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Speaker 1: Sometimes I'll bump into a stranger, maybe on an airplane,

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Speaker 1: and they'll ask me the inevitable question, what do you

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Speaker 1: do for a living? When I say that I'm a physicist,

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Speaker 1: I often get the reaction, ugh, I hate physics so

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Speaker 1: much math and that makes me think if it's the

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Speaker 1: math you didn't like, then hey, hate the math, but

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Speaker 1: you can still love the physics. But of course the

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Speaker 1: two are closely linked. You can't love Shakespeare if you

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Speaker 1: hate the English language, and that of course makes us

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Speaker 1: wonder why math and physics are so intertwined. I mean,

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Speaker 1: if people can actually enjoy Shakespeare in other languages, then

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Speaker 1: it has something about it that's transcending the original English words.

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Speaker 1: Is it possible for physics to transcend math or are

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Speaker 1: they shackled to each other with math woven deeply into

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Speaker 1: the fabric of physics. Hi, I'm Daniel. I'm a particle

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Speaker 1: physicist and a professor at UC Irvine, and I'll admit

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Speaker 1: that I love math. Some people find it confusing, but

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Speaker 1: when I was a kid, I found it to be

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Speaker 1: crisp and logical in a way that the rest of

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Speaker 1: the world was sort of fuzzy and complicated, like people.

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Speaker 1: For example, people are complicated and hard to understand when

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Speaker 1: you're a kid. Are they going to be mean to

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Speaker 1: you or nice to you if you sit next to

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Speaker 1: them at lunch? It's hard to predict from one day

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Speaker 1: to the next. But the rules of math were cast

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Speaker 1: in iron two plus two equals four every day of

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Speaker 1: the week, and if you know the rules, the answer follows.

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Speaker 1: Math is reliable, it's predictable, and that's what led me

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Speaker 1: to physics, the ability to use math to understand and

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Speaker 1: predict the universe. And welcome to the podcast Daniel and

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Speaker 1: Jorge Explain the Universe, where we do a deep dive

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Speaker 1: into the rules of the universe, doing our best to

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Speaker 1: reveal what science has uncovered in terms of the machinations

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Speaker 1: of the universe, and laying out for you what science

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Speaker 1: and scientists are still puzzling over. We tear the universe

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Speaker 1: down to its smallest bits and put them back together

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Speaker 1: to explain how things work and expose our remaining ignorance.

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Speaker 1: And we can do that thanks in no small part

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Speaker 1: to the power of math. Math underlies all of the

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Speaker 1: stories that we tell ourselves about the universe. If you

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Speaker 1: want to predict the path of a baseball, you can

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Speaker 1: use math to calculate its trajectory and tell you where

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Speaker 1: it will land. Physics can predict the future, but the

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Speaker 1: language and the machinery of it are all mathematical. There

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Speaker 1: are times when our intuition fails us, when the universe

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Speaker 1: does things that don't align with our expectations, like in

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Speaker 1: the case of quantum mechanics, which tries to describe tiny

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Speaker 1: little objects that follow rules that seem alien to us,

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Speaker 1: but they do follow rules, and those rules are mathematical

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Speaker 1: described by equations. So when we've lost our intuition, we

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Speaker 1: can close our intuitive eyes and just follow the math

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Speaker 1: and trust that it will guide us to the right

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Speaker 1: physical answer. On this podcast, we actually usually are trying

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Speaker 1: to do the opposite, to avoid the mathematics. That's partly

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Speaker 1: because it's an audio program not well suited to equations

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Speaker 1: or geometric sketches, but also because we are trying to

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Speaker 1: feed your intuition about how the universe works, to strip

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Speaker 1: away the opaqueness of math and make it all make

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Speaker 1: sense to you. And I'll admit that this is sometimes

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Speaker 1: a struggle to accomplish. For some of the deeper concepts

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Speaker 1: in physics, like gauge invariants, the way I learned them

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Speaker 1: is mathematical, and the way that I understand them is mathematical,

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Speaker 1: which has become part of my intuition. So it's not

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Speaker 1: always easy to know how to translate those concepts into

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Speaker 1: pure intuition and talk about them without math, but you know,

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Speaker 1: finding ways to talk about them intuitively has also led

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Speaker 1: me to a deeper understanding of the ideas. That's one

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Speaker 1: of the underappreciated joys of teaching. It forces you to

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Speaker 1: strengthen your own knowledge. But to me, it raises a

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Speaker 1: really interesting question. Is it possible actually to divorce physics

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Speaker 1: from math? Is math truly the language of physics or

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Speaker 1: is it just useful like a shorthand notation. Is math

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Speaker 1: the language of the universe itself or is it just

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Speaker 1: the way that humans like to think about it. So

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Speaker 1: on today's episode, we'll be asking the question why is

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Speaker 1: math so important for physics? A few weeks ago, we

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Speaker 1: talked to a philosopher of mathematics, Professor Mark Colliban, about

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Speaker 1: whether the universe was mathematical. Today, I've invited someone from

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Speaker 1: the other side of the issue to joy. We'll talk

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Speaker 1: today to a working mathematician, someone who spends his days

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Speaker 1: building mathematical tools and using them to describe the patterns

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Speaker 1: and structures of the universe. So it's my pleasure to

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Speaker 1: welcome Professor Steve Strogatz. He's the Jacob gould Sherman Professor

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Speaker 1: of Applied Mathematics at Cornell University, having talked previously at MIT,

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Speaker 1: and having earned a PhD in math from Harvard, So

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Speaker 1: those are some pretty impressive credentials. But he's also an

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Speaker 1: expert in applying math to the real world, including understanding

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Speaker 1: the math of firefly swarms, choruses of chirping crickets, and

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Speaker 1: the wobbling of bridges. He's also a well known podcaster,

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Speaker 1: host of the podcasts The Joy of X and The

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Speaker 1: Joy of Why, both of which I highly recommend, as

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Speaker 1: well as a prolific author. One of his recent books

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Speaker 1: is Infinite Powers, How Calculus Reveals the Secrets of the Universe,

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Speaker 1: a book I recently read and thoroughly enjoyed, and which

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Speaker 1: inspired me to invite Steve on the podcast to talk

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Speaker 1: about calculus, infinity, and the deep relationship between physics and math. Steve,

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Speaker 1: Welcome to the podcast, and thank you very much for

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Speaker 1: joining us.

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Speaker 4: Thanks a lot, Daniel, it's a great pleasure to be

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Speaker 4: with you. That's going to be fun.

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Speaker 1: It's a treat to have you here, as I've been

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Speaker 1: very much enjoying listening to your podcast series and reading

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Speaker 1: your book, and so I'd like to start by asking

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Speaker 1: you a question I've heard you ask several of your

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Speaker 1: guests about definitions. Your book is about calculus, a word

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Speaker 1: that a lot of people have heard but might not

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Speaker 1: really know what it means. Can you define for us

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Speaker 1: what is calculus?

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Speaker 4: Sure, let's try it in a sequence of definitions, and

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Speaker 4: you could stop me when I get too detailed. So

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Speaker 4: if I were giving it to you in one word,

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Speaker 4: I would say, it's the mathematics of change. That's the

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Speaker 4: key word change. If we want to go a little

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Speaker 4: more into it, it's the mathematics of continuous change, and

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Speaker 4: especially things that are changing at a changing rate.

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Speaker 1: So you say it's the mathematics of change. What exactly

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Speaker 1: is changing there? Like if I just want to describe

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Speaker 1: how a ball is moving through the air, what exactly

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Speaker 1: is changing about the ball's motion?

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Speaker 4: So in that case, what's changing is the position of

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Speaker 4: the ball, or also possibly the speed of the ball.

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Speaker 4: So your listeners will remember from high school algebra, we

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Speaker 4: do problems about change and motion that gets summed up

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Speaker 4: in the mantra distance equals rate times time, and so

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Speaker 4: that's motion at a steady speed or at a steady velocity.

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Speaker 4: And you can handle that with algebra. It's just a

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Speaker 4: matter of multiplication. Distance equals rate times time. The rate

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Speaker 4: is the speed, and you're driving sixty miles an hour.

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Speaker 4: For an hour, you're going to go sixty miles. Okay,

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Speaker 4: So in that case the distance is changing, position of

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Speaker 4: the car on the highway is changing, but the speed

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Speaker 4: of the car is not changing. We said it was

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Speaker 4: a steady sixty miles an hour. And so at the

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Speaker 4: time of Isaac Newton or even Johannes Kepler or Galileo,

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Speaker 4: scientists started to become very interested in motion that was

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Speaker 4: not just simple motion at a constant speed. You know,

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Speaker 4: in connection with the things you mentioned dropping a ball,

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Speaker 4: the apocryphal or maybe true dropping the cannon ball off

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Speaker 4: the leaning tower of Pisa from Galileo certainly Kepler with

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Speaker 4: thinking about the motions of the planets. In all of

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Speaker 4: those cases there were things that were changing. I mean,

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Speaker 4: we should also keep in mind with the planets, another

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Speaker 4: thing that can change is direction. So instead of motion

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Speaker 4: in a straight line, if you have an orbit, then

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Speaker 4: the direction of the planet as it's moving is changing.

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Speaker 4: It's curving as it's going around the Sun. And so

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Speaker 4: geometry is a big part of calculus too. When we

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Speaker 4: start to deal with curved shapes as opposed to shapes

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Speaker 4: made of straight lines or planes.

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Speaker 1: So in this case, do you feel historically like physics

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Speaker 1: was in the lead or mathematics. I mean, people have

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Speaker 1: been thinking about things that were moving and changing for

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Speaker 1: thousands of years. But calculus is just a few hundred

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Speaker 1: years old. Was it invented to solve a particularly difficult

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Speaker 1: problem or did it appear in the minds of intelligent

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Speaker 1: people and then allow us to solve problems that had

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Speaker 1: been standing for thousands of years.

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Speaker 4: That's interesting that you say it's only a few hundred

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Speaker 4: years old. Most historians and certainly most scientists would say, yeah,

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Speaker 4: calculus is from the middle sixteen hundreds, from Isaac Newton

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Speaker 4: and Gottfried Wilhelm Leibniz. But I don't personally want to

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Speaker 4: endorse that position, because I think we can see if

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Speaker 4: you want. I mean, I don't quibble about definitions. But

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Speaker 4: there are definitely ideas of calculus almost two thousand years

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Speaker 4: earlier in the work of Archimedes in Syracuse in what

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Speaker 4: was at the time the Greek Empire two fifty BC.

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Speaker 4: Archimedes is calculating volumes of solids with curved faces, or

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Speaker 4: also areas under a parabola, or he's the one that

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Speaker 4: gives us the volume of a sphere or the surface

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Speaker 4: area of a sphere. Those are all calculus problems. We

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Speaker 4: teach those today in calculus when we're teaching students about integrals,

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Speaker 4: which is a generalization of the idea of area and volume.

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Speaker 4: And so he's totally doing calculus in two fifty BC.

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Speaker 4: In fact, he's doing the harder part of calculus, integral calculus.

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Speaker 4: But we don't usually call it calculus because of I

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Speaker 4: don't know why. Actually, I mean, i'd think it is calculus.

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Speaker 4: So back to your question, what is calculus? I mean,

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Speaker 4: another way of talking about it is it's the systematic

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Speaker 4: use of infinity and infinitesimals to solve problems about curved shapes,

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Speaker 4: about motion at a non constant speed, and about anything

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Speaker 4: else that's changing in a non constant way. It could

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Speaker 4: be amount of virus in your bloodstream if you have HIV.

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Speaker 4: It could be a population you know, of the earth

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Speaker 4: going up. Any all of these things are grist for calculus.

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Speaker 1: So why is it that infinity is such an important

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Speaker 1: and powerful concept that lets us now tackle new problems

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Speaker 1: that we couldn't tackle before. I want to think about

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Speaker 1: it in terms of like the ball flying through the air,

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Speaker 1: and you're talking about something changing about its motion, but

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Speaker 1: you're also referring to like calculating the volume of spheres.

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Speaker 1: What's changing in that aspect? Why do we need infinity

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Speaker 1: to help us tackle these problems? I mean, the sphere

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Speaker 1: is not infinitely big, the ball is not moving infinitely fast.

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Speaker 1: What exactly does infinity come into play?

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Speaker 4: The main point is probably infinitesimals rather than infinity of testimals.

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Speaker 4: Let us pretend that a sphere is made up of

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Speaker 4: flat pieces, maybe easier to visualize with a circle. Some

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Speaker 4: of your listeners will have probably played this game. If

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Speaker 4: you put a bunch of dots on a circle and

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Speaker 4: connect them with straight lines, it almost looks like a

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Speaker 4: you know, it'll make a polygon. For instance, you could

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Speaker 4: picture putting four equally spaced points on a circle and

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Speaker 4: connect them. They'll make a square. If you put eight,

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Speaker 4: then you're making an octagon. You know, the more points

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Speaker 4: you put, the more it starts to look like a circle.

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Speaker 4: And from ancient times people had this intuition that a

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Speaker 4: circle is kind of like an infinite polygon. It's got

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Speaker 4: infinitely many corners. It's connected by sides that are infinitesimally small.

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Speaker 4: Now that doesn't seem right because we think of a

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Speaker 4: circle as perfectly smooth it doesn't have any corners at all.

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Speaker 4: But in a certain sense, it's the limit of a

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Speaker 4: polygon as you take more and more points on the

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Speaker 4: polygon at the corners and more and more sides. And

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Speaker 4: so that was the key insight that Archimedes had, that

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Speaker 4: you could calculate the area of a circle the formula

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Speaker 4: we all learn in high school pi are squared. He's

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Speaker 4: the first one to really prove that, and he did

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Speaker 4: it by thinking in this calculus way, by looking at

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Speaker 4: the limit of polygons. So similarly, in the case of Galileo,

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Speaker 4: in the motion of say javelin or something thrown that's

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Speaker 4: going to execute parabolic flight to make the problem easier,

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Speaker 4: gal Well, actually Galileo didn't really have this idea, but

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Speaker 4: later in Newton we would think of the parabola as

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Speaker 4: made up of infinitely many, infinitesimally small excursions along the

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Speaker 4: path that are basically straight lines in the particle or

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Speaker 4: the javelin is moving at a constant speed. For that

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Speaker 4: infinitesimal amount of time, So it breaks the problem down

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Speaker 4: into something that we already know how to solve. Everything

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Speaker 4: becomes distance equals right times time again, except only over

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Speaker 4: an infinitesimal segment.

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Speaker 1: So you solve a problem you can't solve by turning

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Speaker 1: it into an infinite number of problems that you can solve.

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Speaker 4: Bingo, you've really encapsulated the heart of calculus in that sense,

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Speaker 4: in infinite powers. I called that the infinity principle that

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Speaker 4: to solve any difficult problem involving curved shapes or these

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Speaker 4: complicated motions, if you reconceptualize it as an infinite number

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Speaker 4: of smaller, simpler problems in which you have straight lines

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Speaker 4: or motion at a constant speed, you can solve incredibly

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Speaker 4: hard and important problems with this trick. The only problem

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Speaker 4: is you have to somehow put all those infinitesimals back

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Speaker 4: together again to reconstitute the original motion or the original shape.

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Speaker 4: And that's the hard part of calculus. The subdivision part

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Speaker 4: is easy. It's the reassembly part that's hard.

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Speaker 1: Right, And so it's fascinating to me that infinity sort

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Speaker 1: of appears in two places there one as you chop

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Speaker 1: it into little pieces and then again as you put

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Speaker 1: it back together. And to me, it's fascinating because the

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Speaker 1: infinity appears in only the intermediate stages. Like the ball

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Speaker 1: doesn't have infinite velocity or infinite acceleration or infinite anything,

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Speaker 1: but we've used infinity in calculating its very non infinite motion,

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Speaker 1: and so it's fascinating to me that infinity is such

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Speaker 1: a powerful mathematical tool. We don't actually observe it in

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Speaker 1: nature really very often. Or some people might say, ever.

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Speaker 4: That's really a great point you could. I mean, if

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Speaker 4: we were doing this on video, your listeners would see

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Speaker 4: me smiling. I really like that. It's almost like in

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Speaker 4: those old cartoons with the enter stage left and exit

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Speaker 4: stage right, that infinity comes onto the stage and the infinitesimals,

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Speaker 4: but only as you sort of say, like an apparatus.

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Speaker 4: It lets us solve the problem, but it's sort of

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Speaker 4: not really there, it's not real.

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Speaker 1: In physics, we're often seeing infinities in the final answer

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Speaker 1: as a sign of failure. Right in particle physics, a

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Speaker 1: prediction of infinity is unphysical. You can't have infinite probabilities

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Speaker 1: for some outcome in quantum mechanics, or you can't have

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Speaker 1: an infinite force on a particle, and in general relativity

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Speaker 1: we think of a prediction of a singularity infinite density

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Speaker 1: as the breakdown of the physical theory. We try to

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Speaker 1: avoid infinities. We hide them under renormalization whatever possible. So

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Speaker 1: then my question to you is, in your mind, are

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Speaker 1: these infinities real? I mean, do they just exist in

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Speaker 1: the intermediate steps of the mathmad methods we're using. Are

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Speaker 1: they only in our minds? Are they a half finished calculation?

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Speaker 1: Or is this something real about the universe that calculus

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Speaker 1: is capturing, This smooth and infinitely varying motion of a

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Speaker 1: ball or changing of the velocity of a planet. Is

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Speaker 1: infinity real? Is it part of our minds?

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Speaker 4: Such a great, deep question. I don't even know what

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Speaker 4: I'm going to say to the answer. I mean, I've

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Speaker 4: been thinking about this for forty to fifty years, and

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Speaker 4: I still don't really know what the answer is. I mean,

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Speaker 4: the principal person in me, the philosophically tenable person, wants

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Speaker 4: to say it's not real, it's a fiction, it's a

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Speaker 4: useful device. Let's just try to make that argument first,

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Speaker 4: before the more wild eyed person in me makes the

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Speaker 4: counter argument. So the rational person would say, yeah, I mean,

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Speaker 4: from our best understanding of physics today, there are no infinitesimals.

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Speaker 4: You can't subdivide matter arbitrarily finely. That's the whole concept

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Speaker 4: of atoms, those things which are indivisible. You guys tell us,

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Speaker 4: I say you. The physicists tell us that there is

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Speaker 4: even a smallest amount of time and space that is

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Speaker 4: referred to as the Plank scale, the smallest. You know,

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Speaker 4: we don't really, of course, I believe understand how to

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Speaker 4: unify quantum theory. Yet with general relativity there is candidates.

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Speaker 4: But anyway, the cool thing is that, just on dimensional grounds,

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Speaker 4: if you look at the fundamental constants like the speed

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Speaker 4: of light and planks constant that governs quantum phenomena, and

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Speaker 4: Newton's gravitational constant for the strength of gravity, those can

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Speaker 4: only be put together in one way to make a

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Speaker 4: unit of length. That's the plank length, and it's about

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Speaker 4: ten to the minus thirty five meters, And that's sort

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Speaker 4: of the smallest conceivable distance that has any physical meaning.

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Speaker 4: Wouldn't you say, whatever the theory ends up.

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Speaker 1: Being, that's certainly an attempt to describe what might be

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Speaker 1: the shortest distance. In my view, it's a not very

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Speaker 1: clever attempt, but also the most clever attempt we have.

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Speaker 1: We have no better way to do it, and so

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Speaker 1: this is the only thing. You know, we do this

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Speaker 1: all the time in physics. We say, let's start with

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Speaker 1: the most naive idea and then try to build on it,

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Speaker 1: and we're sort of still there with the shortest distance,

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Speaker 1: you know. I mean, if you try to estimate, like

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Speaker 1: how many candy bars a person eats in a year,

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Speaker 1: just by combining various quantities with the right units, you

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Speaker 1: might get an answer that's off by a factor of

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Speaker 1: a thousand, and that would feel like a pretty wrong answer.

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Speaker 1: In the case of the plank length, I think we're

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Speaker 1: just sort of groping generally for where in the space

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Speaker 1: that answer might be. But I think the point you're

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Speaker 1: making is we have the sense that the universe is

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Speaker 1: discrete and not continuous. E Quanto mechanics tells us that

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Speaker 1: you can't infinitely chop up the universe, and therefore mathematics

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Speaker 1: of calculus that assumes that might not actually be describing

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Speaker 1: what's happening in the universe.

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Speaker 4: Fine, I mean, I take your point that we don't

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Speaker 4: know that the plank length of ten to the minus

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Speaker 4: thirty five is right. There could be factors of a

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Speaker 4: thousand in one direction or another or more. I mean,

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Speaker 4: we don't really know what the prefactor is, so okay,

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Speaker 4: I accept that. Nevertheless, as you say, also from quantum theory,

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Speaker 4: we have reasons to think that nature is fundamentally discrete

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Speaker 4: in every aspect, whether it's matter or space or time.

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Speaker 4: And so if that turns out to be correct, that

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Speaker 4: will mean that real numbers are not real. Real numbers

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Speaker 4: are the things that we use in calculus all day long.

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Speaker 4: They are numbers that have infinitely many digits after the

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Speaker 4: decimal point, like pi. Right, people know you can keep

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Speaker 4: calculating and you'll never know all the digits of pi

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Speaker 4: because there's infinitely many of them. Is that real? Like

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Speaker 4: In fact, you could ask that question about all of math,

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Speaker 4: our circles real, you'd have to say no. Circles are

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Speaker 4: not real either, because as you zoom in on them,

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Speaker 4: you know what's there. It's all jiggly and there's fluctuations

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Speaker 4: of the subatomic particles. So there's no material circle in

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Speaker 4: the real world. But nevertheless, going back to Plato or others,

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Speaker 4: we can think about perfection. In our minds, we can

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Speaker 4: think about the concept of a perfect circle, and we

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Speaker 4: can think about the concept of pie, and even the

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Speaker 4: concept of infinity. And this is the uncanny part. These

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Speaker 4: things are not real from the standpoint of physics, yet

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Speaker 4: they give us our best understanding of the physical universe

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Speaker 4: that we've achieved, you know, as a species. And that's

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Speaker 4: just a fact. I mean, that's just a historical fact.

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Speaker 4: The calculus based on this fiction of infinitely subdivisible quantities

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Speaker 4: works pretty darn well. While I was walking my dog

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Speaker 4: this morning, I tried to figure out how many orders

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Speaker 4: of magnitude if you tell us the universe is about

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Speaker 4: ten to the twenty five meters big the visible universe,

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Speaker 4: that's the estimate I looked. According to when I asked

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Speaker 4: Siri on my iPhone, she said, the visible universe ten

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Speaker 4: to the twenty five meters, and the typical scale of

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Speaker 4: a hydrogen atom is something like ten to the minus

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Speaker 4: ten meters. So you've got thirty five orders of magnitude,

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Speaker 4: very well described by calculus, all the way from the

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Speaker 4: Schrodinger equation at the lowest scale to general relativity at

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Speaker 4: the highest scale, all built on calculus. So it's kind

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Speaker 4: of capturing the truth. Okay, you couldn't. Now it's going

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Speaker 4: to start screwing up at the scale of quantum gravity,

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Speaker 4: whatever that ends up being, we think. But I think

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Speaker 4: that's a pretty good notch in the belt of calculous

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Speaker 4: that it works over such a vast range of scales.

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Speaker 1: Absolutely, it's incredible because it powers not just you know,

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Speaker 1: quantum field theory, which is full of integrals, but also

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Speaker 1: general relativity and talking about you know, galaxies and black holes.

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Speaker 1: All Right, I have a lot more questions about math

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Speaker 1: and physics for our guest, but first, let's take a

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465
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466
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467
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482
00:26:01,359 --> 00:26:04,919
Speaker 1: and we're talking with Professor Steve Strogatz about why math

483
00:26:05,080 --> 00:26:08,359
Speaker 1: is so important for physics. And it makes me think

484
00:26:08,480 --> 00:26:12,120
Speaker 1: about the connection in physics and math of the concept

485
00:26:12,160 --> 00:26:15,679
Speaker 1: of emergence. You know, some simple behavior at the scale

486
00:26:15,720 --> 00:26:17,840
Speaker 1: of like me and you or a bowl of soup

487
00:26:18,240 --> 00:26:22,680
Speaker 1: that neatly and compactly summarizes the almost infinite details going

488
00:26:22,720 --> 00:26:25,359
Speaker 1: on underneath. I mean, even if you don't believe that

489
00:26:25,520 --> 00:26:28,440
Speaker 1: a ball is infinitely divisible into bits, we know this

490
00:26:28,600 --> 00:26:31,119
Speaker 1: a huge number of bits with a huge number of details.

491
00:26:31,160 --> 00:26:34,520
Speaker 1: But it's almost like the equations and the simplicity of calculus,

492
00:26:34,560 --> 00:26:37,719
Speaker 1: the parabolic motion of that ball emerge somehow from all

493
00:26:37,760 --> 00:26:40,520
Speaker 1: of these infinite testimals doing their bit together to tell

494
00:26:40,520 --> 00:26:43,440
Speaker 1: a fairly simple story. And in physics, to me, it's

495
00:26:43,440 --> 00:26:46,640
Speaker 1: something of a mystery, like why this happens? Why can

496
00:26:46,680 --> 00:26:50,159
Speaker 1: we describe the universe in simple mathematical stories when we

497
00:26:50,240 --> 00:26:53,320
Speaker 1: know that the details are crazy and gory and intense,

498
00:26:53,480 --> 00:26:55,919
Speaker 1: and calculus really wraps this up. So do you have

499
00:26:55,960 --> 00:26:58,080
Speaker 1: an instinct or an intuition or even a guess for

500
00:26:58,520 --> 00:27:02,520
Speaker 1: why it's possible to rank go these almost infinities into

501
00:27:02,560 --> 00:27:05,400
Speaker 1: fairly simple stories that make sense to our human minds.

502
00:27:05,680 --> 00:27:07,480
Speaker 4: That's another tough one.

503
00:27:09,880 --> 00:27:11,280
Speaker 1: I don't mean to put you on the spot.

504
00:27:11,320 --> 00:27:14,560
Speaker 4: Well, they're all great questions, they're so deep. My first

505
00:27:14,600 --> 00:27:18,720
Speaker 4: instinct to that one after I don't know, is is

506
00:27:18,720 --> 00:27:21,879
Speaker 4: it a question of the measuring apparatus meaning us that

507
00:27:21,920 --> 00:27:25,280
Speaker 4: we happen to be macroscopic and so for us space

508
00:27:25,400 --> 00:27:28,720
Speaker 4: is perceived as smooth and time as smooth and so on.

509
00:27:28,760 --> 00:27:32,600
Speaker 4: But if we were Plank scale creatures, we wouldn't. You know,

510
00:27:32,680 --> 00:27:34,400
Speaker 4: of course we don't know what's going on down there,

511
00:27:34,400 --> 00:27:38,080
Speaker 4: but under our current understanding, you wouldn't have the concept

512
00:27:38,080 --> 00:27:41,200
Speaker 4: of space time as smooth. So, as you say it emerges,

513
00:27:41,440 --> 00:27:44,760
Speaker 4: it appears smooth only at our scale, or well down

514
00:27:44,760 --> 00:27:48,040
Speaker 4: to even atomic scales. But it's still twenty five orders

515
00:27:48,080 --> 00:27:50,520
Speaker 4: of magnitude bigger than the Plank scale to go to

516
00:27:50,560 --> 00:27:53,359
Speaker 4: the hydrogen atoms diameter. So yeah, it might just be

517
00:27:53,560 --> 00:27:57,000
Speaker 4: where you know, all those jitters, their quantum gravitational jitters

518
00:27:57,000 --> 00:27:59,639
Speaker 4: are invisible, they get smoothed out, or they start to

519
00:27:59,640 --> 00:28:03,480
Speaker 4: look space time emerges. Right. That's the latest talk that

520
00:28:03,600 --> 00:28:06,760
Speaker 4: space time as a manifold in the jargon of differential

521
00:28:06,760 --> 00:28:10,399
Speaker 4: geometry as this smooth structure. That's another fiction. That's an

522
00:28:10,440 --> 00:28:14,560
Speaker 4: emergent property of something about quantum fluctuations, maybe having to

523
00:28:14,560 --> 00:28:17,480
Speaker 4: do with entanglement. Anyway, I don't know about that stuff.

524
00:28:17,520 --> 00:28:19,760
Speaker 4: You probably have other guests who could address that better.

525
00:28:19,840 --> 00:28:23,800
Speaker 4: But yeah, so we're probably studying the emergent theory that

526
00:28:24,200 --> 00:28:27,879
Speaker 4: just the way thermodynamics works well, even those statistical mechanics

527
00:28:27,920 --> 00:28:32,240
Speaker 4: is the deeper theory calculus and all of smooth classical physics,

528
00:28:32,240 --> 00:28:35,520
Speaker 4: and even the smooth parts of quantum physics, say the

529
00:28:35,560 --> 00:28:39,160
Speaker 4: Schrodinger equation or the direct equation, those things are emergent.

530
00:28:39,240 --> 00:28:41,280
Speaker 4: But I guess your question is why does emergence work

531
00:28:41,360 --> 00:28:44,360
Speaker 4: so well, that's something about a different branch of math,

532
00:28:44,400 --> 00:28:48,240
Speaker 4: that's about statistics, about laws of large numbers. And it's

533
00:28:48,280 --> 00:28:50,880
Speaker 4: a very fortunate accident. I mean, maybe it's not an accident.

534
00:28:50,880 --> 00:28:54,560
Speaker 4: Maybe we couldn't exist as intelligent creatures except at that scale.

535
00:28:54,640 --> 00:28:58,520
Speaker 4: If we were these hypothetical quantum gravitational scale creatures at

536
00:28:58,520 --> 00:29:01,080
Speaker 4: the Plank scale, we'd be so it would be hard

537
00:29:01,080 --> 00:29:03,320
Speaker 4: to keep a thought in our heads. You know what

538
00:29:03,560 --> 00:29:05,360
Speaker 4: I mean, I'm being silly. We wouldn't have heads.

539
00:29:06,200 --> 00:29:08,760
Speaker 1: Podcast episodes would be ten to the minus thirty four

540
00:29:08,800 --> 00:29:09,400
Speaker 1: seconds long.

541
00:29:13,040 --> 00:29:16,280
Speaker 4: So I guess I'm giving an anthropic principle style argument here,

542
00:29:16,280 --> 00:29:18,920
Speaker 4: aren't they. But it's hard to answer these deep questions.

543
00:29:18,960 --> 00:29:20,640
Speaker 1: It is hard, and to me it really goes to

544
00:29:20,680 --> 00:29:23,800
Speaker 1: the heart of these questions about whether we are describing

545
00:29:23,840 --> 00:29:27,320
Speaker 1: the universe as it is or just our view of it,

546
00:29:27,360 --> 00:29:30,520
Speaker 1: and whether our view of it is somehow human centric

547
00:29:30,640 --> 00:29:33,000
Speaker 1: in a way that we can't unravel and can't peel

548
00:29:33,120 --> 00:29:36,080
Speaker 1: back because we only have our human view and the

549
00:29:36,080 --> 00:29:38,840
Speaker 1: appearance of calculus and like short simple stories to me

550
00:29:38,960 --> 00:29:41,600
Speaker 1: like our interesting clue to grab onto. So let me

551
00:29:41,600 --> 00:29:43,600
Speaker 1: steer us back the other direction. Because we've sort of

552
00:29:43,760 --> 00:29:46,920
Speaker 1: described calculus as a useful fiction. We've said it's a

553
00:29:46,960 --> 00:29:49,120
Speaker 1: handy tool for doing calculations, but as you say, it

554
00:29:49,160 --> 00:29:51,920
Speaker 1: comes on the stage and disappears before the answer is revealed.

555
00:29:52,000 --> 00:29:55,320
Speaker 1: And yet it is really really powerful, right. Calculus and

556
00:29:55,320 --> 00:29:58,200
Speaker 1: math in general is sometimes described as like being unreasonably

557
00:29:58,240 --> 00:30:00,920
Speaker 1: effective in your book, I really like this line you wrote.

558
00:30:00,920 --> 00:30:03,880
Speaker 1: You said, what fascinates me as an applied mathematician is

559
00:30:03,920 --> 00:30:06,360
Speaker 1: the push and pull between the real world around us

560
00:30:06,520 --> 00:30:09,760
Speaker 1: and the ideal world in our heads. Phenomena out there

561
00:30:09,800 --> 00:30:13,440
Speaker 1: guide the mathematical questions we ask. Conversely, the math we

562
00:30:13,520 --> 00:30:17,520
Speaker 1: imagine sometimes foreshadows what actually happens out there in reality.

563
00:30:17,600 --> 00:30:20,880
Speaker 1: When it does, the effect is uncanny. And later you

564
00:30:20,920 --> 00:30:24,640
Speaker 1: wrote it's eerie. The calculus can mimic nature. So well,

565
00:30:25,080 --> 00:30:26,800
Speaker 1: can you elaborate on that a little bit? Why do

566
00:30:26,840 --> 00:30:29,960
Speaker 1: you think math is so good at describing the universe

567
00:30:30,000 --> 00:30:32,160
Speaker 1: if it's just sort of a fiction in our minds?

568
00:30:32,640 --> 00:30:35,440
Speaker 1: And why do we then describe it as unreasonable or

569
00:30:35,560 --> 00:30:38,640
Speaker 1: uncanny or eerie when that happens? Why are we surprised

570
00:30:38,680 --> 00:30:38,959
Speaker 1: by that?

571
00:30:39,200 --> 00:30:42,240
Speaker 4: Well? Should we stipulate that we believe in all this?

572
00:30:42,320 --> 00:30:44,360
Speaker 4: I mean, is it worth going into any case studies

573
00:30:44,360 --> 00:30:47,040
Speaker 4: of the eerie effectiveness? Or do you think we should

574
00:30:47,080 --> 00:30:48,040
Speaker 4: just assume that we know it?

575
00:30:48,160 --> 00:30:49,760
Speaker 1: No? Please give us some examples.

576
00:30:49,880 --> 00:30:52,000
Speaker 4: Well, okay, yeah, let's talk about a few. Because I

577
00:30:52,040 --> 00:30:54,640
Speaker 4: did feel myself recoiling a bit. I felt like you

578
00:30:54,680 --> 00:30:58,320
Speaker 4: were almost verging toward a kind of circular reasoning claim

579
00:30:58,440 --> 00:31:01,320
Speaker 4: that we as human beings can only think a certain

580
00:31:01,320 --> 00:31:04,120
Speaker 4: way or perceive certain things, and so it all kind

581
00:31:04,160 --> 00:31:07,240
Speaker 4: of comes out tidy because of our own limitations, like

582
00:31:07,280 --> 00:31:10,120
Speaker 4: we're convincing ourself. I don't think you were saying that exactly,

583
00:31:10,160 --> 00:31:12,360
Speaker 4: but if some people heard it like that, I would

584
00:31:12,360 --> 00:31:14,520
Speaker 4: have to push back on that. Because of the concept

585
00:31:14,520 --> 00:31:17,400
Speaker 4: of prediction. We use our math, We use all of

586
00:31:17,400 --> 00:31:21,320
Speaker 4: our scientific laws and observations to make predictions of things

587
00:31:21,320 --> 00:31:24,000
Speaker 4: we haven't seen before or haven't measured. And there's no

588
00:31:24,280 --> 00:31:27,800
Speaker 4: circular aspect to what we predict. Either nature does what

589
00:31:27,840 --> 00:31:30,120
Speaker 4: we predict or it doesn't. And there have been plenty

590
00:31:30,120 --> 00:31:32,920
Speaker 4: of cases of you know, flogiston theories and all kinds

591
00:31:32,920 --> 00:31:34,880
Speaker 4: of other things that turned out to be wrong. So

592
00:31:34,920 --> 00:31:37,320
Speaker 4: science is done in good faith. We make predictions and

593
00:31:37,360 --> 00:31:39,479
Speaker 4: they sometimes come out wrong. And yeah, I mean there

594
00:31:39,480 --> 00:31:41,760
Speaker 4: are old people who will hang onto the theory after

595
00:31:41,760 --> 00:31:43,400
Speaker 4: they should have given it up. But it's a self

596
00:31:43,400 --> 00:31:46,960
Speaker 4: correcting enterprise, it really is, I think over the long run.

597
00:31:47,160 --> 00:31:50,239
Speaker 4: So I don't think there's any circularity happening here. And

598
00:31:50,480 --> 00:31:53,080
Speaker 4: you know, for me, the eerie examples are things like,

599
00:31:53,360 --> 00:31:57,040
Speaker 4: you know, take Maxwell, James Clerk, Maxwell, who has these

600
00:31:57,040 --> 00:32:01,720
Speaker 4: empirical laws from people like Ampere and Faraday and I

601
00:32:01,720 --> 00:32:04,040
Speaker 4: don't know Bosavr. All these laws that we learn about

602
00:32:04,040 --> 00:32:07,720
Speaker 4: in electricity and magnetism courses for what happens with magnets,

603
00:32:07,720 --> 00:32:10,360
Speaker 4: with electric currents and circuits and stuff. So these laws

604
00:32:10,360 --> 00:32:13,880
Speaker 4: then could be rewritten in a certain mathematical language, and

605
00:32:13,960 --> 00:32:16,720
Speaker 4: Maxwell did that using the language at the time, which

606
00:32:16,800 --> 00:32:21,240
Speaker 4: was called quaternions, but nowadays we would use vectors vector calculus.

607
00:32:21,280 --> 00:32:23,800
Speaker 4: And he saw certain things in those laws that looked

608
00:32:23,840 --> 00:32:26,680
Speaker 4: a little contradictory to him. That led him to introduce

609
00:32:26,720 --> 00:32:29,560
Speaker 4: a new concept, the displacement current. And when he put

610
00:32:29,600 --> 00:32:33,040
Speaker 4: that in the known laws and started cranking the mathematical

611
00:32:33,120 --> 00:32:36,480
Speaker 4: crank just manipulating the equations. Now in the world of

612
00:32:36,520 --> 00:32:40,520
Speaker 4: pure idealization, in the world of calculus, he saw that

613
00:32:40,560 --> 00:32:44,400
Speaker 4: those equations predicted something, which is that electric fields and

614
00:32:44,440 --> 00:32:47,640
Speaker 4: magnetic fields could move through empty space, although for him

615
00:32:47,680 --> 00:32:50,120
Speaker 4: it was the ether, but nowadays we would say empty

616
00:32:50,120 --> 00:32:53,160
Speaker 4: space in this kind of dance, with the electric field

617
00:32:53,280 --> 00:32:56,000
Speaker 4: changing and generating a magnetic field that would change and

618
00:32:56,040 --> 00:32:58,720
Speaker 4: regenerate the electric field, and the whole thing would propagate

619
00:32:58,800 --> 00:33:01,400
Speaker 4: at a certain speed governed by an equation that in

620
00:33:01,760 --> 00:33:05,600
Speaker 4: calculus we call the wave equation. So he's predicting electromagnetic

621
00:33:05,600 --> 00:33:09,080
Speaker 4: waves those were not known. That's a prediction, and his

622
00:33:09,200 --> 00:33:11,920
Speaker 4: math gives him a prediction for the speed of those waves,

623
00:33:12,200 --> 00:33:14,680
Speaker 4: and when he calculates it using the known physics, it

624
00:33:14,680 --> 00:33:16,400
Speaker 4: comes out to be the speed of light. So it's

625
00:33:16,440 --> 00:33:18,640
Speaker 4: one of the biggest aha moments in the history of

626
00:33:18,720 --> 00:33:23,320
Speaker 4: humanity that light is an electromagnetic wave. And Maxwell's the

627
00:33:23,360 --> 00:33:25,760
Speaker 4: first to realize that, and it turns out it's right.

628
00:33:26,200 --> 00:33:28,760
Speaker 4: You know. Years later his predictions get checked out in

629
00:33:28,800 --> 00:33:33,400
Speaker 4: the lab, hurts measures that really are electromagnetic waves, and

630
00:33:33,440 --> 00:33:36,600
Speaker 4: pretty soon after that, Marconi and Tesla are building telegraphs

631
00:33:36,640 --> 00:33:39,680
Speaker 4: and we've got wireless communication across the ocean, and all

632
00:33:39,720 --> 00:33:42,160
Speaker 4: this stuff is real. But it was born out of

633
00:33:42,200 --> 00:33:45,400
Speaker 4: calculus combined with physics. Let's be clear. It's not calculus

634
00:33:45,440 --> 00:33:48,440
Speaker 4: on its own. It's calculus supplemented, not supplement I mean,

635
00:33:48,600 --> 00:33:50,920
Speaker 4: calculus are more like the supporting player. The real stars

636
00:33:50,960 --> 00:33:54,000
Speaker 4: are Michael Faraday and Ampere and the rest. But their

637
00:33:54,160 --> 00:33:57,680
Speaker 4: laws of nature have these logical implications that lead to

638
00:33:57,720 --> 00:33:59,800
Speaker 4: predictions that turn out to be right. And so what's

639
00:33:59,840 --> 00:34:03,120
Speaker 4: on canny there is that nature is obeying logic that's

640
00:34:03,240 --> 00:34:07,400
Speaker 4: not necessary right. This is puny primate logic. This is us.

641
00:34:07,440 --> 00:34:10,120
Speaker 4: We're not the best imaginable thing under the sun. But

642
00:34:10,200 --> 00:34:14,120
Speaker 4: our logic somehow is enough to make these predictions. And

643
00:34:14,160 --> 00:34:16,560
Speaker 4: you know, well, there's countless examples of this. So but

644
00:34:16,640 --> 00:34:18,280
Speaker 4: maybe that Maxwell one makes the point.

645
00:34:18,360 --> 00:34:20,680
Speaker 1: I'm wondering if you know anymore about the history of it,

646
00:34:20,719 --> 00:34:23,960
Speaker 1: because I've heard this story about Maxwell's AHA moment, and

647
00:34:24,000 --> 00:34:27,560
Speaker 1: I wonder historically, was there a moment. It's such an

648
00:34:27,640 --> 00:34:30,440
Speaker 1: incredible realization. I'd like to imagine that he was sitting

649
00:34:30,480 --> 00:34:32,960
Speaker 1: there by lantern light at his desk and it all

650
00:34:32,960 --> 00:34:35,640
Speaker 1: clicked together and he had this epiphany where like he

651
00:34:35,719 --> 00:34:38,080
Speaker 1: saw the universe in a way nobody'd ever seen it before.

652
00:34:38,120 --> 00:34:39,560
Speaker 1: Do you know if there was such a moment, if

653
00:34:39,560 --> 00:34:41,600
Speaker 1: we're sort of a gradual coming together.

654
00:34:41,640 --> 00:34:43,440
Speaker 4: I don't know. I want to know that too, And

655
00:34:43,520 --> 00:34:46,760
Speaker 4: that's funny. I have the same fantasy image of the lantern,

656
00:34:47,160 --> 00:34:50,880
Speaker 4: the little hovel in Scotland, So I don't know. I

657
00:34:50,920 --> 00:34:53,600
Speaker 4: think it is known. I think this is another point

658
00:34:53,600 --> 00:34:56,640
Speaker 4: that history of science is such a rich and detailed

659
00:34:56,680 --> 00:35:00,680
Speaker 4: and often non logical thing. Like we you and I

660
00:35:00,760 --> 00:35:02,840
Speaker 4: are telling ourselves this story a certain way, and I

661
00:35:02,920 --> 00:35:04,520
Speaker 4: just told it a certain way, and I don't really

662
00:35:04,520 --> 00:35:07,600
Speaker 4: know what I'm talking about. For instance, I read somewhere

663
00:35:07,600 --> 00:35:10,279
Speaker 4: fairly recently, that he knew that light was going to

664
00:35:10,360 --> 00:35:13,160
Speaker 4: turn out to be an electromagnetic wave before his math

665
00:35:13,200 --> 00:35:16,680
Speaker 4: showed him that just on dimensional grounds. You earlier were

666
00:35:16,719 --> 00:35:20,000
Speaker 4: talking about the Planck scale and the cancelation of units

667
00:35:20,000 --> 00:35:22,640
Speaker 4: and stuff, or not cancelation, but you can get arguments

668
00:35:22,680 --> 00:35:25,880
Speaker 4: based on dimensional just by monkeying around with units. I

669
00:35:25,880 --> 00:35:28,879
Speaker 4: think he knew that mew not and epsilon not, these

670
00:35:28,920 --> 00:35:32,200
Speaker 4: properties of the vacuum having to do with its magnetic

671
00:35:32,200 --> 00:35:34,800
Speaker 4: and electrical properties, that they could be combined in a

672
00:35:34,840 --> 00:35:36,880
Speaker 4: certain way to make a speed And I think he

673
00:35:36,920 --> 00:35:40,240
Speaker 4: did that calculation about a decade before he actually derived

674
00:35:40,239 --> 00:35:40,960
Speaker 4: the wave equation.

675
00:35:41,200 --> 00:35:43,360
Speaker 1: Wow, it it'd be delicious to understand the history of

676
00:35:43,400 --> 00:35:45,120
Speaker 1: that a little bit better. But I love the argument

677
00:35:45,160 --> 00:35:48,759
Speaker 1: you're making here that essentially the math guide to the physics,

678
00:35:48,760 --> 00:35:53,720
Speaker 1: that he saw something that wasn't symmetric, that looked imbalanced mathematically,

679
00:35:54,000 --> 00:35:56,720
Speaker 1: and he patched it up just because of his mathematical intuition,

680
00:35:56,880 --> 00:35:59,200
Speaker 1: and the physics sort of followed suit. That I was

681
00:35:59,200 --> 00:36:03,000
Speaker 1: a better discription of the universe because mathematically it hung

682
00:36:03,080 --> 00:36:06,480
Speaker 1: together more crisply than the previous ideas. That the math

683
00:36:06,640 --> 00:36:09,680
Speaker 1: really did guide us to truth about the universe? Is

684
00:36:09,719 --> 00:36:10,760
Speaker 1: that the core of the argument.

685
00:36:11,000 --> 00:36:13,880
Speaker 4: Yeah, And the part that is spooky is, look who's

686
00:36:13,920 --> 00:36:18,040
Speaker 4: behind it. It's this creature that has evolved on this

687
00:36:18,120 --> 00:36:21,719
Speaker 4: planet in an ordinary galaxy, you know. I mean, it's

688
00:36:21,719 --> 00:36:24,320
Speaker 4: not like we have godlike intelligence. The thing that's so

689
00:36:24,880 --> 00:36:28,279
Speaker 4: spooky is we're so bounded in our understanding. We can

690
00:36:28,400 --> 00:36:32,120
Speaker 4: understand so much through the help of this crazy fictional

691
00:36:32,200 --> 00:36:34,640
Speaker 4: thing that involves infinity. It's almost like we're in the

692
00:36:34,640 --> 00:36:37,920
Speaker 4: sweet spot for pleasure in doing science and math. If

693
00:36:37,960 --> 00:36:41,160
Speaker 4: we were much smarter than we are, we wouldn't be surprised.

694
00:36:41,200 --> 00:36:43,840
Speaker 4: Everything would be trivial, Like playing tic tac toe is

695
00:36:43,840 --> 00:36:46,640
Speaker 4: not interesting for someone who understands it, and so grown

696
00:36:46,680 --> 00:36:49,960
Speaker 4: ups don't play tic tac toe for fun because it's boring.

697
00:36:50,120 --> 00:36:52,759
Speaker 4: And if we were just a bit smarter, physics and

698
00:36:52,840 --> 00:36:55,680
Speaker 4: math might be boring in the same way. But it's

699
00:36:55,680 --> 00:36:58,160
Speaker 4: fun for us because we're in this place where we're

700
00:36:58,160 --> 00:37:00,680
Speaker 4: not as stupid as a lobster. I mean, a lobster

701
00:37:00,760 --> 00:37:04,920
Speaker 4: is not inventing calculus. We're at this happy resonant place

702
00:37:05,280 --> 00:37:09,040
Speaker 4: where we're smart enough to get it, but sort of

703
00:37:09,040 --> 00:37:11,240
Speaker 4: stupid enough to be surprised all the time.

704
00:37:12,640 --> 00:37:15,080
Speaker 1: It is amazing. It's a really fun game, but it's

705
00:37:15,200 --> 00:37:18,120
Speaker 1: also teaching us things about the universe, which is incredible.

706
00:37:18,160 --> 00:37:20,960
Speaker 1: As I was hearing you talk about that Scottish mathematician,

707
00:37:21,120 --> 00:37:24,719
Speaker 1: I was reminded of another Scotsman more than a century later,

708
00:37:24,760 --> 00:37:27,759
Speaker 1: Peter Higgs, who made sort of a similar realization. He

709
00:37:27,840 --> 00:37:31,239
Speaker 1: was looking at the mathematics of not just electromagnetism, but

710
00:37:31,360 --> 00:37:34,400
Speaker 1: electromagnetism and the weak force, how they clicked together, and

711
00:37:34,440 --> 00:37:37,640
Speaker 1: realizing there was a missing piece and predicting the existence

712
00:37:37,680 --> 00:37:39,560
Speaker 1: of a field we now call the Higgs field. So

713
00:37:39,920 --> 00:37:41,880
Speaker 1: you know, maybe it's something in the water in Scotland.

714
00:37:42,080 --> 00:37:45,279
Speaker 4: Ah. Well, it's another great example because it took a

715
00:37:45,320 --> 00:37:48,400
Speaker 4: long time for that prediction to be checked in the

716
00:37:48,480 --> 00:37:51,759
Speaker 4: lab and tremendous effort and cost from great teams of

717
00:37:51,840 --> 00:37:57,640
Speaker 4: physicists and engineers at the Large Hadron Collider. Is that right? Yeah? Detected?

718
00:37:57,800 --> 00:38:00,600
Speaker 4: So I didn't have to be there. And some things

719
00:38:00,640 --> 00:38:04,200
Speaker 4: aren't there, right, like supersymmetry. Is this other beautiful set

720
00:38:04,200 --> 00:38:06,520
Speaker 4: of ideas that so far has not turned out to

721
00:38:06,560 --> 00:38:09,600
Speaker 4: be in the experimental data. It may be in the future,

722
00:38:09,640 --> 00:38:11,720
Speaker 4: but I'm just saying that this is a very honest

723
00:38:11,840 --> 00:38:15,120
Speaker 4: enterprise in science. It's not circular reasoning. It's not like

724
00:38:15,160 --> 00:38:19,000
Speaker 4: we're convincing ourself. We're really doing fair play. And the

725
00:38:19,120 --> 00:38:22,480
Speaker 4: universe either does what we imagine or not, and frequently

726
00:38:22,520 --> 00:38:26,279
Speaker 4: and uncannily it does if we use calculus and feed in.

727
00:38:26,360 --> 00:38:27,919
Speaker 4: I mean, that's the other thing. Like you'll hear people

728
00:38:27,960 --> 00:38:30,920
Speaker 4: say calculus is a language or math is the language

729
00:38:30,920 --> 00:38:34,319
Speaker 4: of science. Partly true, but it's much more than that.

730
00:38:34,400 --> 00:38:38,479
Speaker 4: Math and calculus in particular are a calculating machine. They're

731
00:38:38,560 --> 00:38:42,400
Speaker 4: a logical prosthesis. I mean, there's something which lets us

732
00:38:42,440 --> 00:38:46,960
Speaker 4: take our logic again puny primate logic, and strengthen it

733
00:38:47,320 --> 00:38:51,239
Speaker 4: by introducing symbols and letting us do logical manipulations like

734
00:38:51,400 --> 00:38:53,960
Speaker 4: you know, solving equations. That kind of thing is a

735
00:38:53,960 --> 00:38:56,440
Speaker 4: big extension to what we can hold in our heads.

736
00:38:56,520 --> 00:38:58,640
Speaker 4: That's why we have paper and pencil. You can make

737
00:38:58,680 --> 00:39:01,120
Speaker 4: these arguments much more more elaborate than you could have

738
00:39:01,239 --> 00:39:04,000
Speaker 4: easily held. Like think of algebra. Before we had symbols

739
00:39:04,000 --> 00:39:06,040
Speaker 4: and it was all verbal, it was a much weaker thing.

740
00:39:06,160 --> 00:39:08,560
Speaker 4: So now we just shove these symbols around on paper.

741
00:39:08,600 --> 00:39:11,440
Speaker 4: According to certain rules, and out we get predictions for

742
00:39:11,920 --> 00:39:15,239
Speaker 4: electromagnetic waves or the existence of the Higgs particle. I

743
00:39:15,320 --> 00:39:17,880
Speaker 4: find that very uncanny. I just get I don't know

744
00:39:17,880 --> 00:39:19,839
Speaker 4: how else to say it. To me, it's the spookiest

745
00:39:19,840 --> 00:39:22,440
Speaker 4: and most profound thing there is that this works. And

746
00:39:22,480 --> 00:39:24,560
Speaker 4: I want to emphasize in case people are saying this

747
00:39:24,680 --> 00:39:27,280
Speaker 4: is just math. Why do I harp on calculus so much?

748
00:39:27,400 --> 00:39:29,920
Speaker 4: I really do think calculus has a singular place in

749
00:39:29,960 --> 00:39:33,080
Speaker 4: the landscape of math, in that the laws of nature

750
00:39:33,160 --> 00:39:36,840
Speaker 4: are written in a subdialect of math. It's calculus. And

751
00:39:37,040 --> 00:39:39,680
Speaker 4: even there it's the particular part of calculus we call

752
00:39:39,719 --> 00:39:43,400
Speaker 4: differential equations. So from f equals Ma and Newton to

753
00:39:43,480 --> 00:39:47,520
Speaker 4: Einstein's general relativity to Schrodinger's you know, wave equation, those

754
00:39:47,560 --> 00:39:50,560
Speaker 4: are all differential equations. So it's not like we're using

755
00:39:50,800 --> 00:39:54,440
Speaker 4: combinatorics or some other part of discrete math that is

756
00:39:54,480 --> 00:39:57,680
Speaker 4: not the language of the universe. Sorry, maybe it is

757
00:39:57,719 --> 00:40:00,200
Speaker 4: at the smallest scale, Okay, maybe it will turn out

758
00:40:00,200 --> 00:40:03,920
Speaker 4: the combinatorics is the answer to the Planck scale stuff,

759
00:40:04,000 --> 00:40:07,560
Speaker 4: and calculus is just this emergent, smoothed out version of

760
00:40:07,560 --> 00:40:10,160
Speaker 4: what's really going on, which is combinatorics if we get

761
00:40:10,160 --> 00:40:12,239
Speaker 4: down to the bottom. But for the thirty five orders

762
00:40:12,239 --> 00:40:16,520
Speaker 4: of magnitude that we've done science on so far, it's calculus. Baby.

763
00:40:18,800 --> 00:40:21,400
Speaker 1: Well. I had in my own aha moment as a

764
00:40:21,640 --> 00:40:25,360
Speaker 1: junior in quantum physics, seeing the prediction of properties of

765
00:40:25,400 --> 00:40:29,120
Speaker 1: the electron muon ow to ten decimal places, and then

766
00:40:29,160 --> 00:40:33,240
Speaker 1: seeing the experiments which verify those predictions digit after digit

767
00:40:33,280 --> 00:40:36,360
Speaker 1: after digit, and feeling for the first time that maybe

768
00:40:36,400 --> 00:40:39,759
Speaker 1: math wasn't just a description of what was happening out

769
00:40:39,800 --> 00:40:42,920
Speaker 1: there in our language, but it really was the essential

770
00:40:43,000 --> 00:40:46,640
Speaker 1: underlying machinery of the universe itself, that the universe was

771
00:40:46,800 --> 00:40:50,320
Speaker 1: using these laws, that we weren't describing them but revealing

772
00:40:50,360 --> 00:40:53,880
Speaker 1: them somehow. And I know that it's a philosophical position,

773
00:40:53,920 --> 00:40:56,360
Speaker 1: but I had this moment as an undergrad of feeling this,

774
00:40:56,480 --> 00:40:57,880
Speaker 1: and I thought of that moment when I read this

775
00:40:57,960 --> 00:41:01,520
Speaker 1: passage in your book. You wrote, quote, the results are

776
00:41:01,640 --> 00:41:04,759
Speaker 1: there waiting for us. They have been inherent in the

777
00:41:04,760 --> 00:41:08,000
Speaker 1: figures all along. We are not inventing them like Bob

778
00:41:08,080 --> 00:41:10,520
Speaker 1: Dylan or Tony Morrison, and we are not creating music

779
00:41:10,600 --> 00:41:13,520
Speaker 1: or novels that never existed before. We are discovering facts

780
00:41:13,520 --> 00:41:16,319
Speaker 1: that already exist. And as I was reading your book,

781
00:41:16,320 --> 00:41:18,560
Speaker 1: I was wondering, you know, Steve a realist or is

782
00:41:18,600 --> 00:41:20,799
Speaker 1: he not a realist? And I sort of went back

783
00:41:20,840 --> 00:41:22,840
Speaker 1: and forth a few times as I read these passages.

784
00:41:23,080 --> 00:41:26,120
Speaker 4: Oh, really, was I not clear where I stand on that? Well,

785
00:41:26,120 --> 00:41:28,239
Speaker 4: that's earlier what I was saying with these two people.

786
00:41:28,320 --> 00:41:30,440
Speaker 4: I guess I didn't make the argument for both sides

787
00:41:30,560 --> 00:41:33,200
Speaker 4: that there's the chicken hearted person in me who is

788
00:41:33,239 --> 00:41:35,319
Speaker 4: the one that thinks it's just a language and it's

789
00:41:35,440 --> 00:41:37,399
Speaker 4: just you know. But in my heart, I think it's

790
00:41:37,400 --> 00:41:40,480
Speaker 4: what you're calling realism, which is that the universe isn't

791
00:41:40,560 --> 00:41:44,000
Speaker 4: just described by calculus. The universe actually runs on calculus.

792
00:41:44,040 --> 00:41:46,200
Speaker 4: I really do, in my heart of hearts think that.

793
00:41:46,800 --> 00:41:48,880
Speaker 4: And I don't know why that would be true. I

794
00:41:48,920 --> 00:41:51,360
Speaker 4: think the answer could be, again some kind of anthropic

795
00:41:51,640 --> 00:41:55,000
Speaker 4: argument that a universe that doesn't run on math in

796
00:41:55,080 --> 00:41:58,680
Speaker 4: some way is such a disorganized, higgledy piggledy universe that

797
00:41:58,719 --> 00:42:02,840
Speaker 4: it can't support life intelligent enough to ask questions. So

798
00:42:02,880 --> 00:42:04,720
Speaker 4: I sort of think just the fact that we exist

799
00:42:04,760 --> 00:42:07,279
Speaker 4: and we're here pondering it tells you the universe has

800
00:42:07,320 --> 00:42:10,880
Speaker 4: to obey a certain amount of orderliness, and calculus is

801
00:42:10,920 --> 00:42:13,840
Speaker 4: going to come up in such universes. So it's not

802
00:42:13,880 --> 00:42:16,279
Speaker 4: the most convincing argument. I don't like that argument, but

803
00:42:16,320 --> 00:42:18,080
Speaker 4: that's the best I can do. I mean, obviously, you

804
00:42:18,080 --> 00:42:21,520
Speaker 4: could give a theological argument that God knew calculus better

805
00:42:21,520 --> 00:42:23,799
Speaker 4: than anybody and chose to make a universe that runs

806
00:42:23,800 --> 00:42:27,520
Speaker 4: on calculus. Okay, if that satisfies you, then that's that.

807
00:42:27,560 --> 00:42:29,440
Speaker 4: You could use that argument. But to me, that just

808
00:42:29,520 --> 00:42:31,600
Speaker 4: raises a lot more questions. But I don't have the

809
00:42:31,640 --> 00:42:34,120
Speaker 4: answers to why was it designed this way or built

810
00:42:34,120 --> 00:42:36,640
Speaker 4: this way, or why did it evolve to be this way?

811
00:42:36,680 --> 00:42:39,040
Speaker 4: I don't have any idea, But yeah, that's interesting. I

812
00:42:39,080 --> 00:42:41,719
Speaker 4: mean that ten digit example you give from quantum field theory,

813
00:42:41,719 --> 00:42:45,600
Speaker 4: from quantum electro dynamics, that's really the poster child for

814
00:42:45,800 --> 00:42:49,120
Speaker 4: the claim that the universe is running on math and

815
00:42:49,160 --> 00:42:51,799
Speaker 4: that we happen to have stumbled across that math. That's

816
00:42:51,840 --> 00:42:54,080
Speaker 4: also fun to think about that. Just think of the

817
00:42:54,120 --> 00:42:58,399
Speaker 4: story there's Archimedes in Syracuse pondering circles and spheres two

818
00:42:58,440 --> 00:43:02,160
Speaker 4: fifty BC, and he's stumbling across the math that turns

819
00:43:02,160 --> 00:43:07,400
Speaker 4: out to describe sub atomic particles like muons. Ultimately, a

820
00:43:07,400 --> 00:43:10,600
Speaker 4: few thousand years later, it's that same math and he

821
00:43:10,719 --> 00:43:14,080
Speaker 4: wasn't thinking about that. It's really spooky that that should work,

822
00:43:14,360 --> 00:43:15,040
Speaker 4: but it did.

823
00:43:15,280 --> 00:43:17,520
Speaker 1: It is pretty amazing. All right, I'm really excited about

824
00:43:17,520 --> 00:43:24,520
Speaker 1: these topics. But let's take another quick break. When you

825
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826
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Speaker 1: Okay, we are here talking with Professor Steve's drogads about

872
00:45:50,600 --> 00:45:54,480
Speaker 1: why math and physics are so closely intertwined. In your

873
00:45:54,600 --> 00:45:57,320
Speaker 1: episode of The Joy of Why You inviewed Kevin Buzzard,

874
00:45:57,360 --> 00:46:00,880
Speaker 1: a mathematician, and he described math as a single player

875
00:46:01,000 --> 00:46:04,240
Speaker 1: puzzle game. And I was actually expecting you to object

876
00:46:04,280 --> 00:46:06,959
Speaker 1: a little bit because it makes it sound like math

877
00:46:07,080 --> 00:46:09,640
Speaker 1: is just this game we play. It's fun to use

878
00:46:09,680 --> 00:46:12,759
Speaker 1: to describe the universe, but not actually fundamentally important. It

879
00:46:12,840 --> 00:46:14,759
Speaker 1: makes it sound like Checkers or chess, you know, just

880
00:46:14,840 --> 00:46:18,240
Speaker 1: a game that we invented rather than something physical and true.

881
00:46:19,040 --> 00:46:22,000
Speaker 4: Well, that may be me As a podcast host, I

882
00:46:22,200 --> 00:46:24,959
Speaker 4: probably ought to push back more and maybe it would

883
00:46:24,960 --> 00:46:28,200
Speaker 4: make for lively or discussion. I try to be even handed,

884
00:46:28,280 --> 00:46:30,320
Speaker 4: unfair to the guest. And there is an aspect of

885
00:46:30,400 --> 00:46:34,279
Speaker 4: math that is game playing, especially in pure math, and

886
00:46:34,400 --> 00:46:37,719
Speaker 4: that's not to be sneezed at. Just playing games for

887
00:46:37,880 --> 00:46:40,960
Speaker 4: the intellectual pleasure of playing games and the fun and

888
00:46:41,040 --> 00:46:43,239
Speaker 4: the curiosity of how does the game turn out or

889
00:46:43,520 --> 00:46:45,480
Speaker 4: what happens if I change the rules in this way

890
00:46:45,600 --> 00:46:48,719
Speaker 4: or that way. That's all part of the scientific enterprise

891
00:46:49,000 --> 00:46:51,480
Speaker 4: as well as the mathematical enterprise. And it's a healthy

892
00:46:51,520 --> 00:46:53,120
Speaker 4: one for one thing. I mean, if you want to

893
00:46:53,160 --> 00:46:56,080
Speaker 4: be utilitarian about it, A lot of great discoveries in

894
00:46:56,200 --> 00:46:58,719
Speaker 4: science have come from playing games like that. You know,

895
00:46:58,880 --> 00:47:01,120
Speaker 4: you could think about all those centuries that we thought

896
00:47:01,160 --> 00:47:04,800
Speaker 4: Euclidean geometry was the one true geometry, and then people

897
00:47:04,880 --> 00:47:06,919
Speaker 4: started playing games and asked, well, what if we don't

898
00:47:06,960 --> 00:47:09,360
Speaker 4: have the parallel postulate? What if we allow, you know,

899
00:47:09,520 --> 00:47:12,400
Speaker 4: infinitely many parallel lines to a given line, or what

900
00:47:12,480 --> 00:47:14,239
Speaker 4: if we say there are no parallel lines to a

901
00:47:14,320 --> 00:47:16,880
Speaker 4: given line, you know, through a specific point. Well, then

902
00:47:16,920 --> 00:47:21,360
Speaker 4: you invent hyperbolic geometry and curved spherical or elliptic geometry.

903
00:47:21,520 --> 00:47:24,320
Speaker 4: Those are games for a few hundred years until it

904
00:47:24,360 --> 00:47:27,360
Speaker 4: turns out the universe uses them. In Einstein's work, so

905
00:47:27,600 --> 00:47:30,320
Speaker 4: you could say, let the people play the games, because

906
00:47:30,360 --> 00:47:32,200
Speaker 4: it's going to turn out that the universe is going

907
00:47:32,280 --> 00:47:34,239
Speaker 4: to use them, and they'll be very practical, you know.

908
00:47:34,400 --> 00:47:37,080
Speaker 4: Or similarly, games about prime numbers have led to the

909
00:47:37,360 --> 00:47:39,400
Speaker 4: way that we can do encryption on the internet for

910
00:47:39,480 --> 00:47:42,520
Speaker 4: all of our financial transactions or for keeping secrets. So

911
00:47:42,640 --> 00:47:45,960
Speaker 4: gameplaying is not to be sneezed out on utilitarian grounds.

912
00:47:46,000 --> 00:47:49,040
Speaker 4: It turns out it's often very practical and useful maybe

913
00:47:49,080 --> 00:47:51,759
Speaker 4: a few centuries later. But I wouldn't want to just

914
00:47:51,880 --> 00:47:55,200
Speaker 4: make the utilitarian argument. It's also part of the human spirit.

915
00:47:55,480 --> 00:47:57,640
Speaker 4: Just be curious for the sake of curiosity, and it

916
00:47:57,680 --> 00:47:59,720
Speaker 4: may never turn out to be useful, and that's okay.

917
00:48:00,239 --> 00:48:02,480
Speaker 4: That's what makes it good to be alive for me.

918
00:48:02,640 --> 00:48:05,759
Speaker 1: One way to make this question less philosophical and more

919
00:48:05,880 --> 00:48:09,200
Speaker 1: concrete is to think about aliens. I know it makes

920
00:48:09,239 --> 00:48:11,720
Speaker 1: people snicker to talk about aliens, but instead of asking

921
00:48:11,840 --> 00:48:14,680
Speaker 1: you know, is math universal or is it cultural? Which

922
00:48:14,760 --> 00:48:17,360
Speaker 1: is a question philosophers have been chewing on for millennia

923
00:48:17,480 --> 00:48:21,120
Speaker 1: without making that much progress. I wonder like, if technological

924
00:48:21,320 --> 00:48:24,880
Speaker 1: scientific aliens arrive, it's a question we're actually going to

925
00:48:24,960 --> 00:48:28,000
Speaker 1: have to face whether they do math. We asked Noam

926
00:48:28,080 --> 00:48:30,279
Speaker 1: Chomsky about it on the podcast recently, you know, how

927
00:48:30,320 --> 00:48:32,880
Speaker 1: do you get started talking to aliens in that scenario?

928
00:48:33,040 --> 00:48:35,360
Speaker 1: And he went with the math. He said we should

929
00:48:35,400 --> 00:48:39,200
Speaker 1: start with arithmetic because one plus one equals too everywhere,

930
00:48:39,680 --> 00:48:42,840
Speaker 1: And he was suggesting that any intelligent being in the

931
00:48:42,960 --> 00:48:45,719
Speaker 1: universe is going to end up being mathematical, which is

932
00:48:45,840 --> 00:48:48,880
Speaker 1: essentially making the argument that math is not just human right,

933
00:48:48,960 --> 00:48:51,239
Speaker 1: that it's part of the universe itself. So I don't

934
00:48:51,239 --> 00:48:52,880
Speaker 1: know if you've given this question any thought. What do

935
00:48:52,960 --> 00:48:55,520
Speaker 1: you think if aliens arrive? Are you volunteering to be

936
00:48:56,160 --> 00:48:58,640
Speaker 1: one of the envoys? And should we send our mathematicians

937
00:48:58,719 --> 00:48:59,760
Speaker 1: to talk to the aliens?

938
00:49:00,840 --> 00:49:03,279
Speaker 4: I've seen too many Twilight Zone episodes. I know how

939
00:49:03,360 --> 00:49:07,640
Speaker 4: this turns out, but yeah, I've seen the ending of

940
00:49:07,680 --> 00:49:10,480
Speaker 4: that one. Well, it's probably the best suggestion there is

941
00:49:11,400 --> 00:49:15,120
Speaker 4: that math would be the most universal possible language in

942
00:49:15,200 --> 00:49:18,080
Speaker 4: this scenario. I'm not totally convinced that they would know

943
00:49:18,160 --> 00:49:20,560
Speaker 4: about one plus one, because you could make up stories

944
00:49:20,600 --> 00:49:24,520
Speaker 4: about intelligent life based on plasma or fluid dynamics where

945
00:49:24,520 --> 00:49:26,960
Speaker 4: they don't have discrete particles, so they don't really have

946
00:49:27,160 --> 00:49:29,640
Speaker 4: one plus one. Maybe it's all continuum for them and

947
00:49:29,719 --> 00:49:33,520
Speaker 4: they would rather talk about calculus rather than I'm hammering

948
00:49:33,560 --> 00:49:36,120
Speaker 4: again on the discrete stuff. But no, I mean, basically,

949
00:49:36,200 --> 00:49:38,359
Speaker 4: if the point is that we would could communicate through

950
00:49:38,440 --> 00:49:41,680
Speaker 4: math better than any other way, yeah, maybe so. I

951
00:49:41,760 --> 00:49:43,680
Speaker 4: tend to think they would have to have some version

952
00:49:43,719 --> 00:49:46,040
Speaker 4: of math, or they couldn't have built their rocket ships

953
00:49:46,160 --> 00:49:48,920
Speaker 4: or teleportation devices or however they got here. I think

954
00:49:48,960 --> 00:49:51,240
Speaker 4: they have to have math. I do think the math

955
00:49:51,480 --> 00:49:53,560
Speaker 4: is inherent in the universe. I like the quote you

956
00:49:53,680 --> 00:49:56,600
Speaker 4: gave earlier. There's a psychological dimension to this that I

957
00:49:56,719 --> 00:49:59,080
Speaker 4: want to bring up, which is that there's what philosophers

958
00:49:59,160 --> 00:50:02,719
Speaker 4: talk about like philosophy, but there's also what working physicists

959
00:50:02,760 --> 00:50:06,160
Speaker 4: and mathematicians feel when they're doing math or making discoveries.

960
00:50:06,480 --> 00:50:09,040
Speaker 4: It really feels like the results are out there waiting

961
00:50:09,120 --> 00:50:11,480
Speaker 4: for you. I mean, maybe it's a fiction, maybe it's

962
00:50:11,520 --> 00:50:15,400
Speaker 4: a psychological self deception, but it's very profound and it

963
00:50:15,480 --> 00:50:18,160
Speaker 4: goes way back. Archimedes says it two thousand years ago.

964
00:50:18,280 --> 00:50:20,800
Speaker 4: He says that the things he discovers about the sphere

965
00:50:21,040 --> 00:50:23,960
Speaker 4: are not his inventions, they're inherent in the figures themselves.

966
00:50:24,239 --> 00:50:28,279
Speaker 4: So he expresses very clearly a philosophy of math, which

967
00:50:28,320 --> 00:50:30,520
Speaker 4: I find kind of heartwarming because it makes me feel

968
00:50:30,560 --> 00:50:33,040
Speaker 4: like I'm having a conversation with this person thousands of

969
00:50:33,120 --> 00:50:35,399
Speaker 4: years ago, and that he's feeling some of the same

970
00:50:35,480 --> 00:50:38,200
Speaker 4: things I'm feeling as a mathematician today. And also that

971
00:50:38,320 --> 00:50:40,560
Speaker 4: he's very humble that he doesn't know how to solve

972
00:50:40,600 --> 00:50:42,960
Speaker 4: certain problems, and he just says he hopes his methods

973
00:50:42,960 --> 00:50:46,280
Speaker 4: will help future generations solve the things that he cannot

974
00:50:46,320 --> 00:50:46,799
Speaker 4: figure out.

975
00:50:46,880 --> 00:50:48,480
Speaker 1: I think it's an important lesson there. I mean, we

976
00:50:48,520 --> 00:50:51,360
Speaker 1: can talk about math as inherent to the universe, but

977
00:50:51,560 --> 00:50:54,200
Speaker 1: also there's a human aspect to it. I mean, we

978
00:50:54,320 --> 00:50:57,800
Speaker 1: really appreciate the beauty of math the way we appreciate

979
00:50:57,840 --> 00:51:00,120
Speaker 1: the beauty of a gorgeous view from the top of

980
00:51:00,160 --> 00:51:02,160
Speaker 1: a mountain. Some of my favorite bits in your book

981
00:51:02,239 --> 00:51:05,640
Speaker 1: are when you write very elegantly about your appreciation for

982
00:51:05,840 --> 00:51:08,960
Speaker 1: understanding something and seeing things come together and making these

983
00:51:09,040 --> 00:51:11,920
Speaker 1: connections with ancient mathematicians and knowing that you have this

984
00:51:12,239 --> 00:51:14,360
Speaker 1: joy in common with them. I mean, I think a

985
00:51:14,400 --> 00:51:17,600
Speaker 1: lot of people often see math portrayed as like cold

986
00:51:17,680 --> 00:51:19,959
Speaker 1: and crisp and rigorous. But in your book you write

987
00:51:19,960 --> 00:51:23,399
Speaker 1: about the creativity necessary to play this game. You said,

988
00:51:23,600 --> 00:51:27,920
Speaker 1: quote rigorcomes second, Math is creative. Why do you think

989
00:51:27,960 --> 00:51:30,360
Speaker 1: that is that we find beauty in math? Is it

990
00:51:30,440 --> 00:51:33,000
Speaker 1: the same reason we find beauty in nature? Is it

991
00:51:33,120 --> 00:51:35,880
Speaker 1: necessary that we would have found math to be beautiful?

992
00:51:36,120 --> 00:51:38,080
Speaker 1: Is it possible we could have evolved and all found

993
00:51:38,160 --> 00:51:40,239
Speaker 1: math to be like a horrible chore, even if it

994
00:51:40,320 --> 00:51:40,840
Speaker 1: is useful.

995
00:51:42,120 --> 00:51:45,440
Speaker 4: Well, this sensation of beauty is not universal. There are

996
00:51:45,480 --> 00:51:47,480
Speaker 4: people who don't have much patience for that kind of

997
00:51:47,560 --> 00:51:49,759
Speaker 4: talk who are still good mathematicians. There are a lot

998
00:51:49,800 --> 00:51:52,680
Speaker 4: of reasons to love math. Some people do love the

999
00:51:52,719 --> 00:51:56,000
Speaker 4: beauty of it. Some, you know, like the human struggle.

1000
00:51:56,080 --> 00:51:58,759
Speaker 4: Some like the social aspect that you get to do

1001
00:51:58,840 --> 00:52:01,279
Speaker 4: it with your friends, about it together and you can

1002
00:52:01,320 --> 00:52:04,239
Speaker 4: surprise each other. Some people like the competitive aspect. I'm

1003
00:52:04,280 --> 00:52:06,880
Speaker 4: smarter than the other person because I figured out beauty

1004
00:52:07,000 --> 00:52:09,800
Speaker 4: is one side. I think there's a tendency to go

1005
00:52:09,920 --> 00:52:12,480
Speaker 4: on a little too much about beauty, especially because it

1006
00:52:12,560 --> 00:52:15,719
Speaker 4: can be very exclusionary. People who aren't seeing math as

1007
00:52:15,760 --> 00:52:19,520
Speaker 4: beautiful are even more excluded when they don't get what's

1008
00:52:19,560 --> 00:52:22,080
Speaker 4: beautiful about it. You know that it can be a

1009
00:52:22,200 --> 00:52:25,680
Speaker 4: kind of cudgel or a gatekeeping bit of language. So

1010
00:52:25,760 --> 00:52:28,440
Speaker 4: I know that when we harp on about beauty or

1011
00:52:28,520 --> 00:52:31,239
Speaker 4: trying to make the subject appealing to people and say, hey,

1012
00:52:31,280 --> 00:52:33,239
Speaker 4: it's just like music. You like music, you should like

1013
00:52:33,320 --> 00:52:36,160
Speaker 4: math maybe, but you have to be very sensitive to

1014
00:52:36,680 --> 00:52:40,240
Speaker 4: helping a person appreciate the beauty. I'm reminded of like opera,

1015
00:52:40,840 --> 00:52:43,800
Speaker 4: where I don't get opera. When I hear opera, it

1016
00:52:43,880 --> 00:52:47,239
Speaker 4: sounds like a lot of hysterical carrying on and I

1017
00:52:47,400 --> 00:52:49,719
Speaker 4: just think, you know, get over yourself. But I see

1018
00:52:49,760 --> 00:52:52,840
Speaker 4: other people weeping from it, and they understand it, so

1019
00:52:52,960 --> 00:52:55,640
Speaker 4: it's beautiful to them. It's very profound and emotional, and

1020
00:52:55,719 --> 00:52:58,200
Speaker 4: I feel like I'm missing something but by not getting it,

1021
00:52:58,480 --> 00:53:00,560
Speaker 4: so you know, I actually there is this one commercial

1022
00:53:00,600 --> 00:53:02,600
Speaker 4: for wine. I think it was Ernest and Julia o

1023
00:53:02,680 --> 00:53:06,400
Speaker 4: Gallo where they're singing somebody singing, oh, mio, bambinocaro, and

1024
00:53:06,440 --> 00:53:09,480
Speaker 4: it's so beautiful. Even I got it okay, But other

1025
00:53:09,560 --> 00:53:11,880
Speaker 4: than that, I mostly don't get opera. But anyway, my

1026
00:53:12,000 --> 00:53:16,160
Speaker 4: point here is silly point is you know, as educators

1027
00:53:16,320 --> 00:53:18,960
Speaker 4: or as communicators, like through your podcast or the one

1028
00:53:19,000 --> 00:53:20,920
Speaker 4: that I try to do or when I write books,

1029
00:53:21,080 --> 00:53:24,120
Speaker 4: I want to be careful about this beauty argument. There

1030
00:53:24,160 --> 00:53:26,480
Speaker 4: are a lot of ways in to our subjects. Like

1031
00:53:26,560 --> 00:53:28,920
Speaker 4: I'm trying to press every possible button, so I might

1032
00:53:29,040 --> 00:53:31,359
Speaker 4: hit somebody's button at a given time.

1033
00:53:31,480 --> 00:53:34,120
Speaker 1: Well, let's talk a little bit about the button of creativity.

1034
00:53:34,680 --> 00:53:38,200
Speaker 1: Some folks feel like math and science and physics are

1035
00:53:38,200 --> 00:53:42,240
Speaker 1: a different kind of intellectual venture than things like music

1036
00:53:42,600 --> 00:53:45,719
Speaker 1: or art. But there's a creative side to science or

1037
00:53:45,840 --> 00:53:48,479
Speaker 1: and to math and to intellect. We do sometimes feel

1038
00:53:48,480 --> 00:53:50,399
Speaker 1: like you're playing a game you wrote in your book.

1039
00:53:50,719 --> 00:53:54,480
Speaker 1: Mathematicians don't come up with proofs. First comes intuition, and

1040
00:53:54,600 --> 00:53:57,080
Speaker 1: rigor comes later. Can you talk a little bit about

1041
00:53:57,120 --> 00:53:59,839
Speaker 1: the element of creativity that's involved in your works?

1042
00:54:00,920 --> 00:54:03,719
Speaker 4: Oh, well, before I say anything about my work specifically,

1043
00:54:03,840 --> 00:54:07,399
Speaker 4: I do appreciate you bringing up that point, because in math,

1044
00:54:07,520 --> 00:54:10,759
Speaker 4: especially in high school geometry, we're taught the proof has

1045
00:54:10,840 --> 00:54:14,000
Speaker 4: to be rigorous, it has to follow logic. Sometimes teachers

1046
00:54:14,040 --> 00:54:16,480
Speaker 4: will even have students write out statements in the left

1047
00:54:16,560 --> 00:54:19,839
Speaker 4: column and reasons in the right column. There's a point

1048
00:54:19,880 --> 00:54:22,000
Speaker 4: to that to help young students learn how to get

1049
00:54:22,120 --> 00:54:25,800
Speaker 4: organized in their thinking and construct logical arguments. And so

1050
00:54:25,920 --> 00:54:28,719
Speaker 4: that is definitely a part of math. Mathematicians are very

1051
00:54:28,800 --> 00:54:31,719
Speaker 4: proud of being able to have absolute proof in a

1052
00:54:31,800 --> 00:54:35,920
Speaker 4: way that scientists cannot. Right, sciences get revised as more

1053
00:54:35,960 --> 00:54:38,560
Speaker 4: information comes in. But in math, the theorems that were

1054
00:54:38,640 --> 00:54:41,000
Speaker 4: proven thousands of years ago are still true, and the

1055
00:54:41,080 --> 00:54:43,440
Speaker 4: proofs if they were correct back then, they're still correct.

1056
00:54:43,520 --> 00:54:46,560
Speaker 4: Some of us like this absolute nature of the subject,

1057
00:54:46,760 --> 00:54:50,160
Speaker 4: but that's only half of the story. And how do

1058
00:54:50,239 --> 00:54:51,919
Speaker 4: you come up with the proof in the first place,

1059
00:54:52,239 --> 00:54:54,120
Speaker 4: or how do you dream up what theorem you're even

1060
00:54:54,160 --> 00:54:57,840
Speaker 4: trying to prove? Those things are more akin to music

1061
00:54:57,960 --> 00:55:05,080
Speaker 4: and poetry and art and other creative parts of human activity.

1062
00:55:05,320 --> 00:55:07,640
Speaker 4: I mean, you have to have imagination, and you have

1063
00:55:07,760 --> 00:55:10,799
Speaker 4: to dream, and you have to have wishful hopes. All

1064
00:55:10,880 --> 00:55:13,160
Speaker 4: that kind of stuff is a big part of math.

1065
00:55:13,280 --> 00:55:15,960
Speaker 4: And anyone who does math or physics or any other

1066
00:55:16,120 --> 00:55:18,160
Speaker 4: part of science knows all of that. I mean, when

1067
00:55:18,200 --> 00:55:20,759
Speaker 4: you're doing it. You're still a person, you still have

1068
00:55:20,920 --> 00:55:23,680
Speaker 4: dreams and hopes. So I don't know why we don't

1069
00:55:23,719 --> 00:55:26,319
Speaker 4: teach that more. I mean, you learn it when you're

1070
00:55:26,360 --> 00:55:29,160
Speaker 4: in as an apprentice, as a young scientist or mathematician,

1071
00:55:29,239 --> 00:55:31,640
Speaker 4: and you're in the lab. You feel it. You all

1072
00:55:32,080 --> 00:55:34,200
Speaker 4: want something, But we don't do a great job in

1073
00:55:34,280 --> 00:55:37,480
Speaker 4: our textbooks or our lecturing at conveying that. And I

1074
00:55:37,560 --> 00:55:39,120
Speaker 4: think that's why a lot of people, you know, they

1075
00:55:39,200 --> 00:55:41,920
Speaker 4: might think it's a cold subject that wouldn't hold any

1076
00:55:41,960 --> 00:55:43,640
Speaker 4: appeal to them, But once they get in the lab

1077
00:55:43,760 --> 00:55:46,320
Speaker 4: or actually do some math, they'll see it's just like

1078
00:55:46,400 --> 00:55:50,480
Speaker 4: anything else. It's really fun and occupies your whole human spirit.

1079
00:55:50,600 --> 00:55:53,080
Speaker 1: I want to talk a little bit about accessibility of math.

1080
00:55:53,440 --> 00:55:55,719
Speaker 1: You tell a story in your book about a novelist

1081
00:55:55,960 --> 00:55:57,799
Speaker 1: who received the advice that if he wanted to write

1082
00:55:57,800 --> 00:56:00,640
Speaker 1: about physics, he needed to understand calculus, but as a

1083
00:56:00,719 --> 00:56:03,160
Speaker 1: non technical person, he was unable to find his way in,

1084
00:56:03,560 --> 00:56:06,040
Speaker 1: even going so far as to audit a high school class.

1085
00:56:06,160 --> 00:56:07,880
Speaker 1: And you say that your book is for people like

1086
00:56:07,960 --> 00:56:10,560
Speaker 1: him who want to understand the ideas and the beauty

1087
00:56:10,600 --> 00:56:13,200
Speaker 1: of math but can't otherwise find their way in. Do

1088
00:56:13,239 --> 00:56:15,160
Speaker 1: you think there's a wide spread appetite for this. Do

1089
00:56:15,160 --> 00:56:17,800
Speaker 1: you think if we taught math differently, it might have

1090
00:56:18,160 --> 00:56:20,840
Speaker 1: more supporters and you might less often find people on

1091
00:56:20,880 --> 00:56:23,479
Speaker 1: airplanes who go uugh, I hated math in high school.

1092
00:56:23,920 --> 00:56:27,000
Speaker 4: Yes, unequivocal yes to that question. There is a hunger

1093
00:56:27,120 --> 00:56:29,200
Speaker 4: for it. I know it as a fact. I've done

1094
00:56:29,239 --> 00:56:32,440
Speaker 4: the experiment. The New York Times back in twenty ten

1095
00:56:32,719 --> 00:56:35,480
Speaker 4: opinion page of all things, not the science page, but

1096
00:56:35,600 --> 00:56:38,480
Speaker 4: the opinion page. Editor David Shipley asked me to write

1097
00:56:38,560 --> 00:56:42,200
Speaker 4: a series of columns about math, starting with preschool math

1098
00:56:42,239 --> 00:56:44,799
Speaker 4: about numbers, and going as far as I could up

1099
00:56:44,840 --> 00:56:48,600
Speaker 4: to grad school level topics for his readers, for a

1100
00:56:48,719 --> 00:56:51,080
Speaker 4: curious person who like the kind of person who would

1101
00:56:51,120 --> 00:56:55,120
Speaker 4: read the opinion page, but who like him, fell off

1102
00:56:55,160 --> 00:56:57,800
Speaker 4: the math train somewhere, you know, just didn't see the

1103
00:56:57,840 --> 00:57:01,400
Speaker 4: point of it, didn't like it anymore, or found it

1104
00:57:01,480 --> 00:57:04,759
Speaker 4: hard or repelling in some way, repulsive anyway. So I

1105
00:57:04,880 --> 00:57:08,000
Speaker 4: tried to write for that audience, and there was a

1106
00:57:08,040 --> 00:57:10,239
Speaker 4: big audience, and they liked it, and they were very

1107
00:57:10,280 --> 00:57:14,320
Speaker 4: grateful and appreciative and their comments, you know, because on

1108
00:57:14,400 --> 00:57:17,560
Speaker 4: the Internet people can talk back, and they did, and

1109
00:57:17,760 --> 00:57:19,800
Speaker 4: Of course, there were some people who talked back saying

1110
00:57:19,880 --> 00:57:22,080
Speaker 4: they had a better explanation or they think I got

1111
00:57:22,160 --> 00:57:24,640
Speaker 4: it wrong. But for the most part, there was a

1112
00:57:24,680 --> 00:57:27,280
Speaker 4: big audience that was very grateful and said things like,

1113
00:57:27,440 --> 00:57:29,080
Speaker 4: you know, I wish you were my high school teacher.

1114
00:57:29,200 --> 00:57:31,440
Speaker 4: I wish math was taught this way. Why wasn't it

1115
00:57:31,520 --> 00:57:34,120
Speaker 4: taught this way? And that's a good question, why isn't

1116
00:57:34,160 --> 00:57:37,240
Speaker 4: it taught in a way that engages people more? You know,

1117
00:57:37,320 --> 00:57:40,960
Speaker 4: it's complicated about the story of education in the United States.

1118
00:57:41,600 --> 00:57:45,120
Speaker 4: There's a lot of demands on teachers to get their

1119
00:57:45,160 --> 00:57:48,520
Speaker 4: students to learn certain things that the government requires or

1120
00:57:48,640 --> 00:57:51,120
Speaker 4: wants people to learn by a certain age. There's all

1121
00:57:51,160 --> 00:57:53,800
Speaker 4: the pressure of getting into college. I mean, there's a

1122
00:57:53,880 --> 00:57:57,080
Speaker 4: million things. Also, think of the position of teachers in

1123
00:57:57,160 --> 00:58:00,960
Speaker 4: our society. How much reverence is or not accorded to

1124
00:58:01,080 --> 00:58:04,520
Speaker 4: the profession of teaching at the elementary or high school level,

1125
00:58:04,960 --> 00:58:07,960
Speaker 4: So what people are attracted to it, how much teachers

1126
00:58:08,000 --> 00:58:09,720
Speaker 4: are paid. I mean, there's a million things we could

1127
00:58:09,720 --> 00:58:11,760
Speaker 4: talk about that we don't have time to talk about.

1128
00:58:11,800 --> 00:58:15,000
Speaker 4: But for all kinds of reasons, we aren't teaching math

1129
00:58:15,160 --> 00:58:16,120
Speaker 4: in the optimal way.

1130
00:58:16,560 --> 00:58:19,520
Speaker 1: Well, I certainly appreciate your efforts to translate some of

1131
00:58:19,600 --> 00:58:22,800
Speaker 1: these deep ideas and the historical stories of mathematics. Even

1132
00:58:22,840 --> 00:58:24,880
Speaker 1: as a physicist who thinks about math all day long,

1133
00:58:25,000 --> 00:58:27,680
Speaker 1: I certainly gain and benefit from your efforts, and I

1134
00:58:27,720 --> 00:58:29,600
Speaker 1: think a very wide group of people do as well.

1135
00:58:29,680 --> 00:58:31,680
Speaker 1: And I want to ask you a personal question about

1136
00:58:32,120 --> 00:58:35,000
Speaker 1: why you're a little bit unusual. I mean, there are

1137
00:58:35,040 --> 00:58:38,080
Speaker 1: people who write for the public about science and math,

1138
00:58:38,640 --> 00:58:41,880
Speaker 1: but you're also somebody who's doing that. You're actively researching,

1139
00:58:41,960 --> 00:58:45,320
Speaker 1: you're publishing papers, you're an academic, you're participating in these

1140
00:58:45,360 --> 00:58:47,640
Speaker 1: studies yourself. What is that like for you, sort of

1141
00:58:47,760 --> 00:58:53,120
Speaker 1: living in both worlds. Is your academic intellectual professorial community

1142
00:58:53,160 --> 00:58:55,240
Speaker 1: supportive of this or do you have to sort of

1143
00:58:55,280 --> 00:58:58,479
Speaker 1: push back against trends that encourage you not to spend

1144
00:58:58,520 --> 00:58:59,920
Speaker 1: your time doing this kind of outreach.

1145
00:59:00,400 --> 00:59:03,520
Speaker 4: That's a happy story. Actually the community is pretty supportive,

1146
00:59:03,560 --> 00:59:05,600
Speaker 4: I would say, And I'd be curious your own take

1147
00:59:05,680 --> 00:59:08,360
Speaker 4: on this too, because you must be encountering it. A

1148
00:59:08,440 --> 00:59:11,200
Speaker 4: lot of us fear that if we go into public

1149
00:59:11,240 --> 00:59:13,960
Speaker 4: communication of physics or math, that some of our colleagues

1150
00:59:14,000 --> 00:59:16,560
Speaker 4: would think we're getting soft or we're selling out or

1151
00:59:16,640 --> 00:59:21,280
Speaker 4: we're pandering or dumbing it down or whatever, and that

1152
00:59:21,480 --> 00:59:24,440
Speaker 4: seems to be mostly a misplaced fear. If colleagues do

1153
00:59:24,560 --> 00:59:26,920
Speaker 4: feel that way, they've been polite enough to not tell

1154
00:59:27,000 --> 00:59:31,400
Speaker 4: me so that I appreciate that. But mostly people seem

1155
00:59:31,480 --> 00:59:34,160
Speaker 4: to take it in a good spirit, like, you know,

1156
00:59:34,320 --> 00:59:36,880
Speaker 4: thanks for trying to do this. It's difficult and it's

1157
00:59:36,960 --> 00:59:39,640
Speaker 4: worth trying to do, and the public certainly seems to

1158
00:59:39,680 --> 00:59:42,640
Speaker 4: appreciate it. But no, I haven't found much resistance or

1159
00:59:42,720 --> 00:59:47,640
Speaker 4: even antagonism from colleagues about it. It's also very much

1160
00:59:47,760 --> 00:59:50,760
Speaker 4: fun for me as a perpetual student. I learn a

1161
00:59:50,840 --> 00:59:54,200
Speaker 4: lot from interviewing guests on the podcast in fields I

1162
00:59:54,240 --> 00:59:56,880
Speaker 4: don't know anything about. I talk to people about inflammation

1163
00:59:57,320 --> 00:59:59,880
Speaker 4: or the origin of life or whatever on this Joy

1164
01:00:00,160 --> 01:00:03,360
Speaker 4: Why podcast. So I'm constantly in school, you know, for

1165
01:00:03,440 --> 01:00:05,680
Speaker 4: anyone out there who's had this feeling like, now that

1166
01:00:05,800 --> 01:00:08,000
Speaker 4: I know so much more, I wish I could be

1167
01:00:08,040 --> 01:00:10,360
Speaker 4: a student at this age. I was so busy. I

1168
01:00:10,520 --> 01:00:13,240
Speaker 4: was so young and had all those hormones raging, and

1169
01:00:13,280 --> 01:00:15,040
Speaker 4: I had so many things on my mind. Now that

1170
01:00:15,160 --> 01:00:20,000
Speaker 4: I'm old and I can think straight anyway, I'm just

1171
01:00:20,080 --> 01:00:22,480
Speaker 4: saying that it's fun for me as a student to

1172
01:00:22,640 --> 01:00:24,560
Speaker 4: be able to do this, and I think it actually

1173
01:00:24,640 --> 01:00:27,680
Speaker 4: helps my research too. It's giving me a broader perspective.

1174
01:00:28,000 --> 01:00:30,640
Speaker 4: I'm thinking about questions that never occurred to me before.

1175
01:00:30,680 --> 01:00:31,920
Speaker 4: So no, I think it's all to the good.

1176
01:00:32,120 --> 01:00:35,240
Speaker 1: I have the same feeling. I really appreciate the license

1177
01:00:35,360 --> 01:00:38,280
Speaker 1: to explore topics I wouldn't otherwise feel like I had

1178
01:00:38,320 --> 01:00:41,280
Speaker 1: time to dig into and to educate myself about them

1179
01:00:41,400 --> 01:00:43,600
Speaker 1: to a level where I feel comfortable explaining them in

1180
01:00:43,680 --> 01:00:46,000
Speaker 1: intuitive terms. It's a lot of fun. I really feel

1181
01:00:46,000 --> 01:00:48,160
Speaker 1: like it's broadened my understanding. But let me ask you

1182
01:00:48,240 --> 01:00:50,600
Speaker 1: one more, maybe even more pointed question. What would be

1183
01:00:50,680 --> 01:00:54,240
Speaker 1: your advice to a young person whose career isn't as

1184
01:00:54,360 --> 01:00:57,520
Speaker 1: well established as yours but is excited about outreach, you know,

1185
01:00:57,640 --> 01:00:59,880
Speaker 1: maybe a postdoc or a graduate student. Would you reckon

1186
01:01:00,080 --> 01:01:02,800
Speaker 1: man that they not participate in that and focus on

1187
01:01:02,880 --> 01:01:05,840
Speaker 1: their academics until they're better established, or is this something

1188
01:01:05,880 --> 01:01:08,280
Speaker 1: you think we should be encouraging in young people as well.

1189
01:01:08,560 --> 01:01:12,200
Speaker 4: That's a hard one because realistically, I don't think it

1190
01:01:12,400 --> 01:01:15,200
Speaker 4: will really help a person's chance in the academic life

1191
01:01:15,280 --> 01:01:17,840
Speaker 4: at a young stage. It's not the answer I want

1192
01:01:17,920 --> 01:01:20,240
Speaker 4: to give, but I think it is the honest answer

1193
01:01:20,400 --> 01:01:23,120
Speaker 4: that the culture of the academic world for a person

1194
01:01:23,120 --> 01:01:25,840
Speaker 4: who wants to become a professor is such that you

1195
01:01:25,960 --> 01:01:28,240
Speaker 4: have to focus on research, depending what kind of place

1196
01:01:28,240 --> 01:01:30,240
Speaker 4: you want to work at. So if you're working at

1197
01:01:30,240 --> 01:01:33,720
Speaker 4: a place that considers itself a research powerhouse or aspires

1198
01:01:33,800 --> 01:01:35,760
Speaker 4: to be one, then you got to focus on your

1199
01:01:35,840 --> 01:01:41,280
Speaker 4: research and there wouldn't be much benefit to doing outreach work. Honestly.

1200
01:01:41,400 --> 01:01:45,520
Speaker 4: I mean the priorities are first research, second teaching, third service,

1201
01:01:46,120 --> 01:01:49,240
Speaker 4: of which outreach is considered one of the aspects of service.

1202
01:01:49,520 --> 01:01:52,080
Speaker 4: So yeah, don't do it for that reason. Now that's

1203
01:01:52,120 --> 01:01:54,080
Speaker 4: not to say you shouldn't do it. There are people

1204
01:01:54,120 --> 01:01:56,600
Speaker 4: who decide why should I be a professor? I can

1205
01:01:56,800 --> 01:02:01,080
Speaker 4: make money supporting myself on YouTube, and there are fantastic

1206
01:02:01,840 --> 01:02:05,120
Speaker 4: streamers on YouTube. I mean, think of Grant Sanderson on

1207
01:02:05,240 --> 01:02:08,120
Speaker 4: three Blue One Brown, who's producing some of the best

1208
01:02:08,560 --> 01:02:12,440
Speaker 4: math explanations on the planet through his wizardly use of

1209
01:02:13,040 --> 01:02:16,880
Speaker 4: computer graphics and his brilliant pedagogy. I mean, that guy

1210
01:02:16,920 --> 01:02:19,200
Speaker 4: would be the best teacher at any university where he

1211
01:02:19,360 --> 01:02:22,360
Speaker 4: was a professor, but he's chosen not to be a professor,

1212
01:02:22,360 --> 01:02:24,760
Speaker 4: at least not yet, and he's reaching millions or tens

1213
01:02:24,800 --> 01:02:27,480
Speaker 4: of millions of people. So I'm not sure someone with

1214
01:02:27,600 --> 01:02:30,320
Speaker 4: those aspirations needs to be an academic. You know, there

1215
01:02:30,400 --> 01:02:33,160
Speaker 4: is an ecosystem only in recent years where you can

1216
01:02:33,240 --> 01:02:36,440
Speaker 4: actually thrive and do really good work for humanity, as

1217
01:02:36,480 --> 01:02:38,240
Speaker 4: he and a bunch of other people are doing. So

1218
01:02:38,640 --> 01:02:40,320
Speaker 4: I guess I would say for a person who wants

1219
01:02:40,360 --> 01:02:41,720
Speaker 4: to do that, if you're going to do it in

1220
01:02:41,800 --> 01:02:45,440
Speaker 4: the academic setting, get tenure first, do your research, and

1221
01:02:45,520 --> 01:02:48,280
Speaker 4: then you know, go wild. But if you're doing it

1222
01:02:48,360 --> 01:02:51,400
Speaker 4: outside of the academic world, you could make money creating

1223
01:02:51,440 --> 01:02:53,560
Speaker 4: companies that do it. You may have to get lucky,

1224
01:02:53,960 --> 01:02:57,680
Speaker 4: like say con Academy teaching math and science to the world,

1225
01:02:57,840 --> 01:03:02,640
Speaker 4: but what a great service has provided too, So there's

1226
01:03:02,640 --> 01:03:04,040
Speaker 4: a lot of possibilities today.

1227
01:03:04,080 --> 01:03:06,280
Speaker 1: All right, great, Well, thanks very much for coming on

1228
01:03:06,360 --> 01:03:09,520
Speaker 1: the podcast and talking with us about an incredible breadth

1229
01:03:09,640 --> 01:03:12,240
Speaker 1: of topics, from the beauty of math to communicating with

1230
01:03:12,360 --> 01:03:16,160
Speaker 1: aliens to advice for young researchers. Really appreciate your frank

1231
01:03:16,240 --> 01:03:17,160
Speaker 1: and open conversation.

1232
01:03:17,400 --> 01:03:19,640
Speaker 4: Well, thank you, Daniel. This is a really great pleasure

1233
01:03:19,720 --> 01:03:22,080
Speaker 4: for me and I'm very grateful to you for having

1234
01:03:22,120 --> 01:03:22,680
Speaker 4: me on the show.

1235
01:03:22,920 --> 01:03:25,400
Speaker 1: So you see that the question of why math is

1236
01:03:25,440 --> 01:03:28,640
Speaker 1: so important for physics is a difficult one to answer,

1237
01:03:28,840 --> 01:03:31,520
Speaker 1: even for a physicist and a mathematician talking about it

1238
01:03:31,600 --> 01:03:34,760
Speaker 1: for almost an hour. Hope you enjoyed that conversation. Tune

1239
01:03:34,800 --> 01:03:45,360
Speaker 1: in next time. Thanks for listening, and remember that Daniel

1240
01:03:45,360 --> 01:03:48,800
Speaker 1: and Jorge Explain the Universe is a production of iHeart Radio.

1241
01:03:49,120 --> 01:03:54,200
Speaker 1: For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts,

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Speaker 1: or wherever you listen to your favorite shows.

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