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What's the amplituhedron? · Daniel and Kelly’s Extraordinary Universe

0:08
Speaker 1: Ay, Daniel, do you sometimes think that physics is too complicated? Yeah?
0:12
Speaker 1: Sometimes I think it's amazing that we can understand anything
0:16
Speaker 1: at all that's going on out there in the universe.
0:19
Speaker 1: Don't you think there might be a simpler answer to
0:21
Speaker 1: everything out there? That does strike me sometimes if I'm
0:24
Speaker 1: like doing a calculation and I get a whole page
0:26
Speaker 1: of mathematical symbols, that I wonder, like, did I miss
0:29
Speaker 1: a mind is sign somewhere or a factor too? Yeah? Right,
0:32
Speaker 1: Like maybe there's a better way of looking at things
0:34
Speaker 1: that might be simpler. Yeah, Like maybe we should just
0:37
Speaker 1: do physics with cartoons instead of math exactly. Basically my
0:42
Speaker 1: messages you should hire more cartoonists. Well, you know, we
0:46
Speaker 1: do try to do that a little bit with Finnman diagrams.
0:48
Speaker 1: They're basically cartoons. Oh, there you go. Feinneman was a cartoonist,
0:52
Speaker 1: although his punch lines MA not so funny, and so
0:55
Speaker 1: maybe cartoons are actually the problem. Yeah, that's the simple answer,
0:59
Speaker 1: isn't it land the cartoonists. It's all because of big
1:02
Speaker 1: cartoon Hi. I'm jorgem and cartoonists and the co author
1:20
Speaker 1: of Frequently Asked Questions about the Universe. Hi I'm Daniel.
1:23
Speaker 1: I'm a particle physicist and a professor at u C Irvine,
1:26
Speaker 1: and I'm always amazed that we can understand anything about
1:29
Speaker 1: the universe. I'm always amazed that I understand anything at all.
1:33
Speaker 1: Welcome to our podcast, Daniel and Jorge Explain the Universe,
1:36
Speaker 1: a production of I Heart Radio, in which we think
1:38
Speaker 1: about the biggest questions in the universe, the hardest questions,
1:41
Speaker 1: the easiest questions, the most confusing questions, and we try
1:45
Speaker 1: to explain all of them to you. So it's some
1:49
Speaker 1: questions you don't want the answer to. But I look
1:51
Speaker 1: out at the universe and I wonder, why is it
1:54
Speaker 1: possible to use our kind of little brains to come
1:56
Speaker 1: up with these little stories that can actually tell us
1:59
Speaker 1: something about what's going on out there in the universe.
2:02
Speaker 1: We fight these intellectual battles with the chaos of the universe,
2:05
Speaker 1: and sometimes we come out with a nice little story. Well,
2:08
Speaker 1: you're assuming we know the answer to things. Maybe we don't.
2:10
Speaker 1: Maybe what we think about the universe is actually wrong,
2:13
Speaker 1: or actually much simpler than what we think. Well, it's
2:16
Speaker 1: definitely true that everything we think about the universe is
2:18
Speaker 1: probably wrong, but we hope that the degree of wrongness
2:22
Speaker 1: is decreasing with time, that we're like asymptotically approaching some
2:26
Speaker 1: kind of truth, you know, the way that like Newton's
2:28
Speaker 1: theory of gravity wasn't wrong, it just wasn't as close
2:31
Speaker 1: to the truth as Einstein's right. But wouldn't you need science,
2:34
Speaker 1: you know, if you're getting less wrong, in which case
2:36
Speaker 1: that science could also be wrong. Yeah. Actually there's a
2:39
Speaker 1: whole field of philosophy and how to quantify scientific wrongness,
2:44
Speaker 1: and a lot of people argue but exactly how to
2:46
Speaker 1: do those calculations. So yeah, there's the science of new
2:48
Speaker 1: in science. It sounds like relying on philosophy to tell
2:52
Speaker 1: you if science is right, and I don't know that's
2:54
Speaker 1: the best idea. I think. In the end, everything relies
2:57
Speaker 1: on philosophy. It's the foundation of everything. Maybe not breakfast,
3:01
Speaker 1: but it's a foundation of all intellectual pursuits. Doesn't sound
3:05
Speaker 1: very scientific though, Yeah, philosophy is definitely not scientific. You know.
3:08
Speaker 1: Sometimes you talk about ideas that you can't test, but
3:11
Speaker 1: they're still important for understanding the way we think about things.
3:15
Speaker 1: I guess technically all PhDs are philosophers, right, that's what
3:18
Speaker 1: the pH PhD means right, that's right. Yeah, you have
3:21
Speaker 1: a philosophy degree in mechanical engineering, don't you. Yeah, I
3:24
Speaker 1: think I think about mechanical engineering all the time, philosophy
3:28
Speaker 1: of mechanical engineering. I'm thinking of giving myself a PhD
3:31
Speaker 1: in cartooning from a cartoon university. Yeah, why don't you
3:34
Speaker 1: just found your own university? Absolutely? You know. I once
3:36
Speaker 1: went to the crackpot session at the American Physical Society
3:39
Speaker 1: annual meeting. This is the meeting where they have to
3:41
Speaker 1: give you a presentation if you're a member. If you
3:44
Speaker 1: pay a hundred bucks, you can give a talk at
3:45
Speaker 1: the American Physical Society. And there's always one session where
3:48
Speaker 1: they put all the people who are like Einstein was
3:50
Speaker 1: wrong and everything is worldpools man. And one of my
3:53
Speaker 1: favorite talks at that meeting was given by a guy
3:56
Speaker 1: who came from a university he named after himself, where
3:59
Speaker 1: he was the honor or a chair named after himself,
4:01
Speaker 1: and he had given himself the prize named after himself.
4:06
Speaker 1: Isn't that what all universities are anyways? I mean, Stanford
4:09
Speaker 1: just made one and named it after himself. But is
4:12
Speaker 1: that really a session? It's called the crackpot session. Or
4:14
Speaker 1: is that just what you're calling those people? That's what
4:17
Speaker 1: I call it, But I think officially on the schedule,
4:19
Speaker 1: it's like miscellanea. On the schedule, it's Daniel's colleagues. It's
4:25
Speaker 1: definitely one of the funnest sessions to go to. It's
4:27
Speaker 1: a lot of creative ideas there. Yeah, well some of
4:29
Speaker 1: the ideas might sound crack, but but but sometimes you know,
4:31
Speaker 1: looking at things in a different way can be the
4:33
Speaker 1: right way to kind of push science forward. Right, absolutely,
4:36
Speaker 1: that's right. We need creativity and a basic element of
4:39
Speaker 1: doing science is thinking about new ways to do things,
4:42
Speaker 1: new ways to think about the universe, new ways to
4:44
Speaker 1: tackle problems. Yeah, sometimes the biggest discoveries in science come
4:48
Speaker 1: when people think about new ways or new descriptions of
4:51
Speaker 1: what they already know or they think they know. Yeah,
4:54
Speaker 1: And there are lots of times in the history of
4:56
Speaker 1: science when people are struggling with something. Things seem confused, using,
5:00
Speaker 1: or complicated or getting really elaborate, and then somebody has
5:03
Speaker 1: a new idea and all of a sudden it seems
5:05
Speaker 1: simple again, like when people were trying to understand the
5:07
Speaker 1: motion of the planets and putting the Earth at the
5:10
Speaker 1: center of the solar system required all these complicated shenanigans,
5:14
Speaker 1: you know, loops within loops within loops. But if you
5:17
Speaker 1: just put the Sun at the center of the solar system, boom,
5:19
Speaker 1: you had a much simpler mathematical explanation for what you
5:23
Speaker 1: were seeing. So there are these moments when just another
5:26
Speaker 1: way of looking at things, a different way of doing calculations,
5:28
Speaker 1: a different starting point, can really simplify what was once
5:33
Speaker 1: very difficult. I thought you were going to say, it's
5:35
Speaker 1: simpler if you just give up or change careers or
5:38
Speaker 1: become a philosopher, then you're just run into new kinds
5:41
Speaker 1: of problems. Man, you can't run away from your problems.
5:45
Speaker 1: New kind of financial problems usually be switched to philosophy.
5:48
Speaker 1: But it is interesting how in science sometimes you do
5:51
Speaker 1: sort of need that kind of change in perspective and
5:53
Speaker 1: then it all sort of makes sense. I imagine the
5:55
Speaker 1: quantum revolution was kind of like that too. Absolutely that
5:58
Speaker 1: required a complete evolution in our very understanding of the
6:02
Speaker 1: nature of the universe at its most microscopic. But as
6:06
Speaker 1: soon as Plunk and Einstein thought about light as made
6:09
Speaker 1: out of these little quantized packets instead of just like
6:12
Speaker 1: classical waves, then all of a sudden, the photoelectric effect
6:16
Speaker 1: made a lot of sense, and black body radiation suddenly
6:20
Speaker 1: didn't have a catastrophe in it. So all sorts of
6:22
Speaker 1: problems that were plaguing people for a long time just
6:24
Speaker 1: sort of went away as soon as you took a
6:26
Speaker 1: new approach at things. And you can sometimes get the
6:29
Speaker 1: sense of this yourself. If you're ever doing a calculation
6:32
Speaker 1: and things are just like going horribly wrong, then maybe
6:35
Speaker 1: you've made a little mistake, or maybe you sort of
6:37
Speaker 1: like tried it the wrong way. You know, you're using
6:39
Speaker 1: the wrong mathematical tool, or you're thinking about in an
6:42
Speaker 1: overly complicated way. There's just sometimes a simpler solution at hand. Yeah,
6:46
Speaker 1: and so I guess scientists are always looking for better
6:49
Speaker 1: ways of looking at things. I guess you're always trying
6:50
Speaker 1: to simplify your life, right, Nobody wants to complicated life. Yeah,
6:54
Speaker 1: that's right. We have a certain set of mathematical tools
6:56
Speaker 1: that we can use to do calculations, to try to
6:58
Speaker 1: figure stuff out, to answer questions that we have, and
7:01
Speaker 1: sometimes they work beautifully and it's just like a few
7:03
Speaker 1: lines on a page and boom you get an answer,
7:05
Speaker 1: and then you can test it with the experiment and
7:07
Speaker 1: you can learn something about the universe. Sometimes they get
7:09
Speaker 1: bogged down and you end up with like pages upon
7:12
Speaker 1: pages of calculations or thousands upon thousands of lines of
7:15
Speaker 1: computer programs just to get a sample answer. And that
7:18
Speaker 1: makes you wonder, like are we going in the right direction,
7:21
Speaker 1: or maybe we need a new kind of tool you know,
7:24
Speaker 1: should you be trying to describe the motion of a
7:26
Speaker 1: baseball by thinking about all the tiny little particles inside
7:29
Speaker 1: of it? Or is there a simpler equation that describes
7:32
Speaker 1: the trajectory of an object under free fall? Right? Right?
7:35
Speaker 1: The old like goes up, must come down wall, and
7:37
Speaker 1: it's an incredible thing in our universe, right that, Sometimes
7:41
Speaker 1: a new approach can make things much easier. You know,
7:44
Speaker 1: you can solve almost any problem in lots of different ways.
7:47
Speaker 1: Students of physics know this. If you're tackling a homework problem,
7:50
Speaker 1: you can start it in some way that gives you
7:52
Speaker 1: pages of equations, and other ways you can find the
7:54
Speaker 1: answer in just three lines. So we have lots of
7:57
Speaker 1: different mathematical toolkits, and some of them are appropriate are
8:00
Speaker 1: some problems, but not so appropriate for others. Right, And
8:03
Speaker 1: that's kind of where particle physics is these days, right,
8:05
Speaker 1: I mean sometimes you need supercomputers, right to sort of
8:08
Speaker 1: predict what's going to happen at some particle collisions. Yeah,
8:11
Speaker 1: we use these little cartoons, these finming diagrams to describe
8:14
Speaker 1: what we can happens when particles collide. But in complicated
8:17
Speaker 1: situations sometimes you need thousands or millions of these diagrams
8:21
Speaker 1: that lead to huge calculations that are really hard to do.
8:24
Speaker 1: We can't do them by hand anymore. We have to
8:26
Speaker 1: use supercomputers. And that makes people wonder like, maybe this
8:29
Speaker 1: isn't the way the universe is doing this calculation. Maybe
8:32
Speaker 1: instead of adding up all these time a little bits,
8:34
Speaker 1: we need to step back and get a more global view.
8:36
Speaker 1: Maybe there's a simpler approach. Yeah, maybe there's a simpler
8:39
Speaker 1: way to do Daniel's job. And so to the on
8:42
Speaker 1: the program, we'll be asking the question, what is an
8:50
Speaker 1: AMPLU two hedrawn? Well, that's a hard word to say.
8:54
Speaker 1: How many syllables is that? Like? Ten? It's like the
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Speaker 1: most complicated word for an idea that's supposed to simplify things,
9:01
Speaker 1: all right, I want to just call it a d
9:05
Speaker 1: I don't know if somebody need to call you up
9:06
Speaker 1: and ask you for advice about how to name this thing. Obviously, Yeah,
9:09
Speaker 1: I do have a PhD and naming things in physics
9:12
Speaker 1: by now. It's given to me by Daniel Whites in university.
9:16
Speaker 1: That's right, philosophy of naming things two pH pH PhD.
9:23
Speaker 1: But this is a really fun new idea in physical
9:26
Speaker 1: It's sort of a glimmer of an idea. It's like
9:29
Speaker 1: a potential new way forward that might make things that
9:32
Speaker 1: once we're very, very complicated, nearly impossible, suddenly just snap
9:37
Speaker 1: into focus. And it involves a lot of geometry and
9:41
Speaker 1: possibly quantum field theory. So we're gonna have a lot
9:43
Speaker 1: of fun here on this audio podcast. Exactly what's better
9:46
Speaker 1: for talking about geometry than an audio format. It's like
9:52
Speaker 1: talking about architecture or describing geometry. It's the same concept.
9:56
Speaker 1: Are you saying there aren't architecture podcasts. I'm sure there are.
10:00
Speaker 1: I'm sure they'll go as well as today. But it
10:03
Speaker 1: is a long word, and it's also an interesting word,
10:05
Speaker 1: maybe one that a lot of people haven't heard before.
10:07
Speaker 1: So as usually, we were wondering how many out there
10:10
Speaker 1: had heard of this concept. So thank you very much
10:12
Speaker 1: to everybody who volunteers to answer these questions without a
10:15
Speaker 1: chance to prepare at all. It's very valuable for us
10:18
Speaker 1: to hear what you guys are thinking about, and also
10:20
Speaker 1: very helpful for other listeners to know whether or not
10:23
Speaker 1: this is something other people have heard about. So thanks
10:26
Speaker 1: very much for participating, and if you would like to
10:28
Speaker 1: hear your voice on the podcast, please don't be shy
10:31
Speaker 1: right to us. Two questions at Daniel and Jorge dot com.
10:34
Speaker 1: So Dannon went out there into the wilds of the
10:36
Speaker 1: internet to ask people what do you think and amply
10:39
Speaker 1: to hedron is or is pronounced? Here's what people have
10:44
Speaker 1: to say. It sounds like a shape, I guess, but
10:47
Speaker 1: a made up one. So now it's the shape the
10:49
Speaker 1: sound waves make when my husband plays guitar out of
10:51
Speaker 1: a two vamp. What is I've never even seen this
10:54
Speaker 1: word before and full of pedro uh uh amplute, hedron,
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Speaker 1: amplitude something. Is it some kind of weird amplitude particle?
11:07
Speaker 1: That's that's mine. That's my guess. I can even pronounce that,
11:11
Speaker 1: but um, you know again the word head drawn. I'm
11:15
Speaker 1: guessing it has something to do with the shape that
11:17
Speaker 1: has multiple sides. An amplitude hedron is a quasi three
11:23
Speaker 1: dimensional shape where all of the faces, instead of being
11:27
Speaker 1: two dimensional surfaces, all right, forces with varying amplitudes. If
11:34
Speaker 1: I look at the two base words amplitude heedron, I
11:37
Speaker 1: know a heedron is a geometric shape with a number
11:41
Speaker 1: of facets or faces um. Amplitude looks like the word amplitude,
11:46
Speaker 1: meaning strength or degree um. Putting their two words together, However,
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Speaker 1: I simply have no idea. It sounds like a geometric shape,
11:55
Speaker 1: and I would say it has to do with the
11:58
Speaker 1: amplitude of something I couldn't tell. Unfortunately, I don't know
12:04
Speaker 1: what it is, but it sounds cool, and I would
12:09
Speaker 1: really know, I really really want to know what it is.
12:13
Speaker 1: I think a head drown is a kind of particle,
12:16
Speaker 1: so it must have maybe something to do with the
12:21
Speaker 1: amplitude of a particle. That's my best guest. And note,
12:25
Speaker 1: of course that I didn't pronounce it for these people, right,
12:28
Speaker 1: I sent them an email, so they had to deduce
12:30
Speaker 1: for themselves how to say this word. Oh man, it
12:33
Speaker 1: was like a double quiz. Can you guess what it
12:37
Speaker 1: is and how it's pronounce or even spelled? Yeah, and
12:39
Speaker 1: a lot of people saw he drawn and thought about
12:42
Speaker 1: had drawn, because of course we're talking about had drawns
12:45
Speaker 1: all the time on this podcast, so that's a reasonable misunderstanding,
12:50
Speaker 1: right right. It sounds like you named the hadron a
12:53
Speaker 1: little bit confusing there. Do you think we should have
12:55
Speaker 1: had a large he drawn collider? I think that's how
12:58
Speaker 1: a lot of people pronounce it. Anyways, you might as well.
13:01
Speaker 1: Today we are smashing polygons and triangles, smashing geometry. But
13:06
Speaker 1: it is sounds like a lot of people have heard
13:07
Speaker 1: of the word before, although they are a lot of
13:09
Speaker 1: people sort have caught on that it has maybe something
13:11
Speaker 1: to do with amplitude. Yeah, there's some intuition here that
13:13
Speaker 1: the basic ideas involved our amplitudes and geometry, and in
13:18
Speaker 1: fact that's the core idea. It's a way to try
13:20
Speaker 1: to use geometry to help calculate particle amplitudes like how
13:25
Speaker 1: wide they are or what sized pants they were? Is
13:28
Speaker 1: that what you mean? Well, particle amplitudes are what tell
13:30
Speaker 1: us what's likely to happen when you smash two particles together.
13:34
Speaker 1: To say, for example, you throw an electron at a positron,
13:38
Speaker 1: and you wonder like what's going to happen Each possible
13:41
Speaker 1: outcome has an amplitude. One possible outcome is that they
13:44
Speaker 1: bounce off each other and go back the other direction.
13:46
Speaker 1: Another possible outcome is that they annihilate and turn into
13:49
Speaker 1: a photon, which then turns into something else. There's a
13:52
Speaker 1: whole list of possible outcomes from quantum mechanics and quantum mechanics.
13:55
Speaker 1: A scigns each of these things an amplitude. That's actually
13:58
Speaker 1: what you get out of the shorting or equation, and
14:00
Speaker 1: the larger the amplitude, the more likely it is for
14:03
Speaker 1: that outcome to happen. So it's sort of like a
14:06
Speaker 1: way of calculating the probabilities for an outcome of a
14:09
Speaker 1: particle collision. As a shorthand is the amplitude, because that's
14:12
Speaker 1: what comes from the wave function, right, Because that is
14:15
Speaker 1: the best possible name you could give to the probability
14:19
Speaker 1: of an outcome, is the amplitude, which normally means the
14:23
Speaker 1: width of something right right, Well, in this case, it's
14:25
Speaker 1: talking about the height of the wave function. So if
14:27
Speaker 1: you solve the Shorteninger equation for some situation, you get
14:30
Speaker 1: the wave function, and the amplitude of that wave function
14:33
Speaker 1: is what we're talking about here. To get the probability,
14:36
Speaker 1: you take the amplitude square, you take it to magnitude,
14:38
Speaker 1: because the amplitude can be a complex number, though the
14:41
Speaker 1: probability is one step beyond the amplitude, and the amplitude
14:44
Speaker 1: does in fact talk about sort of the height of
14:47
Speaker 1: the wave function. Well, this might get a little bit
14:49
Speaker 1: abstract and complicated, so maybe let's start with the basics
14:52
Speaker 1: and start with the question we're asking, which is what
14:55
Speaker 1: is an amplitue hedrawn? So how would you describe what
14:58
Speaker 1: this thing is? So an amplitude heedraw and isn't like
15:00
Speaker 1: an abstract geometric object. Imagine some high dimensional space, you know,
15:05
Speaker 1: not just two dimensions or three dimensions, but like ten
15:08
Speaker 1: or eleven dimensions. Let's not let's no, that doesn't help
15:12
Speaker 1: me much. Let's start with just three dimensions. Like what
15:15
Speaker 1: would an amplitudehedron look like or is or would be
15:18
Speaker 1: in just like three dimensional space? So an amplitude hedron
15:21
Speaker 1: in three dimensional space is just a polygon, right, Just
15:25
Speaker 1: it's like a bunch of points with lines in between them.
15:27
Speaker 1: So it's a shape like a triangle or a pyramid.
15:30
Speaker 1: Triangle could be one, a tetrahedron could be one. You know,
15:33
Speaker 1: it depends on what kind of thing you're trying to calculate,
15:36
Speaker 1: you know, a decahedron, All these kind of things could
15:38
Speaker 1: be amplitude heedrons. The point is it's a geometric object.
15:42
Speaker 1: So it's like a shape like just the a connection
15:45
Speaker 1: of dots in space, kind of like if you did
15:47
Speaker 1: a connected dots and three dimensional space, you would get
15:50
Speaker 1: some kind of weird polygon, you know, geometric shape exactly.
15:55
Speaker 1: So put a cloud of dots in space and now
15:58
Speaker 1: connect them with lines and then put planes between those lines.
16:01
Speaker 1: You have like a shape, like a three D shape, right,
16:04
Speaker 1: like a surface, you know, imagined like a mesh of
16:06
Speaker 1: points that make a surface. And so you have this object.
16:09
Speaker 1: It's just like a three D object in space. And
16:12
Speaker 1: it turns out that there's a connection between the geometry
16:16
Speaker 1: of this object, meaning like how you calculate its volume
16:19
Speaker 1: and things we want to know about particles. So if
16:23
Speaker 1: the points you created represent the particles that you're interested in,
16:26
Speaker 1: then the volume of this object that that's created helps
16:29
Speaker 1: you calculate what's going to happen to those particles when
16:31
Speaker 1: they collide. So that's the amplitu hege on. It's like
16:34
Speaker 1: a geometric object that helps you calculate what's going to
16:37
Speaker 1: happen to particles when they smash together. Right, But the
16:39
Speaker 1: points in the geometric shape are not the actual particles, right,
16:43
Speaker 1: They just represent points in some space that you're doing
16:47
Speaker 1: your math in for the particles, Like, they're not the
16:49
Speaker 1: actual particles floating in space. They're not the actual particles
16:52
Speaker 1: floating in space. You know, they're like possibilities. They are
16:54
Speaker 1: things that you're connecting together in some space that you're
16:57
Speaker 1: doing your meth in, right exactly. And often we create
17:01
Speaker 1: abstract spaces to do calculations, Like a lot of normal
17:05
Speaker 1: vanilla quantum mechanics is in complex space, meaning you have
17:09
Speaker 1: real numbers and imaginary numbers, and you have to keep
17:12
Speaker 1: track of both of them. Does it actually exist in reality?
17:15
Speaker 1: Like the complex numbers are imaginary, right, they're not real,
17:19
Speaker 1: but we keep them around to do these calculations. So
17:21
Speaker 1: we do this all the time in physics. We create
17:23
Speaker 1: an abstract space, something which isn't real, but where mathematical
17:27
Speaker 1: objects live, so we can do calculations in that space
17:30
Speaker 1: that give us answers about what happens in our universe. Right,
17:33
Speaker 1: Like a particle in space might have a place and
17:36
Speaker 1: a velocity, but maybe you're doing your math in some
17:39
Speaker 1: other properties of that particle or some other kind of
17:43
Speaker 1: space that describes the particle. Yeah, like the wave function, right,
17:46
Speaker 1: where is the wave function for the particle. It's in
17:49
Speaker 1: some abstract space because it's gonna have weird values like
17:52
Speaker 1: two plus five I. It doesn't exist in the universe.
17:55
Speaker 1: You can't look at it and say this is where
17:56
Speaker 1: the wave function is. It's right here, doesn't have a location,
18:00
Speaker 1: exists in some sort of abstract space. Okay, So an
18:03
Speaker 1: amplitude heedron is like a geometric shape in some kind
18:06
Speaker 1: of space that you're doing your meth in that somehow
18:09
Speaker 1: represents particles. And I think you're saying the d the
18:12
Speaker 1: idea is that maybe this shape in this space of
18:15
Speaker 1: math that you're doing could somehow make calculating things about
18:18
Speaker 1: particles easier. Yeah. The thing that we want to calculate
18:21
Speaker 1: is what happens when we run our collider, when we
18:23
Speaker 1: smash particles together. What happens We want to be able
18:27
Speaker 1: to calculate that because we're gonna do those experiments and
18:29
Speaker 1: we need to be able to predict what's going to
18:31
Speaker 1: happen and compare our predictions to the experiment, and so
18:35
Speaker 1: these amplitude heedrons make those calculations much much simpler. Those
18:39
Speaker 1: calculations which turn out to be really complicated and burden
18:42
Speaker 1: some in a lot of basic situations, can become really
18:45
Speaker 1: simple if you use the amplitude heedron. Well, maybe step
18:48
Speaker 1: us through this. Why is it complicated? I mean, you're
18:50
Speaker 1: just smashing like two protons. Why is that hard to
18:52
Speaker 1: figure out what's gonna happen. It's hard to figure out
18:54
Speaker 1: what's going to happen because lots of different things can happen.
18:57
Speaker 1: Say you're smashing two particles together. Let's not use photons
19:00
Speaker 1: from the moment, because they're actually even more complicated because
19:03
Speaker 1: they're not actually fundamental particles, their bags of particles. So
19:06
Speaker 1: let's say you're smashing together to fundamental particles like an
19:09
Speaker 1: electron and a positron. So what can happen? While they
19:12
Speaker 1: can turn into a photon, and that photon can turn
19:15
Speaker 1: into another pair of particles. But along the way that
19:17
Speaker 1: photon can do other things. It can create other virtual
19:20
Speaker 1: particles which then spawn other photons, or before the collision happens,
19:24
Speaker 1: you know, one of the electrons could radiate an extra photon.
19:27
Speaker 1: There's all sorts of different things that can happen, and
19:30
Speaker 1: we can calculate that. We calculate each of those things
19:32
Speaker 1: by drawing a little fine min diagram that describes what's
19:36
Speaker 1: going to happen in that situation. But to figure out
19:38
Speaker 1: what is the overall chances for something that happen, you
19:40
Speaker 1: have to add up all the different possibilities. You have
19:43
Speaker 1: to account for all the different ways that each thing
19:45
Speaker 1: can happen. So if you want to know, for example,
19:47
Speaker 1: all right, what's the probability that if I smash my
19:50
Speaker 1: electron and positron together, I'm going to get a photon
19:54
Speaker 1: of this energy? Get to figure out all the different
19:56
Speaker 1: ways that can happen and add them all up, and
19:59
Speaker 1: technically there's an infinite number of ways that that can happen.
20:03
Speaker 1: Do you end up adding up lots of little pieces
20:05
Speaker 1: to try to get this answer, So it becomes really
20:08
Speaker 1: complicated if you want precise answers about even pretty basic interactions, right,
20:13
Speaker 1: because I think maybe one thing people don't understand or
20:15
Speaker 1: know about particle physics is that it's not like you
20:17
Speaker 1: just smash particles and then you see what comes out.
20:20
Speaker 1: I mean, you do see what comes out. But sometimes
20:22
Speaker 1: you don't really know what actually happened even though you
20:24
Speaker 1: have the bits of the remaining bits that that came out.
20:27
Speaker 1: Why could have happened between the actual smashing and the
20:30
Speaker 1: debris that you get afterwards. There can be a lot
20:33
Speaker 1: of possibilities there, Right, Yeah, we don't see the actual collision.
20:36
Speaker 1: We can't trace all of the details. So if all
20:39
Speaker 1: you see is what came out, like you put an
20:40
Speaker 1: electron opositron in and out came a muan and an antimuan,
20:45
Speaker 1: you don't know exactly what happened in the intermediate step.
20:48
Speaker 1: There's lots of different ways to go from your initial
20:51
Speaker 1: step electron apositron to your final outcome. And in order
20:55
Speaker 1: to calculate the chances of seeing that, in order to
20:57
Speaker 1: figure out how often you expect to see that outcome,
21:01
Speaker 1: you need to account for all the different ways that
21:03
Speaker 1: it can happen, and so you have to add up
21:05
Speaker 1: all those possibilities, and that can become really complicated. Right, Like,
21:09
Speaker 1: maybe can you step us through an example like the
21:11
Speaker 1: Higgs boson? Right, Like, you don't actually see or catch
21:14
Speaker 1: a Higgs boson when you smash particles together, but you
21:17
Speaker 1: can sort of figure out that it was likely that
21:19
Speaker 1: there was a Higgs boson somewhere in the middle. Using
21:22
Speaker 1: all of the possible ways or knowing all the possible
21:25
Speaker 1: things that could have happened, Yeah, we can talk about
21:27
Speaker 1: the Higgs boson. For example, we discovered the Higgs just
21:29
Speaker 1: about ten years ago, actually on this day, by seeing
21:32
Speaker 1: how it turned into two photons. So we don't see
21:35
Speaker 1: the Higgs boson itself, We see two photons that come
21:38
Speaker 1: out from the detector. We take those two photons and
21:40
Speaker 1: we add them together and we see that they probably
21:42
Speaker 1: came from a particle at about a mass of a
21:44
Speaker 1: hundred and twenty five GV. But there's lots of ways
21:47
Speaker 1: for that Higgs boson to be created. You can have
21:50
Speaker 1: that Higgs boson created because two quarks from the protons
21:53
Speaker 1: fused together. You can have that Higgs boson be created
21:56
Speaker 1: because a couple of gluons fused together. And before the
21:59
Speaker 1: blue ones fused together. They can do all sorts of
22:01
Speaker 1: really complicated things like turn into top corks or turn
22:04
Speaker 1: into other corks. So if you want to write down
22:06
Speaker 1: the ways that this can happen, you start to get
22:09
Speaker 1: a pretty long list of ways that can explain just
22:11
Speaker 1: this pretty simple thing of producing the Higgs boson and
22:14
Speaker 1: seeing it turn into two photons. Right, it's like you
22:17
Speaker 1: gotta know all of the possible things that could happen
22:19
Speaker 1: so you can duce would actually happen. Yeah, and even
22:22
Speaker 1: more important, you have to understand the other things that
22:25
Speaker 1: can come out that word from a Higgs boson, Like
22:27
Speaker 1: it's possible to produce two photons without involving a Higgs boson.
22:31
Speaker 1: There's lots of ways to do that. In fact that
22:33
Speaker 1: that's much more common. So if you're gonna say I've
22:36
Speaker 1: discovered the Higgs boson, you need to understand all those
22:38
Speaker 1: collisions that produced Higgs boson looking like things that weren't
22:42
Speaker 1: actually Higgs boson. So we need to understand, like the background,
22:45
Speaker 1: how often do we expect to see these kinds of
22:47
Speaker 1: things if there wasn't a Higgs boson. Those calculations are
22:50
Speaker 1: even more important if we're going to claim discovery of
22:53
Speaker 1: a new particle. We need to understand how often we'd
22:56
Speaker 1: see this kind of signature without the Higgs, and those
22:59
Speaker 1: calculations and require lots and lots of these Fineman diagrams
23:02
Speaker 1: to add up, because the Fineman diagrams can only describe
23:04
Speaker 1: like the most basic interaction. One particle comes in, another
23:07
Speaker 1: one comes in, and they do something. But most things
23:10
Speaker 1: that happen in nature require lots of these things. It's
23:13
Speaker 1: like putting together legos to build something complicated, right, Anything
23:16
Speaker 1: that's interesting or complicated requires lots of these pieces to
23:20
Speaker 1: come together, right, Because in a way, you're sort of
23:22
Speaker 1: like you're just kind of guessing that the Higgs boson
23:24
Speaker 1: was there, right, But to make it a good guest,
23:27
Speaker 1: to make sure that it's the best guest possible, you
23:29
Speaker 1: kind of have to rule out or take into account
23:31
Speaker 1: everything else it could possibly happen. And that's the complicated
23:34
Speaker 1: part to caltily. Right. Yeah, you could call it a guest,
23:37
Speaker 1: or you could say, you know, it's a statistical statement.
23:39
Speaker 1: We never know anything for sure, as we were saying
23:41
Speaker 1: philosophically earlier, but we can make a statistical statement about
23:44
Speaker 1: the probability of having seen this kind of data if
23:47
Speaker 1: there wasn't a Higgs boson, and we claim discovery of
23:50
Speaker 1: the Higgs, when that probability is very very small, and
23:52
Speaker 1: we're very confident that if the Higgs wasn't there, it's
23:56
Speaker 1: very unlikely that we would have seen this peak in
23:58
Speaker 1: our data, and so you're right, we need to calculate
24:01
Speaker 1: that very precisely. And to do that, we need to
24:03
Speaker 1: understand exactly what we expect to see without the Higgs boson.
24:06
Speaker 1: So seeing all those collisions that would produce things that
24:09
Speaker 1: look sort of similar to the Higgs, we need to
24:11
Speaker 1: understand that really, really well. And to do those calculations
24:15
Speaker 1: is hard, and it gets harder and harder as our
24:18
Speaker 1: energy goes up and as the number of particles involved
24:20
Speaker 1: in the collision goes up, and so it becomes really important. Okay, cool,
24:24
Speaker 1: So let's dig into what makes it such a hard
24:26
Speaker 1: calculation and how this amplitude hedron could maybe simplified. But first,
24:31
Speaker 1: let's take a quick break. All right, we're talking about
24:46
Speaker 1: an amplate two heedron, which I'm guessing, or at least
24:49
Speaker 1: I'm making a statistical statement that, Um, it's a complicated word.
24:55
Speaker 1: It's a complicated word for sort of a beautiful and
24:57
Speaker 1: simplistic geometric idea. Wish they would have chosen a beautiful
25:01
Speaker 1: and simplistic geometric word for it. Yeah, let's try it, Dannie,
25:07
Speaker 1: what would you have called it? That is not my
25:10
Speaker 1: area of skills. How about just an ahedron that sort
25:14
Speaker 1: of sounds like an antihedron, like you collid to heedron
25:17
Speaker 1: and ahedron together and boom. About just a geometric shape,
25:22
Speaker 1: a symmetron or something that but that probably exists already.
25:25
Speaker 1: There you go, Yeah, it's good transformers. But I guess
25:28
Speaker 1: the basic idea is that making predictions in particle collisions
25:32
Speaker 1: is really hard and you need a lot of masks.
25:34
Speaker 1: Nowadays you need supercomputers, and people argue for years over
25:39
Speaker 1: whether you're accurate to the right decimal place, and so
25:41
Speaker 1: it's kind of complicated. And maybe step us through Daniel,
25:43
Speaker 1: then why is it so complicated to calculate everything that
25:46
Speaker 1: can happen in a particle collision? It's complicated just because
25:49
Speaker 1: there are so many different ways that you have to
25:52
Speaker 1: account for, you know. I think a good analogy is
25:54
Speaker 1: thinking about, like how our comedies figured out how to
25:58
Speaker 1: calculate the volume of a really complicated shape, right. I
26:01
Speaker 1: think the story is he wanted to be able to
26:02
Speaker 1: figure out what the volume was of the king's crown
26:05
Speaker 1: so we could figure out what the mass and the
26:07
Speaker 1: density was to see if it was real gold. But
26:09
Speaker 1: it's hard to do calculations with weird shapes. You know,
26:11
Speaker 1: it has like curved and triangles, and how could you
26:14
Speaker 1: do this? Well, one thing you could do is like
26:16
Speaker 1: laboriously measure every tiny little shape of the crown and
26:21
Speaker 1: think about it as a little triangles and squares and
26:23
Speaker 1: add them all up. It would take you a long
26:25
Speaker 1: long time, but in principle, you could add up the
26:27
Speaker 1: volume of the crown. The other way to do it
26:29
Speaker 1: is just like sink it in a bathtub of water
26:32
Speaker 1: and see how much the water goes up. And that
26:34
Speaker 1: gives you the same answer because the water like feels
26:36
Speaker 1: in all the cracks and so like, that's an example
26:39
Speaker 1: of how you can use the universe. Use this trick
26:41
Speaker 1: in the universe to make what seemed to be like
26:43
Speaker 1: a hard calculation much simpler. And so in particle physics,
26:46
Speaker 1: it's sort of the same story. Figure out like what
26:49
Speaker 1: happens when two gluons smashed together. You have to think
26:52
Speaker 1: about all the different ways that they can smash together,
26:55
Speaker 1: in all the different ways that they can produce results,
26:57
Speaker 1: And so it's adding up lots and lots and lots
26:59
Speaker 1: of little bits. Each little bit is not hard. It's
27:01
Speaker 1: like calculating the volume of a cube is not hard.
27:04
Speaker 1: Each individual one is not hard. But when you have
27:06
Speaker 1: billions of them and you have to multiply them against
27:09
Speaker 1: each other to get trillions of diagrams, then it becomes
27:12
Speaker 1: really difficult to do these calculations right. And I think
27:15
Speaker 1: part of what makes these calculations difficult is that they're
27:17
Speaker 1: kind of recursive, or they're kind of like almost like
27:20
Speaker 1: a fractal, Like two particles can smash and they turn
27:23
Speaker 1: into one thing, but then that thing could also turn
27:25
Speaker 1: into something else in the meantime, But then the two
27:27
Speaker 1: things that that thing turned into could also turn into
27:30
Speaker 1: something else, and then it can actually loop back and
27:31
Speaker 1: turn into the original particles, and so you get these
27:34
Speaker 1: kind of infinite loops of things that could happen during
27:37
Speaker 1: that closion. Yeah, the loops are especially tricky because they
27:40
Speaker 1: don't involve anything that you see and imagine, for example,
27:43
Speaker 1: two particles coming in and two particles coming out. You
27:45
Speaker 1: might imagine the simplest possible thing, which is just like
27:47
Speaker 1: put too fine and diagrams together and you get that
27:50
Speaker 1: kind of interaction. But you can also add a loop
27:52
Speaker 1: where like in between some new particles created and it
27:55
Speaker 1: only exists briefly and then it's reabsorbed, right, So it
27:58
Speaker 1: creates this like loop in the Fineman diagram, which otherwise
28:01
Speaker 1: just looks like a tree structure. And those loops require
28:04
Speaker 1: integrals because you have to sum overall that if impossible
28:07
Speaker 1: momentum that loop could have. And then as you say,
28:09
Speaker 1: you could have interactions involved two of those loops, or
28:12
Speaker 1: three of those loops, or five and twenty seven of
28:15
Speaker 1: those loops. So it gets to be really laborious to
28:17
Speaker 1: get an exact answer. In fact, to get an exact answer,
28:20
Speaker 1: you have to include an infinite number of diagrams. So
28:23
Speaker 1: we never actually do that, right. I wonder if it's
28:25
Speaker 1: kind of like playing chess, you know, like to know
28:27
Speaker 1: if a good move is the right move, you would
28:29
Speaker 1: have to kind of calculate all of the possible things
28:31
Speaker 1: that could happen after you make your move, right, And
28:34
Speaker 1: so you get into these branching kind of scenarios where
28:37
Speaker 1: there's like an infinite number of possibilities and you only
28:40
Speaker 1: really know if this one is the right move if
28:42
Speaker 1: it gives you a winning strategy in all of them. Yeah,
28:45
Speaker 1: and there's lots of different ways to get to a win, right,
28:47
Speaker 1: and so in a similar way, you need to think
28:49
Speaker 1: about all the possible intermediate things that could happen from
28:52
Speaker 1: here to where you want to go, Like is it
28:54
Speaker 1: possible from my opponent to derailist strategy? So you have
28:56
Speaker 1: to think about lots of different possibilities. Absolutely, So if
28:59
Speaker 1: you could come up with a way to very simply
29:02
Speaker 1: calculate the probability of winning or losing when you make
29:04
Speaker 1: a move, that would be tremendously helpful in chess. Right,
29:08
Speaker 1: it would make chess a very simple game. That's why
29:10
Speaker 1: chess is hard, because it's difficult to calculate these possible
29:13
Speaker 1: outcomes for every given move, Right, Like, maybe there's a
29:16
Speaker 1: move where you can just stand up and punch your
29:18
Speaker 1: opponent and win, and then that's a much simpler way
29:21
Speaker 1: to solve the whole scenario. Right, is that still chess?
29:24
Speaker 1: Though I'm not. That's m M a chess. There's this
29:27
Speaker 1: moment in particle physics a couple of decades ago when
29:30
Speaker 1: folks were working on one of these calculations involved like
29:33
Speaker 1: billions of terms, billions of terms to the billions. Wait
29:37
Speaker 1: is it infinite actually? And so billions billion is actually
29:40
Speaker 1: just an approximation or is is billion, like all of it.
29:43
Speaker 1: The full calculation would be an infinite number, but to
29:46
Speaker 1: get a reasonably accurate calculation, they needed to use about
29:48
Speaker 1: a billion terms. Yeah yeah, and each term is like
29:51
Speaker 1: a possibility of what can happen during a collision, right exactly.
29:54
Speaker 1: To calculate these probabilities, you have to take these things
29:56
Speaker 1: and square them, which means you get all these cross terms.
29:59
Speaker 1: So the number of terms just getting really really large.
30:01
Speaker 1: But these guys were working really hard and they took
30:03
Speaker 1: these billion terms. They're really good with symbols, right there
30:07
Speaker 1: is how this special skill like know how to manipulate
30:09
Speaker 1: symbols on the page. And they were able through like
30:12
Speaker 1: just sweat and blood and fought to reduce this thing
30:16
Speaker 1: down to a nine page formula, which means like it
30:19
Speaker 1: took nine pages just to write down the expression, right,
30:22
Speaker 1: the algorithm expression for the answer to this thing. They
30:25
Speaker 1: reduced her from a billion terms down to a nine
30:27
Speaker 1: page formula, which is already really impressive. Well that depends
30:31
Speaker 1: that did they use both sides and what size font
30:33
Speaker 1: did they use? Like, if he's a big enough font,
30:36
Speaker 1: anything can be a nonpage formula. You know, this is
30:39
Speaker 1: standard ltech on an eight and a half by eleven,
30:41
Speaker 1: or maybe it was a four. It's one of those
30:43
Speaker 1: European But the really cool thing about it was not
30:46
Speaker 1: that they got it down to a nine page formula,
30:48
Speaker 1: which is totally unwieldy, but that then they took an
30:50
Speaker 1: intuitive guess. They're like, you know what, I think that
30:53
Speaker 1: this probably could be reduced to a simple single expression,
30:56
Speaker 1: like a very small short expression but just a few
30:59
Speaker 1: variables in they that gives you the same answer. They
31:01
Speaker 1: made this guess based on their experience because they're like
31:04
Speaker 1: familiar with these kinds of calculations and they've seen things before,
31:08
Speaker 1: and they said, maybe this is similar to other results
31:10
Speaker 1: we've gotten. Is it possible it just works like this?
31:13
Speaker 1: So they guessed the answer, and then they checked it
31:15
Speaker 1: with a computer. Right, They said, well, does this give
31:17
Speaker 1: the same result in every single case? And the computer
31:19
Speaker 1: said that it was right. So that means that there
31:22
Speaker 1: is an answer, right, There is a simple mathematical expression
31:26
Speaker 1: that gives you the answer you want that doesn't require
31:29
Speaker 1: a billion terms, It doesn't require a nine page formula.
31:32
Speaker 1: It is just a simple thing you can write down
31:34
Speaker 1: in like one second. Well, that's crazy. They just guess
31:37
Speaker 1: what it could be yeah, you know, based on a
31:38
Speaker 1: lot of experience and intuition. They guessed based on other
31:42
Speaker 1: similar things that they had looked at. You know, they've
31:44
Speaker 1: done a lot of these calculations in the past. So
31:47
Speaker 1: there is guessing in physics, there is guessing, absolutely, but
31:49
Speaker 1: then they checked it right. And so to me, that's
31:51
Speaker 1: a lot like this Eureka moment of our comedees right
31:55
Speaker 1: figuring out that there is a simpler way to do
31:57
Speaker 1: this calculation, that you don't have to add up all
32:00
Speaker 1: the little pieces one by one, that there is an expression,
32:03
Speaker 1: it's out there, the math is waiting for us, that
32:05
Speaker 1: there is a simpler way to do these things. That
32:08
Speaker 1: was sort of like a real moment of inspiration for
32:10
Speaker 1: a lot of people in particle physics, because it suggested
32:12
Speaker 1: that if we could somehow figure out a mechanical, like
32:15
Speaker 1: a methodological way to get to that short answer quickly,
32:19
Speaker 1: then we wouldn't have to go through this thousands and
32:21
Speaker 1: billions of terms and nine page calculation and then guessing right.
32:24
Speaker 1: It's not like a robust way to do science, right.
32:27
Speaker 1: It's kind of like the baseball analogy you brought up earlier,
32:29
Speaker 1: like to calculate what happens when you throw a baseball.
32:32
Speaker 1: You could maybe like track each and every single particle
32:35
Speaker 1: in the baseball and how it's interacting with each other
32:38
Speaker 1: and all the air molecules. Or you can just use
32:40
Speaker 1: like a parabola, right, and which also tells you the
32:43
Speaker 1: same and sort of where the baseball is gonna land exactly,
32:46
Speaker 1: because a lot of those little details end up averaging out.
32:49
Speaker 1: You know, maybe you need a billion terms. So maybe
32:51
Speaker 1: those billion terms actually half of them pushed this way
32:53
Speaker 1: and the other half pull the other way, and so
32:55
Speaker 1: they basically just cancel out to something simple. And so
32:59
Speaker 1: the path of a bag bolt isn't governed by what
33:01
Speaker 1: an electron is doing on the bottom half of it.
33:03
Speaker 1: It's this big overall average effect that's actually quite simple.
33:06
Speaker 1: You can describe it with a simple differential equation of
33:09
Speaker 1: F equals m A. So that's what we're looking for
33:11
Speaker 1: in particle physics. We feel like maybe we're just dealing
33:13
Speaker 1: with the microscopic little details when what we really want
33:16
Speaker 1: is the big picture. Right when what you really wanted
33:19
Speaker 1: just to get up and punch the other player, all right,
33:23
Speaker 1: I think you imagine physics conferences are a lot more
33:26
Speaker 1: exciting than they really are. I think if you go
33:29
Speaker 1: around calling people crack pots, you might you might get
33:31
Speaker 1: punched in the face. My favorite part about the crack
33:34
Speaker 1: pot session is sitting there, everybody else in the session
33:37
Speaker 1: totally dismisses the other people. They're like, oh, this is
33:39
Speaker 1: crack pottery. I can believe this guy is even in
33:41
Speaker 1: this session. I can't believe it. None of them take
33:43
Speaker 1: each other seriously, Like, everyone in the crap pot session
33:46
Speaker 1: doesn't know it's called the crap pots. That's what you're saying.
33:49
Speaker 1: That's exactly what I'm saying, even you sitting in the audience. Somehow,
33:53
Speaker 1: that's why I was there because I wanted to see it. Well,
33:55
Speaker 1: so then this is where that concept of an amplitud
33:58
Speaker 1: heedron comes in. Right, It's a possible way to simplify
34:01
Speaker 1: this huge calculation that you right now have to do
34:04
Speaker 1: to figure out what's going to happen at a particle collision. Yeah,
34:07
Speaker 1: it's a new recipe. It says, don't start from the
34:10
Speaker 1: Fynman diagrams at all. Instead, put your points together, draw
34:14
Speaker 1: this geometric object, and the volume of that object, this
34:19
Speaker 1: new weird shape that you've made, is the thing that
34:22
Speaker 1: you want is the amplitude of these particles interacting. So
34:26
Speaker 1: if you can figure out a way to calculate the
34:28
Speaker 1: geometry of this object in a simple way that you
34:31
Speaker 1: can go straight to your answer without adding up all
34:34
Speaker 1: the little bits. There's this theorist at Cambridge I really like,
34:37
Speaker 1: David Skinner, and he said that using Fynman diagrams the
34:40
Speaker 1: old way of doing things is sort of like taking
34:42
Speaker 1: a ming vase and smashing it on the floor and
34:45
Speaker 1: then trying to like, you know, add up what it
34:47
Speaker 1: looked like from those little shards, and so instead just like, hey,
34:51
Speaker 1: enjoy the vase, it's beautiful. Well, maybe step us through
34:53
Speaker 1: a little bit of how this amplitude headron comes up
34:56
Speaker 1: and what the connection is to particle physics, like how
35:00
Speaker 1: do you get an ampletohedron of say, an electron smashing
35:03
Speaker 1: into another electron. So the thing is to avoid thinking
35:06
Speaker 1: about it in terms of space and time the way
35:09
Speaker 1: Fynman diagrams do Flyman diagrams think about these particles. If
35:12
Speaker 1: you know how they look at their these line drawings,
35:14
Speaker 1: they think about particles moving through space, right, so like
35:17
Speaker 1: this one comes close to this one, and then when
35:19
Speaker 1: they get really close they turn into something else, very
35:22
Speaker 1: similar to the way we think of our classical objects, right,
35:25
Speaker 1: like two balls flying through the air and then they
35:26
Speaker 1: bounce off each other. It's sort of relying on our intuition.
35:29
Speaker 1: It helps us keep track of like how things work
35:32
Speaker 1: and how things bounce off each other. Right, sort of
35:34
Speaker 1: like a baseball. We know in our heads that it's
35:36
Speaker 1: made up of little particles, and all the particles are
35:38
Speaker 1: flying together at the same time. But you're saying, don't
35:41
Speaker 1: think about all the particles. Maybe think about the baseball
35:43
Speaker 1: as something else. Yeah, And so instead of thinking about
35:46
Speaker 1: in terms of these Finneman diagrams, Roger Penrose came up
35:49
Speaker 1: with a new kind of diagram that thinks about sort
35:52
Speaker 1: of the relationships between the particles and all the possible
35:55
Speaker 1: relationships they can have. And this is something called a
35:57
Speaker 1: twister diagram E W I, S, T O R. And
36:01
Speaker 1: it helps you think about how the particles can be
36:04
Speaker 1: related to each other. And it doesn't think about the
36:06
Speaker 1: particles in our kind of three D space, you know,
36:10
Speaker 1: like X, Y and Z, the kind of space that
36:12
Speaker 1: we live in. It thinks about them in some sort
36:14
Speaker 1: of like abstract space, like we're talking about before space
36:17
Speaker 1: that doesn't represent our universe and where you are. It's
36:21
Speaker 1: just sort of like a mathematical kind of calculation. How
36:24
Speaker 1: do you get to that space? Like how do you
36:25
Speaker 1: transform a particle which has an x y z and
36:29
Speaker 1: I'm guessing a probability in a way function, how do
36:31
Speaker 1: you get into that new abstract space. So in that
36:34
Speaker 1: abstract space, a particle has a different kind of representation
36:37
Speaker 1: and our kind of space, a particle is like a
36:39
Speaker 1: dot in three dimensional space, but in this twister space.
36:42
Speaker 1: First of all, that space is complex, which means like
36:45
Speaker 1: things in that space can have imaginary values, are not
36:47
Speaker 1: limited to physical numbers, you know, like one, two, three, four,
36:51
Speaker 1: or even like three, one four, one, five, nine, But
36:53
Speaker 1: you can represent them in this kind of space. And
36:55
Speaker 1: this is a kind of mathematical thing physicists do all
36:57
Speaker 1: the time, like invent a whole new space and then
37:00
Speaker 1: and figure out how to represent particles in that space.
37:02
Speaker 1: And if you can invent the space and you can
37:04
Speaker 1: invent the representation, like how you write down particles in
37:07
Speaker 1: that space, then you can play all sorts of new
37:09
Speaker 1: games in that space. And sometimes those new games are useful,
37:13
Speaker 1: sometimes they're just mathematical silliness. And sometimes they're actually very
37:17
Speaker 1: related to what's happening in the real world, and so
37:19
Speaker 1: that's what's going on here. Penrose invented this new space.
37:22
Speaker 1: I wonder if it's a little bit like radar coordinates,
37:24
Speaker 1: Like you can think of as a point as having
37:26
Speaker 1: an x y in two dimensional space, or you can
37:29
Speaker 1: think of it as having it like a direction and
37:31
Speaker 1: a speed or for example m Those are still physical though, right,
37:34
Speaker 1: that's still embedded in the same physical space. But there
37:37
Speaker 1: must be some sort of transformation between the two, right
37:40
Speaker 1: that it does take the physical into these this abstract space,
37:44
Speaker 1: or not at all. There is a transformation in the
37:46
Speaker 1: sense that you're still representing things like particles. But this
37:49
Speaker 1: new space doesn't respect space and time in the same way.
37:52
Speaker 1: Space and time the way we think about them don't
37:55
Speaker 1: exist in this abstract space. And that actually turns out
37:57
Speaker 1: to be something of a breakthrough for this because it
38:00
Speaker 1: helps us think about like where space and time come from.
38:02
Speaker 1: It might be that thinking about the universe in terms
38:05
Speaker 1: of space and time is sort of the mistake we
38:07
Speaker 1: made why we can't, for example, get to a theory
38:10
Speaker 1: of quantum gravity, because it makes us think about how
38:12
Speaker 1: things bounce against each other in a certain way. Thinking
38:15
Speaker 1: about it in terms of this more abstract space allows
38:18
Speaker 1: us to get rid of concepts like space and time
38:20
Speaker 1: and then to do these calculations. But yeah, there definitely
38:23
Speaker 1: is a connection between particles in our space, the things
38:26
Speaker 1: that we think about, and particles in this sort of
38:29
Speaker 1: abstract space. It's sort of similar to the idea we
38:31
Speaker 1: talked about once the universe as a hologram, like maybe
38:35
Speaker 1: this three dimensional space that we think about, this information
38:38
Speaker 1: in this three dimensional space is actually encoded in another
38:41
Speaker 1: kind of space, like a two dimensional space with different
38:44
Speaker 1: kinds of wiggles on it, and so it's possible, for example,
38:47
Speaker 1: to describe a three dimensional space in terms of information
38:50
Speaker 1: on a two D surface. So it's sort of like that.
38:53
Speaker 1: It's like map the whole universe to a new way
38:55
Speaker 1: to organize information, and then the ideas that maybe in
38:58
Speaker 1: this new space, this super accomplished calculation is a lot simpler.
39:02
Speaker 1: So let's get into what these twisters are and what
39:06
Speaker 1: it could all mean for the future of particle physics.
39:08
Speaker 1: But first, let's take another quick break. Are we're talking
39:23
Speaker 1: about ample two heedrons, which I think it's taken us
39:27
Speaker 1: as long just to figure out how to pronounce it.
39:29
Speaker 1: I'm trying to avoid saying it if at all possible.
39:33
Speaker 1: Let's let's have a whole podcast where we avoid talking
39:35
Speaker 1: about the subject. Isn't that what we do every episode?
39:39
Speaker 1: Usually we avoid the subject. Here, I'm actually avoiding the
39:41
Speaker 1: word itself. Oh boy, it's it's like Baltimore, the thing
39:46
Speaker 1: that must not be named. Okay, so you're saying this.
39:49
Speaker 1: This ampl two heedron might simplify a lot how you
39:52
Speaker 1: do particle collisions, because it's sort of maybe cuts through
39:55
Speaker 1: the fog of all the possibilities, Like it's somehow looked
39:58
Speaker 1: at things in a much more simple or or maybe
40:01
Speaker 1: um broader way. And it's based on these things called twisters,
40:04
Speaker 1: which I guess is just kind of like a mathematical thing. Yeah,
40:07
Speaker 1: it's a new mathematical construct invented by Roger Penrose, and
40:11
Speaker 1: he described them as sort of like square roots of
40:14
Speaker 1: space time, which is sort of like, you know, I
40:16
Speaker 1: understand those words, but what does it mean when can
40:18
Speaker 1: put them together? It's sort of like think about again
40:21
Speaker 1: imaginary numbers, Like imaginary numbers are like the square root
40:24
Speaker 1: of minus one, So is an imaginary number real? Like
40:27
Speaker 1: is I out there somewhere in the universe. It's not,
40:31
Speaker 1: but we can still do math with that. We can
40:32
Speaker 1: play with it. It helps us do calculations, and it
40:35
Speaker 1: is the square root of minus one. So now think
40:38
Speaker 1: about these twisters is like not spacetime itself. You can't
40:42
Speaker 1: think about them as space time. But if you put
40:44
Speaker 1: them together in sort of a way, then spacetime comes
40:47
Speaker 1: out of it the way like minus one can come
40:49
Speaker 1: out of two imaginary numbers. And so these twisters are like,
40:52
Speaker 1: you know, basic components that you could put together to
40:55
Speaker 1: make space time. But it's sort of a more natural,
40:58
Speaker 1: underlying way to think about the univer Earth. And so
41:01
Speaker 1: these twisters exist in this abstract space or the astract space.
41:04
Speaker 1: Is these twisters, twister and diagrams help us do calculations
41:08
Speaker 1: in this abstract space. So you create these points in
41:11
Speaker 1: that space, you can make these shapes in that space.
41:14
Speaker 1: You can calculate the volume of those shapes in that space,
41:17
Speaker 1: and the volume of those shapes helps us predict what
41:19
Speaker 1: happens like in our universe, in our space time. WHOA
41:23
Speaker 1: what do you mean? Like you you find the volume
41:25
Speaker 1: of the space and it tells you, hey, um a
41:28
Speaker 1: Higgs boson came out, yeah, or it tells you here's
41:30
Speaker 1: the probability of a Higgs boson to come out. It's
41:33
Speaker 1: really cool because calculating volumes is typically pretty easy. Like
41:36
Speaker 1: if you have three dimensional cube, the volume is easy
41:38
Speaker 1: to calculate if you know the sides right, and there's
41:40
Speaker 1: a little bit of magic there. Right, you're adding up
41:42
Speaker 1: like an infinite number of infinitesimals to get the volume
41:46
Speaker 1: of this thing. But it's a very simple calculation. It's
41:49
Speaker 1: length times with time's height. It's very simple. There's a
41:51
Speaker 1: little bit of like calculational magic that happens there. And
41:54
Speaker 1: so in this twister space, calculating the volume of these
41:58
Speaker 1: weird amplitude hedrawn EAPs is also pretty straightforward. Nima Arkani Hammed,
42:03
Speaker 1: one of the guys who invented this thing, showed how
42:05
Speaker 1: to write them down in this compact notation where you
42:08
Speaker 1: calculate the volume, and then there's this connection. Here's the
42:11
Speaker 1: beautiful part between this volume and all the possible things
42:14
Speaker 1: that can happen to these particles in the same way
42:17
Speaker 1: that like the volume of a cube adds of all
42:19
Speaker 1: the infinitesimal bits inside the cube. Now, the volume of
42:23
Speaker 1: this amplitude, he john represents all the possible things that
42:26
Speaker 1: the particles represented by the points can do with each other.
42:30
Speaker 1: And it works without having to know all of the
42:32
Speaker 1: things that can happen, you know, without having to catalog
42:35
Speaker 1: all of the possibilities. Yeah, you just sweep them all
42:37
Speaker 1: into the volume, right, because you don't really care how
42:40
Speaker 1: many loops of gluons were created when this happened, or
42:43
Speaker 1: how many photons happened. Like, we can't see those things.
42:46
Speaker 1: We don't really care what happens. We care but the
42:48
Speaker 1: input and the output. And so this lets you go
42:50
Speaker 1: from the input to the output much quicker without having
42:53
Speaker 1: to make all those little calculations along the way. In
42:55
Speaker 1: another mathematical analogy, like think about calculus. You need to
42:59
Speaker 1: integrate some function, right, x squared plus two. How could
43:02
Speaker 1: you do it? Well? One way you could do is
43:04
Speaker 1: like draw the function and add up all the little
43:07
Speaker 1: slices to get the area under the curve. But calculus
43:10
Speaker 1: gives you a formula. It says, oh, here's a way
43:12
Speaker 1: to manipulate that expression to give you a simple expression
43:15
Speaker 1: for the answer. Right, we know how to integrate x
43:17
Speaker 1: squared plus two, And it's like you know, excute or
43:20
Speaker 1: three plus two x right, there's an expression that just
43:22
Speaker 1: gives you the answer. You don't have to do all
43:24
Speaker 1: the calculations. And so in the same way, the amplitude
43:26
Speaker 1: heatron is like that shortcut to the answer. Right. Although
43:29
Speaker 1: I'm not sure a lot of people agree that calculus
43:31
Speaker 1: makes things simpler in their lives. I guess it sounds
43:34
Speaker 1: really cool and it sounds really amazing, this amplituo headron.
43:37
Speaker 1: It sounds like it would solve a lot of problems
43:39
Speaker 1: and make things simpler. Is it real is does it
43:41
Speaker 1: actually work or is it still kind of a tentative
43:44
Speaker 1: maybe possibility of how things could be done, or has
43:47
Speaker 1: it been proven right? So it does work in some
43:49
Speaker 1: scenarios and makes some calculations very very simple. It hasn't
43:53
Speaker 1: been proven to be totally correct in every single case.
43:55
Speaker 1: People are still playing with it. It's like a very
43:57
Speaker 1: new mathematical tool. But it has a lot of promise,
44:00
Speaker 1: you know, and in the calculations people have done, it's
44:03
Speaker 1: come out correct. There aren't a whole lot of folks
44:05
Speaker 1: in the universe who know how to use this thing,
44:07
Speaker 1: Like I can't sit down and do a calculation with
44:10
Speaker 1: this thing. It's you know, beyond my level of calculational
44:12
Speaker 1: abilities is probably like a dozen or two dozen people
44:15
Speaker 1: in the world who are like actually know how to
44:17
Speaker 1: use this new mathematical tool. Wait, what do you mean
44:19
Speaker 1: only a few people know how to how it works
44:21
Speaker 1: or how to use it. Don't they print out a
44:23
Speaker 1: recipe or something for how to use it? I mean
44:25
Speaker 1: there are recipes, but it involves like kind of esoteric
44:28
Speaker 1: mathematics that are just not very familiar to most people,
44:31
Speaker 1: even particle physicists, like particle theorists here in my department.
44:34
Speaker 1: I don't think they could sit down calculate amplitude he
44:37
Speaker 1: dron volumes. I'm sure if they spend some time they
44:39
Speaker 1: can figure out how to do it. But it's not
44:41
Speaker 1: like a very widespread technique so far. All right, So
44:44
Speaker 1: then it's proven to work in some cases, but maybe
44:47
Speaker 1: not all or or is it just it hasn't been
44:49
Speaker 1: applied to other cases yet? You know one case it
44:52
Speaker 1: hasn't been applied to yet, for example, is quantum gravity.
44:55
Speaker 1: You know, it's been applied to quantum field theory. When
44:58
Speaker 1: we have these calculations and alving these little particles smashing together,
45:02
Speaker 1: these are the kind of calculations we already know how
45:04
Speaker 1: to do. This would be sort of a shortcut. People
45:07
Speaker 1: are excited because it might also apply to quantum gravity.
45:10
Speaker 1: It might help us do things like figure out what
45:13
Speaker 1: the gravitational attraction is between two quantum particles, which currently
45:17
Speaker 1: we just don't know how to do. We don't have
45:19
Speaker 1: a theory of quantum gravity that works. So one thing
45:22
Speaker 1: that hasn't been done yet is developed the amplitude he
45:25
Speaker 1: drawn to figure out if it can be applied to
45:28
Speaker 1: do calculations for quantum gravity. Also, there are some promising
45:32
Speaker 1: hints there, things that make people think maybe it is
45:35
Speaker 1: a new way forward. Well, that'd be interesting if it
45:38
Speaker 1: can solve quantum gravity. But I thought the main problem
45:40
Speaker 1: was it quantum and relativity that didn't really play well together.
45:44
Speaker 1: Like one assumes spacespendable, the other one assumes it's not,
45:47
Speaker 1: and so they really just don't play it well together.
45:50
Speaker 1: Is this a possible way to bridge the two things. Yeah,
45:52
Speaker 1: because a lot of those problems revolve around starting with space. Right,
45:57
Speaker 1: you have space which general relativity defour worms, and you
46:01
Speaker 1: have space which particles move through. And there are a
46:04
Speaker 1: lot of assumptions that go along with starting from space.
46:06
Speaker 1: One assumption is locality. We assume that things can, for example,
46:11
Speaker 1: only perturb other things that are near them. You know,
46:14
Speaker 1: so for example, you can't do something here which instantaneously
46:17
Speaker 1: affects something in andromeda. You can have sort of like
46:20
Speaker 1: short range connections between things by exchanging particles. But if
46:24
Speaker 1: your calculations don't start from assuming that space is a thing,
46:28
Speaker 1: they just start from this like abstract twister space, then
46:31
Speaker 1: you have a new kind of freedom and how you
46:33
Speaker 1: like build your theory, and maybe space sort of emerges
46:37
Speaker 1: from it, but you don't have to follow all the
46:39
Speaker 1: same rules that you thought you had to follow before.
46:41
Speaker 1: Maybe we can get rid of this requirement of locality.
46:44
Speaker 1: Maybe it's not actually an absolute thing in the universe,
46:48
Speaker 1: but eventually you have to be able to transform it
46:50
Speaker 1: back from the afflex space to the real space time
46:54
Speaker 1: that we live in. Wouldn't that be a problem then
46:56
Speaker 1: probably not. If you're concerned, is like, well, locality is
46:59
Speaker 1: a thing. We're pretty sure or that the universe is local.
47:01
Speaker 1: You know, we've seen that these things work in this
47:03
Speaker 1: sort of way. There feels like there is space in
47:05
Speaker 1: our universe. We're not talking about breaking that open and
47:08
Speaker 1: saying space isn't the thing at all. We're just talking
47:11
Speaker 1: about breaking those rules sometimes, you know, in the same
47:13
Speaker 1: way that like Newtonian theory worked and then it was
47:16
Speaker 1: replaced by Einstein's gravity, which disagreed with it only sometimes right,
47:21
Speaker 1: sometimes it to totally agree. And so if you can
47:23
Speaker 1: now have a new description of, for example, what happens
47:25
Speaker 1: inside black holes or what happened at the very beginning
47:28
Speaker 1: of the universe, that doesn't make all the same assumptions
47:31
Speaker 1: that we're trying to force quantum gravity into. You're a
47:34
Speaker 1: little bit more freedom to do something crazy. And you know,
47:36
Speaker 1: we don't know what's inside black holes. We don't know
47:38
Speaker 1: what happened at the early universe, So there's room there
47:41
Speaker 1: for crazy stuff to have happened which wouldn't be allowed
47:44
Speaker 1: by our current ideas of quantum gravity. And then maybe
47:47
Speaker 1: like quantum gravity or unified theory of quantum gravity in
47:50
Speaker 1: the real world, maybe emerges from all of this math
47:53
Speaker 1: in the abstract space. Is that kind of what might happen. Yeah,
47:56
Speaker 1: in the end, you have to be able to shuggle
47:57
Speaker 1: all of these calculations back over to our world to
48:00
Speaker 1: predict experiments, to say does this actually work? You know,
48:04
Speaker 1: math is fun, but in the end we're hoping that
48:06
Speaker 1: it describes the universe. There's another like deep philosophical question
48:10
Speaker 1: no one knows the answer to, like why does math
48:12
Speaker 1: work at all? Why does it seem to describe our universe?
48:14
Speaker 1: We don't know, But as physicists were excited when a
48:18
Speaker 1: piece of mathematics helps us calculate something about the universe,
48:21
Speaker 1: not just do some fancy geometry in an abstract space.
48:24
Speaker 1: So it has to in the end predict something we
48:26
Speaker 1: can test to prove that it really is a description
48:30
Speaker 1: of the universe. That's useful, and you know, speaking philosophically,
48:33
Speaker 1: if it does work, if it turns out this is
48:35
Speaker 1: a very useful piece of mathematics, then a lot of
48:38
Speaker 1: people take that to be something real. You know. I
48:41
Speaker 1: think about the other geometrical revolution in physics, which was
48:44
Speaker 1: general relativity. General relativity says, no, gravity is not a force.
48:48
Speaker 1: It's actually just a consequence of this complex geometry of
48:52
Speaker 1: space time, which was invisible to us until now. But
48:55
Speaker 1: we don't just think about that it's like an abstract calculation.
48:58
Speaker 1: We think about that is real. We think about space
49:01
Speaker 1: is actually really being curved. So in the same way,
49:03
Speaker 1: if this turns out to be right. If it turns
49:05
Speaker 1: out that calculations in this abstract twister space are the
49:09
Speaker 1: things that actually determine what happens in our space, that
49:12
Speaker 1: this abstract twister space is like somehow more fundamental. There'll
49:16
Speaker 1: be people who will say that's the real universe, man,
49:19
Speaker 1: that the universe really is in this abstract space without
49:23
Speaker 1: our kind of physical space and time, and that what
49:25
Speaker 1: we're experiencing is sort of like a hologram. It's just
49:28
Speaker 1: sort of like a construct that emerges from that. Like
49:32
Speaker 1: maybe we're all living inside of the amplitude heedron kind
49:35
Speaker 1: of and are what we see every day is is
49:37
Speaker 1: not real or it's just some kind of projection of
49:39
Speaker 1: the amplitudehedro. Yeah, and those two things are not the same, Right.
49:42
Speaker 1: It can be very real but also just to be
49:45
Speaker 1: a projection of the amplitude hedron. It can be real
49:48
Speaker 1: without being fundamental, Like I'm real, you're real. Doesn't mean
49:52
Speaker 1: that we're like basic elements of the universe. We arise
49:55
Speaker 1: from the complex to ing and frowing of all the
49:57
Speaker 1: little particles that make us up. Doesn't make us less real,
50:00
Speaker 1: just means that we're not inherent possible for there to
50:02
Speaker 1: be a universe without me and without you and without
50:05
Speaker 1: a podcast. It might be it's possible to have a
50:07
Speaker 1: universe without space and time, but with this abstract twister space,
50:11
Speaker 1: and then we'll all be forced to say the word
50:13
Speaker 1: amplicto heatron all the time. That'll be real fun. It
50:16
Speaker 1: would be the only word in the universe. But as
50:18
Speaker 1: you said, it does seem to work for certain cases,
50:21
Speaker 1: and that means that it has a promising future, like
50:24
Speaker 1: maybe it will sort of let you predict particle collisions
50:27
Speaker 1: from now on. Yeah, it's just fun to have a
50:28
Speaker 1: new mathematical tools something which is really good at this
50:31
Speaker 1: kind of calculation that's really important and the kind of
50:34
Speaker 1: calculation that we're bad at right now. And so it's
50:37
Speaker 1: just sort of like another tool in our arsenal. You
50:39
Speaker 1: know how, sometimes when you're solving a problem, you'd like
50:41
Speaker 1: to solve it using equations on a piece of paper,
50:43
Speaker 1: because the rules of algebra guide you there. And sometimes
50:46
Speaker 1: it's easier to use geometry to like envision how two
50:48
Speaker 1: lines cross or how a plane intersects a circle. So
50:52
Speaker 1: it's good to have lots of different mathematical tools in
50:55
Speaker 1: your toolkit because sometimes one of them makes a problem
50:58
Speaker 1: easy when other ones would make it hard. Right, right,
51:01
Speaker 1: I just have to learn how to draw cartoons in
51:03
Speaker 1: with twisters, I guess, or twisty pens in abstract twelve
51:07
Speaker 1: dimensional space amplitude cartoons. There you go. Yeah, and so
51:12
Speaker 1: in this twister space, locality is not fundamental, and also unitarity,
51:16
Speaker 1: this requirement that quantum information not be destroyed in the universe,
51:20
Speaker 1: and that might help us explain things like what happens
51:23
Speaker 1: to information that flows into a black hole, you know,
51:25
Speaker 1: which we talked about on the podcast a few times.
51:27
Speaker 1: So nima Ar Kannie Hahmed, one of the smart guys
51:29
Speaker 1: who came up with this, He says that locality and
51:32
Speaker 1: unitarity are both suspect. He doesn't believe that they really
51:35
Speaker 1: are fundamental elements of our universe. He thinks they're like
51:38
Speaker 1: almost approximate quantities that we've come to rely on, but
51:41
Speaker 1: aren't real and deep and true. They're just sort of
51:44
Speaker 1: real maybe in the amplitudehedral projection that we live in,
51:48
Speaker 1: but in the real three universe maybe they don't matter.
51:51
Speaker 1: That's what you're saying. Yeah, exactly, there's sus as my
51:53
Speaker 1: kids would say, And this is exciting because it's a
51:58
Speaker 1: pattern in physics. We tear the ail away and reveal
52:01
Speaker 1: the reality is different from the way that we expected.
52:04
Speaker 1: And those are the kind of discoveries that I live for. Cool.
52:07
Speaker 1: If only you knew how to use it exactly, maybe
52:09
Speaker 1: you should be spending some one time trying to learn
52:11
Speaker 1: it rather than talking about person in the world who
52:15
Speaker 1: knows how to calculate with these things. There you go,
52:17
Speaker 1: a small rarefied. It's supposed to being one of the
52:20
Speaker 1: three people who have podcasts, right exactly, one of the
52:23
Speaker 1: few rare people who have a podcast and who can
52:26
Speaker 1: pronounce amplitude heedron three times. Quite man, Yeah, that's an
52:29
Speaker 1: even harder thing. I think they can give you a
52:31
Speaker 1: PhD for that from the amplitudhedro and University. All right, well,
52:36
Speaker 1: it sounds like it's another stay tuned whether this new
52:39
Speaker 1: way of looking at things can actually revolutionize our view
52:43
Speaker 1: of reality and what actually happens when two particles collide.
52:46
Speaker 1: And sometimes progress is made by people smashing things together
52:50
Speaker 1: and discovering new phenomena in the universe, and sometimes it's
52:53
Speaker 1: made just by people thinking mathematically about patterns and shapes
52:57
Speaker 1: and relationships and coming up with new mathematical tricks to
53:01
Speaker 1: solve those problems. Yeah, a lot of people are probably thinking, man,
53:04
Speaker 1: I should have paid more attention in geology class. I
53:06
Speaker 1: could change the universe. Well, we hope you enjoyed that.
53:09
Speaker 1: Thanks for joining us, see you next time. Thanks for listening,
53:20
Speaker 1: and remember that Daniel and Jorge Explain the Universe is
53:23
Speaker 1: a production of I Heart Radio. For more podcast from
53:26
Speaker 1: my Heart Radio, visit the I heart Radio app, Apple Podcasts,
53:30
Speaker 1: or wherever you listen to your favorite shows. H