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Is infinity real or just mathematical? · Daniel and Kelly’s Extraordinary Universe

0:08
Speaker 1: Hey, Katie, how many pets do you have living with
0:11
Speaker 1: you at home? That depends on your definition. Does it
0:14
Speaker 1: include all living creatures in my house? Does it include
0:17
Speaker 1: the mites in my eyelashes? Maybe not, like all the
0:20
Speaker 1: microobs and the tardy grades and all the bacteria in
0:23
Speaker 1: your gut? What about my husband? That's your call. Depends
0:26
Speaker 1: on your relationship, personal choice. Okay, then I've got a
0:30
Speaker 1: dog named Cookie, I've got to fish. I'm going to
0:35
Speaker 1: name them right now, called Bill and Head. So three
0:39
Speaker 1: or four, depending on the definition of my husband. All right,
0:41
Speaker 1: well that's more than I've got. And I got a
0:43
Speaker 1: question for you about pets. At what point do you
0:46
Speaker 1: say you have too many pets? I think that's the
0:49
Speaker 1: wrong way to look at it. Once you have, you know,
0:53
Speaker 1: two or three, like one more, there's no difference, right,
0:56
Speaker 1: It's the cat principle, like once you have two cats,
0:59
Speaker 1: there's no difference between two cats for cats tin cats.
1:03
Speaker 1: I think that sounds dangerous. You're gonna mathematically induce yourself
1:07
Speaker 1: to having an infinite number of cats. Exactly if you
1:10
Speaker 1: already have infinite pets, you can add more and more
1:13
Speaker 1: and still have infinite pets. Hi, I'm Daniel, I'm a
1:31
Speaker 1: particle physicist, and I have an infinite number of questions
1:35
Speaker 1: about the nature of our universe. And I am Katie Golden.
1:40
Speaker 1: I like pets, but I am not a particle physicist,
1:43
Speaker 1: and I still have infinite questions about the universe and
1:48
Speaker 1: about how many cats I can have and get away with.
1:51
Speaker 1: How many cats can there be in the universe? Could
1:54
Speaker 1: we have an infinite universe field with infinite cats. I
1:57
Speaker 1: think that if you replace the sort of building blocks
2:01
Speaker 1: of the universe with cats, it would be a lot cuter.
2:05
Speaker 1: But yeah, I come to the show with a little
2:07
Speaker 1: bit of background in a psychology and evolutionary biology, and
2:11
Speaker 1: that's why I like to talk about cats all the time.
2:14
Speaker 1: And welcome then to the podcast Daniel and Jorge Explain
2:18
Speaker 1: the Universe with its Infinite variety of Cats, a podcast
2:22
Speaker 1: in which we talk about all the crazy, amazing things
2:25
Speaker 1: that are out there in the universe. Not just the
2:27
Speaker 1: things in the universe. We talk about the very nature
2:30
Speaker 1: of the universe. We talk about the universe that's in
2:33
Speaker 1: our minds, that mental model of what's going on outside,
2:36
Speaker 1: and we talk about the real, actual universe, if it
2:39
Speaker 1: actually exists, and what it means what's in it, how
2:43
Speaker 1: it all works, and we try to explain all of
2:45
Speaker 1: it to you. We tackled the biggest questions, the even
2:48
Speaker 1: bigger questions, and the absolute biggest of big questions on
2:52
Speaker 1: the podcast. I think we can do all of that
2:54
Speaker 1: in an hour. I think we can. You know, I
2:56
Speaker 1: was thinking as we were talking about this question of
2:59
Speaker 1: an infinite universe is filled with infinite cats. And you know,
3:02
Speaker 1: probably there was some like ancient Greek philosopher who first
3:05
Speaker 1: raised this question. You know how the Greek philosophers had
3:08
Speaker 1: like the craziest ideas about how the universe might work,
3:11
Speaker 1: and basically every idea that is out there, some old
3:14
Speaker 1: dude in a robe thought of his first thousands of
3:16
Speaker 1: years ago. Yeah, just Plato surrounded by his cats thinking
3:20
Speaker 1: about infinity as they're all me owing. The thing that
3:23
Speaker 1: bugs me about the Greeks is that they had so
3:25
Speaker 1: many ideas that even though only like one or two
3:28
Speaker 1: of them turned out to be correct. Like Democratus, he's
3:32
Speaker 1: the first one to name the adam and think about
3:33
Speaker 1: the universe is made of tiny bits. People give him
3:36
Speaker 1: credit for that because he had a right idea, but
3:38
Speaker 1: he had like a million wrong totally idea. If you
3:42
Speaker 1: just like spew ideas, eventually one of them is going
3:45
Speaker 1: to be right. Statistically speaking, exactly, It's like Nostradamus, like
3:49
Speaker 1: he predicted everything because he made a bunch of false
3:52
Speaker 1: predictions as well, exactly. And so if I wrote down
3:55
Speaker 1: literally every possible thing that could happen, if I made
3:58
Speaker 1: an infinite number of predictions, then one of them would
4:01
Speaker 1: be correct. I could predict the whole future of the
4:03
Speaker 1: university if I had an infinite number predictions, and one
4:06
Speaker 1: of those would be the actual theories of events of
4:09
Speaker 1: the future, right exactly. If you think about, like if
4:12
Speaker 1: you make a random noise in your head, like, the
4:15
Speaker 1: chances are someone else is going to think that same
4:18
Speaker 1: random noise in your head at some point in an
4:20
Speaker 1: infinite universe. And that's what we're gonna talk about today
4:24
Speaker 1: on the podcast. These big concepts, the concepts that are
4:28
Speaker 1: bigger than big, the ones that are so hard that
4:30
Speaker 1: we can only grapple with them in our minds. Today's
4:34
Speaker 1: episode will be focused on this concept of infinity. Katie,
4:38
Speaker 1: what do you think of when I say the word infinity?
4:41
Speaker 1: Just real big, you know, really really big, actually, you know,
4:46
Speaker 1: in a serious answer to that. When I was a
4:48
Speaker 1: kid first learning about infinity, it was almost like the
4:53
Speaker 1: concepts of infinity and nothing were very similar to me
4:56
Speaker 1: because both kind of made my brain feel fuzzy. So
5:00
Speaker 1: thinking about an infinite amount of stuff and thinking about
5:04
Speaker 1: the absence of stuff, it's like a similar feeling to me,
5:08
Speaker 1: where it's like my brain just gets this prickly static
5:10
Speaker 1: feeling when I try to think too hard about it.
5:13
Speaker 1: It's amazing that you can hold an idea in your
5:15
Speaker 1: mind that also sort of confuses your mind. I also
5:19
Speaker 1: remember learning about infinity as a kid, and you know,
5:21
Speaker 1: my dad was really into math, and so this is
5:23
Speaker 1: a very simple proof of like, all right, give me
5:25
Speaker 1: a number. I can give you a bigger number, and
5:27
Speaker 1: then I can give you a bigger number than that
5:29
Speaker 1: shows you pretty quickly that there's like no biggest number.
5:34
Speaker 1: And to me that was a crazy concept lying in
5:36
Speaker 1: bed thinking about super big numbers and imagining, well, you know,
5:39
Speaker 1: there's always one bigger than that. So it's super fun
5:41
Speaker 1: to think about, like how your brain gets stretched by
5:44
Speaker 1: the ideas that you stick inside of it. Yeah, it's like,
5:47
Speaker 1: how do you fit a concept like infinity inside of
5:50
Speaker 1: a finite brain with a finite number of neurons, so
5:54
Speaker 1: you can't It's not something that you can really conceive
5:57
Speaker 1: of without using some kind of shortcut, because our brains
6:01
Speaker 1: aren't infinite, so you can't fit infinity in there. Well,
6:04
Speaker 1: I haven't met you in person, so I don't know
6:05
Speaker 1: if your brain is infinite or not, but I definitely
6:07
Speaker 1: know that mine is finite in its capacity. But this
6:10
Speaker 1: really goes to the heart of what we're trying to
6:12
Speaker 1: do with the whole project of physics or of science,
6:15
Speaker 1: which is to understand that external universe out there and
6:19
Speaker 1: represent it in our minds. And so we do that
6:22
Speaker 1: often using mathematics. Right, we have seen so many beautiful
6:26
Speaker 1: moments when crazy things happening out there in the universe
6:29
Speaker 1: can be represented with mathematical representations in our minds. Newton's
6:34
Speaker 1: laws of motion, for example, tell us about the crazy
6:36
Speaker 1: motions of all the planets and sort of lock them
6:39
Speaker 1: into place to some mathematical rigor. So we know that
6:42
Speaker 1: mathematics is very helpful in helping us understand what's going
6:46
Speaker 1: on out there, that we can represent the craziness, the insanity,
6:49
Speaker 1: the beauty, the complexity of the chaos of the universe
6:52
Speaker 1: using simpler mathematical representations in our minds. But if we
6:56
Speaker 1: know that everything that's physical has to be mathematical, do
7:00
Speaker 1: we know that everything that's mathematical has to be physical? Like?
7:04
Speaker 1: Is everything that you can imagine physically possible? Right? Right?
7:08
Speaker 1: Because you can have something in math that's theoretical, but
7:14
Speaker 1: it's not necessarily a tangible thing that you can like
7:18
Speaker 1: observe or hold in your hands, Like can you pick
7:21
Speaker 1: up a chunk of infinity and have that in your hand? Yeah,
7:25
Speaker 1: And it seems like math is definitely sort of larger
7:28
Speaker 1: than physics. A very simple example is I can come
7:32
Speaker 1: up with a theory of particles that's wrong. It would
7:36
Speaker 1: be mathematically correct, it could work, you know, it doesn't
7:39
Speaker 1: generate nonsense or whatever. It just doesn't describe our universe.
7:43
Speaker 1: So there are more theories. There are more mathematical theories
7:46
Speaker 1: of the universe than actual physical laws that govern the universe. Right,
7:51
Speaker 1: And so far we don't even think we found the one.
7:53
Speaker 1: We have lots of really nice theories of the universe
7:56
Speaker 1: that are beautiful but are probably not correct. So it
7:59
Speaker 1: seems like not everything that's mathematical has to be physical, right.
8:03
Speaker 1: I think for me. One of the simplest examples is,
8:06
Speaker 1: just as you were saying before, things that are perfect,
8:09
Speaker 1: like a circle, like a perfect circle. You can hold
8:12
Speaker 1: that idea in your mind somehow there's a representation in
8:15
Speaker 1: your brain to this concept of a perfect idealized circle.
8:18
Speaker 1: But I've never seen a perfect circle in reality of you. Ah, well,
8:24
Speaker 1: when I eat enough food, maybe, but no, I guess
8:26
Speaker 1: that any kind of drawing or depiction of a circle,
8:30
Speaker 1: even if it looks perfect, if you look at it
8:33
Speaker 1: with like an electron microscope, you're gonna find imperfections. Yeah,
8:37
Speaker 1: and everything is made out of particles, out of atoms
8:40
Speaker 1: at a discrete chunks. Right, So you can't have a
8:43
Speaker 1: perfectly continuous circle in reality. But of course you can
8:47
Speaker 1: hold one in your mind, and you can write down
8:49
Speaker 1: in just a few letters the equation for one right
8:53
Speaker 1: x where it puss wise square, it equals four. That's
8:55
Speaker 1: the equation that describes a perfect circle. But where is
8:59
Speaker 1: that circle? Right? Have the equation? I have the idea
9:01
Speaker 1: in my mind is this set of neurons in my
9:04
Speaker 1: brain that's now representing that concept, But there is no
9:07
Speaker 1: circle actually out there in the universe. It's sort of
9:10
Speaker 1: hard to grapple with and even in our brains, like
9:13
Speaker 1: that circle that you can kind of visualize is just
9:17
Speaker 1: made up of the firing of your neurons, and so
9:21
Speaker 1: is that circle in your brain even perfect? Who knows?
9:24
Speaker 1: Who knows? And we'll dig into that in another episode.
9:26
Speaker 1: But today I want to focus on this biggest concept
9:29
Speaker 1: in mathematics, infinity, because it's something that pops up all
9:33
Speaker 1: the time in physics. It's something that really tickles our
9:36
Speaker 1: brain and makes us ask these really big questions. So
9:38
Speaker 1: today on the podcast, we'll be asking is infinity real?
9:47
Speaker 1: Is it physical? Or is it just mathematical? And people
9:51
Speaker 1: have some answers to this question, which we're going to
9:54
Speaker 1: listen to right now. That's right. Thank you very much
9:57
Speaker 1: to those of you who answered my tough physics questions
10:00
Speaker 1: with no preparation for the podcast. If you like to
10:03
Speaker 1: participate for a future virtual Person on the Street interviews,
10:06
Speaker 1: please write to me two questions at Daniel and Jorge
10:10
Speaker 1: dot com. I promise it's fun. Here's what people have
10:13
Speaker 1: to say. I think that infinity is definitely real. I
10:18
Speaker 1: I believe that the universe is infinite in its size,
10:21
Speaker 1: so that there is the real infinite in the universe
10:24
Speaker 1: that we live in. And also if we believe in
10:26
Speaker 1: the Einstein's theory about black holes, that also inside a
10:30
Speaker 1: black hole we have a singularity that is a point
10:34
Speaker 1: of infinite density. So there we go. We have another
10:37
Speaker 1: very real infinite The only situation in which I can
10:41
Speaker 1: think of um from a physics point of view, where
10:44
Speaker 1: infinity might be real is if the universe has been internal,
10:50
Speaker 1: if it's been around forever. Maybe if there is a
10:56
Speaker 1: singularity in black holes and that might also be considered
11:02
Speaker 1: a point of infinite density. I guess, well, that was
11:07
Speaker 1: very interesting. I do like the idea of the universe
11:11
Speaker 1: being eternal. I think that's kind of one of my
11:13
Speaker 1: concepts of infinity, is that existence of something some you know, universe,
11:20
Speaker 1: even if it's not our universe, but just the existence
11:22
Speaker 1: of stuff has to be infinite, right, Like, there can't
11:25
Speaker 1: be a start and an endpoint to stuff being around.
11:30
Speaker 1: There can't be such an appeal to naturalism. Right, you're
11:32
Speaker 1: just saying, like it's obvious that it must be this way.
11:35
Speaker 1: You're basically a Greek philosopher. That's how they argued. Also, right,
11:38
Speaker 1: I don't know whether to be insulted or not. But yeah,
11:41
Speaker 1: I mean that's how I feel. This is not based
11:44
Speaker 1: on science. It's just how I feel of like, well,
11:47
Speaker 1: we can't just have stuff come out of nothing, go
11:51
Speaker 1: do its thing for a while and then end and
11:53
Speaker 1: then there'll be nothing again. But there's not any scientific
11:58
Speaker 1: reason for that. That's coming from my human feelings of existence.
12:02
Speaker 1: And maybe even that's what I want to believe, because
12:05
Speaker 1: it's very comforting to think there's an infinite universe that
12:08
Speaker 1: doesn't die, and I think it tells you something about
12:11
Speaker 1: yourself and how your mind works and your understanding of
12:14
Speaker 1: the universe to answer these questions that it feels natural
12:17
Speaker 1: to you that the universe is infinite, or that it's
12:19
Speaker 1: not that there are infinities or that there aren't. But remember,
12:23
Speaker 1: of course, that the process of science is to question
12:26
Speaker 1: all that intuition, is to go the opposite direction and
12:29
Speaker 1: to start from the data and say, well, universe, tell
12:31
Speaker 1: us what's out there, and then from that will build
12:34
Speaker 1: our model of the universe, instead of saying like, well,
12:37
Speaker 1: this just has to be this way. But it's hard
12:39
Speaker 1: to sort of understand where those limits are. You can't
12:42
Speaker 1: like question every single thing all the time. You can
12:45
Speaker 1: do experiments every day about every tiny detail. So it's
12:48
Speaker 1: hard to know sometimes when a question is this hard
12:50
Speaker 1: to grapple with exactly how to figure it out. And
12:53
Speaker 1: that's what I think we hear our listeners grappling with
12:55
Speaker 1: whether it can be, whether it must be, whether it
12:58
Speaker 1: can't be. Tricky stuff. Are you saying that I, Katie Golden,
13:02
Speaker 1: could be wrong about one of the most difficult concepts
13:05
Speaker 1: in the universe. I'm saying, basically, everybody is probably wrong
13:09
Speaker 1: about almost everything you know. But those are the best
13:12
Speaker 1: parts of science, right When your intuition is confronted with data,
13:15
Speaker 1: that's when you learn something. That's when the universe is
13:18
Speaker 1: telling you are n't I get why you think this
13:21
Speaker 1: is true, but it turns out it's not. Works a
13:24
Speaker 1: totally different way, And that's why we do science, right,
13:26
Speaker 1: That's why we have this methodological approach to revealing the
13:29
Speaker 1: truth about the universe, rather than just you know, eating
13:32
Speaker 1: olives and lying around in robes and saying maybe it's
13:35
Speaker 1: made of tiny cats, as fun as that is. So
13:39
Speaker 1: say I'm Plato and I'm trying to conceive of infinity.
13:44
Speaker 1: Am I just thinking of like a really really long
13:48
Speaker 1: line of olives? What's going on with that. No, you're right,
13:52
Speaker 1: the Greeks actually do have records of thinking about infinity.
13:56
Speaker 1: And you know, probably people before that thought about infinity.
13:59
Speaker 1: Who knows, But the earliest records we have about infinity
14:02
Speaker 1: go back to about six hundred BC. And you know,
14:06
Speaker 1: there are some examples there are people thinking about infinity,
14:08
Speaker 1: not necessarily in terms of an infinite number of olives.
14:11
Speaker 1: But for example Zeno's paradox. You know, when you say
14:14
Speaker 1: I'm gonna walk first halfway home, and then how much
14:18
Speaker 1: distance do I have to get to the rest of
14:19
Speaker 1: my house, Well half the distance, and before I can
14:22
Speaker 1: get home, I have to then walk half of that distance.
14:25
Speaker 1: Then I have to walk half of that distance and
14:27
Speaker 1: half of that distance, And there's no limit to the
14:29
Speaker 1: number of times you can divide the rest of your
14:32
Speaker 1: distance between yourself and your home. So in principle, there's
14:36
Speaker 1: an infinite number of steps you need to take between
14:38
Speaker 1: yourself and your house if every step is half as
14:41
Speaker 1: long as the previous one. This is Zeno's famous paradox.
14:45
Speaker 1: Of course, right, if there's an infinite number of steps
14:47
Speaker 1: between you and your house, how do you ever get there?
14:49
Speaker 1: You can't, But of course you do. This is how
14:51
Speaker 1: I approach eating a cookie, because I think, well, I'm
14:54
Speaker 1: not going to eat this whole cookie, so I'll just
14:56
Speaker 1: eat half of this cookie. And I'm like, well, I
14:59
Speaker 1: want a little more of this cookie, so we'll eat
15:01
Speaker 1: half of the half of the cookie, and then half
15:03
Speaker 1: of that half and so on and so that way
15:05
Speaker 1: I get to say, like, well, I didn't eat the
15:07
Speaker 1: whole cookie, even though there's only an infintestimally small chrome
15:11
Speaker 1: left of the cookie. Yeah, that's a mathematical proof of
15:14
Speaker 1: converging series. Right. You could have an infinite number of
15:18
Speaker 1: terms and still have it converged to a finite number. Unfortunately,
15:21
Speaker 1: my cookie eating strategy is a divergent series. I started
15:24
Speaker 1: with great intentions. I'm like, I'm just gonna have one,
15:27
Speaker 1: and then I'm like, well I had one, so mighty
15:28
Speaker 1: will just have another one. And then I'm like, well
15:30
Speaker 1: I've had two, so i can just grab a couple more.
15:32
Speaker 1: And then I'm like, might it will just finished the box?
15:35
Speaker 1: Because we all know where this is going, so let's
15:37
Speaker 1: just get there right now. But the Greeks really struggled
15:42
Speaker 1: with this idea. They didn't know if infinity was real,
15:45
Speaker 1: and they had two different concepts. They talked about actual
15:49
Speaker 1: infinity and potential infinity, and they separated these two concepts.
15:52
Speaker 1: They're like, well, this potential infinity, we can think about
15:55
Speaker 1: that for like proofs and geometry and stuff like that.
15:58
Speaker 1: But you know, actual infinity, that's something they actually shied
16:01
Speaker 1: away from. They didn't even want to talk about it.
16:04
Speaker 1: They try to avoid it ever coming up in their
16:06
Speaker 1: proofs and in their logic and in their thought. That
16:08
Speaker 1: like saying sort of a naughty word, like what about
16:12
Speaker 1: actual infinity? And then you get kicked out of class,
16:15
Speaker 1: out of Greek class. Yeah, and they called it the
16:18
Speaker 1: horror of the infinite. They did all these proofs where
16:21
Speaker 1: you could have, you know, used infinity as a mathematical step,
16:24
Speaker 1: but they took all these extra steps to make these
16:27
Speaker 1: proofs happen without needing to resort infinity, without infinity appearing
16:31
Speaker 1: anywhere in their math, because they thought, well, that must
16:34
Speaker 1: be nonsense. That's so interesting. So they had a concept
16:38
Speaker 1: of the potential for infinity, but actually discussing infinity itself
16:45
Speaker 1: was taboo because it makes your brain feel bad. Because
16:48
Speaker 1: I think they thought it wasn't real, you know. I
16:51
Speaker 1: think they thought as a mathematical curiosity, and if you
16:55
Speaker 1: invoked it, if you had to invoke it, then it's
16:56
Speaker 1: somehow made your proofs invalid. And now, of course, you know,
17:00
Speaker 1: we have the same sort of relationship with infinity, Like
17:02
Speaker 1: it's a thing. We can think about it, we can
17:04
Speaker 1: understand it, but it is difficult for us to wrap
17:07
Speaker 1: our minds around, at least to all sorts of like
17:09
Speaker 1: counterintuitive concepts, and infinity has many, many interesting layers. You know.
17:14
Speaker 1: The basic notion of infinity is just the one we
17:16
Speaker 1: talked about before, Like the number of numbers. Right, if
17:20
Speaker 1: you start from zero and you keep going, you'll never
17:22
Speaker 1: get to a point where you can't add another number.
17:25
Speaker 1: Our number system just has that flexibility is no limit,
17:29
Speaker 1: so that you can always make a bigger number. And
17:31
Speaker 1: that's like a really powerful concept. It also makes me
17:34
Speaker 1: wonder sometimes, like what's the biggest number any human has
17:37
Speaker 1: ever thought of? Right? There isn't the biggest number in
17:40
Speaker 1: principle that there might be a biggest number anybody has
17:42
Speaker 1: ever like written down or held in their head. Yeah,
17:45
Speaker 1: I mean, but then once you find that out, you
17:47
Speaker 1: can just add one to it and then you've got
17:50
Speaker 1: the record. Right, you're the human who's thought the biggest
17:52
Speaker 1: number ever. That would be super cool. Yeah, like a googleplex,
17:56
Speaker 1: a google plex plus one, that's it. You're the chain,
18:00
Speaker 1: So that's super fun. And there's all these really interesting
18:03
Speaker 1: exercises to get your brain used to the counterintuitive nature
18:06
Speaker 1: of infinity, because the mathematics of infinity are quite slippery, right,
18:10
Speaker 1: you can think about infinity plus one, but like infinity
18:13
Speaker 1: plus one really is just infinity. One of my favorite
18:16
Speaker 1: examples comes from David Hilbert. The guy invented Hilbert Space
18:19
Speaker 1: like hundred years ago, and this is called Hilbert's Hotel.
18:23
Speaker 1: And in Hilbert's Hotel, he's got a hotel with an
18:26
Speaker 1: infinite number of rooms, right, but he's also got an
18:29
Speaker 1: infinite number of guests. So every room in the hotel
18:32
Speaker 1: has somebody in it. It's all occupied. And you might think, well,
18:35
Speaker 1: if I had a thousand rooms and a thousand guests,
18:37
Speaker 1: then I'm filled up, and if somebody shows up and
18:39
Speaker 1: asked for a room, I would have to say no.
18:41
Speaker 1: But Hilbert's Hotel is different because infinity is really different
18:45
Speaker 1: from other numbers. If he's in the office, he's got
18:47
Speaker 1: infinite rooms and infinite guests, and somebody shows up, he
18:50
Speaker 1: can make room. What he has to do is this
18:53
Speaker 1: special trick and sell everybody to pack up, leave your room,
18:55
Speaker 1: and move over to the next room. So the person
18:58
Speaker 1: in room number one goes to number two. Person room
19:01
Speaker 1: number five hundred forty seven goes through room five hundred,
19:05
Speaker 1: and in this way, room number one now becomes vacant.
19:08
Speaker 1: What happens at the very very end, like in room infinity,
19:12
Speaker 1: will room infinity goes through Room infinity plus one, right,
19:16
Speaker 1: and I think, well that room didn't exist before. Well
19:19
Speaker 1: it did because there were an infinite number of rooms.
19:22
Speaker 1: And so in this weird way you can still make
19:24
Speaker 1: room even if you had an infinite number of guests.
19:27
Speaker 1: But you know, it sounds like this is going to
19:29
Speaker 1: only get a two point five stars on Yell because
19:32
Speaker 1: Albert's making you pack up and move your rooms all
19:34
Speaker 1: the time. Terrible stay. Yeah, and he can even accommodate
19:38
Speaker 1: an infinite number of guests, Like if an infinite number
19:41
Speaker 1: of people show up and want rooms, he can just say,
19:43
Speaker 1: all right, everybody, leave your room and go to twice
19:47
Speaker 1: your room number right to then person in room four
19:50
Speaker 1: goes to room eight for example, leaving three rooms open,
19:54
Speaker 1: and so there's a lot of flexibility there left in infinity.
19:57
Speaker 1: It's really fascinating, but of course it feels unfa of all,
20:00
Speaker 1: this doesn't feel like something that could actually exist because
20:03
Speaker 1: hotels have a certain number of rooms. Even if there
20:06
Speaker 1: are very very large numbers, there is a number, and
20:10
Speaker 1: so that shows you that, like infinity really not a
20:12
Speaker 1: number in the same way that other big numbers are. Right,
20:15
Speaker 1: when we try to apply something like infinity to something
20:21
Speaker 1: that in our human minds is a finite thing, like
20:24
Speaker 1: physical space of a hotel rooms, you know, those little
20:28
Speaker 1: mints they put under your pillow, it's very difficult to
20:31
Speaker 1: actually try to translate that concept into infinity, Like I
20:35
Speaker 1: can't think of infinity mints. That's just not you know,
20:39
Speaker 1: infinite meus. Like, although that would be a good brand
20:41
Speaker 1: for those little hotel ments in the infinity, we are
20:44
Speaker 1: copyrighting that right here. And you can play other fun
20:47
Speaker 1: games to really blow your mind, because it turns out
20:49
Speaker 1: that there are different sizes of infinity. Like you know,
20:53
Speaker 1: I think a whole lot of infinity is everything is
20:55
Speaker 1: the biggest thing. There can't be anything bigger than that.
20:58
Speaker 1: But you can't actually take an infinite list and then
21:01
Speaker 1: make something bigger than that infinite list. There's another really
21:05
Speaker 1: clever example in mathematics, like say, for example, you write
21:08
Speaker 1: down all of the numbers between one and two. How
21:12
Speaker 1: many numbers are there between one and two? Well, is
21:15
Speaker 1: an infinite number because you can always add another digit
21:18
Speaker 1: to subdivice, like Zeno's paradox. If you have one point
21:21
Speaker 1: seven and one point eight, you can always go one
21:23
Speaker 1: point seven five, and then one point seven two five
21:25
Speaker 1: and one point seven one seven five or whatever. So
21:28
Speaker 1: there's an infinite number of numbers there because you can
21:30
Speaker 1: always take half of a half exactly. So we have
21:33
Speaker 1: an infinite number of numbers, and each of those numbers
21:36
Speaker 1: can have an infinite number of digits. So between one
21:39
Speaker 1: and two there's an infinite number of numbers, each of
21:42
Speaker 1: which have an infinite number of digits, right, just like pie.
21:45
Speaker 1: And so that's amazing just to think about. Now, if
21:48
Speaker 1: you take that list, I can always find a number
21:51
Speaker 1: that's not on that list. There's always one more number
21:55
Speaker 1: between one and two that's not on that list. How
21:58
Speaker 1: do you do that? Well, it's sort of just like
22:01
Speaker 1: taking the biggest number and adding one which you need.
22:03
Speaker 1: Is a recipe for generating a new number that's not
22:06
Speaker 1: on that list, and that's not actually that hard. You
22:09
Speaker 1: just take the first digit from the first number and
22:12
Speaker 1: you add one to it, and you take the second
22:14
Speaker 1: digit from the second number and you add one to it,
22:17
Speaker 1: and the third digit from the third number, and you
22:18
Speaker 1: add one to it, and then you're making a number
22:21
Speaker 1: which disagrees with every number on your list in one
22:24
Speaker 1: of the digits. So it wasn't on your list, which
22:27
Speaker 1: means that you had an infinite number of numbers on
22:29
Speaker 1: your list, but you can make it bigger. And so
22:33
Speaker 1: that's an example of a kind of infinity we call
22:36
Speaker 1: uncountable infinity, where you can't like associate all the things
22:40
Speaker 1: on your list with the natural numbers. With one, six, seven,
22:44
Speaker 1: it's bigger than the infinity of all the numbers. So,
22:47
Speaker 1: for those of us who are less numerically inclined, you're saying, basically,
22:53
Speaker 1: you could have a pilot cats, but it's an infinite
22:57
Speaker 1: pilot cat, like, well, this is infinity cats. But then
23:01
Speaker 1: you find just one more cat and it looks so
23:05
Speaker 1: cute that you have to add it to the pile
23:07
Speaker 1: of infinity cats that you're hoarding, And now you have
23:10
Speaker 1: an even bigger pile of cats, but they're both piles
23:13
Speaker 1: of infinite cats, that's right. And you can have a
23:15
Speaker 1: pile of cats that's so infinite that you can't even
23:19
Speaker 1: assign them all numbers. You can't give them all unique numbers.
23:22
Speaker 1: There's more cats on that list than there are numbers
23:25
Speaker 1: in the infinite number line. At a certain point, you
23:28
Speaker 1: just gotta start calling them all minute, mitten seventy two,
23:33
Speaker 1: Come get your pill. That's a lot of being a
23:37
Speaker 1: cat mom. So there's these crazy concept we have countable infinity,
23:40
Speaker 1: which is like the natural numbers, and then we have
23:42
Speaker 1: uncountable infinities, which are even bigger and hard to grapple with. Well,
23:46
Speaker 1: I think one thing we can grapple with, though, is
23:49
Speaker 1: a very finite break before we talk more about the
23:53
Speaker 1: infinity of infinity after the break, which won't be infinity.
23:57
Speaker 1: So don't worry, and we are back, And I hope
24:13
Speaker 1: that break did not feel like an infinity being separated
24:16
Speaker 1: from our lovely voices telling you about infinity. We are
24:20
Speaker 1: having a lot of fun thinking and talking about infinities,
24:23
Speaker 1: and so far we've been talking about infinity sort of
24:26
Speaker 1: mathematically right in terms of like what the number means
24:30
Speaker 1: and how big it is and how hard that is
24:31
Speaker 1: to get your mind around. But now let's talk about
24:34
Speaker 1: infinity in physics, because physics and theoretical physics specifically has
24:40
Speaker 1: infinities all the time, right like their infinities all over
24:44
Speaker 1: the place in theoretical physics. And so first let's talk
24:48
Speaker 1: about infinities and theoretical physics, and then we'll figure out
24:50
Speaker 1: whether any of those are actually real out there in
24:53
Speaker 1: the universe. So when I think of physics, I think
24:57
Speaker 1: of you know, you drop a ball off of a build,
25:00
Speaker 1: and hey, you can figure out how fast that ball
25:02
Speaker 1: is going, or even particle physics, you are looking at
25:06
Speaker 1: the interaction of particles with each other. It's hard for
25:10
Speaker 1: me to conceptualize what infinity looks like. How do you
25:14
Speaker 1: have infinity tall building with the infinity balls dropping off
25:20
Speaker 1: of it, or how do you have infinity particles interacting
25:23
Speaker 1: with each other? Yeah, that's really as hard to think about,
25:25
Speaker 1: but it entered into physics very very early with Newton. Like,
25:29
Speaker 1: as you're saying, Newton is thinking of like an apple
25:31
Speaker 1: falling off of the tree or the motion of something.
25:34
Speaker 1: In order to solve those physics problems, he had to
25:37
Speaker 1: invent a new kind of mathematics, calculus. Calculus is adding
25:41
Speaker 1: up what we call infinitesimals, lots of tiny little contributions.
25:46
Speaker 1: You know, for example, when the apple is falling from
25:48
Speaker 1: the tree, it's not moving a constant velocity, is not
25:51
Speaker 1: falling with the same speed all the time. It's falling
25:54
Speaker 1: faster and then faster, and then faster. And so to
25:57
Speaker 1: do those calculations to figure out like how long does
26:00
Speaker 1: to take the apple to fall from the tree and
26:02
Speaker 1: hit the ground means adding up lots of changing velocities.
26:06
Speaker 1: So we have to invent a new kind of mathematics
26:09
Speaker 1: called calculus, which allows you to add up an infinite
26:12
Speaker 1: number of little slices of time to get the right answer.
26:17
Speaker 1: And that's the way calculus works. It's like the limit
26:19
Speaker 1: of taking a big sum when that limit becomes infinite,
26:22
Speaker 1: when you have an infinite number of things you're adding up.
26:24
Speaker 1: And so calculus is all about infinitesimals. It's everywhere around us.
26:28
Speaker 1: So here's a potentially stupid question. If you had an
26:32
Speaker 1: infinitely tall tree, and you had an apple fall from
26:36
Speaker 1: an infinitely tall branch onto Newton, who was infinitely below
26:42
Speaker 1: that apple, with that apple without when resistance become infinitely
26:47
Speaker 1: fast and just pulverized Newton into infinitely nothing. Well, if
26:51
Speaker 1: we're living in this universe, then there's a speed limit
26:54
Speaker 1: and so it can't go infinitely fast. Right, that's a
26:58
Speaker 1: really fascinating question about infinite because in theoretical physics, you
27:02
Speaker 1: can't have infinite velocity. Right, there is a speed limit
27:06
Speaker 1: to the universe. You can't go infinite velocity. So if
27:09
Speaker 1: he's infinitely far away from the apple, then they would
27:12
Speaker 1: never hit him. So is there some kind of like
27:14
Speaker 1: space cops that are like space highway patrol enforcing this
27:19
Speaker 1: space speed limit, because that seems like they're really harsh
27:23
Speaker 1: and my mellow, No, it's just a fact of the universe.
27:26
Speaker 1: But fascinatingly, there is no limit on the energy of
27:30
Speaker 1: a particle, and so these particles can't go infinitely fast,
27:33
Speaker 1: but they can have infinite energy. Like if you build
27:36
Speaker 1: a particle accelerator, you can just keep pumping these particles
27:39
Speaker 1: to have higher and higher energy even though they don't
27:42
Speaker 1: go faster and faster. The relationship between energy and speed
27:46
Speaker 1: changes as you approach the speed of light, and you
27:48
Speaker 1: can like double the amount of energy a particle has
27:50
Speaker 1: and it just goes a tiny little bit faster. So
27:53
Speaker 1: there is no limit to the energy a particle can have,
27:56
Speaker 1: but there is a limit to the speed it can have,
27:58
Speaker 1: which is interesting sort of counterplay there between finite and infinite.
28:02
Speaker 1: So what is the universal speed limit? Is it like
28:05
Speaker 1: a hundred miles per hour or like KOs per hour?
28:09
Speaker 1: I don't want to be too exclusive to our European listeners,
28:13
Speaker 1: it's a three times ten the eight meters per second,
28:16
Speaker 1: So three hundred million meters per second is the speed
28:20
Speaker 1: limit for the speed of light in a vacuum, of course,
28:23
Speaker 1: and that's the fastest that anything can move relative to
28:25
Speaker 1: any other object in the universe. But again, no limit
28:28
Speaker 1: on the energy, which is amazing. Wow. Well that's good
28:32
Speaker 1: to know though, so we don't get a speeding ticket.
28:34
Speaker 1: And theoretical physics also deals with infinity in terms of
28:38
Speaker 1: the particles. As you were saying, you know what happens
28:41
Speaker 1: when two particles bump against each other, Well, they're not
28:44
Speaker 1: like physically actually touching each other. In our model, we
28:48
Speaker 1: have them passing particles back and forth like two electrons
28:51
Speaker 1: repel each other. How while they do it by emitting
28:54
Speaker 1: a photon and passing that photon from one to the other,
28:57
Speaker 1: which gives it a little push. It's a little momentum,
29:00
Speaker 1: it's firm. But it's not just one photon. The electron
29:02
Speaker 1: is constantly emitting photons. Most of the photons aren't like big,
29:07
Speaker 1: heavy duty photons they're gonna do anything. Most of them
29:09
Speaker 1: are very very very low energy, infinitesimally small energy. But
29:14
Speaker 1: then there's an infinite number of them. So every photon
29:17
Speaker 1: is constantly emitting an infinite number of tiny, tiny, tiny photons.
29:21
Speaker 1: So that's like if you have a kitten who's got
29:26
Speaker 1: a very weak little swipe of the paw, but if
29:29
Speaker 1: you have infinity little kittens, it's gonna have an impact
29:32
Speaker 1: on you exactly. And these infinite little photons or kittens
29:36
Speaker 1: just add up to a normal number, and they don't
29:39
Speaker 1: like give you a divergence. They don't give you an
29:41
Speaker 1: infinite amount of force between the electrons. That's the key
29:44
Speaker 1: that sometimes in these calculations you have an infinite number
29:47
Speaker 1: of steps in the calculation, but you still get a
29:50
Speaker 1: finite answer, right. The electron pushes against the other electron
29:54
Speaker 1: with a certain finite number, and that's sort of like
29:56
Speaker 1: Zeno's paradox, it tells you that the infinity isn't real.
30:00
Speaker 1: It's just an artifact of how you're doing the calculation.
30:03
Speaker 1: You can take any finite number and slice it up
30:06
Speaker 1: into infinite pieces doesn't mean there's a real infinity there.
30:09
Speaker 1: It just means that you've cut it into an infinite
30:11
Speaker 1: number of pieces, because, like if you cut a single
30:15
Speaker 1: cookie into infinitely small pieces, it's still just a single
30:20
Speaker 1: cookie unfortunately exactly and now probably doesn't even taste as good,
30:24
Speaker 1: because you've separated all the ingredients, right, And it's that
30:27
Speaker 1: magical mixture of ingredients that makes a cookie what it is.
30:30
Speaker 1: And often in theoretical physics, when you do get a
30:32
Speaker 1: real infinity, when all the particles add up to give you,
30:36
Speaker 1: like an infinite force between the two electrons, that's when
30:39
Speaker 1: you know you've done something wrong that we call a divergence, right,
30:42
Speaker 1: because you can have an infinite series that does diverge. Say,
30:46
Speaker 1: for example, you just add up all the natural numbers
30:48
Speaker 1: between one and infinity, that some if you add them
30:52
Speaker 1: all up, is going to be infinity. If you add
30:54
Speaker 1: up you know, one and then plus a half and
30:56
Speaker 1: a fourth and an eighth, that's not going to be
30:58
Speaker 1: an infinite number that's going to current verge. And so
31:01
Speaker 1: in physics, when we do a calculation and it gives
31:04
Speaker 1: us infinity, we usually think of that as a failure.
31:07
Speaker 1: It's sort of like the Greeks, you know, like actual infinities,
31:11
Speaker 1: like the horror of the infinite, because we don't think
31:13
Speaker 1: that particles push against each other with infinite force. So
31:16
Speaker 1: when buzz light year says to infinity and beyond, that's
31:19
Speaker 1: like horrific. Physicists we're like, no, don't go there, fix
31:25
Speaker 1: your calculation. You must have missed a minus sign or something.
31:29
Speaker 1: And so it does pop up all the time, and
31:31
Speaker 1: usually it's a sign that something is wrong. You've done
31:33
Speaker 1: your calculation wrong, and so your series is like diverged
31:36
Speaker 1: instead of converged. You know, you missed a minus sign maybe.
31:39
Speaker 1: And this is how we know, for example, that a
31:41
Speaker 1: theory isn't working, because we don't see these infinities in nature.
31:45
Speaker 1: You don't see particles with infinite electric charge or pushing
31:49
Speaker 1: against other particles with infinite forces. And so that's why
31:53
Speaker 1: like the lack of seeing infinity in the physical universe
31:55
Speaker 1: tells us that we can't have a cropping up in
31:57
Speaker 1: our theoretical concepts as well. That also happens in biology.
32:02
Speaker 1: You have like a Fibonacci sequence perhaps where you get
32:06
Speaker 1: these fractals in nature, like you'll see them in plants
32:10
Speaker 1: often where or like even if you see like a cauliflower,
32:13
Speaker 1: or if you have ever had a romanesco it's this
32:16
Speaker 1: very beautiful green plant that has tastes like cauliflower. It's
32:20
Speaker 1: quite quite delicious when you fried up, and it has
32:24
Speaker 1: a natural fractal that occurs with it. And with mathematical fractals,
32:29
Speaker 1: they are theoretically infinite, but of course there's not infinite
32:34
Speaker 1: amount of romanesco. So even though that fractal is repeating
32:39
Speaker 1: and is you know, following the mathematical model of like
32:43
Speaker 1: of an infinite pattern, at a certain point it tapers off.
32:47
Speaker 1: There is a smallest, like little particle of romanesco that
32:51
Speaker 1: we're not even getting to the particle physics. You're getting
32:54
Speaker 1: to biology, which has a much larger cutoff for how
32:58
Speaker 1: small an individual unit, because it can only be as
33:01
Speaker 1: small as like a cell. Yeah, exactly, And so I
33:04
Speaker 1: love that you just said the phrase particle of romanesquo.
33:08
Speaker 1: You're right, we don't see those infinities and so we
33:10
Speaker 1: have to sort of like try to cut them out
33:11
Speaker 1: of our theory. But you know, in some cases we
33:13
Speaker 1: don't know, And we have infinities in theories, we don't
33:16
Speaker 1: know if they are real or they're just mathematical. I
33:18
Speaker 1: think one of the most famous ones are infinities in
33:21
Speaker 1: general relativity. Right, general relativity tells us that space is curved,
33:27
Speaker 1: and that it gets curved when you're in the presence
33:29
Speaker 1: of mass or energy, and if you have a huge
33:31
Speaker 1: amount of mass, incredibly compact mass, then the curvature of space,
33:36
Speaker 1: which determines how strong gravity feels, can get infinite. And
33:40
Speaker 1: that's what we mean by, for example, a singularity. Singularity
33:44
Speaker 1: is infinite curvature, essentially infinite gravitational force at that point.
33:48
Speaker 1: So does that mean that a black hole is evidence
33:52
Speaker 1: that there is actual tangible infinity. We just don't know,
33:57
Speaker 1: because we don't know if there's a real singularity inside there.
34:00
Speaker 1: There's a singularity in the theory, and that singularity predicts
34:03
Speaker 1: black holes, and we see black holes. But also we
34:07
Speaker 1: don't think those singularities are probably there because they're in
34:09
Speaker 1: conflict with quantum mechanics, which says you can't have an
34:12
Speaker 1: infinitely dense point at a certain location. So we're really
34:16
Speaker 1: pretty confused about what's going on inside black holes, and
34:19
Speaker 1: we'd love to see one because if an answer not
34:21
Speaker 1: just the question of you know, our infinity is real,
34:24
Speaker 1: but also tell us you know how general relativity works.
34:28
Speaker 1: But if you talk to people who do general relativity,
34:30
Speaker 1: they don't say this is a physical prediction. They don't
34:32
Speaker 1: say general relativity predicts the existence of physical infinities and singularities.
34:37
Speaker 1: They say this is a failure of the theory. This
34:40
Speaker 1: is they say, we can't predict what happens there because
34:43
Speaker 1: infinite curvature is like nonsense. It's like the theory breaks down.
34:47
Speaker 1: It's like you have a hole in your fabric of
34:49
Speaker 1: space where you don't know what to do. Instead of
34:51
Speaker 1: like actually predicting an infinite singularity, I mean that seems
34:56
Speaker 1: kind of like a bummer. And I guess until we
34:59
Speaker 1: can get a big enough black hole where it's safe
35:01
Speaker 1: to kind of float around on like a space inflatable
35:05
Speaker 1: life jacket and then just kind of cruise right in, Like,
35:09
Speaker 1: how would you even see, though, whether there's an infinite
35:12
Speaker 1: singularity even if you could cruise around in a black
35:16
Speaker 1: hole like how would you identify that. Yeah, we actually
35:18
Speaker 1: need a fun podcast episode a few months ago about
35:21
Speaker 1: seeing singularities. They're called naked singularities. And you could try
35:25
Speaker 1: to take a black hole that's spinning and make it
35:27
Speaker 1: spin faster and faster, so the event horizon sort of
35:30
Speaker 1: shrinks and it might reveal the singularity, but nobody knows,
35:33
Speaker 1: and that would take a crazy amount of energy. Until then, though,
35:36
Speaker 1: we are trying to come up with a better theory,
35:39
Speaker 1: one that can describe what's going on in the inside
35:42
Speaker 1: of a black hole and be consistent with quantum mechanics,
35:45
Speaker 1: and the category of theories are called quantum gravity. And
35:48
Speaker 1: some of these theories are pretty good, but most of
35:50
Speaker 1: them fail because they have infinities. Like you try to
35:54
Speaker 1: calculate what happens when you have two big masses they
35:57
Speaker 1: get close together, and they predict infinite horses and you're like, well,
36:00
Speaker 1: we know that's not right, and so these theories break down,
36:04
Speaker 1: like it doesn't agree with what we see, and so
36:06
Speaker 1: their infinities are also a failure. So we have infinities
36:09
Speaker 1: in these theories. But again it's the horror of the
36:12
Speaker 1: infinite is the failure of the theory. We're trying to
36:14
Speaker 1: remove those infinities so we can make predictions for what
36:17
Speaker 1: happens in the actual physical world instead. Okay, so we
36:21
Speaker 1: don't have a theory yet that doesn't have that mistake,
36:26
Speaker 1: that oopsie of infinity. But we are going to take
36:29
Speaker 1: a quick break about a minute, so everyone listening out there. Daniel,
36:35
Speaker 1: I'll get out a calculator. Let's see if we can
36:37
Speaker 1: get this before we get back from our quick break.
36:53
Speaker 1: All right, we're back. Has anyone come up with the
36:56
Speaker 1: theory without infinity as an answer? We should totally crowd
37:00
Speaker 1: source the theory of quantum gravity. All our listeners, all
37:02
Speaker 1: that brain power together approaches infinite genius exactly. And so
37:07
Speaker 1: we've been wrestling with the concept of infinity. We know
37:09
Speaker 1: it's a mathematical idea. We can do equations with it.
37:12
Speaker 1: We use it all the time in our mathematics. We
37:15
Speaker 1: even have it inside our physical theories as we're like
37:18
Speaker 1: doing calculus and summing over an infinite number of particles.
37:21
Speaker 1: But really the question is whether it's just something in
37:24
Speaker 1: our minds or whether it actually exists out there in
37:27
Speaker 1: the universe as well. So, Katie, you were talking earlier
37:31
Speaker 1: about the infinity of time, like whether the universe could
37:34
Speaker 1: go on forever, right, which I like the idea of
37:38
Speaker 1: because it seems to indicate to me there's an infinite
37:41
Speaker 1: amount of possibilities, such as a universe in which I
37:45
Speaker 1: Katie forty one b is surrounded by an infinite number
37:49
Speaker 1: of cats. But I do like the idea of a
37:52
Speaker 1: universe going on forever because it feels, you know, the
37:57
Speaker 1: idea of the death of the universe is maybe even
38:00
Speaker 1: scarier to me than my own mortality. In some ways,
38:03
Speaker 1: the idea that things could just stop existing is quite terrifying, right,
38:07
Speaker 1: And it is terrifying, and it's hard to imagine not
38:10
Speaker 1: existing anymore. But we all know that it happens, right
38:13
Speaker 1: There are people who were alive and are now not
38:15
Speaker 1: alive anymore. And so you can apply that same sort
38:20
Speaker 1: of concept to the universe and wonder like, even though
38:22
Speaker 1: the universe exists now, doesn't mean it always will. And
38:26
Speaker 1: the biggest argument against the universe being infinite in time
38:30
Speaker 1: to the future is that we don't know if the
38:32
Speaker 1: universe was infinite in time in the past, right, Like,
38:36
Speaker 1: we look back at the history of the universe and
38:38
Speaker 1: we see what looks like a beginning fourteen billion years
38:42
Speaker 1: ago the universe began. We don't know if there was
38:45
Speaker 1: anything before that, or if the universe actually literally started there.
38:49
Speaker 1: A lot of theories of general relativity have like the
38:51
Speaker 1: clock beginning at that moment, and before that there was
38:54
Speaker 1: no clock, there was no universe, there was no space,
38:57
Speaker 1: there was nothing. Doesn't mean we know how that happened.
39:00
Speaker 1: But in that concept, the universe has a finite age
39:03
Speaker 1: so far, why would it make sense for it to
39:05
Speaker 1: then go on for infinity. It's interesting because this is
39:09
Speaker 1: sort of what I was saying earlier, where trying to
39:12
Speaker 1: think about infinity gives me that same brain tingle sensation
39:18
Speaker 1: as trying to think about nothingness. So trying to think
39:20
Speaker 1: about nothing existing before the universe started and then nothing
39:26
Speaker 1: existing after, I would almost say that's a harder concept
39:29
Speaker 1: for me to think about than infinity, like thinking of like, well,
39:33
Speaker 1: how could just there suddenly be an explosion of things
39:37
Speaker 1: out of nothing and then how could all that stuff
39:40
Speaker 1: suddenly become nothing again? And what does that even mean?
39:44
Speaker 1: And it was hard for people to accept this idea
39:46
Speaker 1: before we understood that the universe was expanding, and that
39:49
Speaker 1: suggested that it was once younger and denser and hotter,
39:52
Speaker 1: and therefore might have had a beginning. People thought the
39:55
Speaker 1: universe was infinitely old, and that was just a much
39:57
Speaker 1: more natural idea. But of course can't just accept physics
40:01
Speaker 1: because it sounds natural. It has to be right. And
40:04
Speaker 1: so now we've accepted the concept that maybe the universe
40:07
Speaker 1: has a finite age so far, so we just don't know,
40:10
Speaker 1: like will the universe go on forever or will it
40:13
Speaker 1: come to an end? And there's some really weird possibilities,
40:15
Speaker 1: like it might be that the universe doesn't come to
40:18
Speaker 1: a dramatic end. It might be the universe doesn't like
40:21
Speaker 1: reverse the Big Bang and end up as a big crunch.
40:23
Speaker 1: One possibility is that the universe just sort of like
40:26
Speaker 1: spreads out into an evenly tempered muck so that everything
40:30
Speaker 1: is the same temperature. You don't have like hot spots
40:32
Speaker 1: and cold spots anymore. This is called the heat death
40:35
Speaker 1: in the universe. So in the universe is maximally disordered.
40:38
Speaker 1: You have maximum entropy, and there's some folks out there
40:41
Speaker 1: that think that entropy and time are so closely connected
40:44
Speaker 1: that it's entropy that's driving time forward. And when you
40:48
Speaker 1: get to this heat death, this equally spaced muck of
40:51
Speaker 1: the universe, that time itself comes to an end, that
40:55
Speaker 1: nothing can happen anymore. And so it might be that
40:57
Speaker 1: the universe has a dramatic beginning and then very undramatic
41:01
Speaker 1: sort of end like a lion, and then France is
41:05
Speaker 1: out like muck, like entropy muck. So that's a possibility, right.
41:10
Speaker 1: We just can't say whether the universe will exist forever
41:14
Speaker 1: forward in time. We don't know if it existed forever
41:18
Speaker 1: backwards in time, but current thinking is probably not. But
41:21
Speaker 1: you know, there are other dimensions, of course, of infinity.
41:24
Speaker 1: One of my favorites is thinking about the universe is
41:26
Speaker 1: infinite in space, right, Like if you look out into
41:30
Speaker 1: the universe, can you point your finger which makes a line,
41:34
Speaker 1: and how that line continue out through space and never
41:37
Speaker 1: ever stop right, never like loop back on itself or
41:41
Speaker 1: hit a wall or something. Does that line actually traverse
41:44
Speaker 1: space literally forever? That's what I thought you could do.
41:47
Speaker 1: If you've got a strong enough flashlight and pointed up
41:50
Speaker 1: at the sky, it's like, take that space. All this
41:53
Speaker 1: light is going to go on forever, but probably not. Well,
41:56
Speaker 1: if the universe is infinite in space and in time,
41:58
Speaker 1: then that photon from your flashlight will literally go on forever.
42:02
Speaker 1: I guess it could get absorbed by something, probably a
42:05
Speaker 1: black hole between me and infinity, a black hole made
42:08
Speaker 1: of somebody else's infinite number of cats that collapse on themselves.
42:12
Speaker 1: But this is like a true infinity, right, Regardless of
42:15
Speaker 1: what else is going on in the universe, it makes
42:18
Speaker 1: some sense for the universe to be infinite. It might
42:20
Speaker 1: make more sense for it to be infinite than for
42:22
Speaker 1: it to have an edge or for it to be
42:24
Speaker 1: like looped or closed in on itself. In our theories
42:28
Speaker 1: of the universe, we typically assume that the universe is
42:31
Speaker 1: infinite because it just currently feels like the most natural thing, right,
42:36
Speaker 1: because I've seen like images of maybe the universe is
42:40
Speaker 1: like a doughnut or a cone. And then the hard
42:43
Speaker 1: part for me to wrap around a non infinite universe
42:45
Speaker 1: is like, well, what's outside of that doughnut or cone?
42:49
Speaker 1: I can't my brain just again, it starts to break
42:52
Speaker 1: down when I try to think, well, what would be
42:54
Speaker 1: outside of a universe? Like, what would be that? Nothing? Like?
42:57
Speaker 1: I think that's another I don't remember which Greek philosopher
43:01
Speaker 1: came up with this, but I thought that was another
43:02
Speaker 1: thing of like, well, once you get to the edge
43:05
Speaker 1: of the universe and you pull apart the veil, what's
43:08
Speaker 1: beyond that? Right? And we just don't know. But the
43:10
Speaker 1: fascinating thing is that there's only one answer we could
43:14
Speaker 1: possibly know. Like, we could discover an edge to the universe.
43:18
Speaker 1: We could discover that the university's finite, that it loops
43:21
Speaker 1: around itself or has some weird deformity at the edge,
43:24
Speaker 1: or something like that, but we could never prove that
43:27
Speaker 1: it's infinite. Right, How could you prove that the universe
43:30
Speaker 1: is infinite? It's like proving that it doesn't have an edge.
43:33
Speaker 1: You can't prove a negative. It could just be that
43:36
Speaker 1: the edges beyond where you thought it was, right, because
43:39
Speaker 1: every time you get a government grant to send out
43:42
Speaker 1: like a spaceship to the edge of space, then it's
43:45
Speaker 1: like okay, but there's more, and then you have to
43:47
Speaker 1: write another grant, And so you would need an infinite
43:51
Speaker 1: number of grants to get to the infinite edge of
43:55
Speaker 1: the universe, and nobody wants to go through that. I
43:58
Speaker 1: do feel like I've really a number of grants of
44:00
Speaker 1: my economic career and I've not received an infinite number
44:03
Speaker 1: of dollars. So it's a really fun concept. And you know,
44:06
Speaker 1: some people suggest that you might be able to prove
44:09
Speaker 1: that the universe is infinite if you can come up
44:12
Speaker 1: with a theory of cosmology that describes the universe and
44:16
Speaker 1: is accurate and requires that the universe is infinite, if
44:19
Speaker 1: your theory only works for an infinite universe and you
44:22
Speaker 1: can exclude all other possible theories. But I'm not sure
44:25
Speaker 1: philosophically that's even possible. So this is another like potential infinity.
44:30
Speaker 1: But it's tantalizing because we can never actually know whether
44:34
Speaker 1: the universe is infinite. That Galileo said this hundreds of
44:37
Speaker 1: years ago in some famous letter, that mankind would never
44:40
Speaker 1: be able to know whether the universe is infinite, And
44:43
Speaker 1: so this is like a centuries old puzzle about the
44:46
Speaker 1: infinity of space in the universe. I like to think
44:49
Speaker 1: that because you look through this telescope. You know, one
44:52
Speaker 1: of the first people to use a telescope, he just
44:55
Speaker 1: sees all these stars out there. It's like, yeah, there's
44:57
Speaker 1: no way we're sorting this now. Now, maybe that was
45:01
Speaker 1: in his grand proposal. He's like, folks, I need even
45:03
Speaker 1: a number of dollars, got a lot of work to
45:05
Speaker 1: do up here, and then he probably got sent to jail.
45:09
Speaker 1: But you don't need to look out into space to
45:11
Speaker 1: see potential infinities. Like we were talking about how there's
45:14
Speaker 1: an infinite number of numbers between the numbers one and two.
45:18
Speaker 1: You can just hold your fingers apart and say, well,
45:21
Speaker 1: how many pieces of space are there between my fingers?
45:25
Speaker 1: How many unique locations? How many different possible spots could
45:29
Speaker 1: a particle be at between my fingers? And if space
45:33
Speaker 1: is continuous, then there's an infinite number of places for
45:37
Speaker 1: a particle to be between your fingers. I'm staring at
45:39
Speaker 1: my hand right now and like pulling my fingers apart.
45:42
Speaker 1: I'm just really glad nobody's here right now see me
45:45
Speaker 1: doing this, because like, hey, how's it going? What you
45:48
Speaker 1: doing there? I'm just doing physics, and like, okay, that's
45:50
Speaker 1: where you look physic shut up a science. And so, if,
45:55
Speaker 1: as general relativity suggests, the universe is continuous, then you
45:59
Speaker 1: can divide that space an infinite number of times, and
46:02
Speaker 1: there are real locations for every one of those numbers.
46:05
Speaker 1: Every subdivision is real. But you know, quantum mechanics says
46:09
Speaker 1: not so fast. It says that everything in the universe
46:12
Speaker 1: so far seems to be quantized, and a lot of
46:15
Speaker 1: theories out there suggests that space itself might be quantized.
46:19
Speaker 1: That space might be made out of tiny little space
46:22
Speaker 1: pixels that are so small that you can't see them.
46:25
Speaker 1: It's like a retina screen. They might be like ten
46:27
Speaker 1: to the negative thirty five meters wide. It doesn't really
46:31
Speaker 1: matter how small they are as long as there's a
46:34
Speaker 1: minimum distance. That means that the space between your fingers
46:38
Speaker 1: is not an infinite number of locations, but a large
46:40
Speaker 1: and finite number of possible locations, like little slots that
46:44
Speaker 1: particles can fit into. Thinking about space pixels just makes
46:48
Speaker 1: me feel like we're some aliens computer game, and maybe
46:52
Speaker 1: we are. Maybe our universe is finite, but it's just
46:55
Speaker 1: a simulation inside an infinite universe. That's what I'm thinking.
46:59
Speaker 1: But even if our universe is finite, we still wouldn't
47:04
Speaker 1: know if there are infinite finite universe is right, that's right.
47:09
Speaker 1: Another dimension of infinity is whether our universe itself is
47:14
Speaker 1: all that there is. Right. We think of universe like
47:17
Speaker 1: uni means like all of it, the one thing. But
47:20
Speaker 1: these days we have the concept of the multiverse where
47:23
Speaker 1: it's possible that there are other universes just like ours.
47:27
Speaker 1: In fact, there might be an infinite number of them.
47:30
Speaker 1: This concept comes from like a struggle to understand why
47:33
Speaker 1: our universe is so weird, like why is the speed
47:36
Speaker 1: of light the way that it is. Why are the
47:38
Speaker 1: various numbers the parameters that control physics seem to have
47:41
Speaker 1: kind of weird values. And they answered by saying, well,
47:45
Speaker 1: maybe there's an infinite number of universes and so that
47:47
Speaker 1: all the values are explored and we just happen to
47:49
Speaker 1: be in this one. And you know, that's a fun idea,
47:52
Speaker 1: and it's another concept where it's easy to like create
47:55
Speaker 1: infinity in your mind, but it's not something we can
47:58
Speaker 1: ever really study because as these other universes in the
48:01
Speaker 1: multiverse aren't places we can interact with, there are things
48:05
Speaker 1: we can see, we can't ever get evidence of their existence,
48:08
Speaker 1: and so it might be real there might be other
48:11
Speaker 1: universes out there, but I'm not sure that's something we
48:13
Speaker 1: could ever prove or really know. It seems like the
48:17
Speaker 1: only quote unquote evidence we would have of another universe
48:21
Speaker 1: is just if we can't figure something out about our
48:24
Speaker 1: own universe. So we think that maybe there's another universe
48:29
Speaker 1: somehow interacting with our universe, but we would have no
48:32
Speaker 1: way of measuring that at all, because we're stuck inside
48:37
Speaker 1: our universe like a bunch of fish and a fish bowl,
48:40
Speaker 1: and then we're bonking into another fish bowl, but we
48:43
Speaker 1: can never interact with the fish and that other fish bowl.
48:46
Speaker 1: We only know Maybe I think maybe they could be there,
48:49
Speaker 1: if it's the only way we could explain how our
48:52
Speaker 1: fish bowl is getting jostled around. Yeah, there are some
48:55
Speaker 1: fun ideas about how other bubble universes might have been
48:59
Speaker 1: made near hours and when they were very young, and
49:01
Speaker 1: they could have bumped into each other and left a
49:03
Speaker 1: little imprint like these circles on the cosmic microwave background
49:07
Speaker 1: radiation is left over glow from just after the Big Bang,
49:10
Speaker 1: But nobody's ever observed any evidence of that, so it's
49:13
Speaker 1: just a fun idea so far. So that's another possible
49:16
Speaker 1: infinity that could really be real, but we might never
49:19
Speaker 1: actually know. One that's closest to my heart is this
49:22
Speaker 1: question of infinite number of particles, like how many particles
49:26
Speaker 1: are there in my finger? Well, you know, something like
49:30
Speaker 1: Avagajo's number of atoms and then those are made of
49:33
Speaker 1: electrons and protons and neutrons which are made of quarks.
49:36
Speaker 1: But then you can ask like, well, what are those
49:38
Speaker 1: electrons and quarks made out of? One of the electron
49:41
Speaker 1: is made out of particles, which are made out of particles,
49:44
Speaker 1: which are made out of particles which are made out
49:45
Speaker 1: of particles, And it goes infinitely far down to infinite
49:49
Speaker 1: testimal particles. Then you could say, hey, I made out
49:52
Speaker 1: of an infinite number of particles. Yeah. I mean, it's
49:55
Speaker 1: the cookie problem again, where if you start to cut
49:58
Speaker 1: apart a particle like a cookie, it's not that the
50:02
Speaker 1: particle itself is infinitely large, but it's made up of
50:07
Speaker 1: infinitely nesting particles like a Russian nesting doll. But they're
50:13
Speaker 1: sub atomic particles. Yeah, and so that's certainly a possibility, Like,
50:17
Speaker 1: we can't rule that out. We call the electron and
50:20
Speaker 1: the corks the fundamental particles, meaning that they're not divisible,
50:23
Speaker 1: only because we haven't seen anything smaller inside them, not
50:26
Speaker 1: because we have any evidence that they're actually fundamental. We
50:29
Speaker 1: just haven't built a big enough particle collider to smash
50:32
Speaker 1: them open and see what's inside. In fact, we strongly
50:34
Speaker 1: suspect there are smaller particles inside them that would explain
50:37
Speaker 1: lots of the weird patterns that we see in the
50:39
Speaker 1: universe and in those particles. But we also suspect that
50:43
Speaker 1: there might be the smallest particle that if you keep
50:46
Speaker 1: cracking them open far enough down you get down to
50:48
Speaker 1: the smallest bit. Quantum mechanics again says that everything in
50:52
Speaker 1: the universe is discreet, not continuous, that it comes in
50:55
Speaker 1: grains or in chunks. So we suspect that maybe it's
50:58
Speaker 1: a vibrating string or something else, but at very very
51:00
Speaker 1: short distances there is a smallest thing, which would mean
51:05
Speaker 1: you're made out of a finite number of those little
51:07
Speaker 1: vibrating strings or tiny cosmic kittens or whatever. It's so
51:12
Speaker 1: hard to conceptualize a smallest particle because in the physical
51:17
Speaker 1: world that we interact with, even when we find like
51:19
Speaker 1: a smallest building block like you mentioned, like a pixel,
51:22
Speaker 1: we know that pixel actually you can break apart, like
51:26
Speaker 1: it does have little elements, Like when you have a
51:28
Speaker 1: pixel on a screen, it's actually made up of Well,
51:31
Speaker 1: now I don't know how computers work, so I'm just
51:34
Speaker 1: gonna assume it's it's made out of you know, light
51:37
Speaker 1: coming through a little square on your screen. That's exactly
51:41
Speaker 1: how they do it. They build thingies. They put a
51:43
Speaker 1: bunch of little thingies on your screen and little tiny
51:46
Speaker 1: lights that come through the thingies. I'm sure someone who
51:48
Speaker 1: knows how a computer screen work could explain that better.
51:51
Speaker 1: But you know, it's the same thing like with the
51:53
Speaker 1: human brain when you break it up, like the smallest
51:56
Speaker 1: unit of a thought is the action that happens in
52:00
Speaker 1: a synapse, like from one end of a neuron to another.
52:04
Speaker 1: But then you can break that apart because you can
52:07
Speaker 1: look at the molecular structure of a neurotransmitter. I mean
52:11
Speaker 1: you could say though that like if you look at
52:14
Speaker 1: the space between two neurons and the synaps, that could
52:17
Speaker 1: potentially be broken down into infinitely smaller halves of a space.
52:22
Speaker 1: So maybe there's an infinity whenever we have a single thought,
52:26
Speaker 1: because you know, you have an infinite haves that your
52:30
Speaker 1: neurotransmitters have to traverse over your synaps. But again it's
52:35
Speaker 1: kind of like that would according to the mathematics converge,
52:38
Speaker 1: but it's also sort of the goal, Like we feel
52:41
Speaker 1: that if we found the smallest unit, we'd be seeing
52:44
Speaker 1: something like the source code of the universe would reveal
52:46
Speaker 1: something deep and true. Everything above that is just like
52:49
Speaker 1: how those pieces tend to fit together and turn into stuff,
52:52
Speaker 1: right like ice cream is not fundamentalists and teach you
52:55
Speaker 1: something about the universe, regardless of how delicious it is.
52:58
Speaker 1: We want to figure out what is the smallest thing,
53:00
Speaker 1: so we can like look at the deepest nature of
53:02
Speaker 1: the universe. But we don't know if there is the
53:05
Speaker 1: smallest thing or if it just goes on forever. Alright,
53:08
Speaker 1: So we've talked about the potential infinities. I think the
53:11
Speaker 1: most promising ones are the spatial infinities, like maybe the
53:15
Speaker 1: universe really is infinite and goes on forever, or the
53:18
Speaker 1: temporal ones, like maybe the universe can last forever. I
53:22
Speaker 1: think it's pretty unlikely that space can be infinitely divided
53:26
Speaker 1: into bits, or that particles can be infinitely broken into
53:29
Speaker 1: smaller particles. But I think there really is a chance
53:31
Speaker 1: that the universe is infinitely big. But what's amazing to
53:34
Speaker 1: me is that for all these hundreds and thousands of
53:36
Speaker 1: years that we've been thinking about infinity, that we've had
53:39
Speaker 1: it in our minds, we've still never seen actual infinity.
53:43
Speaker 1: No human has ever witnessed laid eyes on anything that
53:47
Speaker 1: is truly infinite. It might be out there and there
53:50
Speaker 1: are universe hiding from us, waiting inside black holes or
53:53
Speaker 1: out past the edge, but we have never seen it.
53:56
Speaker 1: I mean, if you ever stare into a dog's eyes though,
53:59
Speaker 1: and see the love of there, I'd say that's infinite.
54:03
Speaker 1: All right. Well, there you having, folks. If you are
54:05
Speaker 1: a seeker of infinity, then get an infinite number of
54:08
Speaker 1: pets and feel an infinite amount of love from all
54:11
Speaker 1: of them. Until then, keep infiniting in your mind and
54:14
Speaker 1: let us know if you see it out there in
54:16
Speaker 1: the universe. Thanks very much Katie for joining us again
54:18
Speaker 1: on the podcast. Thank you so much for having me.
54:21
Speaker 1: This was infinitely fun. And don't forget to check out
54:24
Speaker 1: her other awesome podcast, Creature Feature, which she talks about
54:27
Speaker 1: the infinite, amazing, nous and complexity of biology. And until then,
54:30
Speaker 1: thank you very much for sharing us your curiosity and
54:33
Speaker 1: tune in next time. Thanks for listening, and remember that
54:43
Speaker 1: Daniel and Jorge explained. The Universe is a production of
54:46
Speaker 1: I Heart Radio. For more podcast from my Heart Radio,
54:49
Speaker 1: visit the i Heart Radio app, Apple Podcasts, or wherever
54:53
Speaker 1: you listen to your favorite shows. No.