinite genius exactly. And so

681
00:37:07,360 --> 00:37:09,719
Speaker 1: we've been wrestling with the concept of infinity. We know

682
00:37:09,840 --> 00:37:12,640
Speaker 1: it's a mathematical idea. We can do equations with it.

683
00:37:12,920 --> 00:37:15,120
Speaker 1: We use it all the time in our mathematics. We

684
00:37:15,280 --> 00:37:17,800
Speaker 1: even have it inside our physical theories as we're like

685
00:37:18,120 --> 00:37:21,280
Speaker 1: doing calculus and summing over an infinite number of particles.

686
00:37:21,680 --> 00:37:24,400
Speaker 1: But really the question is whether it's just something in

687
00:37:24,520 --> 00:37:27,759
Speaker 1: our minds or whether it actually exists out there in

688
00:37:27,880 --> 00:37:30,960
Speaker 1: the universe as well. So, Katie, you were talking earlier

689
00:37:31,000 --> 00:37:34,680
Speaker 1: about the infinity of time, like whether the universe could

690
00:37:34,719 --> 00:37:38,040
Speaker 1: go on forever, right, which I like the idea of

691
00:37:38,239 --> 00:37:41,440
Speaker 1: because it seems to indicate to me there's an infinite

692
00:37:41,480 --> 00:37:45,040
Speaker 1: amount of possibilities, such as a universe in which I

693
00:37:45,880 --> 00:37:49,719
Speaker 1: Katie forty one b is surrounded by an infinite number

694
00:37:49,719 --> 00:37:52,719
Speaker 1: of cats. But I do like the idea of a

695
00:37:52,840 --> 00:37:57,000
Speaker 1: universe going on forever because it feels, you know, the

696
00:37:57,120 --> 00:38:00,239
Speaker 1: idea of the death of the universe is maybe even

697
00:38:00,360 --> 00:38:03,440
Speaker 1: scarier to me than my own mortality. In some ways,

698
00:38:03,560 --> 00:38:07,759
Speaker 1: the idea that things could just stop existing is quite terrifying, right,

699
00:38:07,800 --> 00:38:10,000
Speaker 1: And it is terrifying, and it's hard to imagine not

700
00:38:10,160 --> 00:38:13,160
Speaker 1: existing anymore. But we all know that it happens, right

701
00:38:13,440 --> 00:38:15,680
Speaker 1: There are people who were alive and are now not

702
00:38:15,920 --> 00:38:19,920
Speaker 1: alive anymore. And so you can apply that same sort

703
00:38:20,000 --> 00:38:22,480
Speaker 1: of concept to the universe and wonder like, even though

704
00:38:22,480 --> 00:38:26,480
Speaker 1: the universe exists now, doesn't mean it always will. And

705
00:38:26,640 --> 00:38:30,600
Speaker 1: the biggest argument against the universe being infinite in time

706
00:38:30,840 --> 00:38:32,840
Speaker 1: to the future is that we don't know if the

707
00:38:32,920 --> 00:38:36,040
Speaker 1: universe was infinite in time in the past, right, Like,

708
00:38:36,280 --> 00:38:38,600
Speaker 1: we look back at the history of the universe and

709
00:38:38,680 --> 00:38:42,120
Speaker 1: we see what looks like a beginning fourteen billion years

710
00:38:42,160 --> 00:38:45,000
Speaker 1: ago the universe began. We don't know if there was

711
00:38:45,200 --> 00:38:49,160
Speaker 1: anything before that, or if the universe actually literally started there.

712
00:38:49,400 --> 00:38:51,719
Speaker 1: A lot of theories of general relativity have like the

713
00:38:51,840 --> 00:38:54,840
Speaker 1: clock beginning at that moment, and before that there was

714
00:38:54,920 --> 00:38:57,320
Speaker 1: no clock, there was no universe, there was no space,

715
00:38:57,400 --> 00:38:59,960
Speaker 1: there was nothing. Doesn't mean we know how that happened.

716
00:39:00,440 --> 00:39:03,440
Speaker 1: But in that concept, the universe has a finite age

717
00:39:03,600 --> 00:39:05,800
Speaker 1: so far, why would it make sense for it to

718
00:39:05,920 --> 00:39:09,680
Speaker 1: then go on for infinity. It's interesting because this is

719
00:39:09,960 --> 00:39:12,560
Speaker 1: sort of what I was saying earlier, where trying to

720
00:39:12,680 --> 00:39:17,360
Speaker 1: think about infinity gives me that same brain tingle sensation

721
00:39:18,080 --> 00:39:20,719
Speaker 1: as trying to think about nothingness. So trying to think

722
00:39:20,760 --> 00:39:26,160
Speaker 1: about nothing existing before the universe started and then nothing

723
00:39:26,280 --> 00:39:29,720
Speaker 1: existing after, I would almost say that's a harder concept

724
00:39:29,800 --> 00:39:33,680
Speaker 1: for me to think about than infinity, like thinking of like, well,

725
00:39:33,800 --> 00:39:37,200
Speaker 1: how could just there suddenly be an explosion of things

726
00:39:37,680 --> 00:39:40,560
Speaker 1: out of nothing and then how could all that stuff

727
00:39:40,880 --> 00:39:44,080
Speaker 1: suddenly become nothing again? And what does that even mean?

728
00:39:44,360 --> 00:39:46,440
Speaker 1: And it was hard for people to accept this idea

729
00:39:46,560 --> 00:39:49,600
Speaker 1: before we understood that the universe was expanding, and that

730
00:39:49,680 --> 00:39:52,560
Speaker 1: suggested that it was once younger and denser and hotter,

731
00:39:52,920 --> 00:39:55,440
Speaker 1: and therefore might have had a beginning. People thought the

732
00:39:55,560 --> 00:39:57,799
Speaker 1: universe was infinitely old, and that was just a much

733
00:39:57,840 --> 00:40:01,160
Speaker 1: more natural idea. But of course can't just accept physics

734
00:40:01,200 --> 00:40:04,160
Speaker 1: because it sounds natural. It has to be right. And

735
00:40:04,400 --> 00:40:07,120
Speaker 1: so now we've accepted the concept that maybe the universe

736
00:40:07,280 --> 00:40:10,239
Speaker 1: has a finite age so far, so we just don't know,

737
00:40:10,560 --> 00:40:13,000
Speaker 1: like will the universe go on forever or will it

738
00:40:13,080 --> 00:40:15,759
Speaker 1: come to an end? And there's some really weird possibilities,

739
00:40:15,840 --> 00:40:18,279
Speaker 1: like it might be that the universe doesn't come to

740
00:40:18,360 --> 00:40:20,920
Speaker 1: a dramatic end. It might be the universe doesn't like

741
00:40:21,080 --> 00:40:23,600
Speaker 1: reverse the Big Bang and end up as a big crunch.

742
00:40:23,960 --> 00:40:26,320
Speaker 1: One possibility is that the universe just sort of like

743
00:40:26,480 --> 00:40:30,640
Speaker 1: spreads out into an evenly tempered muck so that everything

744
00:40:30,760 --> 00:40:32,920
Speaker 1: is the same temperature. You don't have like hot spots

745
00:40:32,960 --> 00:40:35,319
Speaker 1: and cold spots anymore. This is called the heat death

746
00:40:35,360 --> 00:40:38,160
Speaker 1: in the universe. So in the universe is maximally disordered.

747
00:40:38,200 --> 00:40:41,040
Speaker 1: You have maximum entropy, and there's some folks out there

748
00:40:41,120 --> 00:40:44,360
Speaker 1: that think that entropy and time are so closely connected

749
00:40:44,960 --> 00:40:48,160
Speaker 1: that it's entropy that's driving time forward. And when you

750
00:40:48,239 --> 00:40:51,320
Speaker 1: get to this heat death, this equally spaced muck of

751
00:40:51,400 --> 00:40:54,920
Speaker 1: the universe, that time itself comes to an end, that

752
00:40:55,040 --> 00:40:57,680
Speaker 1: nothing can happen anymore. And so it might be that

753
00:40:57,840 --> 00:41:01,080
Speaker 1: the universe has a dramatic beginning and then very undramatic

754
00:41:01,200 --> 00:41:05,440
Speaker 1: sort of end like a lion, and then France is

755
00:41:05,480 --> 00:41:10,839
Speaker 1: out like muck, like entropy muck. So that's a possibility, right.

756
00:41:10,880 --> 00:41:14,160
Speaker 1: We just can't say whether the universe will exist forever

757
00:41:14,400 --> 00:41:17,920
Speaker 1: forward in time. We don't know if it existed forever

758
00:41:18,040 --> 00:41:21,000
Speaker 1: backwards in time, but current thinking is probably not. But

759
00:41:21,160 --> 00:41:24,360
Speaker 1: you know, there are other dimensions, of course, of infinity.

760
00:41:24,680 --> 00:41:26,640
Speaker 1: One of my favorites is thinking about the universe is

761
00:41:26,719 --> 00:41:30,399
Speaker 1: infinite in space, right, Like if you look out into

762
00:41:30,440 --> 00:41:33,560
Speaker 1: the universe, can you point your finger which makes a line,

763
00:41:34,000 --> 00:41:37,279
Speaker 1: and how that line continue out through space and never

764
00:41:37,520 --> 00:41:41,320
Speaker 1: ever stop right, never like loop back on itself or

765
00:41:41,480 --> 00:41:44,160
Speaker 1: hit a wall or something. Does that line actually traverse

766
00:41:44,239 --> 00:41:47,360
Speaker 1: space literally forever? That's what I thought you could do.

767
00:41:47,640 --> 00:41:50,640
Speaker 1: If you've got a strong enough flashlight and pointed up

768
00:41:50,640 --> 00:41:52,840
Speaker 1: at the sky, it's like, take that space. All this

769
00:41:53,080 --> 00:41:56,120
Speaker 1: light is going to go on forever, but probably not. Well,

770
00:41:56,239 --> 00:41:58,680
Speaker 1: if the universe is infinite in space and in time,

771
00:41:58,760 --> 00:42:02,440
Speaker 1: then that photon from your flashlight will literally go on forever.

772
00:42:02,680 --> 00:42:04,960
Speaker 1: I guess it could get absorbed by something, probably a

773
00:42:05,040 --> 00:42:08,920
Speaker 1: black hole between me and infinity, a black hole made

774
00:42:08,960 --> 00:42:11,880
Speaker 1: of somebody else's infinite number of cats that collapse on themselves.

775
00:42:12,520 --> 00:42:15,200
Speaker 1: But this is like a true infinity, right, Regardless of

776
00:42:15,280 --> 00:42:17,879
Speaker 1: what else is going on in the universe, it makes

777
00:42:18,000 --> 00:42:20,600
Speaker 1: some sense for the universe to be infinite. It might

778
00:42:20,640 --> 00:42:22,560
Speaker 1: make more sense for it to be infinite than for

779
00:42:22,640 --> 00:42:24,600
Speaker 1: it to have an edge or for it to be

780
00:42:24,719 --> 00:42:28,040
Speaker 1: like looped or closed in on itself. In our theories

781
00:42:28,080 --> 00:42:31,480
Speaker 1: of the universe, we typically assume that the universe is

782
00:42:31,600 --> 00:42:35,960
Speaker 1: infinite because it just currently feels like the most natural thing, right,

783
00:42:36,040 --> 00:42:39,880
Speaker 1: because I've seen like images of maybe the universe is

784
00:42:40,000 --> 00:42:43,160
Speaker 1: like a doughnut or a cone. And then the hard

785
00:42:43,320 --> 00:42:45,840
Speaker 1: part for me to wrap around a non infinite universe

786
00:42:45,960 --> 00:42:49,240
Speaker 1: is like, well, what's outside of that doughnut or cone?

787
00:42:49,280 --> 00:42:52,560
Speaker 1: I can't my brain just again, it starts to break

788
00:42:52,600 --> 00:42:54,200
Speaker 1: down when I try to think, well, what would be

789
00:42:54,280 --> 00:42:57,360
Speaker 1: outside of a universe? Like, what would be that? Nothing? Like?

790
00:42:57,600 --> 00:43:01,080
Speaker 1: I think that's another I don't remember which Greek philosopher

791
00:43:01,120 --> 00:43:02,720
Speaker 1: came up with this, but I thought that was another

792
00:43:02,840 --> 00:43:04,879
Speaker 1: thing of like, well, once you get to the edge

793
00:43:05,120 --> 00:43:08,200
Speaker 1: of the universe and you pull apart the veil, what's

794
00:43:08,280 --> 00:43:10,800
Speaker 1: beyond that? Right? And we just don't know. But the

795
00:43:10,920 --> 00:43:14,359
Speaker 1: fascinating thing is that there's only one answer we could

796
00:43:14,480 --> 00:43:18,120
Speaker 1: possibly know. Like, we could discover an edge to the universe.

797
00:43:18,200 --> 00:43:21,680
Speaker 1: We could discover that the university's finite, that it loops

798
00:43:21,719 --> 00:43:24,640
Speaker 1: around itself or has some weird deformity at the edge,

799
00:43:24,719 --> 00:43:26,960
Speaker 1: or something like that, but we could never prove that

800
00:43:27,080 --> 00:43:30,200
Speaker 1: it's infinite. Right, How could you prove that the universe

801
00:43:30,480 --> 00:43:33,560
Speaker 1: is infinite? It's like proving that it doesn't have an edge.

802
00:43:33,560 --> 00:43:35,920
Speaker 1: You can't prove a negative. It could just be that

803
00:43:36,000 --> 00:43:39,040
Speaker 1: the edges beyond where you thought it was, right, because

804
00:43:39,080 --> 00:43:42,000
Speaker 1: every time you get a government grant to send out

805
00:43:42,200 --> 00:43:45,879
Speaker 1: like a spaceship to the edge of space, then it's

806
00:43:45,920 --> 00:43:47,840
Speaker 1: like okay, but there's more, and then you have to

807
00:43:47,920 --> 00:43:51,000
Speaker 1: write another grant, And so you would need an infinite

808
00:43:51,080 --> 00:43:55,920
Speaker 1: number of grants to get to the infinite edge of

809
00:43:55,960 --> 00:43:58,520
Speaker 1: the universe, and nobody wants to go through that. I

810
00:43:58,640 --> 00:44:00,759
Speaker 1: do feel like I've really a number of grants of

811
00:44:00,800 --> 00:44:03,479
Speaker 1: my economic career and I've not received an infinite number

812
00:44:03,480 --> 00:44:05,920
Speaker 1: of dollars. So it's a really fun concept. And you know,

813
00:44:06,040 --> 00:44:09,360
Speaker 1: some people suggest that you might be able to prove

814
00:44:09,600 --> 00:44:12,480
Speaker 1: that the universe is infinite if you can come up

815
00:44:12,480 --> 00:44:16,040
Speaker 1: with a theory of cosmology that describes the universe and

816
00:44:16,200 --> 00:44:19,239
Speaker 1: is accurate and requires that the universe is infinite, if

817
00:44:19,239 --> 00:44:22,440
Speaker 1: your theory only works for an infinite universe and you

818
00:44:22,520 --> 00:44:25,680
Speaker 1: can exclude all other possible theories. But I'm not sure

819
00:44:25,760 --> 00:44:30,240
Speaker 1: philosophically that's even possible. So this is another like potential infinity.

820
00:44:30,480 --> 00:44:33,960
Speaker 1: But it's tantalizing because we can never actually know whether

821
00:44:34,000 --> 00:44:37,400
Speaker 1: the universe is infinite. That Galileo said this hundreds of

822
00:44:37,520 --> 00:44:40,480
Speaker 1: years ago in some famous letter, that mankind would never

823
00:44:40,560 --> 00:44:43,560
Speaker 1: be able to know whether the universe is infinite, And

824
00:44:43,680 --> 00:44:46,200
Speaker 1: so this is like a centuries old puzzle about the

825
00:44:46,239 --> 00:44:49,359
Speaker 1: infinity of space in the universe. I like to think

826
00:44:49,440 --> 00:44:52,319
Speaker 1: that because you look through this telescope. You know, one

827
00:44:52,360 --> 00:44:54,960
Speaker 1: of the first people to use a telescope, he just

828
00:44:55,080 --> 00:44:57,480
Speaker 1: sees all these stars out there. It's like, yeah, there's

829
00:44:57,480 --> 00:45:01,520
Speaker 1: no way we're sorting this now. Now, maybe that was

830
00:45:01,560 --> 00:45:03,759
Speaker 1: in his grand proposal. He's like, folks, I need even

831
00:45:03,760 --> 00:45:05,360
Speaker 1: a number of dollars, got a lot of work to

832
00:45:05,440 --> 00:45:08,040
Speaker 1: do up here, and then he probably got sent to jail.

833
00:45:09,560 --> 00:45:11,440
Speaker 1: But you don't need to look out into space to

834
00:45:11,480 --> 00:45:14,520
Speaker 1: see potential infinities. Like we were talking about how there's

835
00:45:14,520 --> 00:45:17,960
Speaker 1: an infinite number of numbers between the numbers one and two.

836
00:45:18,520 --> 00:45:20,680
Speaker 1: You can just hold your fingers apart and say, well,

837
00:45:21,239 --> 00:45:25,000
Speaker 1: how many pieces of space are there between my fingers?

838
00:45:25,040 --> 00:45:29,640
Speaker 1: How many unique locations? How many different possible spots could

839
00:45:29,640 --> 00:45:33,520
Speaker 1: a particle be at between my fingers? And if space

840
00:45:33,680 --> 00:45:36,920
Speaker 1: is continuous, then there's an infinite number of places for

841
00:45:37,000 --> 00:45:39,799
Speaker 1: a particle to be between your fingers. I'm staring at

842
00:45:39,840 --> 00:45:42,160
Speaker 1: my hand right now and like pulling my fingers apart.

843
00:45:42,239 --> 00:45:45,120
Speaker 1: I'm just really glad nobody's here right now see me

844
00:45:45,280 --> 00:45:48,200
Speaker 1: doing this, because like, hey, how's it going? What you

845
00:45:48,280 --> 00:45:50,759
Speaker 1: doing there? I'm just doing physics, and like, okay, that's

846
00:45:50,760 --> 00:45:55,160
Speaker 1: where you look physic shut up a science. And so, if,

847
00:45:55,440 --> 00:45:59,400
Speaker 1: as general relativity suggests, the universe is continuous, then you

848
00:45:59,560 --> 00:46:01,920
Speaker 1: can divide that space an infinite number of times, and

849
00:46:02,000 --> 00:46:05,400
Speaker 1: there are real locations for every one of those numbers.

850
00:46:05,440 --> 00:46:09,240
Speaker 1: Every subdivision is real. But you know, quantum mechanics says

851
00:46:09,320 --> 00:46:12,160
Speaker 1: not so fast. It says that everything in the universe

852
00:46:12,239 --> 00:46:15,239
Speaker 1: so far seems to be quantized, and a lot of

853
00:46:15,320 --> 00:46:19,440
Speaker 1: theories out there suggests that space itself might be quantized.

854
00:46:19,880 --> 00:46:22,320
Speaker 1: That space might be made out of tiny little space

855
00:46:22,360 --> 00:46:24,719
Speaker 1: pixels that are so small that you can't see them.

856
00:46:25,000 --> 00:46:27,719
Speaker 1: It's like a retina screen. They might be like ten

857
00:46:27,800 --> 00:46:31,759
Speaker 1: to the negative thirty five meters wide. It doesn't really

858
00:46:31,800 --> 00:46:34,080
Speaker 1: matter how small they are as long as there's a

859
00:46:34,239 --> 00:46:37,760
Speaker 1: minimum distance. That means that the space between your fingers

860
00:46:38,040 --> 00:46:40,800
Speaker 1: is not an infinite number of locations, but a large

861
00:46:40,920 --> 00:46:44,320
Speaker 1: and finite number of possible locations, like little slots that

862
00:46:44,480 --> 00:46:47,959
Speaker 1: particles can fit into. Thinking about space pixels just makes

863
00:46:48,000 --> 00:46:52,840
Speaker 1: me feel like we're some aliens computer game, and maybe

864
00:46:52,920 --> 00:46:55,600
Speaker 1: we are. Maybe our universe is finite, but it's just

865
00:46:55,680 --> 00:46:59,440
Speaker 1: a simulation inside an infinite universe. That's what I'm thinking.

866
00:46:59,680 --> 00:47:04,280
Speaker 1: But even if our universe is finite, we still wouldn't

867
00:47:04,320 --> 00:47:09,200
Speaker 1: know if there are infinite finite universe is right, that's right.

868
00:47:09,440 --> 00:47:14,120
Speaker 1: Another dimension of infinity is whether our universe itself is

869
00:47:14,239 --> 00:47:17,120
Speaker 1: all that there is. Right. We think of universe like

870
00:47:17,320 --> 00:47:20,239
Speaker 1: uni means like all of it, the one thing. But

871
00:47:20,440 --> 00:47:23,799
Speaker 1: these days we have the concept of the multiverse where

872
00:47:23,840 --> 00:47:27,080
Speaker 1: it's possible that there are other universes just like ours.

873
00:47:27,160 --> 00:47:29,640
Speaker 1: In fact, there might be an infinite number of them.

874
00:47:30,120 --> 00:47:33,000
Speaker 1: This concept comes from like a struggle to understand why

875
00:47:33,160 --> 00:47:36,280
Speaker 1: our universe is so weird, like why is the speed

876
00:47:36,320 --> 00:47:38,120
Speaker 1: of light the way that it is. Why are the

877
00:47:38,200 --> 00:47:41,680
Speaker 1: various numbers the parameters that control physics seem to have

878
00:47:41,920 --> 00:47:44,839
Speaker 1: kind of weird values. And they answered by saying, well,

879
00:47:45,040 --> 00:47:47,279
Speaker 1: maybe there's an infinite number of universes and so that

880
00:47:47,400 --> 00:47:49,920
Speaker 1: all the values are explored and we just happen to

881
00:47:49,960 --> 00:47:52,840
Speaker 1: be in this one. And you know, that's a fun idea,

882
00:47:52,960 --> 00:47:55,880
Speaker 1: and it's another concept where it's easy to like create

883
00:47:55,960 --> 00:47:58,680
Speaker 1: infinity in your mind, but it's not something we can

884
00:47:58,760 --> 00:48:01,719
Speaker 1: ever really study because as these other universes in the

885
00:48:01,840 --> 00:48:05,200
Speaker 1: multiverse aren't places we can interact with, there are things

886
00:48:05,320 --> 00:48:08,640
Speaker 1: we can see, we can't ever get evidence of their existence,

887
00:48:08,880 --> 00:48:11,560
Speaker 1: and so it might be real there might be other

888
00:48:11,680 --> 00:48:13,920
Speaker 1: universes out there, but I'm not sure that's something we

889
00:48:13,960 --> 00:48:17,440
Speaker 1: could ever prove or really know. It seems like the

890
00:48:17,640 --> 00:48:21,480
Speaker 1: only quote unquote evidence we would have of another universe

891
00:48:21,560 --> 00:48:24,640
Speaker 1: is just if we can't figure something out about our

892
00:48:24,760 --> 00:48:29,120
Speaker 1: own universe. So we think that maybe there's another universe

893
00:48:29,440 --> 00:48:32,320
Speaker 1: somehow interacting with our universe, but we would have no

894
00:48:32,480 --> 00:48:36,760
Speaker 1: way of measuring that at all, because we're stuck inside

895
00:48:37,120 --> 00:48:40,520
Speaker 1: our universe like a bunch of fish and a fish bowl,

896
00:48:40,600 --> 00:48:43,600
Speaker 1: and then we're bonking into another fish bowl, but we

897
00:48:43,719 --> 00:48:46,160
Speaker 1: can never interact with the fish and that other fish bowl.

898
00:48:46,200 --> 00:48:49,560
Speaker 1: We only know Maybe I think maybe they could be there,

899
00:48:49,680 --> 00:48:52,359
Speaker 1: if it's the only way we could explain how our

900
00:48:52,400 --> 00:48:55,279
Speaker 1: fish bowl is getting jostled around. Yeah, there are some

901
00:48:55,560 --> 00:48:59,200
Speaker 1: fun ideas about how other bubble universes might have been

902
00:48:59,239 --> 00:49:01,520
Speaker 1: made near hours and when they were very young, and

903
00:49:01,600 --> 00:49:03,600
Speaker 1: they could have bumped into each other and left a

904
00:49:03,719 --> 00:49:07,360
Speaker 1: little imprint like these circles on the cosmic microwave background

905
00:49:07,480 --> 00:49:10,719
Speaker 1: radiation is left over glow from just after the Big Bang,

906
00:49:10,880 --> 00:49:13,680
Speaker 1: But nobody's ever observed any evidence of that, so it's

907
00:49:13,760 --> 00:49:16,560
Speaker 1: just a fun idea so far. So that's another possible

908
00:49:16,640 --> 00:49:19,359
Speaker 1: infinity that could really be real, but we might never

909
00:49:19,480 --> 00:49:22,440
Speaker 1: actually know. One that's closest to my heart is this

910
00:49:22,640 --> 00:49:26,800
Speaker 1: question of infinite number of particles, like how many particles

911
00:49:26,920 --> 00:49:30,120
Speaker 1: are there in my finger? Well, you know, something like

912
00:49:30,360 --> 00:49:33,600
Speaker 1: Avagajo's number of atoms and then those are made of

913
00:49:33,680 --> 00:49:36,720
Speaker 1: electrons and protons and neutrons which are made of quarks.

914
00:49:36,960 --> 00:49:38,919
Speaker 1: But then you can ask like, well, what are those

915
00:49:38,960 --> 00:49:41,720
Speaker 1: electrons and quarks made out of? One of the electron

916
00:49:41,800 --> 00:49:44,000
Speaker 1: is made out of particles, which are made out of particles,

917
00:49:44,000 --> 00:49:45,560
Speaker 1: which are made out of particles which are made out

918
00:49:45,600 --> 00:49:49,240
Speaker 1: of particles, And it goes infinitely far down to infinite

919
00:49:49,239 --> 00:49:52,399
Speaker 1: testimal particles. Then you could say, hey, I made out

920
00:49:52,400 --> 00:49:55,359
Speaker 1: of an infinite number of particles. Yeah. I mean, it's

921
00:49:55,400 --> 00:49:58,440
Speaker 1: the cookie problem again, where if you start to cut

922
00:49:58,520 --> 00:50:02,000
Speaker 1: apart a particle like a cookie, it's not that the

923
00:50:02,200 --> 00:50:06,520
Speaker 1: particle itself is infinitely large, but it's made up of

924
00:50:07,120 --> 00:50:12,640
Speaker 1: infinitely nesting particles like a Russian nesting doll. But they're

925
00:50:13,040 --> 00:50:17,279
Speaker 1: sub atomic particles. Yeah, and so that's certainly a possibility, Like,

926
00:50:17,400 --> 00:50:20,200
Speaker 1: we can't rule that out. We call the electron and

927
00:50:20,239 --> 00:50:23,320
Speaker 1: the corks the fundamental particles, meaning that they're not divisible,

928
00:50:23,480 --> 00:50:26,239
Speaker 1: only because we haven't seen anything smaller inside them, not

929
00:50:26,320 --> 00:50:29,320
Speaker 1: because we have any evidence that they're actually fundamental. We

930
00:50:29,440 --> 00:50:32,120
Speaker 1: just haven't built a big enough particle collider to smash

931
00:50:32,200 --> 00:50:34,600
Speaker 1: them open and see what's inside. In fact, we strongly

932
00:50:34,640 --> 00:50:37,720
Speaker 1: suspect there are smaller particles inside them that would explain

933
00:50:37,800 --> 00:50:39,600
Speaker 1: lots of the weird patterns that we see in the

934
00:50:39,719 --> 00:50:43,480
Speaker 1: universe and in those particles. But we also suspect that

935
00:50:43,520 --> 00:50:45,960
Speaker 1: there might be the smallest particle that if you keep

936
00:50:46,040 --> 00:50:48,560
Speaker 1: cracking them open far enough down you get down to

937
00:50:48,640 --> 00:50:52,040
Speaker 1: the smallest bit. Quantum mechanics again says that everything in

938
00:50:52,080 --> 00:50:55,120
Speaker 1: the universe is discreet, not continuous, that it comes in

939
00:50:55,280 --> 00:50:58,279
Speaker 1: grains or in chunks. So we suspect that maybe it's

940
00:50:58,280 --> 00:51:00,880
Speaker 1: a vibrating string or something else, but at very very

941
00:51:00,920 --> 00:51:04,640
Speaker 1: short distances there is a smallest thing, which would mean

942
00:51:05,080 --> 00:51:07,560
Speaker 1: you're made out of a finite number of those little

943
00:51:07,719 --> 00:51:11,920
Speaker 1: vibrating strings or tiny cosmic kittens or whatever. It's so

944
00:51:12,080 --> 00:51:16,719
Speaker 1: hard to conceptualize a smallest particle because in the physical

945
00:51:17,080 --> 00:51:19,480
Speaker 1: world that we interact with, even when we find like

946
00:51:19,560 --> 00:51:22,440
Speaker 1: a smallest building block like you mentioned, like a pixel,

947
00:51:22,880 --> 00:51:25,960
Speaker 1: we know that pixel actually you can break apart, like

948
00:51:26,080 --> 00:51:28,360
Speaker 1: it does have little elements, Like when you have a

949
00:51:28,480 --> 00:51:31,920
Speaker 1: pixel on a screen, it's actually made up of Well,

950
00:51:31,960 --> 00:51:34,759
Speaker 1: now I don't know how computers work, so I'm just

951
00:51:34,840 --> 00:51:37,520
Speaker 1: gonna assume it's it's made out of you know, light

952
00:51:37,680 --> 00:51:41,040
Speaker 1: coming through a little square on your screen. That's exactly

953
00:51:41,080 --> 00:51:43,239
Speaker 1: how they do it. They build thingies. They put a

954
00:51:43,320 --> 00:51:46,240
Speaker 1: bunch of little thingies on your screen and little tiny

955
00:51:46,400 --> 00:51:48,759
Speaker 1: lights that come through the thingies. I'm sure someone who

956
00:51:48,800 --> 00:51:51,480
Speaker 1: knows how a computer screen work could explain that better.

957
00:51:51,600 --> 00:51:53,480
Speaker 1: But you know, it's the same thing like with the

958
00:51:53,600 --> 00:51:56,640
Speaker 1: human brain when you break it up, like the smallest

959
00:51:56,880 --> 00:52:00,880
Speaker 1: unit of a thought is the action that happens in

960
00:52:00,960 --> 00:52:04,280
Speaker 1: a synapse, like from one end of a neuron to another.

961
00:52:04,440 --> 00:52:06,920
Speaker 1: But then you can break that apart because you can

962
00:52:07,040 --> 00:52:11,560
Speaker 1: look at the molecular structure of a neurotransmitter. I mean

963
00:52:11,640 --> 00:52:14,440
Speaker 1: you could say though that like if you look at

964
00:52:14,480 --> 00:52:17,799
Speaker 1: the space between two neurons and the synaps, that could

965
00:52:17,840 --> 00:52:22,480
Speaker 1: potentially be broken down into infinitely smaller halves of a space.

966
00:52:22,680 --> 00:52:26,160
Speaker 1: So maybe there's an infinity whenever we have a single thought,

967
00:52:26,360 --> 00:52:30,000
Speaker 1: because you know, you have an infinite haves that your

968
00:52:30,080 --> 00:52:35,279
Speaker 1: neurotransmitters have to traverse over your synaps. But again it's

969
00:52:35,360 --> 00:52:38,800
Speaker 1: kind of like that would according to the mathematics converge,

970
00:52:38,880 --> 00:52:41,680
Speaker 1: but it's also sort of the goal, Like we feel

971
00:52:41,719 --> 00:52:44,080
Speaker 1: that if we found the smallest unit, we'd be seeing

972
00:52:44,160 --> 00:52:46,600
Speaker 1: something like the source code of the universe would reveal

973
00:52:46,760 --> 00:52:49,160
Speaker 1: something deep and true. Everything above that is just like

974
00:52:49,560 --> 00:52:52,680
Speaker 1: how those pieces tend to fit together and turn into stuff,

975
00:52:52,760 --> 00:52:55,239
Speaker 1: right like ice cream is not fundamentalists and teach you

976
00:52:55,320 --> 00:52:57,719
Speaker 1: something about the universe, regardless of how delicious it is.

977
00:52:58,080 --> 00:52:59,880
Speaker 1: We want to figure out what is the smallest thing,

978
00:53:00,239 --> 00:53:02,680
Speaker 1: so we can like look at the deepest nature of

979
00:53:02,760 --> 00:53:05,120
Speaker 1: the universe. But we don't know if there is the

980
00:53:05,200 --> 00:53:08,640
Speaker 1: smallest thing or if it just goes on forever. Alright,

981
00:53:08,680 --> 00:53:11,880
Speaker 1: So we've talked about the potential infinities. I think the

982
00:53:11,920 --> 00:53:15,279
Speaker 1: most promising ones are the spatial infinities, like maybe the

983
00:53:15,400 --> 00:53:18,400
Speaker 1: universe really is infinite and goes on forever, or the

984
00:53:18,480 --> 00:53:22,279
Speaker 1: temporal ones, like maybe the universe can last forever. I

985
00:53:22,360 --> 00:53:25,960
Speaker 1: think it's pretty unlikely that space can be infinitely divided

986
00:53:26,040 --> 00:53:29,000
Speaker 1: into bits, or that particles can be infinitely broken into

987
00:53:29,040 --> 00:53:31,319
Speaker 1: smaller particles. But I think there really is a chance

988
00:53:31,360 --> 00:53:34,320
Speaker 1: that the universe is infinitely big. But what's amazing to

989
00:53:34,400 --> 00:53:36,640
Speaker 1: me is that for all these hundreds and thousands of

990
00:53:36,760 --> 00:53:39,400
Speaker 1: years that we've been thinking about infinity, that we've had

991
00:53:39,480 --> 00:53:43,480
Speaker 1: it in our minds, we've still never seen actual infinity.

992
00:53:43,760 --> 00:53:47,160
Speaker 1: No human has ever witnessed laid eyes on anything that

993
00:53:47,520 --> 00:53:50,040
Speaker 1: is truly infinite. It might be out there and there

994
00:53:50,080 --> 00:53:53,400
Speaker 1: are universe hiding from us, waiting inside black holes or

995
00:53:53,440 --> 00:53:55,719
Speaker 1: out past the edge, but we have never seen it.

996
00:53:56,000 --> 00:53:59,000
Speaker 1: I mean, if you ever stare into a dog's eyes though,

997
00:53:59,160 --> 00:54:01,960
Speaker 1: and see the love of there, I'd say that's infinite.

998
00:54:03,840 --> 00:54:05,880
Speaker 1: All right. Well, there you having, folks. If you are

999
00:54:05,920 --> 00:54:08,279
Speaker 1: a seeker of infinity, then get an infinite number of

1000
00:54:08,320 --> 00:54:11,400
Speaker 1: pets and feel an infinite amount of love from all

1001
00:54:11,480 --> 00:54:14,600
Speaker 1: of them. Until then, keep infiniting in your mind and

1002
00:54:14,800 --> 00:54:16,279
Speaker 1: let us know if you see it out there in

1003
00:54:16,320 --> 00:54:18,680
Speaker 1: the universe. Thanks very much Katie for joining us again

1004
00:54:18,760 --> 00:54:21,000
Speaker 1: on the podcast. Thank you so much for having me.

1005
00:54:21,440 --> 00:54:24,040
Speaker 1: This was infinitely fun. And don't forget to check out

1006
00:54:24,120 --> 00:54:27,000
Speaker 1: her other awesome podcast, Creature Feature, which she talks about

1007
00:54:27,040 --> 00:54:30,600
Speaker 1: the infinite, amazing, nous and complexity of biology. And until then,

1008
00:54:30,760 --> 00:54:33,080
Speaker 1: thank you very much for sharing us your curiosity and

1009
00:54:33,280 --> 00:54:43,440
Speaker 1: tune in next time. Thanks for listening, and remember that

1010
00:54:43,600 --> 00:54:46,360
Speaker 1: Daniel and Jorge explained. The Universe is a production of

1011
00:54:46,480 --> 00:54:49,799
Speaker 1: I Heart Radio. For more podcast from my Heart Radio,

1012
00:54:49,960 --> 00:54:53,520
Speaker 1: visit the i Heart Radio app, Apple Podcasts, or wherever

1013
00:54:53,640 --> 00:55:00,920
Speaker 1: you listen to your favorite shows. No.