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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?

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Speaker 4: Pet? Depends on your definition. Does it include all living

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Speaker 4: creatures in my house? Does it include the mites in

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Speaker 4: my eyelashes?

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Speaker 1: Maybe not? Like all the microbes and the Tardi grades

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Speaker 1: and all the bacteria in your gut?

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Speaker 4: What about my husband?

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Speaker 1: That's your call. Depends on your relationship personal choice.

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Speaker 4: Okay, then I've got a dog named Cookie. I've got

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Speaker 4: two fish. I'm gonna name them right now, called Bill

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Speaker 4: and Ted. So three or four depending on the definition

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Speaker 4: of my husband.

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Speaker 1: All right, well that's more than I've got. And I

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

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Speaker 1: do you say you have too many pets?

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Speaker 4: I think that's the wrong way to look at it.

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Speaker 4: Once you have, you know, two or three, like one more,

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Speaker 4: there's no difference, right, It's the cat principle, like once

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Speaker 4: you have two cats, there's no difference between two cats,

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Speaker 4: four cats, ten cats.

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Speaker 1: I think that sounds dangerous. You're going to mathematically induce

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Speaker 1: yourself to having an infinite number of cats exactly.

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Speaker 4: If you already have infinite pets, can add more and

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Speaker 4: more and still have infinite pets.

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Speaker 1: Hi, I'm Daniel, I'm a particle physicist, and I have

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Speaker 1: an infinite number of questions about the nature of our universe.

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Speaker 4: And I am Katie Golden. I like pets, but I

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Speaker 4: am not a particle physicist, and I still have infinite

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Speaker 4: questions about the universe and about how many cats I

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Speaker 4: 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 filled with infinite cats?

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Speaker 4: I think that if you replaced the building blocks of

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Speaker 4: the universe with cats, it would be a lot cuter.

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Speaker 4: But yeah, I come to the show with a little

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Speaker 4: bit of background in psychology and evolutionary biology, and that's

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Speaker 4: 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.

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Speaker 4: I think we can do all that in an hour.

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Speaker 1: I think we can. You know, I was thinking as

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Speaker 1: we were talking about this question of an infinite universe

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Speaker 1: filled with infinite cats, and you know, probably there was

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Speaker 1: some like ancient Greek philosopher who first raised this question.

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Speaker 1: You know how the Greek philosophers had like the craziest

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Speaker 1: ideas about how the universe might work. Basically every idea

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Speaker 1: that's out there, some old dude in a robe thought

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Speaker 1: of it first thousands of years ago.

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Speaker 4: Yeah, just Plato surrounded by his cats thinking about infinity

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Speaker 4: as they're all meowing.

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Speaker 1: The thing that bugs me about the Greeks is that

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Speaker 1: they had so many ideas that even though only like

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Speaker 1: one or two of them turned out to be correct.

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Speaker 1: Like Democratus, he's the first one to name the atom

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Speaker 1: and think about the universes made of tiny bits. People

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

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Speaker 1: but he had like a million wrong, totally monkers ideas.

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Speaker 1: If you just like spew ideas, eventually one of them

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Speaker 1: is going to be right.

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Speaker 4: Statistically speaking, exactly, It's like Nostra Damus, like he predicted

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Speaker 4: everything because he made a bunch of false predictions as well, exactly.

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Speaker 1: And so if I wrote down literally every possible thing

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Speaker 1: that could happen, if I made an infinite number of predictions,

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Speaker 1: then one of them would be correct. I could predict

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Speaker 1: the whole future of the universe if I had an

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Speaker 1: infinite number of predictions, and one of those would be

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Speaker 1: the actual series of events of the.

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Speaker 4: Future, right exactly. If you think about, like if you

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Speaker 4: make a random noise in your head, like, the chances

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Speaker 4: are someone else is going to think that same random

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Speaker 4: noise in your head at some point in an infinite universe.

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Speaker 1: And that's what we're going to talk about today on

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

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

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

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

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

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Speaker 4: Ah, just real big, you know, really really big actually,

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Speaker 4: you know, in a serious answer to that. When I

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Speaker 4: was a kid first learning about infinity, it was almost

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Speaker 4: like the concepts of infinity and nothing were very similar

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Speaker 4: to me because both kind of made my brain feel fuzzy.

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Speaker 4: So thinking about an infinite amount of stuff and thinking

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Speaker 4: about the absence of stuff, it's like a similar feeling

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Speaker 4: to me, where it's like my brain just gets this

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Speaker 4: prickly static feeling when I try to think 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.

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Speaker 4: Yeah, it's like, how do you fit a concept like

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Speaker 4: infinity inside of a finite brain with a finite number

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Speaker 4: of neurons? So you can't. It's not something that you

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Speaker 4: can really conceive of without using some kind of shortcut

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Speaker 4: because our brains aren't infinite, so you can't fit infinity

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Speaker 4: in there.

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

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

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

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

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Speaker 1: to 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: emotions 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?

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Speaker 5: Like?

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

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Speaker 4: Right? Because you can have something in math that's theoretical,

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Speaker 4: but it's not necessarily a tangible thing that you can

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Speaker 4: like observe or hold in your hands, Like can you

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Speaker 4: pick up a chunk of infinity and have that in

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Speaker 4: your hands.

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

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

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

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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 of this concept of a perfect idealized circle.

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Speaker 1: But I've never seen a perfect circle in reality.

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Speaker 5: Have you.

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Speaker 4: Ah, Well, when I eat enough food, maybe, but no,

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Speaker 4: I guess that any kind of drawing or depiction of

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Speaker 4: a circle even if it looks perfect, if you look

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Speaker 4: at it with like an electron microscope, you're gonna find imperfections.

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

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

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Speaker 1: a perfectly continuous circle in reality, But of course you

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

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

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Speaker 1: right x W plus y square it equals for 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?

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Speaker 2: Right?

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Speaker 1: Have the equation? I have the idea in my mind,

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Speaker 1: there is this set of neurons in my brain that's

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Speaker 1: now representing that concept, But there is no circle actually

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Speaker 1: out there in the universe. It's sort of hard to

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Speaker 1: grabble with.

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Speaker 4: Even in our brains. Like that circle that you can

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Speaker 4: kind of visualize is just made up of the firing

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Speaker 4: of your neurons. And so is that circle in your

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Speaker 4: brain even perfect?

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

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Speaker 1: another episode. But today I want to focus on this

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Speaker 1: biggest concept in mathematics, infinity, because it's something that pops

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Speaker 1: up all the time in physics. It's something that really

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

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Speaker 1: So 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?

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Speaker 4: And people have some answers to this question, which we're

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Speaker 4: going to listen to right now.

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Speaker 1: That's right. Thank you very much to those of you

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Speaker 1: who answered my tough physics questions with no preparation for

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Speaker 1: the podcast. If you'd like to participate for a future

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Speaker 1: virtual Person on the Street interviews, please write to me

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Speaker 1: too questions at Danielianjorge dot com. I promise it's fun.

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Speaker 1: Here's what people had to say.

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Speaker 6: I think that infinity is definitely real. I believe that

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Speaker 6: the universe is infinite in its size, so that there

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Speaker 6: is the real infinite in the universe that we live in.

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Speaker 6: And also, if we believe in the Einstein's theory about

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Speaker 6: black holes, that also inside a black hole we have

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Speaker 6: a singularity that is a point of infinite density. So

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Speaker 6: there you go, you have another very real infinite.

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Speaker 7: The early situation in which I can think of from

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Speaker 7: a physics point of view, where infinity might be real

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Speaker 7: is if the universe has been eternal, if it's been

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Speaker 7: around forever, maybe if there is a singularity in black holes,

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Speaker 7: then that might also be considered a point of infinite density.

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Speaker 4: I guess, well, that is very interesting. I do like

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Speaker 4: the idea of the universe being a turn well, I

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Speaker 4: think that's kind of one of my concepts of infinity

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Speaker 4: is that existence of something some you know, universe, even

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Speaker 4: if it's not our universe, but just the existence of

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Speaker 4: stuff has to be infinite, right, Like, there can't be

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Speaker 4: 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.

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Speaker 4: Also, right, I don't know whether to be insulted or not,

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Speaker 4: but yeah, I mean that's how I feel. This is

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Speaker 4: not based on science. It's just how I feel of like, well,

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Speaker 4: we can't just have stuff come out of nothing, go

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Speaker 4: do its thing for a while and then end and

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Speaker 4: then there be nothing again. But there's not any scientific

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Speaker 4: reason for that. That's coming from my human feelings of existence.

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Speaker 4: And maybe even that's what I want to believe because

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Speaker 4: it's very comforting to think there's an infinite universe that

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Speaker 4: doesn't die, And.

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Speaker 1: I think it tells you something about yourself and how

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Speaker 1: your mind works and your understanding of the universe to

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Speaker 1: answer these questions that it feels natural to you that

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Speaker 1: the universe is infinite, or that it's not that there

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

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

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Speaker 1: is to go the opposite direction, to start from the

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Speaker 1: data and say, well, universe, tell us what's out there,

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Speaker 1: and then from that will build our model of the universe,

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Speaker 1: instead of saying like, well, this just has to be

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Speaker 1: this way. But it's hard to sort of understand where

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Speaker 1: those limits are. You can't like question every single thing

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Speaker 1: all the time. You can do experiments every day about

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Speaker 1: every tiny detail, so it's hard to know sometimes when

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Speaker 1: a question is this hard to grapple with exactly how

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Speaker 1: to figure it out. And that's what I think we

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Speaker 1: hear our listeners grappling with whether it can be, whether

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Speaker 1: it must be, whether it can't be. Tricky stuff.

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Speaker 4: Are you saying that I, Katie Golden, could be wrong

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Speaker 4: about one of the most difficult concepts in the universe.

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Speaker 1: I'm saying, basically, everybody is probably wrong about almost everything.

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Speaker 1: You know, those are the best parts of science, right,

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Speaker 1: When your intuition is confronted with data, that's when you

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Speaker 1: learn something. That's when the universe is telling you all right,

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Speaker 1: I get why you think this is true, but it

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Speaker 1: turns out it's not. Works a totally different way, And

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Speaker 1: that's why we do science, right, That's why we have

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Speaker 1: this methodological approach to revealing the truth about the universe,

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Speaker 1: rather than just you know, eating olives and lying around

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Speaker 1: in robes and saying maybe it's made of tiny cats,

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Speaker 1: as fun as that is.

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Speaker 4: So say I'm Plato and I'm trying to conceive of infinity.

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Speaker 4: Am I just thinking of like a really really long

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Speaker 4: line of olives? What's going on with that?

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Speaker 6: 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 BCE, and you know,

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Speaker 1: there are some examples there of 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, Xeno'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.

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Speaker 4: This is how I approach eating a cookie because I think, well,

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Speaker 4: I'm not going to eat this whole cookie, so I'll

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Speaker 4: just eat half of this cookie. And I'm like, well,

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Speaker 4: I want a little more of this cookie, so I'll

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Speaker 4: eat half of a half of a cookie, and then

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Speaker 4: half of that half and so on, and so that

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Speaker 4: way I get to say, like, well, I didn't eat

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Speaker 4: the whole cookie, even though there's only an infinitesimally small

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Speaker 4: chrome left of cookie.

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Speaker 1: Yeah, that's a mathematical proof of converging series. Right, you

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Speaker 1: could have an infinite number of terms and still have

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Speaker 1: it converged to a finite number. Unfortunately, my cookie eating

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Speaker 1: strategy is a divergent series. I start out with great intentions.

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Speaker 1: I'm like, I'm just gonna have one, and then I'm like, well,

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Speaker 1: I had one, so mighty, we'll just have another one.

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Speaker 1: And then I'm like, well, I've had two, so I

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Speaker 1: can just grab a couple more. And then I'm like, mighty,

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Speaker 1: well just finished the box, because we all know where

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Speaker 1: this is going, so let's just get there right now.

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Speaker 1: But the Greeks really struggled with this idea. They didn't

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Speaker 1: know if infinity was real, and they had two different concepts.

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Speaker 1: They talked about actual infinity and potential infinity, and they

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Speaker 1: separated these two concepts. They were like, well, this potential infinity,

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Speaker 1: we can think about that for like proofs and geometry

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Speaker 1: and stuff like that, but you know, actual infinity, that's

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Speaker 1: something they actually shied away from. They didn't even want

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Speaker 1: to talk about it. They try to avoid it ever

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Speaker 1: coming up in their proofs and in their logic and

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Speaker 1: in their thought.

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Speaker 4: Like saying sort of a naughty word, like what about

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Speaker 4: actual infinity? And then you get kicked out of class,

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Speaker 4: out of Greek class.

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Speaker 1: Yeah, and they called it the horror of the infinite.

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Speaker 1: They did all these proofs where you could have you know,

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Speaker 1: used infinity as a mathematical step, but they took all

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Speaker 1: these extra steps to make these proofs happen without needing

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Speaker 1: to resort infinity, without infinity appearing anywhere in their math,

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Speaker 1: because they thought, well, that must be nonsense.

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Speaker 4: That's so interesting. So they had a concept of the

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Speaker 4: potential for infinity, but actually discussing infinity itself was taboo

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Speaker 4: because it makes your brain feel bad.

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

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Speaker 1: I think they thought it was a mathematical curiosity and

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Speaker 1: if you invoked it, if you had to invoke it,

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Speaker 1: then it's somehow made your proofs invalid. And now, of

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Speaker 1: course we you know, we have the same sort of

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Speaker 1: relationship with infinity, like it's a thing. We can think

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Speaker 1: about it, we can understand it, but it is difficult

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Speaker 1: for us to wrap our minds around, at least to

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Speaker 1: all sorts of like counterintuitive concepts, and has many many

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Speaker 1: interesting layers, you know, the basic notion of infinity is

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Speaker 1: just the one we talked about before, like the number

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Speaker 1: of numbers. Right, if you start from zero and you

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Speaker 1: keep going, you'll never get to a point where you

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Speaker 1: can't add another number. Our number system just has that

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Speaker 1: flexibility is no limit, so that you can always make

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Speaker 1: a bigger number, And that's like a really powerful concept.

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Speaker 1: It also makes me wonder sometimes, like what's the biggest

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Speaker 1: number any human has ever thought of? Right, there isn't

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Speaker 1: a biggest number in principle that there might be a

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Speaker 1: biggest number anybody's ever like written down or held in

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Speaker 1: their head.

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Speaker 4: Yeah, I mean, but then once you find that out,

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Speaker 4: you can just add one to it.

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Speaker 1: And then you've got the record. Right, you're the human

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Speaker 1: who's thought the biggest number ever. That'd be super cool.

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Speaker 4: Yeah, like a google plex, a google plex plus one.

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Speaker 1: That's it. You're the champ now. So that's super fun.

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Speaker 1: And there's all these really interesting exercises to get your

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Speaker 1: brain used to the counterintuitive nature of infinity, because the

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Speaker 1: mathematics of infinity are quite slippery. Right, you can think

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Speaker 1: about infinity plus but like if phinty plus one really

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Speaker 1: is just infinity. One of my favorite examples comes from

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Speaker 1: David Hilbert, the guy invented Hilbert Space, like one hundred

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Speaker 1: years ago, and this is called Hilbert's Hotel. And in

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Speaker 1: Hilbert's Hotel, he's got a hotel with an infinite number

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

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Speaker 1: of guests. So every room in the hotel has somebody

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Speaker 1: 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: asks 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 tells 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 and forty seven goes to room five

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Speaker 1: hundred and forty eight, And in this way, room number

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Speaker 1: one now becomes vacant. What happens at the very very end,

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Speaker 1: like in room infinity. Well, room infinity goes to room

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Speaker 1: infinity plus one, right, and I think, well that room

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Speaker 1: didn't exist before. Well, it did because there were an

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Speaker 1: infinite number of rooms, and so in this weird way,

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Speaker 1: you can still make room even if you had an

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Speaker 1: infinite number of guests.

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Speaker 4: But you know, it sounds like this is gonna only

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Speaker 4: get a two point five stars on Yelp because Albert's

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Speaker 4: making you pack up and move your rooms all the time.

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Speaker 4: Terrible stay.

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Speaker 1: Yeah, and he can even accommodate an infinite number of guests,

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Speaker 1: Like if an infinite number of people show up and

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Speaker 1: want rooms, he can just say, all right, everybody, leave

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Speaker 1: your room and go to twice your room number. Right,

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Speaker 1: So then person in room four goes to room eight,

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Speaker 1: for example, leaving three rooms open. And so there's a

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Speaker 1: lot of flexibility there left in infinity. It's really fascinating,

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Speaker 1: but of course it feels unphysical. This doesn't feel like

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Speaker 1: something that could actually exist because hotels have a certain

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Speaker 1: number of rooms. Even if there are very very large numbers,

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Speaker 1: there is a number, and so that shows you that

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Speaker 1: like infinity really not a number in the same way

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Speaker 1: that other big numbers are.

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Speaker 4: Right when we try to apply something like infinity to

437
00:22:09,160 --> 00:22:12,080
Speaker 4: something that in our human minds is a finite thing,

438
00:22:12,240 --> 00:22:16,160
Speaker 4: like physical space of a hotel rooms. You know, those

439
00:22:16,160 --> 00:22:19,720
Speaker 4: little mints they put under your pillow. It's very difficult

440
00:22:19,760 --> 00:22:23,800
Speaker 4: to actually try to translate that concept into infinity, like

441
00:22:23,880 --> 00:22:27,119
Speaker 4: I can't think of infinity mints. That's just not you know,

442
00:22:27,200 --> 00:22:30,080
Speaker 4: infinemns like, although that would be a good brand for

443
00:22:30,160 --> 00:22:33,359
Speaker 4: those little hotel mins in the infinity.

444
00:22:32,800 --> 00:22:34,880
Speaker 1: We are copywriting that right here. And you can play

445
00:22:35,000 --> 00:22:37,320
Speaker 1: other fun games to really blow your mind because it

446
00:22:37,359 --> 00:22:41,000
Speaker 1: turns out that there are different sizes of infinity. Like

447
00:22:41,200 --> 00:22:43,520
Speaker 1: you know, I think whole lot is Infinity is everything.

448
00:22:43,560 --> 00:22:45,879
Speaker 1: It's the biggest thing. There can't be anything bigger than that.

449
00:22:46,480 --> 00:22:49,840
Speaker 1: But you can't actually take an infinite list and then

450
00:22:50,000 --> 00:22:53,760
Speaker 1: make something bigger than that infinite list. There's another really

451
00:22:53,840 --> 00:22:57,040
Speaker 1: clever example in mathematics, like say, for example, you write

452
00:22:57,080 --> 00:23:00,920
Speaker 1: down all of the numbers between one and two. How

453
00:23:00,920 --> 00:23:03,239
Speaker 1: many numbers are there between one and two? Well, there

454
00:23:03,280 --> 00:23:06,119
Speaker 1: is an infinite number because you can always add another

455
00:23:06,200 --> 00:23:09,280
Speaker 1: digit to subdividce like Zeno's paradox. If you have one

456
00:23:09,280 --> 00:23:11,399
Speaker 1: point seven and one point eight, you can always go

457
00:23:11,480 --> 00:23:13,479
Speaker 1: one point seven five, and then one point seven two

458
00:23:13,640 --> 00:23:16,240
Speaker 1: five and one point seven one seven five or whatever.

459
00:23:16,600 --> 00:23:18,680
Speaker 1: So there's an infinite number of numbers there.

460
00:23:18,520 --> 00:23:21,640
Speaker 4: Because you can always take half of a half exactly.

461
00:23:21,640 --> 00:23:23,880
Speaker 1: So we have an infinite number of numbers, and each

462
00:23:23,880 --> 00:23:26,359
Speaker 1: of those numbers can have an infinite number of digits.

463
00:23:26,600 --> 00:23:30,120
Speaker 1: So between one and two, there's an infinite number of numbers,

464
00:23:30,280 --> 00:23:32,880
Speaker 1: each of which have an infinite number of digits, right,

465
00:23:32,960 --> 00:23:36,320
Speaker 1: just like pi. And so that's amazing just to think about. Now,

466
00:23:36,320 --> 00:23:39,359
Speaker 1: if you take that list, I can always find a

467
00:23:39,480 --> 00:23:42,960
Speaker 1: number that's not on that list. There's always one more

468
00:23:43,040 --> 00:23:46,399
Speaker 1: number between one and two that's not on that list.

469
00:23:46,760 --> 00:23:48,679
Speaker 1: How do you do that? Well, it's sort of just

470
00:23:48,800 --> 00:23:51,320
Speaker 1: like taking the biggest number and adding one which you need.

471
00:23:51,400 --> 00:23:54,679
Speaker 1: Is a recipe for generating a new number that's not

472
00:23:54,920 --> 00:23:57,800
Speaker 1: on that list, and that's not actually that hard. You

473
00:23:57,920 --> 00:24:00,679
Speaker 1: just take the first digit from the first number and

474
00:24:00,760 --> 00:24:02,639
Speaker 1: you add one to it, and you take the second

475
00:24:02,680 --> 00:24:04,919
Speaker 1: digit from the second number and you add one to it,

476
00:24:05,119 --> 00:24:07,040
Speaker 1: and the third digit from the third number and you

477
00:24:07,119 --> 00:24:09,439
Speaker 1: add one to it, and then you're making a number

478
00:24:09,480 --> 00:24:12,520
Speaker 1: which disagrees with every number on your list in one

479
00:24:12,560 --> 00:24:15,639
Speaker 1: of the digits. So it wasn't on your list, which

480
00:24:15,680 --> 00:24:18,040
Speaker 1: means that you had an infinite number of numbers on

481
00:24:18,080 --> 00:24:21,240
Speaker 1: your list, but you can make it bigger. And so

482
00:24:21,440 --> 00:24:23,960
Speaker 1: that's an example of a kind of infinity we call

483
00:24:24,240 --> 00:24:28,760
Speaker 1: uncountable infinity, where you can't like associate all the things

484
00:24:28,800 --> 00:24:31,960
Speaker 1: on your list with the natural numbers with one, two, three, four, five,

485
00:24:31,960 --> 00:24:35,760
Speaker 1: sixty seven. It's bigger than the infinity of all the numbers.

486
00:24:35,880 --> 00:24:39,240
Speaker 4: So, for those of us who are less numerically inclined,

487
00:24:39,600 --> 00:24:44,040
Speaker 4: you're saying, basically, you could have a pile of cats,

488
00:24:44,840 --> 00:24:47,920
Speaker 4: but it's an infinite pile of cats, like, well, this

489
00:24:47,960 --> 00:24:51,600
Speaker 4: is infinity cats. But then you find just one more

490
00:24:51,680 --> 00:24:54,639
Speaker 4: cat and it looks so cute that you have to

491
00:24:54,680 --> 00:24:57,480
Speaker 4: add it to the pile of infinity cats that you're hoarding,

492
00:24:57,760 --> 00:25:00,399
Speaker 4: and now you have an even bigger pile of cats.

493
00:25:00,520 --> 00:25:03,280
Speaker 4: But they're both piles of infinite cats.

494
00:25:03,000 --> 00:25:04,560
Speaker 1: That's right. And you can have a pile of cats

495
00:25:04,560 --> 00:25:08,680
Speaker 1: that's so infinite that you can't even assign them all numbers.

496
00:25:08,720 --> 00:25:11,440
Speaker 1: You can't like give them all unique numbers. There's more

497
00:25:11,520 --> 00:25:14,240
Speaker 1: cats on that list than there are numbers in the

498
00:25:14,359 --> 00:25:15,480
Speaker 1: infinite number line.

499
00:25:15,600 --> 00:25:17,560
Speaker 4: At a certain point, you just got to start calling

500
00:25:17,600 --> 00:25:18,400
Speaker 4: them all Mint.

501
00:25:20,359 --> 00:25:22,840
Speaker 1: Mitten's two hundred and seventy two, Come get your pill.

502
00:25:24,280 --> 00:25:26,400
Speaker 1: That's a lot of being a cat mom. So there's

503
00:25:26,440 --> 00:25:29,080
Speaker 1: these crazy concept. We have countable infinity, which is like

504
00:25:29,119 --> 00:25:32,480
Speaker 1: the natural numbers, and then we have uncountable infinities, which

505
00:25:32,520 --> 00:25:34,240
Speaker 1: are even bigger and hard to grapple with.

506
00:25:34,440 --> 00:25:37,520
Speaker 4: Well, I think one thing we can grapple with, though,

507
00:25:37,600 --> 00:25:41,000
Speaker 4: is a very finite break before we talk more about

508
00:25:41,080 --> 00:25:45,640
Speaker 4: the infinity of infinity after the break, which won't be infinity.

509
00:25:45,680 --> 00:25:51,320
Speaker 4: So don't worry with.

510
00:25:51,359 --> 00:25:54,560
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550
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559
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Speaker 1: pop a piece of cheese into your mouth or enjoy

560
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Speaker 1: a rich spoonful of Greek yogurt, you're probably not thinking

561
00:28:27,080 --> 00:28:30,639
Speaker 1: about the environmental impact of each and every bite, But

562
00:28:30,680 --> 00:28:33,360
Speaker 1: the people in the dairy industry are US Dairy has

563
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Speaker 1: set themselves some ambitious sustainability goals, including being greenhouse gas

564
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565
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566
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567
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Speaker 1: for example, most dairy farms reuse water up to four

568
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Speaker 1: times the same water cools the milk, cleans equipment, washes

569
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Speaker 1: the barn, and irrigates the crops. How is US Dairy

570
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Speaker 1: tackling greenhouse gases? Many farms use anaerobic digestors that turn

571
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Speaker 1: and electric cars. So the next time you grab a

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Speaker 1: slice of pizza or lick an ice cream cone, know

574
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Speaker 1: that dairy farmers and processors around the country are using

575
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576
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Speaker 1: dairy products we love with less of an impact. Visit

577
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578
00:29:28,600 --> 00:29:31,200
Speaker 4: And we are back. And I hope that break did

579
00:29:31,240 --> 00:29:35,360
Speaker 4: not feel like an infinity being separated from our lovely

580
00:29:35,440 --> 00:29:37,360
Speaker 4: voices telling you about infinity.

581
00:29:37,840 --> 00:29:39,760
Speaker 1: We are having a lot of fun thinking and talking

582
00:29:39,800 --> 00:29:43,040
Speaker 1: about infinities. And so far we've been talking about infinity

583
00:29:43,080 --> 00:29:46,400
Speaker 1: sort of mathematically, right in terms of like what the

584
00:29:46,480 --> 00:29:48,840
Speaker 1: number means and how big it is and how hard

585
00:29:48,880 --> 00:29:50,960
Speaker 1: that is to get your minds around. But now let's

586
00:29:50,960 --> 00:29:56,360
Speaker 1: talk about infinity in physics, because physics and theoretical physics

587
00:29:56,400 --> 00:29:59,920
Speaker 1: specifically has infinities all the time, right, Like they're in

588
00:30:00,000 --> 00:30:04,720
Speaker 1: infinities all over the place in theoretical physics. And so

589
00:30:04,840 --> 00:30:07,440
Speaker 1: first let's talk about infinities and theoretical physics, and then

590
00:30:07,440 --> 00:30:09,840
Speaker 1: we'll figure out whether any of those are actually real

591
00:30:10,000 --> 00:30:11,440
Speaker 1: out there in the universe.

592
00:30:11,760 --> 00:30:15,000
Speaker 4: So when I think of physics, I think of you know,

593
00:30:15,080 --> 00:30:17,760
Speaker 4: you drop a ball off of a building, and hey,

594
00:30:17,800 --> 00:30:20,240
Speaker 4: you can figure out how fast that ball is going,

595
00:30:20,720 --> 00:30:24,680
Speaker 4: or even particle physics, you are looking at the interaction

596
00:30:24,840 --> 00:30:28,160
Speaker 4: of particles with each other. It's hard for me to

597
00:30:28,280 --> 00:30:33,080
Speaker 4: conceptualize what infinity looks like. How do you have infinity

598
00:30:34,200 --> 00:30:37,640
Speaker 4: tall building with infinity balls dropping off of it, or

599
00:30:37,720 --> 00:30:40,880
Speaker 4: how do you have infinity particles interacting with each other?

600
00:30:41,160 --> 00:30:43,400
Speaker 1: Yeah, that's really is hard to think about. But it

601
00:30:43,560 --> 00:30:47,200
Speaker 1: entered into physics very very early with Newton. Like, as

602
00:30:47,240 --> 00:30:49,440
Speaker 1: you're saying, Newton is thinking of like an apple falling

603
00:30:49,480 --> 00:30:52,160
Speaker 1: off of the tree or the motion of something. In

604
00:30:52,240 --> 00:30:54,920
Speaker 1: order to solve those physics problems, you get to invent

605
00:30:54,960 --> 00:30:59,239
Speaker 1: a new kind of mathematics, calculus. Calculus is adding up

606
00:30:59,240 --> 00:31:03,200
Speaker 1: what we call infie tesimals, lots of tiny little contributions.

607
00:31:03,320 --> 00:31:05,680
Speaker 1: You know, for example, when the apple is falling from

608
00:31:05,680 --> 00:31:08,840
Speaker 1: the tree, it's not moving a constant velocity. It's not

609
00:31:08,960 --> 00:31:11,880
Speaker 1: falling with the same speed all the time. It's falling

610
00:31:11,960 --> 00:31:14,920
Speaker 1: faster and then faster, and then faster. And so to

611
00:31:14,960 --> 00:31:17,240
Speaker 1: do those calculations to figure out like how long does

612
00:31:17,280 --> 00:31:20,120
Speaker 1: it take the apple to fall from the tree and

613
00:31:20,200 --> 00:31:23,960
Speaker 1: hit the ground means adding up lots of changing velocities.

614
00:31:24,160 --> 00:31:26,440
Speaker 1: So you have to invent a new kind of mathematics

615
00:31:26,480 --> 00:31:30,040
Speaker 1: called calculus, which allows you to add up an infinite

616
00:31:30,200 --> 00:31:33,880
Speaker 1: number of little slices of time to get the right answer.

617
00:31:34,320 --> 00:31:36,560
Speaker 1: And that's the way calculus works. It's like the limit

618
00:31:36,600 --> 00:31:39,320
Speaker 1: of taking a big sum. When that limit becomes infinite,

619
00:31:39,320 --> 00:31:41,560
Speaker 1: when you have an infinite number of things you're adding up.

620
00:31:41,960 --> 00:31:45,160
Speaker 1: And so calculus is all about infinite tesimals. It's everywhere

621
00:31:45,200 --> 00:31:45,719
Speaker 1: around us.

622
00:31:45,880 --> 00:31:49,320
Speaker 4: So here's a potentially stupid question. If you had an

623
00:31:49,400 --> 00:31:53,920
Speaker 4: infinitely tall tree and you had an apple fall from

624
00:31:53,920 --> 00:31:59,640
Speaker 4: an infinitely tall branch onto Newton who was infinitely below

625
00:31:59,760 --> 00:32:04,719
Speaker 4: that apple, with that apple without when resistance become infinitely

626
00:32:04,800 --> 00:32:08,000
Speaker 4: fast and just pulverize Newton into infinitely nothing.

627
00:32:08,240 --> 00:32:10,800
Speaker 1: Well, if we're you living in this universe, then there

628
00:32:10,880 --> 00:32:14,640
Speaker 1: is a speed limit, and so it can't go infinitely fast. Right,

629
00:32:15,000 --> 00:32:19,040
Speaker 1: that's a really fascinating question about infinity because in theoretical physics,

630
00:32:19,120 --> 00:32:22,600
Speaker 1: you can't have infinite velocity. Right, there is a speed

631
00:32:22,640 --> 00:32:26,720
Speaker 1: limit to the universe. You can't go infiniti velocity. So

632
00:32:26,960 --> 00:32:29,360
Speaker 1: if he's infinitely far away from the apple, then it

633
00:32:29,400 --> 00:32:30,280
Speaker 1: would never hit him.

634
00:32:30,440 --> 00:32:33,000
Speaker 4: So is there some kind of like space cops that

635
00:32:33,040 --> 00:32:37,640
Speaker 4: are like space highway patrol enforcing this space speed limit,

636
00:32:37,760 --> 00:32:41,680
Speaker 4: because that seems like they're really harsh in my mellow.

637
00:32:41,920 --> 00:32:44,960
Speaker 1: No, it's just a fact of the universe. But fascinatingly,

638
00:32:45,200 --> 00:32:47,920
Speaker 1: there is no limit on the energy of a particle.

639
00:32:48,120 --> 00:32:50,880
Speaker 1: So these particles can't go infinitely fast, but they can

640
00:32:51,040 --> 00:32:54,760
Speaker 1: have infinite energy, Like if you build a particle accelerator,

641
00:32:54,800 --> 00:32:57,280
Speaker 1: you can just keep pumping these particles to have higher

642
00:32:57,320 --> 00:33:00,200
Speaker 1: and higher energy, even though they don't go fast, stir

643
00:33:00,280 --> 00:33:04,120
Speaker 1: and faster. The relationship between energy and speed changes as

644
00:33:04,120 --> 00:33:06,040
Speaker 1: you approach the speed of light, and you can like

645
00:33:06,120 --> 00:33:08,280
Speaker 1: double the amount of energy a particle has and it

646
00:33:08,360 --> 00:33:11,280
Speaker 1: just goes a tiny little bit faster. So there is

647
00:33:11,320 --> 00:33:13,400
Speaker 1: no limit to the energy a particle can have, but

648
00:33:13,480 --> 00:33:15,480
Speaker 1: there is a limit to the speed it can have,

649
00:33:15,920 --> 00:33:18,720
Speaker 1: which is an interesting sort of counterplay there between finite

650
00:33:18,760 --> 00:33:19,320
Speaker 1: and infinite.

651
00:33:19,440 --> 00:33:22,400
Speaker 4: So what is the universal speed limit? Is it like

652
00:33:22,640 --> 00:33:25,280
Speaker 4: one hundred miles per hour or like one hundred and

653
00:33:25,280 --> 00:33:27,720
Speaker 4: twenty kilometers per hour? I don't want to be too

654
00:33:27,880 --> 00:33:30,000
Speaker 4: exclusive to our europe and listeners.

655
00:33:30,200 --> 00:33:33,840
Speaker 1: It's a three times teny eight meters per second. So

656
00:33:34,000 --> 00:33:37,560
Speaker 1: three hundred million meters per second is the speed limit

657
00:33:37,600 --> 00:33:39,960
Speaker 1: for the speed of light in a vacuum, of course,

658
00:33:40,280 --> 00:33:42,880
Speaker 1: and that's the fastest that anything can move relative to

659
00:33:42,920 --> 00:33:45,880
Speaker 1: any other object in the universe. But again, no limit

660
00:33:46,040 --> 00:33:47,720
Speaker 1: on the energy, which is amazing.

661
00:33:47,880 --> 00:33:50,160
Speaker 4: Wow. Well that's good to know though, so we don't

662
00:33:50,160 --> 00:33:51,080
Speaker 4: get a speeding ticket.

663
00:33:51,800 --> 00:33:55,320
Speaker 1: And theoretical physics also deals with infinity in terms of

664
00:33:55,360 --> 00:33:58,280
Speaker 1: the particles. As you were saying, you know what happens

665
00:33:58,360 --> 00:34:01,400
Speaker 1: when two particles bumping out each other, Well, they're not

666
00:34:01,480 --> 00:34:05,080
Speaker 1: like physically actually touching each other. In our model, we

667
00:34:05,200 --> 00:34:08,640
Speaker 1: have them passing particles back and forth, like two electrons

668
00:34:08,680 --> 00:34:11,680
Speaker 1: repel each other. How while they do it by emitting

669
00:34:11,719 --> 00:34:14,879
Speaker 1: a photon and passing that photon from one to the other,

670
00:34:14,960 --> 00:34:17,520
Speaker 1: which gives it a little push. It's a little momentum transfer.

671
00:34:17,640 --> 00:34:21,000
Speaker 1: But it's not just one photon. The electron is constantly

672
00:34:21,080 --> 00:34:24,520
Speaker 1: emitting photons. Most of the photons aren't like big, heavy

673
00:34:24,600 --> 00:34:26,919
Speaker 1: duty photons they're going to do anything. Most of them

674
00:34:27,000 --> 00:34:31,400
Speaker 1: are very very very low energy, infinitesimally small energy. But

675
00:34:31,440 --> 00:34:34,560
Speaker 1: then there's an infinite number of them. So every photon

676
00:34:34,680 --> 00:34:38,960
Speaker 1: is constantly emitting an infinite number of tiny, tiny, tiny photons.

677
00:34:39,160 --> 00:34:43,399
Speaker 4: So that's like if you have a kitten who's got

678
00:34:43,440 --> 00:34:46,160
Speaker 4: a very weak little swipe of the paw, but if

679
00:34:46,200 --> 00:34:50,320
Speaker 4: you have infinity little kittens, it's gonna have an impact.

680
00:34:49,920 --> 00:34:53,800
Speaker 1: On you exactly. And these infinite little photons or kittens

681
00:34:54,200 --> 00:34:56,399
Speaker 1: just add up to a normal number, and they don't

682
00:34:56,640 --> 00:34:58,760
Speaker 1: give you a divergence. They don't give you an infinite

683
00:34:58,800 --> 00:35:02,040
Speaker 1: amount of force between the electrons that's the key that

684
00:35:02,080 --> 00:35:04,839
Speaker 1: sometimes in these calculations, you have an infinite number of

685
00:35:04,880 --> 00:35:08,960
Speaker 1: steps in the calculation, but you still get a finite answer, right.

686
00:35:08,960 --> 00:35:11,920
Speaker 1: The electron pushes against the other electron with a certain

687
00:35:12,080 --> 00:35:14,960
Speaker 1: finite number, and that's sort of like Zeno's paradox. It

688
00:35:15,000 --> 00:35:18,400
Speaker 1: tells you that the infinity isn't real. It's just an

689
00:35:18,520 --> 00:35:21,560
Speaker 1: artifact of how you're doing the calculation. You could take

690
00:35:21,560 --> 00:35:24,240
Speaker 1: any finite number and slice it up into infinite pieces.

691
00:35:24,520 --> 00:35:27,239
Speaker 1: Doesn't mean there's a real infinity there. It just means

692
00:35:27,239 --> 00:35:29,200
Speaker 1: that you've cut it into an infinite number of.

693
00:35:29,080 --> 00:35:33,120
Speaker 4: Pieces, right, Because like if you cut a single cookie

694
00:35:33,400 --> 00:35:39,840
Speaker 4: into infinitely small pieces, it's still just a single cookie unfortunately.

695
00:35:39,600 --> 00:35:41,839
Speaker 1: Exactly, and that probably doesn't even taste as good, because

696
00:35:41,840 --> 00:35:45,000
Speaker 1: you've separated all the ingredients, right, And it's that magical

697
00:35:45,040 --> 00:35:47,359
Speaker 1: mixture of ingredients that makes a cookie what it is.

698
00:35:47,520 --> 00:35:50,120
Speaker 1: And often in theoretical physics, when you do get a

699
00:35:50,160 --> 00:35:53,080
Speaker 1: real infinity, when all the particles add up to give

700
00:35:53,080 --> 00:35:56,719
Speaker 1: you like an infinite force between the two electrons, that's

701
00:35:56,719 --> 00:35:59,080
Speaker 1: when you know you've done something wrong. That we call

702
00:35:59,120 --> 00:36:02,160
Speaker 1: it divergence, right, because you can have an infinite series

703
00:36:02,200 --> 00:36:04,680
Speaker 1: that does diverge. Say, for example, you just add up

704
00:36:04,680 --> 00:36:08,560
Speaker 1: all the natural numbers between one and infinity, that sum,

705
00:36:08,640 --> 00:36:10,719
Speaker 1: if you add them all up, is going to be infinity.

706
00:36:10,920 --> 00:36:13,239
Speaker 1: If you add up you know, one and then plus

707
00:36:13,280 --> 00:36:15,480
Speaker 1: a half and a fourth and an eighth, that's not

708
00:36:15,560 --> 00:36:17,759
Speaker 1: going to be an infinite number. That's going to converge.

709
00:36:18,200 --> 00:36:21,040
Speaker 1: And so in physics, when we do a calculation and

710
00:36:21,080 --> 00:36:23,839
Speaker 1: it gives us infinity, we usually think of that as

711
00:36:23,840 --> 00:36:26,960
Speaker 1: a failure. It's sort of like the Greeks, you know,

712
00:36:27,120 --> 00:36:29,880
Speaker 1: like actual infinity. It's like the horror of the infinite,

713
00:36:29,960 --> 00:36:32,279
Speaker 1: because we don't think that particles push against each other

714
00:36:32,360 --> 00:36:33,240
Speaker 1: with infinite force.

715
00:36:33,400 --> 00:36:36,520
Speaker 4: So when buzz light year says to infinity and beyond,

716
00:36:36,719 --> 00:36:38,040
Speaker 4: that's like horrific.

717
00:36:38,360 --> 00:36:42,840
Speaker 1: For physicists, we're like, no, don't go there, fix your calculation.

718
00:36:42,880 --> 00:36:46,680
Speaker 1: You must have missed a minus sign or something. And

719
00:36:46,760 --> 00:36:48,839
Speaker 1: so it does pop up all the time, and usually

720
00:36:48,880 --> 00:36:50,880
Speaker 1: it's a sign that something is wrong. You've done your

721
00:36:50,920 --> 00:36:54,000
Speaker 1: calculation wrong, and so your series is like diverged instead

722
00:36:54,000 --> 00:36:56,520
Speaker 1: of converged. You know, you missed a minus sign maybe.

723
00:36:56,560 --> 00:36:58,160
Speaker 1: And this is how we know, for example, that a

724
00:36:58,200 --> 00:37:02,640
Speaker 1: theory isn't working because we don't see these infinities. In nature,

725
00:37:02,719 --> 00:37:06,760
Speaker 1: you don't see particles with infinite electric charge or pushing

726
00:37:06,800 --> 00:37:10,279
Speaker 1: against other particles with infinite forces, And so that's why,

727
00:37:10,360 --> 00:37:12,920
Speaker 1: like the lack of seeing infinity in the physical universe

728
00:37:13,080 --> 00:37:15,120
Speaker 1: tells us that we can't have it cropping up in

729
00:37:15,239 --> 00:37:17,640
Speaker 1: our theoretical concepts as well.

730
00:37:17,800 --> 00:37:21,160
Speaker 4: That also happens in biology. You have like a Fibonacci

731
00:37:21,239 --> 00:37:26,239
Speaker 4: sequence perhaps where you get these fractals in nature, like

732
00:37:26,320 --> 00:37:29,160
Speaker 4: you'll see them in plants often where or like even

733
00:37:29,200 --> 00:37:31,279
Speaker 4: if you see like a cauliflower or if you have

734
00:37:31,360 --> 00:37:35,360
Speaker 4: ever had it romanesco. It's this very beautiful green plant

735
00:37:35,440 --> 00:37:38,640
Speaker 4: that has it tastes like cauliflower. It's quite quite delicious

736
00:37:38,640 --> 00:37:43,000
Speaker 4: when you fried up, and it has a natural fractal

737
00:37:43,120 --> 00:37:47,239
Speaker 4: that occurs with it. And with mathematical fractals, they are

738
00:37:48,000 --> 00:37:52,759
Speaker 4: theoretically infinite, but of course there's not infinite amount of romanesco.

739
00:37:53,840 --> 00:37:57,759
Speaker 4: So even though that fractal is repeating and is you know,

740
00:37:58,000 --> 00:38:02,000
Speaker 4: following the mathematical model of like of an infinite pattern,

741
00:38:02,120 --> 00:38:05,960
Speaker 4: at a certain point it tapers off. There is a smallest,

742
00:38:06,200 --> 00:38:09,200
Speaker 4: like little particle of roman esco that we're not even

743
00:38:09,280 --> 00:38:12,799
Speaker 4: getting to the particle physics you're getting to biology, which

744
00:38:12,840 --> 00:38:17,480
Speaker 4: has a much larger cutoff for how small an individual unit,

745
00:38:17,560 --> 00:38:19,760
Speaker 4: because it can only be as small as like a cell.

746
00:38:20,080 --> 00:38:22,839
Speaker 1: Yeah, exactly, And so I love that you just said

747
00:38:22,880 --> 00:38:26,239
Speaker 1: the phrase particle of romanesco. You're right, we don't see

748
00:38:26,280 --> 00:38:27,839
Speaker 1: those infinities, and so we have to sort of like

749
00:38:27,880 --> 00:38:29,960
Speaker 1: try to cut them out of our theory. But you know,

750
00:38:30,000 --> 00:38:32,720
Speaker 1: in some cases we don't know, And we have infinities

751
00:38:32,760 --> 00:38:34,680
Speaker 1: in theories, we don't know if they are real or

752
00:38:34,680 --> 00:38:36,759
Speaker 1: if they're just mathematical. I think one of the most

753
00:38:36,760 --> 00:38:41,600
Speaker 1: famous ones are infinities in general relativity. Right, General relativity

754
00:38:41,640 --> 00:38:45,000
Speaker 1: tells us that space is curved, and that it gets

755
00:38:45,080 --> 00:38:47,800
Speaker 1: curved when you're in the presence of mass or energy.

756
00:38:47,920 --> 00:38:50,879
Speaker 1: And if you have a huge amount of mass, incredibly

757
00:38:50,960 --> 00:38:54,560
Speaker 1: compact mass, then the curvature of space, which determines how

758
00:38:54,560 --> 00:38:58,120
Speaker 1: strong gravity feels, can get infinite. And that's what we

759
00:38:58,200 --> 00:39:02,680
Speaker 1: mean by for example, a singular singularity is infinite curvature,

760
00:39:02,760 --> 00:39:05,720
Speaker 1: essentially infinite gravitational force at that point.

761
00:39:05,920 --> 00:39:09,520
Speaker 4: So does that mean that a black hole is evidence

762
00:39:09,640 --> 00:39:12,680
Speaker 4: that there is actual tangible infinity.

763
00:39:13,239 --> 00:39:15,480
Speaker 1: We just don't know, because we don't know if there's

764
00:39:15,480 --> 00:39:19,480
Speaker 1: a real singularity inside there. There's a singularity in the theory,

765
00:39:19,719 --> 00:39:23,240
Speaker 1: and that singularity predicts black holes, and we see black holes.

766
00:39:23,480 --> 00:39:26,359
Speaker 1: But also we don't think those singularities are probably there

767
00:39:26,480 --> 00:39:29,239
Speaker 1: because they're in conflict with quantum mechanics, which says you

768
00:39:29,320 --> 00:39:32,680
Speaker 1: can't have an infinitely dense point at a certain location.

769
00:39:33,280 --> 00:39:36,160
Speaker 1: So we're really pretty confused about what's going on inside

770
00:39:36,160 --> 00:39:38,239
Speaker 1: black holes. And we'd love to see one because it

771
00:39:38,239 --> 00:39:40,560
Speaker 1: would answer not just the question of you know, our

772
00:39:40,560 --> 00:39:43,440
Speaker 1: infinity is real, but also it would tell us, you know,

773
00:39:43,640 --> 00:39:46,040
Speaker 1: how general relativity works. But if you talk to people

774
00:39:46,040 --> 00:39:48,880
Speaker 1: who do general relativity, they don't say this is a

775
00:39:48,880 --> 00:39:52,799
Speaker 1: physical prediction. They don't say general relativity predicts the existence

776
00:39:52,840 --> 00:39:56,400
Speaker 1: of physical infinities and singularities. They say this is a

777
00:39:56,440 --> 00:39:59,000
Speaker 1: failure of the theory. This is they say, we can't

778
00:39:59,040 --> 00:40:02,279
Speaker 1: predict what happens there because infinite curvature is like nonsense.

779
00:40:02,480 --> 00:40:04,680
Speaker 1: It's like the theory breaks down. It's like you have

780
00:40:04,719 --> 00:40:07,400
Speaker 1: a hole in your fabric of space where you don't

781
00:40:07,480 --> 00:40:10,239
Speaker 1: know what to do. Instead of like actually predicting an

782
00:40:10,280 --> 00:40:12,120
Speaker 1: infinite singularity, I mean.

783
00:40:12,600 --> 00:40:15,520
Speaker 4: That seems kind of like a bummer, And I guess

784
00:40:15,600 --> 00:40:18,560
Speaker 4: until we can get a big enough black hole where

785
00:40:18,600 --> 00:40:21,200
Speaker 4: it's safe to kind of float around on like a

786
00:40:21,360 --> 00:40:25,800
Speaker 4: space inflatable life jacket, and then just kind of cruise

787
00:40:25,880 --> 00:40:28,760
Speaker 4: right in. Like how would you even see, though, whether

788
00:40:28,800 --> 00:40:32,480
Speaker 4: there's an infinite singularity even if you could cruise around

789
00:40:32,680 --> 00:40:35,000
Speaker 4: in a black hole, Like, how would you identify that?

790
00:40:35,320 --> 00:40:37,560
Speaker 1: Yeah, we actually did a fun podcast episode a few

791
00:40:37,560 --> 00:40:41,840
Speaker 1: months ago about seeing singularities. They're called naked singularities. And

792
00:40:41,920 --> 00:40:44,080
Speaker 1: you could try to take a black hole that's spinning

793
00:40:44,400 --> 00:40:46,600
Speaker 1: and make it spin faster and faster, so the event

794
00:40:46,640 --> 00:40:49,799
Speaker 1: horizon sort of shrinks and it might reveal the singularity,

795
00:40:49,960 --> 00:40:52,560
Speaker 1: but nobody knows, and that would take a crazy amount

796
00:40:52,600 --> 00:40:55,319
Speaker 1: of energy. Until then, though, we are trying to come

797
00:40:55,400 --> 00:40:58,399
Speaker 1: up with a better theory, one that can describe what's

798
00:40:58,440 --> 00:41:00,799
Speaker 1: going on the inside of a black hole and be

799
00:41:00,960 --> 00:41:04,239
Speaker 1: consistent with quantum mechanics, and the category of theories are

800
00:41:04,280 --> 00:41:07,400
Speaker 1: called quantum gravity. And some of these theories are pretty good,

801
00:41:07,440 --> 00:41:11,440
Speaker 1: but most of them fail because they have infinities. Like

802
00:41:11,480 --> 00:41:14,080
Speaker 1: you try to calculate what happens when you have two

803
00:41:14,120 --> 00:41:17,160
Speaker 1: big masses they get close together, and they predict infinite

804
00:41:17,160 --> 00:41:19,000
Speaker 1: forces and you're like, well, we know that's not right,

805
00:41:19,480 --> 00:41:22,480
Speaker 1: and so these theories break down like it doesn't agree

806
00:41:22,520 --> 00:41:25,240
Speaker 1: with what we see, and so their infinities are also

807
00:41:25,280 --> 00:41:28,160
Speaker 1: a failure. So we have infinities in these theories, but

808
00:41:28,280 --> 00:41:30,680
Speaker 1: again it's the horror of the infinite. It's the failure

809
00:41:30,719 --> 00:41:33,400
Speaker 1: of the theory. We try to remove those infinities so

810
00:41:33,440 --> 00:41:35,840
Speaker 1: we can make predictions for what happens in the actual

811
00:41:35,880 --> 00:41:37,040
Speaker 1: physical world instead.

812
00:41:37,320 --> 00:41:42,440
Speaker 4: Okay, so we don't have a theory yet that doesn't

813
00:41:42,480 --> 00:41:46,319
Speaker 4: have that mistake, that oopsie of infinity. But we are

814
00:41:46,360 --> 00:41:49,680
Speaker 4: going to take a quick break about a minute, so

815
00:41:49,880 --> 00:41:54,160
Speaker 4: everyone listening out there. Daniel, I'll get out a calculator.

816
00:41:54,200 --> 00:41:55,960
Speaker 4: Let's see if we can get this before we get

817
00:41:56,000 --> 00:41:57,240
Speaker 4: back from our quick break.

818
00:42:01,640 --> 00:42:03,440
Speaker 1: When you pop a piece of cheese into your mouth

819
00:42:03,520 --> 00:42:06,680
Speaker 1: or enjoy a rich spoonful of Greek yogurt, you're probably

820
00:42:06,719 --> 00:42:10,800
Speaker 1: not thinking about the environmental impact of each and every bite.

821
00:42:10,800 --> 00:42:13,400
Speaker 1: But the people in the dairy industry are us. Dairy

822
00:42:13,440 --> 00:42:17,759
Speaker 1: has set themselves some ambitious sustainability goals, including being greenhouse

823
00:42:17,760 --> 00:42:20,359
Speaker 1: gas neutral by twenty to fifty. That's why they're working

824
00:42:20,360 --> 00:42:22,760
Speaker 1: hard every day to find new ways to reduce waste,

825
00:42:22,800 --> 00:42:27,000
Speaker 1: conserve natural resources, and drive down greenhouse gas emissions. Take water.

826
00:42:27,040 --> 00:42:30,640
Speaker 1: For example, most dairy farms reuse water up to four times.

827
00:42:30,680 --> 00:42:34,080
Speaker 1: The same water cools the milk, cleans equipment, washes the barn,

828
00:42:34,160 --> 00:42:37,880
Speaker 1: and irrigates the crops. How is US dairy tackling greenhouse gases?

829
00:42:37,920 --> 00:42:40,920
Speaker 1: Many farms use anaerobic digestors that turn the methane from

830
00:42:40,920 --> 00:42:44,319
Speaker 1: maneure into renewable energy that can power farms, towns, and

831
00:42:44,360 --> 00:42:46,600
Speaker 1: electric cars. So the next time you grab a slice

832
00:42:46,640 --> 00:42:48,520
Speaker 1: of pizza or lick an ice cream cone, know that

833
00:42:48,600 --> 00:42:51,239
Speaker 1: dairy farmers and processors around the country are using the

834
00:42:51,320 --> 00:42:55,080
Speaker 1: latest practices and innovations to provide the nutrient dense dairy

835
00:42:55,120 --> 00:42:58,120
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836
00:42:58,160 --> 00:43:00,399
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837
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838
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839
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840
00:43:09,600 --> 00:43:13,160
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841
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842
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844
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861
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Speaker 4: All right, we're back. Has anyone come up with the

862
00:44:26,719 --> 00:44:28,880
Speaker 4: theory without infinity as an answer?

863
00:44:29,160 --> 00:44:32,440
Speaker 1: We should totally crowdsource a theory of quantum gravity. All

864
00:44:32,480 --> 00:44:37,040
Speaker 1: our listeners, all that brain power together approaches infinite genius exactly,

865
00:44:37,520 --> 00:44:39,960
Speaker 1: and so we've been wrestling with the concept of infinity.

866
00:44:40,000 --> 00:44:42,880
Speaker 1: We know it's a mathematical idea. We can do equations

867
00:44:42,920 --> 00:44:45,239
Speaker 1: with it, We use it all the time in our mathematics.

868
00:44:45,520 --> 00:44:48,200
Speaker 1: We even have it inside our physical theories as we're

869
00:44:48,239 --> 00:44:51,799
Speaker 1: like doing calculus and summing over an infinite number of particles.

870
00:44:52,120 --> 00:44:54,920
Speaker 1: But really the question is whether it's just something in

871
00:44:55,000 --> 00:44:58,319
Speaker 1: our minds or whether it actually exists out there in

872
00:44:58,360 --> 00:45:01,440
Speaker 1: the universe as well. So, Katie, you were talking earlier

873
00:45:01,440 --> 00:45:05,120
Speaker 1: about the infinity of time, like whether the universe could

874
00:45:05,200 --> 00:45:05,640
Speaker 1: go on.

875
00:45:05,800 --> 00:45:09,239
Speaker 4: Forever, right, which I like the idea of because it

876
00:45:09,320 --> 00:45:13,240
Speaker 4: seems to indicate to me there's an infinite amount of possibilities,

877
00:45:13,280 --> 00:45:17,480
Speaker 4: such as a universe in which I, Katie forty one

878
00:45:17,600 --> 00:45:21,239
Speaker 4: b is surrounded by an infinite number of cats. But

879
00:45:21,640 --> 00:45:24,200
Speaker 4: I do like the idea of a universe going on

880
00:45:24,360 --> 00:45:28,120
Speaker 4: forever because it feels, you know, the idea of the

881
00:45:28,239 --> 00:45:31,719
Speaker 4: death of the universe is maybe even scarier to me

882
00:45:31,840 --> 00:45:34,759
Speaker 4: than my own mortality. In some ways, the idea that

883
00:45:35,000 --> 00:45:38,279
Speaker 4: things could just stop existing is quite terrifying.

884
00:45:38,040 --> 00:45:40,280
Speaker 1: Right, And it is terrifying, and it's hard to imagine

885
00:45:40,440 --> 00:45:43,360
Speaker 1: not existing anymore. But we all know that it happens,

886
00:45:43,440 --> 00:45:45,959
Speaker 1: right there are people who were alive and are now

887
00:45:46,120 --> 00:45:49,840
Speaker 1: not alive anymore. And so you can't apply that same

888
00:45:50,120 --> 00:45:52,759
Speaker 1: sort of concept to the universe and wonder like, even

889
00:45:52,800 --> 00:45:56,240
Speaker 1: though the universe exists now, does it mean it always will?

890
00:45:56,880 --> 00:46:00,560
Speaker 1: And the biggest argument against the universe being infinite in

891
00:46:00,719 --> 00:46:03,200
Speaker 1: time to the future is that we don't know if

892
00:46:03,239 --> 00:46:06,600
Speaker 1: the universe was infinite in time in the past, right, Like,

893
00:46:06,719 --> 00:46:09,080
Speaker 1: we look back at the history of the universe and

894
00:46:09,120 --> 00:46:12,600
Speaker 1: we see what looks like a beginning fourteen billion years

895
00:46:12,600 --> 00:46:15,520
Speaker 1: ago the universe began. We don't know if there was

896
00:46:15,640 --> 00:46:19,640
Speaker 1: anything before that, or if the universe actually literally started there.

897
00:46:19,880 --> 00:46:22,239
Speaker 1: A lot of theories of general relativity have like the

898
00:46:22,320 --> 00:46:25,359
Speaker 1: clock beginning at that moment, and before that there was

899
00:46:25,400 --> 00:46:27,800
Speaker 1: no clock, there was no universe, there was no space,

900
00:46:27,840 --> 00:46:30,600
Speaker 1: there was nothing. Doesn't mean we know how that happened.

901
00:46:30,880 --> 00:46:34,040
Speaker 1: But in that concept, the universe has a finite age

902
00:46:34,080 --> 00:46:36,319
Speaker 1: so far, why would it make sense for it to

903
00:46:36,360 --> 00:46:38,080
Speaker 1: then go on for infinity.

904
00:46:38,320 --> 00:46:41,239
Speaker 4: It's interesting because this is sort of what I was

905
00:46:41,280 --> 00:46:45,480
Speaker 4: saying earlier, where trying to think about infinity gives me

906
00:46:45,600 --> 00:46:50,360
Speaker 4: that same brain tingle sensation as trying to think about nothingness,

907
00:46:50,400 --> 00:46:54,800
Speaker 4: So trying to think about nothing existing before the universe

908
00:46:54,840 --> 00:46:59,040
Speaker 4: started and then nothing existing after. I would almost say

909
00:46:59,040 --> 00:47:01,680
Speaker 4: that's a harder concept up for me to think about.

910
00:47:01,719 --> 00:47:04,880
Speaker 4: Then infinity, like thinking of like, well, how could just

911
00:47:05,000 --> 00:47:09,040
Speaker 4: there suddenly be an explosion of things out of nothing?

912
00:47:09,480 --> 00:47:12,960
Speaker 4: And then how could all the stuff suddenly become nothing again?

913
00:47:13,360 --> 00:47:14,600
Speaker 4: And what does that even mean?

914
00:47:14,800 --> 00:47:16,880
Speaker 1: And it was hard for people to accept this idea.

915
00:47:17,000 --> 00:47:20,120
Speaker 1: Before we understood that the universe was expanding, and that

916
00:47:20,160 --> 00:47:23,000
Speaker 1: suggested that it was once younger and denser and hotter

917
00:47:23,360 --> 00:47:25,920
Speaker 1: and therefore might have had a beginning. People thought the

918
00:47:26,000 --> 00:47:28,279
Speaker 1: universe was infinitely old, and that was just a much

919
00:47:28,320 --> 00:47:31,280
Speaker 1: more natural idea. But of course you can't just accept

920
00:47:31,280 --> 00:47:33,960
Speaker 1: physics because it sounds natural. It has to be right.

921
00:47:34,600 --> 00:47:37,120
Speaker 1: And so now we've accepted the concept that maybe the

922
00:47:37,200 --> 00:47:40,279
Speaker 1: universe has a finite age so far, so we just

923
00:47:40,360 --> 00:47:43,160
Speaker 1: don't know, like will the universe go on forever or

924
00:47:43,200 --> 00:47:45,040
Speaker 1: will it come to an end? And there's some really

925
00:47:45,080 --> 00:47:48,280
Speaker 1: weird possibilities, like it might be that the universe doesn't

926
00:47:48,480 --> 00:47:51,000
Speaker 1: come to a dramatic end. It might be the universe

927
00:47:51,040 --> 00:47:53,359
Speaker 1: doesn't like reverse the big bang and end up as

928
00:47:53,360 --> 00:47:56,400
Speaker 1: a big crunch. One possibility is that the universe just

929
00:47:56,440 --> 00:47:59,879
Speaker 1: sort of like spreads out into an evenly tempered muck,

930
00:48:00,360 --> 00:48:02,520
Speaker 1: and so that everything is the same temperature. You don't

931
00:48:02,560 --> 00:48:04,960
Speaker 1: have like hot spots and cold spots anymore. This is

932
00:48:05,000 --> 00:48:06,880
Speaker 1: called the heat death of the universe. So in the

933
00:48:06,960 --> 00:48:10,680
Speaker 1: universe is maximally disordered, you have maximum entropy. And there's

934
00:48:10,719 --> 00:48:13,240
Speaker 1: some folks out there that think that entropy and time

935
00:48:13,400 --> 00:48:17,880
Speaker 1: are so closely connected that it's entropy that's driving time forward.

936
00:48:18,239 --> 00:48:20,840
Speaker 1: And when you get to this heat death, this equally

937
00:48:20,880 --> 00:48:24,440
Speaker 1: spaced muck of the universe, that time itself comes to

938
00:48:24,480 --> 00:48:27,640
Speaker 1: an end, that nothing can happen anymore. And so it

939
00:48:27,719 --> 00:48:30,239
Speaker 1: might be that the universe has a dramatic beginning and

940
00:48:30,239 --> 00:48:32,280
Speaker 1: then a very undramatic.

941
00:48:31,680 --> 00:48:34,719
Speaker 4: Sort of end, whereas in like a lion, and then

942
00:48:35,400 --> 00:48:38,879
Speaker 4: France is out like muck, like entropy muck.

943
00:48:39,920 --> 00:48:42,720
Speaker 1: So that's a possibility, right. We just can't say whether

944
00:48:42,719 --> 00:48:46,520
Speaker 1: the universe will exist forever forward in time. We don't

945
00:48:46,640 --> 00:48:49,920
Speaker 1: know if it existed forever backwards in time, but current

946
00:48:49,960 --> 00:48:52,879
Speaker 1: thinking is probably not. But you know, there are other

947
00:48:53,000 --> 00:48:56,040
Speaker 1: dimensions of course of infinity. One of my favorites is

948
00:48:56,040 --> 00:48:59,279
Speaker 1: thinking about the universe is infinite in space, right, Like

949
00:48:59,640 --> 00:49:02,440
Speaker 1: if you look out into the universe, can you point

950
00:49:02,480 --> 00:49:05,440
Speaker 1: your finger which makes a line, and have that line

951
00:49:05,520 --> 00:49:09,600
Speaker 1: continue out through space and never ever stop right, never

952
00:49:09,719 --> 00:49:13,080
Speaker 1: like loop back on itself or hit a wall or something.

953
00:49:13,080 --> 00:49:16,560
Speaker 1: Does that line actually traverse space literally forever?

954
00:49:16,760 --> 00:49:18,680
Speaker 4: That's what I thought you could do. If you've got

955
00:49:18,719 --> 00:49:21,520
Speaker 4: a strong enough flashlight and point it up at the sky,

956
00:49:21,600 --> 00:49:24,080
Speaker 4: it's like, take that space. All this light is going

957
00:49:24,160 --> 00:49:26,120
Speaker 4: to go on forever. But probably not.

958
00:49:26,400 --> 00:49:29,160
Speaker 1: Well, if the universe is infinite in space and in time,

959
00:49:29,200 --> 00:49:32,920
Speaker 1: then that photon from your flashlight will literally go on forever.

960
00:49:33,120 --> 00:49:34,640
Speaker 1: I guess it could get absorbed by.

961
00:49:34,520 --> 00:49:38,239
Speaker 4: Something, probably a black hole between me and infinity.

962
00:49:38,520 --> 00:49:40,840
Speaker 1: A black hole made of somebody else's infinite number of

963
00:49:40,880 --> 00:49:43,680
Speaker 1: cats that collapse on themselves. But this is like a

964
00:49:43,760 --> 00:49:46,520
Speaker 1: true infinity, right, Regardless of what else is going on

965
00:49:46,600 --> 00:49:49,880
Speaker 1: in the universe, it makes some sense for the universe

966
00:49:49,920 --> 00:49:52,080
Speaker 1: to be infinite. It might make more sense for it

967
00:49:52,080 --> 00:49:54,040
Speaker 1: to be infinite than for it to have an edge

968
00:49:54,440 --> 00:49:56,759
Speaker 1: or for it to be like looped or closed in

969
00:49:56,920 --> 00:50:00,400
Speaker 1: on itself. In our theories of the universe, we typically

970
00:50:00,480 --> 00:50:04,000
Speaker 1: assume that the universe is infinite because it just currently

971
00:50:04,040 --> 00:50:06,680
Speaker 1: feels like the most natural thing, right.

972
00:50:06,560 --> 00:50:10,360
Speaker 4: Because I've seen like images of maybe the universe is

973
00:50:10,480 --> 00:50:13,680
Speaker 4: like a donut or a cone. And then the hard

974
00:50:13,760 --> 00:50:16,320
Speaker 4: part for me to wrap around a non infinite universe

975
00:50:16,400 --> 00:50:19,720
Speaker 4: is like, well, what's outside of that donut or cone?

976
00:50:19,920 --> 00:50:23,279
Speaker 4: I can't. My brain just again starts to break down

977
00:50:23,320 --> 00:50:25,360
Speaker 4: when I try to think, well, what would be outside

978
00:50:25,400 --> 00:50:27,640
Speaker 4: of a universe? Like what would be that? Nothing?

979
00:50:27,800 --> 00:50:27,880
Speaker 8: Like?

980
00:50:28,080 --> 00:50:31,480
Speaker 4: I think that's another I don't remember which Greek philosopher

981
00:50:31,560 --> 00:50:33,240
Speaker 4: came up with this, but I thought that was another

982
00:50:33,280 --> 00:50:35,319
Speaker 4: thing of like, well, once you get to the edge

983
00:50:35,560 --> 00:50:38,640
Speaker 4: of the universe and you pull apart the veil, what's

984
00:50:38,719 --> 00:50:39,359
Speaker 4: beyond that?

985
00:50:39,840 --> 00:50:40,000
Speaker 5: Right?

986
00:50:40,040 --> 00:50:42,480
Speaker 1: And we just don't know. But the fascinating thing is

987
00:50:42,520 --> 00:50:46,279
Speaker 1: that there's only one answer we could possibly know, Like

988
00:50:46,360 --> 00:50:49,000
Speaker 1: we could discover an edge to the universe. We could

989
00:50:49,080 --> 00:50:52,520
Speaker 1: discover that the universe is finite, that it loops around

990
00:50:52,560 --> 00:50:55,239
Speaker 1: itself or has some weird deformity at the edge or

991
00:50:55,280 --> 00:50:58,560
Speaker 1: something like that, but we could never prove that it's infinite. Right,

992
00:50:58,600 --> 00:51:02,239
Speaker 1: How could you prove that the universe is infinite? It's

993
00:51:02,280 --> 00:51:04,359
Speaker 1: like proving that it doesn't have an edge. You can't

994
00:51:04,400 --> 00:51:06,960
Speaker 1: prove a negative. It could just be that the edges

995
00:51:07,080 --> 00:51:08,080
Speaker 1: beyond where you.

996
00:51:08,080 --> 00:51:10,680
Speaker 4: Thought it was right, because every time you get a

997
00:51:10,719 --> 00:51:14,759
Speaker 4: government grant to send out like a spaceship to the

998
00:51:14,880 --> 00:51:17,600
Speaker 4: edge of space, then it's like okay, but there's more,

999
00:51:17,719 --> 00:51:20,279
Speaker 4: and then you have to write another grant, and so

1000
00:51:20,320 --> 00:51:24,840
Speaker 4: you need an infinite number of grants to get to

1001
00:51:24,960 --> 00:51:28,120
Speaker 4: the infinite edge of the universe, and nobody wants to

1002
00:51:28,120 --> 00:51:28,560
Speaker 4: go through that.

1003
00:51:28,920 --> 00:51:30,840
Speaker 1: I do feel like I've written an infinite number of

1004
00:51:30,880 --> 00:51:33,279
Speaker 1: grants in my economic career, and I've not received an

1005
00:51:33,320 --> 00:51:36,120
Speaker 1: infinite number of dollars. So it's a really fun concept.

1006
00:51:36,160 --> 00:51:38,920
Speaker 1: And you know, some people suggest that you might be

1007
00:51:39,000 --> 00:51:42,319
Speaker 1: able to prove that the universe is infinite if you

1008
00:51:42,360 --> 00:51:45,880
Speaker 1: can come up with a theory of cosmology that describes

1009
00:51:45,920 --> 00:51:48,880
Speaker 1: the universe and is accurate and requires that the universe

1010
00:51:48,960 --> 00:51:51,840
Speaker 1: is infinite, if your theory only works for an infinite

1011
00:51:51,960 --> 00:51:55,400
Speaker 1: universe and you can exclude all other possible theories. But

1012
00:51:55,640 --> 00:51:58,880
Speaker 1: I'm not sure philosophically that's even possible. So this is

1013
00:51:58,920 --> 00:52:02,359
Speaker 1: another like potent infinity, but it's tantalizing because we can

1014
00:52:02,440 --> 00:52:06,319
Speaker 1: never actually know whether the universe is infinite. In fact,

1015
00:52:06,440 --> 00:52:09,560
Speaker 1: Galileo said this hundreds of years ago in some famous letter,

1016
00:52:09,719 --> 00:52:12,200
Speaker 1: that mankind would never be able to know whether the

1017
00:52:12,280 --> 00:52:15,600
Speaker 1: universe is infinite, and so this is like a century's

1018
00:52:15,640 --> 00:52:18,920
Speaker 1: old puzzle. But the infinity of space in the universe.

1019
00:52:19,120 --> 00:52:22,279
Speaker 4: I like to think that because he looked through this telescope,

1020
00:52:22,440 --> 00:52:25,239
Speaker 4: you know, one of the first people to use a telescope.

1021
00:52:25,239 --> 00:52:27,719
Speaker 4: He just sees all these stars out there, and he's like, yeah,

1022
00:52:27,719 --> 00:52:28,880
Speaker 4: there's no way we're sorting this.

1023
00:52:28,960 --> 00:52:33,319
Speaker 1: Nope, No, maybe that was in his grand proposal. He's like,

1024
00:52:33,719 --> 00:52:35,560
Speaker 1: I need infinite number of dollars, got a lot of

1025
00:52:35,560 --> 00:52:35,960
Speaker 1: work to.

1026
00:52:35,880 --> 00:52:38,520
Speaker 4: Do up here, and then he promptly got sent to jail.

1027
00:52:40,000 --> 00:52:41,920
Speaker 1: But you don't need to look out into space to

1028
00:52:41,960 --> 00:52:45,000
Speaker 1: see potential infinities. Like we were talking about how there's

1029
00:52:45,000 --> 00:52:48,439
Speaker 1: an infinite number of numbers between the numbers one and two.

1030
00:52:49,000 --> 00:52:51,240
Speaker 1: You can just hold your fingers apart and say, well,

1031
00:52:51,719 --> 00:52:55,480
Speaker 1: how many pieces of space are there between my fingers,

1032
00:52:55,520 --> 00:53:00,200
Speaker 1: how many unique locations? How many different possible spots could

1033
00:53:00,200 --> 00:53:04,000
Speaker 1: a particle be at between my fingers? And if space

1034
00:53:04,120 --> 00:53:07,400
Speaker 1: is continuous, then there's an infinite number of places for

1035
00:53:07,480 --> 00:53:09,160
Speaker 1: a particle to be between your fingers.

1036
00:53:09,440 --> 00:53:11,760
Speaker 4: I'm staring at my hand right now and like pulling

1037
00:53:11,760 --> 00:53:14,759
Speaker 4: my fingers apart. I'm just really glad nobody's here right

1038
00:53:14,800 --> 00:53:17,640
Speaker 4: now to see me doing this, because like, hey, how's

1039
00:53:17,680 --> 00:53:19,240
Speaker 4: it going? What you doing there?

1040
00:53:19,440 --> 00:53:21,319
Speaker 1: I'm just doing physics. I'm like, oh, okay, that's why

1041
00:53:21,320 --> 00:53:21,759
Speaker 1: you look at this.

1042
00:53:21,920 --> 00:53:24,160
Speaker 4: There's a science. Shut up, it's science.

1043
00:53:24,920 --> 00:53:29,200
Speaker 1: And so, if, as general relativity suggests, the universe is continuous,

1044
00:53:29,600 --> 00:53:32,320
Speaker 1: then you can subdivide that space an infinite number of times,

1045
00:53:32,320 --> 00:53:35,880
Speaker 1: and there are real locations for every one of those numbers.

1046
00:53:35,920 --> 00:53:39,800
Speaker 1: Every subdivision is real. But you know, quantum mechanics says

1047
00:53:39,800 --> 00:53:42,680
Speaker 1: not so fast. It says that everything in the universe

1048
00:53:42,719 --> 00:53:45,719
Speaker 1: so far seems to be quantized, and a lot of

1049
00:53:45,760 --> 00:53:49,920
Speaker 1: theories out there suggest that space itself might be quantized.

1050
00:53:50,320 --> 00:53:52,800
Speaker 1: That space might be made out of tiny little space

1051
00:53:52,840 --> 00:53:55,239
Speaker 1: pixels that are so small that you can't see them.

1052
00:53:55,440 --> 00:53:58,200
Speaker 1: It's like a retina screen. They might be like ten

1053
00:53:58,280 --> 00:54:02,040
Speaker 1: to the negative thirty five meters wide, and it doesn't

1054
00:54:02,040 --> 00:54:04,439
Speaker 1: really matter how small they are as long as there's

1055
00:54:04,480 --> 00:54:07,680
Speaker 1: a minimum distance. Now, that means that the space between

1056
00:54:07,719 --> 00:54:10,640
Speaker 1: your fingers is not an infinite number of locations, but

1057
00:54:10,719 --> 00:54:14,160
Speaker 1: a large and finite number of possible locations, like little

1058
00:54:14,160 --> 00:54:16,000
Speaker 1: slots that particles can fit into.

1059
00:54:16,160 --> 00:54:19,319
Speaker 4: Thinking about space pixels just makes me feel like we're

1060
00:54:19,320 --> 00:54:20,920
Speaker 4: some aliens computer.

1061
00:54:20,600 --> 00:54:25,600
Speaker 1: Game, and maybe we are. Maybe our universe is finite,

1062
00:54:25,680 --> 00:54:29,280
Speaker 1: but it's just a simulation inside an infinite universe, That's.

1063
00:54:29,200 --> 00:54:33,839
Speaker 4: What I'm thinking. But even if our universe is finite,

1064
00:54:33,920 --> 00:54:38,839
Speaker 4: we still wouldn't know if there are infinite, finite universes, right,

1065
00:54:39,200 --> 00:54:39,680
Speaker 4: that's right.

1066
00:54:39,880 --> 00:54:44,600
Speaker 1: Another dimension of infinity is whether our universe itself is

1067
00:54:44,719 --> 00:54:45,799
Speaker 1: all that there is.

1068
00:54:46,280 --> 00:54:46,440
Speaker 6: Right.

1069
00:54:46,480 --> 00:54:49,000
Speaker 1: We think of universe like uni means like all of

1070
00:54:49,040 --> 00:54:51,799
Speaker 1: it with the one thing. But these days we have

1071
00:54:51,880 --> 00:54:55,400
Speaker 1: the concept of the multiverse, where it's possible that there

1072
00:54:55,440 --> 00:54:58,640
Speaker 1: are other universes just lying ours. In fact, there might

1073
00:54:58,680 --> 00:55:01,680
Speaker 1: be an infinite number of them. This concept comes from

1074
00:55:01,719 --> 00:55:05,440
Speaker 1: like a struggle to understand why our universe is so weird,

1075
00:55:05,600 --> 00:55:07,520
Speaker 1: like why is the speed of light the way that

1076
00:55:07,560 --> 00:55:10,520
Speaker 1: it is. Why are the various numbers the parameters that

1077
00:55:10,560 --> 00:55:14,120
Speaker 1: control physics seem to have kind of weird values? And

1078
00:55:14,160 --> 00:55:16,400
Speaker 1: they answered it by saying, well, maybe there's an infinite

1079
00:55:16,480 --> 00:55:18,719
Speaker 1: number of universes, and so that all the values are

1080
00:55:18,760 --> 00:55:21,320
Speaker 1: explored and we just happen to be in this one.

1081
00:55:21,880 --> 00:55:24,360
Speaker 1: And you know, that's a fun idea, and it's another

1082
00:55:24,560 --> 00:55:27,640
Speaker 1: concept where it's easy to like create infinity in your mind,

1083
00:55:28,080 --> 00:55:30,640
Speaker 1: but it's not something we can ever really study because

1084
00:55:31,000 --> 00:55:33,879
Speaker 1: these other universes in the multiverse aren't places we can

1085
00:55:33,960 --> 00:55:36,879
Speaker 1: interact with. There are things we can see, we can't

1086
00:55:36,880 --> 00:55:40,640
Speaker 1: ever get evidence of their existence, and so it might

1087
00:55:40,760 --> 00:55:43,319
Speaker 1: be real, there might be other universes out there, but

1088
00:55:43,360 --> 00:55:45,360
Speaker 1: I'm not sure that's something we could ever prove or

1089
00:55:45,400 --> 00:55:45,840
Speaker 1: really know.

1090
00:55:46,280 --> 00:55:50,560
Speaker 4: It seems like the only quote unquote evidence we would

1091
00:55:50,600 --> 00:55:53,840
Speaker 4: have of another universe is just if we can't figure

1092
00:55:53,880 --> 00:55:57,840
Speaker 4: something out about our own universe. So we think that

1093
00:55:57,960 --> 00:56:02,120
Speaker 4: maybe there's another universe how interacting with our universe, But

1094
00:56:02,200 --> 00:56:05,719
Speaker 4: we would have no way of measuring that at all

1095
00:56:05,920 --> 00:56:09,719
Speaker 4: because we're stuck inside our universe like a bunch of

1096
00:56:09,760 --> 00:56:12,080
Speaker 4: fish in a fish bowl, and then we're bonking into

1097
00:56:12,160 --> 00:56:15,640
Speaker 4: another fish bowl, but we can never interact with the fish,

1098
00:56:15,640 --> 00:56:18,520
Speaker 4: and that other fish bowl we only know. Maybe I

1099
00:56:18,560 --> 00:56:20,959
Speaker 4: think maybe they could be there if it's the only

1100
00:56:21,520 --> 00:56:24,600
Speaker 4: way we could explain how our fishbowl is getting jostled around.

1101
00:56:24,880 --> 00:56:28,480
Speaker 1: Yeah, there are some fun ideas about how other bubble

1102
00:56:28,600 --> 00:56:31,200
Speaker 1: universes might have been made near hours and when they

1103
00:56:31,239 --> 00:56:33,279
Speaker 1: were very young, and they could have bumped into each

1104
00:56:33,320 --> 00:56:36,359
Speaker 1: other and left a little imprint like these circles on

1105
00:56:36,400 --> 00:56:40,279
Speaker 1: the cosmic microwave background radiation. This left overglow from just

1106
00:56:40,360 --> 00:56:43,160
Speaker 1: after the Big Bang, But nobody's ever observed any evidence

1107
00:56:43,200 --> 00:56:45,440
Speaker 1: of that, so it's just a fun idea so far.

1108
00:56:45,680 --> 00:56:48,879
Speaker 1: So that's another possible infinity that could really be real,

1109
00:56:49,000 --> 00:56:51,960
Speaker 1: but we might never actually know. One that's closest to

1110
00:56:52,040 --> 00:56:55,680
Speaker 1: my heart is this question of infinite number of particles,

1111
00:56:56,080 --> 00:56:59,719
Speaker 1: Like how many particles are there in my finger? Well,

1112
00:56:59,760 --> 00:57:03,400
Speaker 1: you know, something like Avagajo's number of atoms, and then

1113
00:57:03,440 --> 00:57:06,359
Speaker 1: those are made of electrons and protons and neutrons which

1114
00:57:06,360 --> 00:57:08,799
Speaker 1: are made of quarks. But then you can ask like, well,

1115
00:57:08,840 --> 00:57:11,560
Speaker 1: what are those electrons and quarks made out of? One

1116
00:57:11,560 --> 00:57:13,719
Speaker 1: of the electron is made out of particles, which are

1117
00:57:13,719 --> 00:57:15,440
Speaker 1: made out of particles, which are made out of particles,

1118
00:57:15,440 --> 00:57:18,200
Speaker 1: which are made out of particles, And it goes infinitely

1119
00:57:18,280 --> 00:57:22,120
Speaker 1: far down to infinite testimal particles. Then you could say, hey,

1120
00:57:22,320 --> 00:57:24,560
Speaker 1: I'm made out of an infinite number of particles.

1121
00:57:24,800 --> 00:57:27,960
Speaker 4: Yeah, I mean it's the cookie problem again, where if

1122
00:57:28,000 --> 00:57:31,400
Speaker 4: you start to cut apart a particle like a cookie.

1123
00:57:31,720 --> 00:57:35,640
Speaker 4: It's not that the particle itself is infinitely large, but

1124
00:57:35,800 --> 00:57:41,560
Speaker 4: it's made up of infinitely nesting particles like a Russian

1125
00:57:41,600 --> 00:57:44,800
Speaker 4: nesting doll. But they're sub atomic particles.

1126
00:57:45,080 --> 00:57:48,520
Speaker 1: Yeah, and so that's certainly a possibility. We can't rule

1127
00:57:48,520 --> 00:57:51,280
Speaker 1: that out. We call the electron and the quarks the

1128
00:57:51,360 --> 00:57:54,520
Speaker 1: fundamental particles, meaning that they're not divisible, only because we

1129
00:57:54,560 --> 00:57:57,200
Speaker 1: haven't seen anything smaller inside them, not because we have

1130
00:57:57,240 --> 00:58:00,840
Speaker 1: any evidence that they're actually fundamental, having build a big

1131
00:58:00,960 --> 00:58:03,960
Speaker 1: enough particle collider to smash them open and see what's inside.

1132
00:58:04,000 --> 00:58:07,240
Speaker 1: In fact, we strongly suspect there are smaller particles inside

1133
00:58:07,240 --> 00:58:09,560
Speaker 1: them that would explain lots of the weird patterns that

1134
00:58:09,600 --> 00:58:12,240
Speaker 1: we see in the universe and in those particles. But

1135
00:58:12,800 --> 00:58:15,760
Speaker 1: we also suspect that there might be a smallest particle

1136
00:58:15,800 --> 00:58:18,280
Speaker 1: that if you keep cracking them open far enough down,

1137
00:58:18,360 --> 00:58:21,480
Speaker 1: you get down to the smallest bit. Quantum mechanics again

1138
00:58:21,560 --> 00:58:25,000
Speaker 1: says that everything in the universe is discrete, not continuous,

1139
00:58:25,040 --> 00:58:27,640
Speaker 1: that it comes in grains or in chunks. So we

1140
00:58:27,680 --> 00:58:30,640
Speaker 1: suspect that maybe it's a vibrating string or something else.

1141
00:58:30,720 --> 00:58:34,120
Speaker 1: But at very very short distances, there is a smallest thing,

1142
00:58:34,320 --> 00:58:37,440
Speaker 1: which would mean you're made out of a finite number

1143
00:58:37,480 --> 00:58:41,520
Speaker 1: of those little vibrating strings or tiny cosmic kittens or whatever.

1144
00:58:42,080 --> 00:58:46,520
Speaker 4: It's so hard to conceptualize a smallest particle because in

1145
00:58:46,560 --> 00:58:49,440
Speaker 4: the physical world that we interact with, even when we

1146
00:58:49,520 --> 00:58:52,280
Speaker 4: find like a smallest building block, like you mentioned, like

1147
00:58:52,320 --> 00:58:55,920
Speaker 4: a pixel, we know that pixel actually you can break

1148
00:58:55,920 --> 00:58:58,600
Speaker 4: apart like it does have little elements, Like when you

1149
00:58:58,640 --> 00:59:01,280
Speaker 4: have a pixel on a screen and it's actually made

1150
00:59:01,320 --> 00:59:04,080
Speaker 4: up of well, now I don't know how computers work,

1151
00:59:04,200 --> 00:59:07,040
Speaker 4: so I'm just going to assume it's it's made out

1152
00:59:07,040 --> 00:59:09,960
Speaker 4: of you know, light coming through a little square on

1153
00:59:10,000 --> 00:59:10,600
Speaker 4: your screen.

1154
00:59:10,920 --> 00:59:12,760
Speaker 1: That's exactly how they do it. They build thingies.

1155
00:59:12,960 --> 00:59:15,640
Speaker 4: They put a bunch of little thingies on your screen,

1156
00:59:15,720 --> 00:59:18,520
Speaker 4: and little tiny lights that come through the thingies. I'm

1157
00:59:18,520 --> 00:59:21,120
Speaker 4: sure someone who knows how a computer screen work could

1158
00:59:21,160 --> 00:59:23,480
Speaker 4: explain that better. But you know, it's the same thing

1159
00:59:23,600 --> 00:59:26,000
Speaker 4: like with the human brain, when you break it up,

1160
00:59:26,080 --> 00:59:30,040
Speaker 4: like the smallest unit of a thought is the action

1161
00:59:30,160 --> 00:59:33,680
Speaker 4: that happens in a synapse, like from one end of

1162
00:59:33,720 --> 00:59:36,000
Speaker 4: a neuron to another. But then you can break that

1163
00:59:36,120 --> 00:59:40,200
Speaker 4: apart because you can look at the molecular structure of

1164
00:59:40,240 --> 00:59:44,200
Speaker 4: a neurotransmitter. I mean you could say though that like

1165
00:59:44,280 --> 00:59:46,760
Speaker 4: if you look at the space between two neurons and

1166
00:59:46,760 --> 00:59:50,920
Speaker 4: a synapse, that could potentially be broken down into infinitely

1167
00:59:50,960 --> 00:59:54,480
Speaker 4: smaller halves of a space. So maybe there's an infinity

1168
00:59:54,960 --> 00:59:58,080
Speaker 4: whenever we have a single thought, because you know, you

1169
00:59:58,160 --> 01:00:02,280
Speaker 4: have an infinite halves that your neurotransmitters have to traverse

1170
01:00:02,920 --> 01:00:06,680
Speaker 4: over your synaps But again, it's kind of like that

1171
01:00:06,760 --> 01:00:09,480
Speaker 4: would according to the mathematics converge, but.

1172
01:00:09,440 --> 01:00:12,240
Speaker 1: It's also sort of the goal. Like we feel that

1173
01:00:12,280 --> 01:00:14,880
Speaker 1: if we found the smallest unit, we'd be seeing something

1174
01:00:14,920 --> 01:00:17,120
Speaker 1: like the source code of the universe. It would reveal

1175
01:00:17,200 --> 01:00:19,720
Speaker 1: something deep and true. Everything above that is just like

1176
01:00:20,040 --> 01:00:23,320
Speaker 1: how those pieces tend to fit together and turn into stuff, right,

1177
01:00:23,360 --> 01:00:25,960
Speaker 1: Like ice cream is not fundamentalist and teach you something

1178
01:00:26,000 --> 01:00:28,600
Speaker 1: about the universe, regardless of how delicious it is. We

1179
01:00:28,640 --> 01:00:30,800
Speaker 1: want to figure out what is the smallest thing, so

1180
01:00:30,880 --> 01:00:33,840
Speaker 1: we can like look at the deepest nature of the universe.

1181
01:00:34,120 --> 01:00:36,280
Speaker 1: But we don't know if there is a smallest thing

1182
01:00:36,360 --> 01:00:39,240
Speaker 1: or if it just goes on forever. All right, So

1183
01:00:39,280 --> 01:00:42,560
Speaker 1: we've talked about the potential infinities I think the most

1184
01:00:42,600 --> 01:00:46,280
Speaker 1: promising ones are the spatial infinities, like maybe the universe

1185
01:00:46,320 --> 01:00:49,800
Speaker 1: really is infinite and goes on forever, or the temporal ones,

1186
01:00:49,840 --> 01:00:53,160
Speaker 1: like maybe the universe can last forever. I think it's

1187
01:00:53,160 --> 01:00:57,120
Speaker 1: pretty unlikely that space can be infinitely divided into bits,

1188
01:00:57,400 --> 01:00:59,960
Speaker 1: or that particles can be infinitely broken into smaller parts.

1189
01:01:00,480 --> 01:01:02,000
Speaker 1: But I think there really is a chance that the

1190
01:01:02,080 --> 01:01:05,160
Speaker 1: universe is infinitely big. But what's amazing to me is

1191
01:01:05,160 --> 01:01:07,520
Speaker 1: that for all these hundreds and thousands of years that

1192
01:01:07,560 --> 01:01:10,200
Speaker 1: we've been thinking about infinity, that we've had it in

1193
01:01:10,320 --> 01:01:14,760
Speaker 1: our minds, we've still never seen actual infinity. No human

1194
01:01:14,800 --> 01:01:19,160
Speaker 1: has ever witnessed laid eyes on anything that is truly infinite.

1195
01:01:19,440 --> 01:01:22,200
Speaker 1: It might be out there in our universe, hiding from us,

1196
01:01:22,320 --> 01:01:25,160
Speaker 1: waiting inside black holes or out past the edge, but

1197
01:01:25,240 --> 01:01:26,240
Speaker 1: we have never seen it.

1198
01:01:26,480 --> 01:01:29,479
Speaker 4: I mean, if you ever stare into a dog's eyes, though,

1199
01:01:29,640 --> 01:01:33,200
Speaker 4: and see the love there, I'd say that's infinite.

1200
01:01:34,280 --> 01:01:36,120
Speaker 1: All right. Well, there you have it, folks. If you

1201
01:01:36,200 --> 01:01:38,680
Speaker 1: are a seeker of infinity, then get an infinite number

1202
01:01:38,680 --> 01:01:41,680
Speaker 1: of pets and feel an infinite amount of love from

1203
01:01:41,720 --> 01:01:44,880
Speaker 1: all of them. Until then, keep infinity in your mind

1204
01:01:45,000 --> 01:01:46,720
Speaker 1: and let us know if you see it out there

1205
01:01:46,720 --> 01:01:48,880
Speaker 1: in the universe. Thanks very much Katie for joining us

1206
01:01:48,880 --> 01:01:50,040
Speaker 1: again on the podcast.

1207
01:01:50,280 --> 01:01:53,160
Speaker 4: Thank you so much for having me. This was infinitely fun.

1208
01:01:53,480 --> 01:01:55,960
Speaker 1: And don't forget to check out her other awesome podcast,

1209
01:01:56,000 --> 01:01:58,960
Speaker 1: Creature Feature, which she talks about the infinite, amazingness and

1210
01:01:59,000 --> 01:02:02,040
Speaker 1: complexity of bio. Until then, Thank you very much for

1211
01:02:02,120 --> 01:02:12,800
Speaker 1: sharing us your curiosity and tune in next time. Thanks

1212
01:02:12,800 --> 01:02:15,400
Speaker 1: for listening, and remember that Daniel and Jorge Explain the

1213
01:02:15,480 --> 01:02:20,320
Speaker 1: Universe is a production of iHeartRadio. For more podcasts from iHeartRadio,

1214
01:02:20,400 --> 01:02:24,600
Speaker 1: visit the iHeartRadio app, Apple Podcasts, or wherever you listen

1215
01:02:24,680 --> 01:02:25,840
Speaker 1: to your favorite shows.

1216
01:02:37,760 --> 01:02:40,640
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1224
01:03:07,960 --> 01:03:09,720
Speaker 1: When you pop a piece of cheese into your mouth,

1225
01:03:09,720 --> 01:03:13,000
Speaker 1: you're probably not thinking about the environmental impact. But the

1226
01:03:13,040 --> 01:03:15,920
Speaker 1: people in the dairy industry are. That's why they're working

1227
01:03:15,960 --> 01:03:18,560
Speaker 1: hard every day to find new ways to reduce waste,

1228
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1229
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Speaker 1: US dairy tackling greenhouse gases. Many farms use anaerobic digestors

1230
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1231
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1232
01:03:34,480 --> 01:03:37,240
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1233
01:03:38,800 --> 01:03:42,320
Speaker 3: There are children, friends, and families walking, riding on passing

1234
01:03:42,320 --> 01:03:44,760
Speaker 3: the roads every day. Remember they're real people with loved

1235
01:03:44,760 --> 01:03:45,560
Speaker 3: ones who need them to.

1236
01:03:45,480 --> 01:03:46,280
Speaker 4: Get home safely.

1237
01:03:46,480 --> 01:03:49,080
Speaker 3: Protect our cyclists and pedestrians because they're people too.

1238
01:03:49,360 --> 01:03:49,880
Speaker 1: Go safely.

1239
01:03:49,960 --> 01:03:52,800
Speaker 3: California from the California Office of Traffic Safety and Caltrans