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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 I hate physics so much math,

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Speaker 1: And that makes me think, if it's the math you

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

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Speaker 1: still love the physics. But of course the two are

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Speaker 1: closely linked. You can't love Shakespeare if you hate the

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Speaker 1: English language, and that of course makes us wonder why

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Speaker 1: math and physics are so intertwined. I mean, if people

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Speaker 1: can actually enjoy Shakespeare and other languages, then it has

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

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

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

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

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Speaker 1: and a professor at U c 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 ex Playing the Universe, where we do a deep

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

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

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

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

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

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

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Speaker 1: And we can do that, thinks, 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, and you

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

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

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

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Speaker 1: There are times when our intuition fails us when the

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

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

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Speaker 1: tiny 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, and that's

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

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

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

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

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

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

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Speaker 1: concepts and physics like gauge invariants. The way I learned

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

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Speaker 1: is mathematical, which has become part of my intuition. So

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Speaker 1: it's not always easy to know how to translate those

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Speaker 1: concepts into pure intuition and talk about the without math,

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Speaker 1: but you know, finding ways to talk about them intuitively

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Speaker 1: has also led me to a deeper understanding of the ideas.

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Speaker 1: That's one of the underappreciated joys of teaching. It forces

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

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Speaker 1: raises a really interesting question. Is it possible actually to

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

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Speaker 1: physics or is it just useful like a shorthand notation.

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Speaker 1: Is math the language of the universe itself or is

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

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

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

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Speaker 1: we talked to a philosopher of mathematics, Professor Mark cole Evan,

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

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Speaker 1: from the other side of the issue to join us.

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Speaker 1: We'll talk today to a working mathematicians some and who

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Speaker 1: spends his day's building mathematical tools and using them to

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Speaker 1: describe the patterns and structures of the universe. So it's

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Speaker 1: my pleasure to welcome Professor Steve Strogatz. He's the Jacob

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Speaker 1: gould Sherman Professor of Applied Mathematics at Cornell University, having

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Speaker 1: taught previously at M I T and having earned a

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Speaker 1: PhD in math from Harvard, So those are some pretty

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Speaker 1: impressive credentials. But he's also an expert in applying math

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Speaker 1: to the real world, including understanding the math of firefly swarms,

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Speaker 1: choruses of chirping crickets, and the wobbling of bridges. He's

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Speaker 1: also a well known podcaster, host of the podcasts The

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Speaker 1: Joy of X and The Joy of Why, both of

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Speaker 1: which I highly recommend, as well as a prolific author.

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Speaker 1: One of his recent books is Infinite Powers, How Calculus

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Speaker 1: Reveals the Secrets of the Universe, the book I recently

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Speaker 1: read and thoroughly enjoyed, and which inspired me to invite

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Speaker 1: Steve on the podcast to talk about calculus, infinity, and

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Speaker 1: the deep relationship between physics and math. Steve, Welcome to

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Speaker 1: the podcast and thank you very much for joining us.

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Speaker 1: Thank it's a lot, Daniel. It's a great pleasure to

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Speaker 1: be with you. That's going to be fun. It's a

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Speaker 1: treat to have you here as I've been very much

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Speaker 1: enjoying listening to your podcast series and reading your book.

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Speaker 1: And so I'd like to start by asking you a

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Speaker 1: question I've heard you ask several of your guests about definitions.

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Speaker 1: Your book is about calculus, a word that a lot

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Speaker 1: of people have heard but might not really know what

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Speaker 1: it means. Can you define for us what is calculus? Sure,

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Speaker 1: let's try it in a sequence of definitions, and you

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Speaker 1: could stop me when I get too detailed. So if

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Speaker 1: I were giving it to you in one word, I

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Speaker 1: would say, it's the mathematics of change. That's the keyword change.

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Speaker 1: If we want to go a little more into it,

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Speaker 1: it's the mathematics of continuous change, and especially things that

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Speaker 1: are changing at a changing rate. So you say it's

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Speaker 1: the mathematics of change. What exactly is changing there? Like

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Speaker 1: if I just want to describe how a ball is

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Speaker 1: moving through the air, what exactly is changing about the

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Speaker 1: ball's motion? So in that case, what's changing is the

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Speaker 1: position of the ball, or also possibly the speed of

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Speaker 1: the ball. So your listeners will remember from high schoo

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Speaker 1: Well algebra, we do problems about change and motion. That

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Speaker 1: gets summed up in the mantra. Distance equals rate times time,

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Speaker 1: and so that's motion at a steady speed or at

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Speaker 1: a steady velocity. And you can handle that with algebra.

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Speaker 1: It's just a matter of multiplication. Distance equals rate times time.

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Speaker 1: The rate is the speed, and you're driving sixty miles

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Speaker 1: an hour. For an hour, you're gonna go sixty miles. Okay,

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Speaker 1: So in that case the distance is changing, position of

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Speaker 1: the car on the highway is changing, but the speed

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Speaker 1: of the car is not changing. We said it was

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Speaker 1: a steady sixty miles an hour. And so at the

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Speaker 1: time of Isaac Newton or even Johannes Kepler or Galileo,

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Speaker 1: scientists started to become very interested in motion that was

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Speaker 1: not just simple motion at a constant speed. You know,

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Speaker 1: in connection with the things you mentioned dropping a ball,

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Speaker 1: the apocryphal or maybe true dropping the cannon ball off

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Speaker 1: the leaning tower of pizza from Galileo, certainly Kepler with

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Speaker 1: thinking about the motions of the planets. In all of

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Speaker 1: those cases there were things that were changing. I mean

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Speaker 1: we should also keep in mind with the planets. Another

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Speaker 1: thing that can change is direction. So instead of motion

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Speaker 1: in a straight line, if you have an orbit, then

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Speaker 1: the direction of the planet as it's moving is changing.

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Speaker 1: It's curving as it's going around the Sun. And so

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Speaker 1: geometry is a big part of calculus too, when we

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Speaker 1: start to deal with curved shapes as opposed to shapes

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Speaker 1: made of straight lines or or planes. So in this case,

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Speaker 1: do you feel historically like physics was in the lead

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Speaker 1: or mathematics. I mean, people have been thinking about things

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Speaker 1: that were moving and changing for thousands of years. But

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Speaker 1: calculus is just a few hundred years old. Was it

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Speaker 1: invented to solve a particularly difficult problem or did it

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Speaker 1: appear in the minds of intelligent people and then allow

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Speaker 1: us to solve problems that had been standing for thousands

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Speaker 1: of years. That's interesting that you say it's only a

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Speaker 1: few hundred years old. Most historians and certainly most scientists

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Speaker 1: would say, yeah, calculus is from the middle sixteen hundreds,

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Speaker 1: from Isaac Newton and Gottfried Wilhelm Leibnitz. But I don't

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Speaker 1: personally I want to endorse that position because I think

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Speaker 1: we can see if you want. I mean, I don't

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Speaker 1: equibble about definitions, but there are definitely ideas of calculus.

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Speaker 1: Almost two thousand years earlier in the work of Archimedes

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Speaker 1: in Syracuse, in what was at the time the Greek

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Speaker 1: Empire Um to fifty BC. Archimedes is calculating volumes of

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Speaker 1: solids with curved faces, or also areas under a parabola.

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Speaker 1: Or he's the one that gives us the volume of

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Speaker 1: a sphere or the surface area of a sphere. Those

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Speaker 1: are all calculus problems. We teach those today in calculus

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Speaker 1: when we're teaching students about integrals, which is a generalization

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Speaker 1: of the idea of area and volume. And so he's

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Speaker 1: totally doing calculus in two fifty BC. In fact, he's

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Speaker 1: doing the harder part of calculus, integral calculus. But we

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Speaker 1: don't usually call it calculus because of I don't know why. Actually,

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Speaker 1: I mean, I think it is calculus. So back to

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Speaker 1: your question, what is calculus, I mean, another way of

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Speaker 1: talking about it is it's the systematic use of infinity

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Speaker 1: and infinitesimals to solve problems about curved shapes, about motion

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Speaker 1: at a non constant speed, and about anything else that's

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Speaker 1: changing in a non constant way. It could be amount

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Speaker 1: of virus in your bloodstream if you have HIV. It

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Speaker 1: could be a population you know, of the Earth going up.

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Speaker 1: Any all of these things are grist for calculus. So

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

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

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

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

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

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Speaker 1: but 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? The main point

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Speaker 1: is probably infinitesimals rather than infinity. So infinitesimals. Let us

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Speaker 1: pretend that us fear is made up of flat pieces.

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Speaker 1: May be easier to visualize with a circle. Some of

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Speaker 1: your listeners will have probably played this game. If you

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Speaker 1: put a bunch of dots on a circle and connect

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Speaker 1: them with straight lines, it almost looks like a you know,

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Speaker 1: it'll make a polygon for instance, you could picture putting

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Speaker 1: four equally space points on a circle and connect them,

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Speaker 1: they'll make a square. If you put eight, then you're

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Speaker 1: making an octagon. You know, the more points you put,

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Speaker 1: the more it starts to look like a circle. And

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Speaker 1: from ancient times people had this intuition that a circle

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Speaker 1: is kind of like an infinite polygon. It's got infinitely

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Speaker 1: many corners, it's connected by sides that are infinitesimally small.

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Speaker 1: Now that doesn't seem right because we think of a

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Speaker 1: circle as perfectly smooth it doesn't have any corners at all.

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Speaker 1: But in a certain sense, it's the limit of a

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Speaker 1: polygon as you take more and more points on the

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Speaker 1: polygon at the corners and more and more sides. And

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Speaker 1: so that was the key insight that Archimedes had, that

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Speaker 1: you could calculate the area of a circle the formula

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Speaker 1: we all learn in high school I R squared. He's

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Speaker 1: the first one to really prove that, and he did

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Speaker 1: it by thinking in this calculus way, by looking at

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Speaker 1: the limit of polygons. So similarly, in the case of Galileo,

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Speaker 1: in the motion of say javelin or something thrown that's

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Speaker 1: going to execute parabolic flight to make the problem easier.

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Speaker 1: Gal Well, actually Galileo didn't really have this idea, but

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Speaker 1: later in Newton we would think of the parabola as

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Speaker 1: made up of infinitely many, infinitesimally small excursions along the

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Speaker 1: path that are basically straight lines in the particle or

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Speaker 1: the javelin is moving at a constant speed for that

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Speaker 1: infinitesimal amount of time, So it breaks the problem down

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Speaker 1: into something that we already know how to solve. Everything

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Speaker 1: becomes distance equals right times time again, except only over

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Speaker 1: an infinitesimal segment. So you solve a problem you can't

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Speaker 1: solve by turning it into an infinite number of problems

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Speaker 1: that you can solve. Bingo, you've really encapsulated the heart

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Speaker 1: of calculus in that sense in infinite powers. I called

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Speaker 1: that the infinity principle that to solve any difficult problem

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Speaker 1: in evolving curve shapes or these complicated motions, if you

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Speaker 1: reconceptualize it as an infinite number of smaller, simpler problems

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Speaker 1: in which you have straight lines or motion at a

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Speaker 1: constant speed, you can solve incredibly hard and important problems

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Speaker 1: with this trick. The only problem is you have to

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Speaker 1: somehow put all those infinite testimals back together again to

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Speaker 1: reconstitute the original motion or the original shape. And that's

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Speaker 1: the hard part of calculus. The subdivision part is easy.

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Speaker 1: It's the reassembly part that's hard, right, And so it's

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Speaker 1: fascinating to me that infinity sort of appears in two

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Speaker 1: places there, one as you chop it into little pieces,

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Speaker 1: and then again as you put it back together. And

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Speaker 1: to me, it's fascinating because the infinity appears in only

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Speaker 1: the intermediate stages. Like the ball doesn't have infinite velocity

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Speaker 1: or infinite acceleration or infinite anything. But we've used infinity

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Speaker 1: in calculating. It's very non infinite motion. And so it's

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Speaker 1: fascinating to me that infinity is such a powerful mathematical tool,

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Speaker 1: yet we don't actually observe it in nature really very often.

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Speaker 1: Or some people might say, ever, that's really a great

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Speaker 1: point you could. I mean, if we were doing this

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Speaker 1: on video, your listeners would see me smiling. I really

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Speaker 1: like that. It's almost like in those old cartoons with

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Speaker 1: the you know, enter stage left and exit stage right,

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Speaker 1: that infinity comes onto the stage and the infinitesimals, but

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Speaker 1: only as you sort of say, like an apparatus. It

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Speaker 1: it lets us solve the problem, but it's sort of

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Speaker 1: not really there, it's not real. In physics, we're often

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Speaker 1: seeing infinities in the final answer as a sign of

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Speaker 1: failure writing particle physics, prediction of infinity is unphysical. You

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Speaker 1: can't have infinite probabilities for some outcome and quantum mechanics,

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Speaker 1: or you can't have an infinite force on a particle.

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Speaker 1: And in general relativity we think of a prediction of

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Speaker 1: a singularity infinite density as the breakdown of the physical theory.

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Speaker 1: We try to avoid infinities. We hide them under renormalization

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Speaker 1: whatever possible. So then my question to you is in

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Speaker 1: your mind are these infinities real? I mean, do they

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Speaker 1: just exist in the intermediate steps of the mathematical methods

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Speaker 1: we're using. Are they only in our minds? Are they

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Speaker 1: half finished calculation? Or is this something real about the

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Speaker 1: universe that calculus is capturing, This smooth and infinitely varying

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Speaker 1: motion of a ball or changing of the velocity of

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

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Speaker 1: Such a great deep question. I don't even know what

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Speaker 1: I'm gonna say to the answer. I mean, I've been

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Speaker 1: thinking about this for forty fifty years, and I still

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Speaker 1: don't really know what the answer is. I I mean,

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Speaker 1: the principal person in me, the philosophically tenable person, wants

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Speaker 1: to say it's not real, it's a fiction, it's a

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Speaker 1: useful device. Let's just try to make that argument first,

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Speaker 1: before the more wild eyed person in me makes the

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Speaker 1: counter argument. So the rational person would say, yeah, I mean,

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Speaker 1: our from our best understanding of physics today, there are

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Speaker 1: no infinitesimals. You can't subdivide matter arbitrarily finely. That's the

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Speaker 1: whole concept of atoms, those things which are indivisible. You

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Speaker 1: guys tell us, I say you. The physicists tell us

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Speaker 1: that there is even a smallest amount of time and

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Speaker 1: space that is referred to as the Planck scale, the smallest.

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Speaker 1: You know, we don't really, of course, I believe understand

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Speaker 1: how to unify quantum theory yet with general relativity. There

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Speaker 1: are candidates. But anyway, the cool thing is that, just

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Speaker 1: on dimensional grounds, if you look at the fundamental constants

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Speaker 1: like the speed of light and planks constant that governs

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Speaker 1: quantum phenomena, and Newton's gravitational constant for the strength of gravity,

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Speaker 1: those can only be put together in one way to

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Speaker 1: make a unit of length. That's the Planck length, and

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Speaker 1: it's about ten to the minus thirty five meters, and

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Speaker 1: that's sort of the smallest conceivable distance that has any

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Speaker 1: physical meaning, wouldn't you say, whatever the theory ends up being,

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

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

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

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

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

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

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Speaker 1: most night 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 a thousand,

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Speaker 1: and that would feel like a pretty wrong answer in

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Speaker 1: the case of the plant length, I think, which is

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

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

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

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Speaker 1: and not continuous. Equantom mechanics tells us that you can't

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Speaker 1: infinitely chop up the universe, and therefore mathematics of calculus

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Speaker 1: that assumes that might not actually be describing what's happening

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Speaker 1: in the universe. Fine, I mean, I take your point

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Speaker 1: that we don't know that the plant length of tend

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Speaker 1: to the minus thirty five is right. There could be

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Speaker 1: factors of a thousand in one direction or another or more.

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Speaker 1: I mean, we don't really know what the pre factor is,

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Speaker 1: So okay, I accept that. Nevertheless, as you say, also

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Speaker 1: from quantum theory, we have reason to think that nature

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Speaker 1: is fundamentally discreet in every aspect, whether it's matter or

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Speaker 1: space or time. And so if that turns out to

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Speaker 1: be correct, that will mean that real numbers are not real.

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Speaker 1: Real numbers are the things that we use in calculus

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Speaker 1: all day long. There are numbers that have infinitely many

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Speaker 1: digits after the decimal point, like pie. Right, people know,

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Speaker 1: you can keep calculating and you'll never know all the

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Speaker 1: digits of pie because there's infinitely many of them. Is

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Speaker 1: that real? Like? In fact, you could ask that question

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Speaker 1: about all of math, our circles real, you'd have to

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Speaker 1: say no. Circles are not real either, because as you

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Speaker 1: zoom in on them, you know what's there. It's all

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Speaker 1: jiggily and there's fluctuations of the sub atomic particles. So

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Speaker 1: there's no material circle in the real world. But nevertheless,

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Speaker 1: going back to Plato or others, we can think about

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Speaker 1: perfection in our minds. We can think about the concept

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Speaker 1: of a perfect circle, and we can think about the

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Speaker 1: concept of pie, and even the concept of infinity. And

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Speaker 1: this is the uncanny part. These things are not real

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Speaker 1: from the standpoint of physics, yet they give us our

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Speaker 1: best understanding of the physical universe that we've achieved in

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Speaker 1: as a species. And that's just a fact. I mean,

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Speaker 1: that's just a historical fact. That calculus based on this

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Speaker 1: fiction of infinitely subdivisible quantities works pretty darn well. While

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Speaker 1: I was walking my dog this morning, I tried to

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Speaker 1: figure out how many orders of magnitude if you tell

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Speaker 1: us the universe is about ten to the twenty five

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Speaker 1: meters big the visible universe, that's the estimate I looked

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Speaker 1: according to When I asked Syria on my iPhone, she said,

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Speaker 1: the visible universe tend to the twenty five ms, and

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Speaker 1: the typical scale of a hydrogen atom is something like

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Speaker 1: ten to the minus ten meters, So you've got thirty

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Speaker 1: five orders of magnitude very well described by calculus, all

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Speaker 1: the way from the Schroedinger equation at the lowest scale

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Speaker 1: to general relativity at the highest scale, all built on calculus.

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Speaker 1: So it's kind of capturing the truth. Okay, you couldn't. No,

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Speaker 1: it's gonna start screwing up at the scale of quantum gravity,

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Speaker 1: whatever that ends up being, we think. But I think

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Speaker 1: that's a pretty good good notch in the belt of

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Speaker 1: calculus that it works over such a vast range of scales. Absolutely,

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

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

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Speaker 1: 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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Speaker 1: quick break. Okay, we're back and we're talking with Professor

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Speaker 1: Steve stroke Gats about why math is so important for physics.

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Speaker 1: And it makes me think about the connection in physics

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Speaker 1: and math of the concept of emergence. You know, some

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Speaker 1: simple behavior at the scale of like me and you

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Speaker 1: are a bowl of soup that neatly and compactly summarizes

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Speaker 1: the almost infinite details going on underneath. I mean, even

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Speaker 1: if you don't believe that a ball is infinitely divisible

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Speaker 1: into bits, we know this is a huge number of

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Speaker 1: bits with a huge number of details. But it's almost

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Speaker 1: like the equations and the simplicity of calculus, the parabolic

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Speaker 1: motion of that ball emerge somehow from all of these

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Speaker 1: infinite testimals doing their bit together to tell a fairly

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Speaker 1: simple story. And in physics, to me, it's something of

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Speaker 1: a mystery, like why this happens? Why can we describe

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Speaker 1: the universe in simple mathematical stories when we know that

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Speaker 1: the details are crazy and gory in intense and calculus

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Speaker 1: really wraps this up. So do you have an instinct

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Speaker 1: or an intuition, or even a guest for why it's

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Speaker 1: possible to wrangle these almost infinities into fairly simple stories

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Speaker 1: that make sense to our human minds. That's another tough one.

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Speaker 1: I don't mean to put you on this spot. Well,

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Speaker 1: they're all great questions, they're so deep. My first instinct

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Speaker 1: to that one after I don't know is Is it

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Speaker 1: a question of the measuring apparatus meaning us that we

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Speaker 1: happened to be macroscopic and so for us space has

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Speaker 1: perceived as smooth, and time as smooth and so on.

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Speaker 1: But if we were playing scale creatures, we wouldn't. Of course,

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Speaker 1: we don't know what's going on down there, but under

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Speaker 1: our current understanding, you wouldn't have the concept of space

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Speaker 1: time as smooth. So, as you say it emerges, it

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Speaker 1: appears smooth only at our scale, or well down to

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Speaker 1: even atomic scales, but it's still twenty five orders of

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Speaker 1: magnitude bigger than the Planck scale to go to the

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Speaker 1: hydrogen atoms diameter. So yeah, it might just be where

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Speaker 1: you know, all those jitters, their quantum gravitational jitters are invisible,

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Speaker 1: they get smoothed out, or they start to look smooth,

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Speaker 1: spacetime emerges. Right. That's the latest talk that spacetime as

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Speaker 1: a as a manifold in the jargon of differential geometry

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Speaker 1: as this smooth structure. That's another fiction. That's an emergent

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Speaker 1: property of something about quantum fluctuations, maybe having to do

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Speaker 1: with entanglement. Anyway, I don't know about that stuff. You

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Speaker 1: probably have other guests who could address that better. But yeah,

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Speaker 1: so we're probably studying the emergent theory that just the

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Speaker 1: way thermodynamics works well, even though statistical mechanics is the

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Speaker 1: deeper theory. Calculus and all of smooth classical physics, and

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Speaker 1: even the smooth parts of quantum physics, say the Schrodinger

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Speaker 1: equation or the direct equation, those things are emergent. But

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Speaker 1: I guess your question was why does emergence work so well?

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Speaker 1: That's something about a different branch of math, that's about statistics,

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Speaker 1: about laws of large numbers. And it's a very fortunate accident.

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Speaker 1: I mean, maybe it's not an accident. Maybe we couldn't

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Speaker 1: exist as intelligent creatures except at that scale. If we

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Speaker 1: were these hypothetical quantum gravitational scale creatures at the Planck scale,

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Speaker 1: we'd be so jiggili it would be hard to keep

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Speaker 1: a thought in our heads. You know what I mean.

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Speaker 1: I'm being simply, We wouldn't have heads. Podcast episodes would

430
00:23:34,960 --> 00:23:40,680
Speaker 1: be tend of the minus thirty four seconds long. So

431
00:23:40,840 --> 00:23:43,679
Speaker 1: I guess I'm giving an anthropic principle style argument here,

432
00:23:43,680 --> 00:23:46,320
Speaker 1: aren't I. But it's hard to answer these deep questions.

433
00:23:46,400 --> 00:23:48,040
Speaker 1: It is hard and to meet. It really goes to

434
00:23:48,119 --> 00:23:51,199
Speaker 1: the heart of these questions about whether we are describing

435
00:23:51,240 --> 00:23:54,760
Speaker 1: the universe as it is or just our view of it,

436
00:23:54,800 --> 00:23:57,960
Speaker 1: and whether our view of it is somehow human centric

437
00:23:58,040 --> 00:24:00,480
Speaker 1: in a way that we can't unravel and can't peeled

438
00:24:00,520 --> 00:24:03,480
Speaker 1: back because we only have our human view, and the

439
00:24:03,480 --> 00:24:06,240
Speaker 1: appearance of calculus and like short simple stories to me

440
00:24:06,359 --> 00:24:08,919
Speaker 1: like are an interesting clue to grab onto. So let

441
00:24:08,960 --> 00:24:10,920
Speaker 1: me steer us back the other direction. Because we've sort

442
00:24:10,920 --> 00:24:14,280
Speaker 1: of described calculus as a useful fiction. We've said it's

443
00:24:14,280 --> 00:24:16,400
Speaker 1: a handy tool for doing calculations, but as you say,

444
00:24:16,440 --> 00:24:18,720
Speaker 1: it comes on the stage and disappears before the answer

445
00:24:18,800 --> 00:24:22,040
Speaker 1: is revealed. And yet it is really really powerful, right,

446
00:24:22,080 --> 00:24:24,639
Speaker 1: Calculus and math and general is sometimes described as like

447
00:24:24,720 --> 00:24:27,639
Speaker 1: being unreasonably effective in your book. I really like this

448
00:24:27,720 --> 00:24:30,000
Speaker 1: line you wrote. You said, what fascinates me as an

449
00:24:30,040 --> 00:24:32,880
Speaker 1: applied mathematician is the push and pull between the real

450
00:24:32,920 --> 00:24:35,919
Speaker 1: world around us and the ideal world in our heads.

451
00:24:36,240 --> 00:24:40,240
Speaker 1: Phenomena out there guide the mathematical questions we ask. Conversely,

452
00:24:40,280 --> 00:24:43,960
Speaker 1: the math we imagine sometimes foreshadows what actually happens out

453
00:24:44,000 --> 00:24:47,480
Speaker 1: there in reality. When it does, the effect is uncanny

454
00:24:47,560 --> 00:24:51,200
Speaker 1: and later you wrote it's eerie that calculus can mimic nature,

455
00:24:51,440 --> 00:24:53,919
Speaker 1: So well, can you elaborate on that a little bit?

456
00:24:53,960 --> 00:24:56,800
Speaker 1: Why do you think math is so good at describing

457
00:24:56,840 --> 00:24:58,840
Speaker 1: the universe if it's just sort of a fiction in

458
00:24:58,880 --> 00:25:01,840
Speaker 1: our minds? And why do we then describe it as

459
00:25:01,960 --> 00:25:05,439
Speaker 1: unreasonable or uncanny or eerie when that happens, why are

460
00:25:05,440 --> 00:25:08,800
Speaker 1: we surprised by that? Well? Should we stipulate that we

461
00:25:08,800 --> 00:25:10,440
Speaker 1: we believe in all this? I mean, is it worth

462
00:25:10,440 --> 00:25:13,199
Speaker 1: going into any case studies of the eerie effectiveness? Or

463
00:25:13,200 --> 00:25:15,480
Speaker 1: do you think we should just assume that we know it?

464
00:25:16,040 --> 00:25:18,320
Speaker 1: Please give us some examples. Well, okay, yeah, let's talk

465
00:25:18,359 --> 00:25:21,240
Speaker 1: about a few. Because I did feel myself recoiling a bit.

466
00:25:21,400 --> 00:25:24,160
Speaker 1: I felt like you were almost verging toward a kind

467
00:25:24,200 --> 00:25:27,880
Speaker 1: of circular reasoning claim that we as human beings can

468
00:25:27,920 --> 00:25:30,720
Speaker 1: only think a certain way or perceive certain things, and

469
00:25:30,800 --> 00:25:33,400
Speaker 1: so it all kind of comes out tidy because of

470
00:25:33,440 --> 00:25:36,400
Speaker 1: our own limitations, like we're convincing ourselves. I don't think

471
00:25:36,400 --> 00:25:38,560
Speaker 1: you were saying that exactly, but if if some people

472
00:25:38,600 --> 00:25:40,520
Speaker 1: heard it like that, I would have to push back

473
00:25:40,560 --> 00:25:43,200
Speaker 1: on that. Because of the concept of prediction, we use

474
00:25:43,240 --> 00:25:46,159
Speaker 1: our math, we use our all of our scientific laws

475
00:25:46,200 --> 00:25:49,440
Speaker 1: and observations to make predictions of things we haven't seen

476
00:25:49,480 --> 00:25:53,119
Speaker 1: before or haven't measured. And there's no circular aspect to

477
00:25:53,240 --> 00:25:56,159
Speaker 1: what we predict. Either nature does what we predict or

478
00:25:56,200 --> 00:25:58,520
Speaker 1: it doesn't. And there's been plenty of cases of you know,

479
00:25:58,600 --> 00:26:01,280
Speaker 1: flagists on theories and kinds of other things that turned

480
00:26:01,280 --> 00:26:03,720
Speaker 1: out to be wrong. So science is done in good faith.

481
00:26:03,760 --> 00:26:06,440
Speaker 1: We make predictions and they sometimes come out wrong. And yeah,

482
00:26:06,480 --> 00:26:08,440
Speaker 1: I mean there are old people who will hang onto

483
00:26:08,480 --> 00:26:10,240
Speaker 1: the theory after they should have given it up. But

484
00:26:10,280 --> 00:26:13,200
Speaker 1: it's a self correcting enterprise, it really is, I think

485
00:26:13,280 --> 00:26:15,840
Speaker 1: over the long run. So I don't think there's any

486
00:26:15,880 --> 00:26:19,080
Speaker 1: circularity happening here. And you know, for me, the eerie

487
00:26:19,119 --> 00:26:23,600
Speaker 1: examples are things like, you know, take Maxwell, James Clerk, Maxwell,

488
00:26:23,680 --> 00:26:26,640
Speaker 1: who has these empirical laws from people like amp Here

489
00:26:26,680 --> 00:26:30,400
Speaker 1: and Faraday and uh, I don't know, Bo Savar, all

490
00:26:30,400 --> 00:26:33,000
Speaker 1: these laws that we learned about in electricity and magnetism

491
00:26:33,040 --> 00:26:36,159
Speaker 1: courses for what happens with magnets with electric currents and

492
00:26:36,200 --> 00:26:38,920
Speaker 1: circuits and stuff. So these laws then could be rewritten

493
00:26:39,040 --> 00:26:42,760
Speaker 1: in a certain mathematical language, and Maxwell did that using

494
00:26:42,920 --> 00:26:45,399
Speaker 1: the language at the time which was called quaternions, but

495
00:26:45,480 --> 00:26:49,680
Speaker 1: nowadays we would use vectors vector calculus, and he saw

496
00:26:49,760 --> 00:26:52,399
Speaker 1: certain things in those laws that looked a little contradictory

497
00:26:52,440 --> 00:26:54,920
Speaker 1: to him. That led him to introduce a new concept,

498
00:26:54,960 --> 00:26:57,399
Speaker 1: the displacement current. And when he put that in the

499
00:26:57,480 --> 00:27:01,399
Speaker 1: known laws and started cranking the math, medical crank, just

500
00:27:01,480 --> 00:27:05,159
Speaker 1: manipulating the equations. Now in the world of pure idealization,

501
00:27:05,440 --> 00:27:08,800
Speaker 1: in the world of calculus, he saw that those equations

502
00:27:08,800 --> 00:27:12,760
Speaker 1: predicted something, which is that electric fields and magnetic fields

503
00:27:12,760 --> 00:27:15,320
Speaker 1: could move through empty space. Although for him it was

504
00:27:15,359 --> 00:27:18,119
Speaker 1: the ether, but nowadays we would say empty space in

505
00:27:18,160 --> 00:27:21,199
Speaker 1: this kind of dance with the electric field changing and

506
00:27:21,240 --> 00:27:24,119
Speaker 1: generating a magnetic field that would change and regenerate the

507
00:27:24,160 --> 00:27:26,439
Speaker 1: electric field, and the whole thing would propagate at a

508
00:27:26,480 --> 00:27:29,840
Speaker 1: certain speed, governed by an equation that in calculus we

509
00:27:29,920 --> 00:27:33,520
Speaker 1: call the wave equation. So he's predicting electromagnetic waves those

510
00:27:33,520 --> 00:27:37,120
Speaker 1: were not known. That's a prediction, and his math gives

511
00:27:37,160 --> 00:27:39,680
Speaker 1: him a prediction for the speed of those waves, and

512
00:27:39,720 --> 00:27:42,280
Speaker 1: when he calculates it using the known physics, it comes

513
00:27:42,320 --> 00:27:44,000
Speaker 1: out to be the speed of light. So it's one

514
00:27:44,000 --> 00:27:46,800
Speaker 1: of the biggest a haa moments in the history of humanity.

515
00:27:46,840 --> 00:27:51,000
Speaker 1: That light is an electromagnetic wave, and Maxwell's the first

516
00:27:51,000 --> 00:27:53,800
Speaker 1: to realize that, and it turns out it's right. You know,

517
00:27:53,920 --> 00:27:56,600
Speaker 1: years later his predictions get checked out in the lab

518
00:27:57,000 --> 00:28:01,360
Speaker 1: Hurts measures there really are electromagnetic waves, and pretty soon

519
00:28:01,400 --> 00:28:04,360
Speaker 1: after that, Marconi and Tesla are building telegraphs and we've

520
00:28:04,359 --> 00:28:07,639
Speaker 1: got wireless communication across the ocean and all this stuff

521
00:28:07,720 --> 00:28:10,800
Speaker 1: is real. But it was born out of calculus combined

522
00:28:10,800 --> 00:28:13,320
Speaker 1: with physics. Let's be clear. It's not calculus on its own.

523
00:28:13,440 --> 00:28:16,679
Speaker 1: It's calculus supplemented, not supplement I mean, calculus is more

524
00:28:16,720 --> 00:28:19,399
Speaker 1: like the supporting player. The real stars are Michael Faraday,

525
00:28:19,520 --> 00:28:22,000
Speaker 1: An amp Here and the rest. But their laws of

526
00:28:22,080 --> 00:28:25,760
Speaker 1: nature have these logical implications that lead to predictions that

527
00:28:25,800 --> 00:28:28,200
Speaker 1: turn out to be right. And so what's uncanny there

528
00:28:28,440 --> 00:28:31,880
Speaker 1: is that nature is obeying logic that's not necessary, right,

529
00:28:31,960 --> 00:28:35,199
Speaker 1: This is puny primate logic. This is us. We're not

530
00:28:35,280 --> 00:28:38,280
Speaker 1: the best imaginable thing under the sun, but our logic

531
00:28:38,440 --> 00:28:41,720
Speaker 1: somehow is enough to make these predictions. And you know,

532
00:28:41,840 --> 00:28:44,880
Speaker 1: there's countless examples of this. So but maybe that Maxwell

533
00:28:44,920 --> 00:28:47,200
Speaker 1: one makes the point. I'm wondering if you know anymore

534
00:28:47,240 --> 00:28:49,800
Speaker 1: about the history of it, because I've heard this story

535
00:28:49,840 --> 00:28:53,440
Speaker 1: about Maxwell's AHA moment, and I wonder historically was their

536
00:28:53,440 --> 00:28:56,760
Speaker 1: own moment. It's such an incredible realization. I'd like to

537
00:28:56,800 --> 00:28:59,520
Speaker 1: imagine that he was sitting there by lantern light at

538
00:28:59,520 --> 00:29:01,440
Speaker 1: his desk and it all clicked together and he had

539
00:29:01,480 --> 00:29:04,080
Speaker 1: this epiphany where like he saw the universe in a

540
00:29:04,080 --> 00:29:05,760
Speaker 1: way nobody had ever seen him before. Do you know

541
00:29:05,800 --> 00:29:07,440
Speaker 1: if there was such a moment for sort of a

542
00:29:07,480 --> 00:29:09,960
Speaker 1: gradual coming together? And I don't know. I want to

543
00:29:10,000 --> 00:29:12,080
Speaker 1: know that too, And it's funny. I have the same

544
00:29:12,160 --> 00:29:16,640
Speaker 1: fantasy image of the lantern, the little hovel in Scotland,

545
00:29:16,880 --> 00:29:19,400
Speaker 1: So I don't know. I think it is known. I

546
00:29:19,440 --> 00:29:22,280
Speaker 1: think this is another point that history of science is

547
00:29:22,320 --> 00:29:26,120
Speaker 1: such a rich and detailed and often non logical thing.

548
00:29:26,880 --> 00:29:29,200
Speaker 1: Like we we you and I are telling ourselves this

549
00:29:29,240 --> 00:29:30,880
Speaker 1: story a certain way, and I just told it a

550
00:29:30,880 --> 00:29:33,040
Speaker 1: certain way, and I don't really know what I'm talking about.

551
00:29:33,120 --> 00:29:36,600
Speaker 1: For instance, I read somewhere fairly recently that he knew

552
00:29:36,640 --> 00:29:38,360
Speaker 1: that light was going to turn out to be an

553
00:29:38,400 --> 00:29:41,920
Speaker 1: electromagnetic wave before his math showed him that just on

554
00:29:42,000 --> 00:29:45,360
Speaker 1: dimensional grounds. You earlier, we're talking about the Planck scale,

555
00:29:45,400 --> 00:29:48,080
Speaker 1: and you know the cancelation of units and stuff or

556
00:29:48,120 --> 00:29:51,080
Speaker 1: not cancelation, but you can get arguments based on dimensional

557
00:29:51,400 --> 00:29:53,960
Speaker 1: just by monkeying around with units. I think he knew

558
00:29:53,960 --> 00:29:57,440
Speaker 1: that me not an epsilon, not these properties of the

559
00:29:57,560 --> 00:30:00,920
Speaker 1: vacuum having to do with its magnetic and elect trical properties,

560
00:30:01,000 --> 00:30:02,840
Speaker 1: that they could be combined in a certain way to

561
00:30:02,880 --> 00:30:05,360
Speaker 1: make a speed. And I think he did that calculation

562
00:30:05,400 --> 00:30:08,800
Speaker 1: about a decade before he actually derived the wave equation. Wow,

563
00:30:08,840 --> 00:30:10,840
Speaker 1: it would be delicious to understand the history of that

564
00:30:10,880 --> 00:30:12,720
Speaker 1: a little bit better. But I love the argument you're

565
00:30:12,760 --> 00:30:16,240
Speaker 1: making here that essentially the math guided the physics. That

566
00:30:16,320 --> 00:30:21,120
Speaker 1: he saw something that wasn't symmetric, that looked imbalanced mathematically,

567
00:30:21,400 --> 00:30:24,240
Speaker 1: and he patched it up just because of his mathematical intuition,

568
00:30:24,280 --> 00:30:26,600
Speaker 1: and the physics sort of followed suit. That that was

569
00:30:26,640 --> 00:30:30,400
Speaker 1: a better description of the universe because mathematically it hung

570
00:30:30,480 --> 00:30:33,920
Speaker 1: together more crisply than the previous ideas. That the math

571
00:30:34,040 --> 00:30:37,120
Speaker 1: really did guide us to truth about the universe. Is

572
00:30:37,120 --> 00:30:39,320
Speaker 1: that the core of the argument. Yeah, And the part

573
00:30:39,360 --> 00:30:43,600
Speaker 1: that the spooky is, Look who's behind it. It's it's

574
00:30:43,680 --> 00:30:46,920
Speaker 1: this creature that has evolved on this planet in an

575
00:30:47,000 --> 00:30:49,560
Speaker 1: ordinary galaxy, you know. I mean, it's not like we

576
00:30:49,640 --> 00:30:52,840
Speaker 1: have godlike intelligence. The thing that so so spooky is

577
00:30:52,880 --> 00:30:56,520
Speaker 1: we're so bounded in our understanding. We can understand so

578
00:30:56,640 --> 00:30:59,880
Speaker 1: much through the help of this crazy fictional thing that

579
00:31:00,040 --> 00:31:02,720
Speaker 1: involves infinity. It's almost like we're in the sweet spot

580
00:31:02,880 --> 00:31:05,640
Speaker 1: for pleasure in doing science and math. If we were

581
00:31:05,720 --> 00:31:08,959
Speaker 1: much smarter than we are, we wouldn't be surprised. Everything

582
00:31:08,960 --> 00:31:11,320
Speaker 1: would be trivial, Like playing tic tac toe is not

583
00:31:11,440 --> 00:31:14,280
Speaker 1: interesting for someone who understands it, and so grown ups

584
00:31:14,320 --> 00:31:17,360
Speaker 1: don't play tic tac toe for fun because it's boring.

585
00:31:17,520 --> 00:31:20,160
Speaker 1: And if we were just a bit smarter, physics and

586
00:31:20,240 --> 00:31:23,080
Speaker 1: math might be boring in the same way. But it's

587
00:31:23,120 --> 00:31:25,560
Speaker 1: fun for us because we're in this place where we're

588
00:31:25,600 --> 00:31:28,080
Speaker 1: not as stupid as a lobster. I mean, a lobster

589
00:31:28,160 --> 00:31:32,360
Speaker 1: is not inventing calculus. We're at this happy, resonant place

590
00:31:32,720 --> 00:31:36,440
Speaker 1: where we're smart enough to get it but sort of

591
00:31:36,480 --> 00:31:40,760
Speaker 1: stupid enough to be surprised all the time. It's amazing.

592
00:31:40,800 --> 00:31:43,640
Speaker 1: It's a really fun game, but it's also teaching us

593
00:31:43,640 --> 00:31:45,960
Speaker 1: things about the universe, which is incredible. As I was

594
00:31:46,080 --> 00:31:49,640
Speaker 1: hearing you talk about that Scottish mathematician. I was reminded

595
00:31:49,680 --> 00:31:52,920
Speaker 1: of another Scotsman more than a century later, Peter Higgs,

596
00:31:52,920 --> 00:31:55,600
Speaker 1: who made sort of a similar realization. He was looking

597
00:31:55,600 --> 00:31:59,800
Speaker 1: at the mathematics of not just electromagnetism, but electromagnetism and

598
00:31:59,800 --> 00:32:02,600
Speaker 1: the weak force, how they clicked together, and realizing there

599
00:32:02,640 --> 00:32:05,280
Speaker 1: was a missing piece and predicting the existence of a

600
00:32:05,320 --> 00:32:07,520
Speaker 1: field we now call the Higgs field. So you know,

601
00:32:07,560 --> 00:32:10,840
Speaker 1: maybe it's something in the water in Scotland. Well, it's

602
00:32:10,840 --> 00:32:13,880
Speaker 1: another great example because it took a long time for

603
00:32:14,000 --> 00:32:17,240
Speaker 1: that prediction to be checked in the lab and tremendous

604
00:32:17,280 --> 00:32:20,680
Speaker 1: effort and cost from great teams of physicists and engineers

605
00:32:20,720 --> 00:32:25,400
Speaker 1: at large Hadron Collider is that right, Yeah, detected? So

606
00:32:26,200 --> 00:32:29,200
Speaker 1: I didn't have to be there. And some things aren't there, right,

607
00:32:29,240 --> 00:32:32,320
Speaker 1: like supersymmetry. Is this other beautiful set of ideas that

608
00:32:32,400 --> 00:32:34,920
Speaker 1: so far has not turned out to be in the

609
00:32:35,000 --> 00:32:37,760
Speaker 1: experimental data. Maybe in the future. But I'm just saying

610
00:32:37,840 --> 00:32:40,680
Speaker 1: that this is a very honest enterprise in science. It's

611
00:32:40,680 --> 00:32:44,400
Speaker 1: not circular reasoning. It's not like we're convincing ourselves. We're

612
00:32:44,440 --> 00:32:47,840
Speaker 1: really doing fair play. And the universe either does what

613
00:32:47,880 --> 00:32:51,240
Speaker 1: we imagine or not, and frequently and uncannily it does

614
00:32:51,400 --> 00:32:54,000
Speaker 1: if we use calculus and and feed in. I mean,

615
00:32:54,000 --> 00:32:56,040
Speaker 1: that's the other thing. Like you'll hear people say calculus

616
00:32:56,120 --> 00:32:59,400
Speaker 1: is a language or math is the language of science.

617
00:32:59,600 --> 00:33:02,280
Speaker 1: Partly true, but it's much more than that. Math and

618
00:33:02,360 --> 00:33:08,080
Speaker 1: calculus in particular are a calculating machine. They're a logical prosthesis.

619
00:33:08,320 --> 00:33:10,720
Speaker 1: I mean, there's something which lets us take our logic

620
00:33:10,920 --> 00:33:16,200
Speaker 1: again puny primate logic, and strengthen it by introducing symbols

621
00:33:16,200 --> 00:33:20,120
Speaker 1: and letting us do logical manipulations, like you know, solving equations.

622
00:33:20,440 --> 00:33:22,640
Speaker 1: That kind of thing is a big extension to what

623
00:33:22,680 --> 00:33:24,560
Speaker 1: we can hold in our heads. That's why we have

624
00:33:24,600 --> 00:33:27,480
Speaker 1: paper and pencil. You can make these arguments much more

625
00:33:27,480 --> 00:33:30,320
Speaker 1: elaborate than you could have easily held. Like think of algebra.

626
00:33:30,400 --> 00:33:32,440
Speaker 1: Before we had symbols and it was all verbal. It

627
00:33:32,520 --> 00:33:34,520
Speaker 1: was a much weaker thing. So now we just shove

628
00:33:34,600 --> 00:33:37,600
Speaker 1: these symbols around on paper according to certain rules, and

629
00:33:37,640 --> 00:33:41,360
Speaker 1: out we get predictions for electromagnetic waves or the existence

630
00:33:41,360 --> 00:33:44,600
Speaker 1: of the Higgs particle. I find that very uncanny. I

631
00:33:44,640 --> 00:33:46,160
Speaker 1: just get I don't know how else to say it

632
00:33:46,200 --> 00:33:48,280
Speaker 1: to me. It's the spooky, est and most profound thing

633
00:33:48,520 --> 00:33:50,760
Speaker 1: there is that this works. And I want to emphasize

634
00:33:50,760 --> 00:33:52,960
Speaker 1: in case people are saying this is just math. Why

635
00:33:52,960 --> 00:33:55,280
Speaker 1: do I harp on calculus so much? I really do

636
00:33:55,360 --> 00:33:58,520
Speaker 1: think calculus has a singular place in the landscape of math,

637
00:33:58,960 --> 00:34:01,360
Speaker 1: in that the laws of nature are written in a

638
00:34:01,440 --> 00:34:05,320
Speaker 1: subdialect of math. It's calculus. And even there it's the

639
00:34:05,360 --> 00:34:08,839
Speaker 1: particular part of calculus we call differential equations. So from

640
00:34:08,880 --> 00:34:12,520
Speaker 1: F equals M A and Newton to Einstein's general relativity

641
00:34:12,600 --> 00:34:16,680
Speaker 1: to Schroedinger's you know, wave equation, those are all differential equations.

642
00:34:16,719 --> 00:34:19,960
Speaker 1: So it's not like we're using combinatorics or some other

643
00:34:20,000 --> 00:34:22,680
Speaker 1: part of discrete math that is not the language of

644
00:34:22,719 --> 00:34:26,520
Speaker 1: the universe. Sorry, maybe it is at the smallest scale, Okay,

645
00:34:26,560 --> 00:34:29,280
Speaker 1: maybe it will turn out the combinatorics is the answer

646
00:34:29,760 --> 00:34:33,080
Speaker 1: to the Planck scale stuff, and calculus is just this emergent,

647
00:34:33,760 --> 00:34:36,279
Speaker 1: smoothed out version of what's really going on, which is

648
00:34:36,280 --> 00:34:38,600
Speaker 1: combinatorics if we get down to the bottom. But for

649
00:34:38,680 --> 00:34:41,320
Speaker 1: the thirty five orders of magnitude that we've done science

650
00:34:41,360 --> 00:34:46,880
Speaker 1: on so far, it's calculus. Baby, Well, I had in

651
00:34:46,920 --> 00:34:50,719
Speaker 1: my own aha moment as a junior in quantum physics,

652
00:34:50,840 --> 00:34:54,359
Speaker 1: seeing the prediction of properties of the electron muan how

653
00:34:54,480 --> 00:34:57,839
Speaker 1: to tend decimal places, and then seeing the experiments which

654
00:34:58,040 --> 00:35:02,200
Speaker 1: verify those predictions digit after digit after digit, and feeling

655
00:35:02,200 --> 00:35:05,080
Speaker 1: for the first time that maybe math wasn't just a

656
00:35:05,239 --> 00:35:08,400
Speaker 1: description of what was happening out there in our language,

657
00:35:08,600 --> 00:35:11,520
Speaker 1: but it really was the essential underlying machinery of the

658
00:35:11,600 --> 00:35:15,360
Speaker 1: universe itself, that the universe was using these laws, that

659
00:35:15,400 --> 00:35:19,160
Speaker 1: we weren't describing them but revealing them somehow. And I

660
00:35:19,280 --> 00:35:21,560
Speaker 1: know that's, you know, it's a philosophical position. But I

661
00:35:21,880 --> 00:35:23,960
Speaker 1: had this moment as an undergrad of feeling this, and

662
00:35:24,000 --> 00:35:25,840
Speaker 1: I thought of that moment when I read this passage

663
00:35:25,840 --> 00:35:29,719
Speaker 1: in your book. You wrote, quote, the results are there

664
00:35:29,719 --> 00:35:32,600
Speaker 1: waiting for us. They have been inherent in the figures

665
00:35:32,600 --> 00:35:35,760
Speaker 1: all along. We are not inventing them like Bob Dylan

666
00:35:35,840 --> 00:35:38,440
Speaker 1: or Tony Morrison. We are not creating music or novels

667
00:35:38,480 --> 00:35:42,320
Speaker 1: that never existed before. We are discovering facts that already exist.

668
00:35:42,560 --> 00:35:44,320
Speaker 1: And as I was reading your book, I was wondering,

669
00:35:44,520 --> 00:35:47,040
Speaker 1: you know, Steve a realist or is he not a realist?

670
00:35:47,239 --> 00:35:48,839
Speaker 1: And I sort of went back and forth a few

671
00:35:48,880 --> 00:35:51,120
Speaker 1: times since I read these passages. Oh really, was I

672
00:35:51,200 --> 00:35:54,200
Speaker 1: not clear where I stand on that? Well, that's earlier

673
00:35:54,200 --> 00:35:56,040
Speaker 1: what I was saying with these two people. I guess

674
00:35:56,040 --> 00:35:58,359
Speaker 1: I didn't make the argument for both sides that there's

675
00:35:58,400 --> 00:36:00,920
Speaker 1: the chicken hearted person in me who is the one

676
00:36:00,960 --> 00:36:03,520
Speaker 1: that thinks it's just a language and it's just you know.

677
00:36:03,640 --> 00:36:06,120
Speaker 1: But in my heart, I think it's what you're calling realism,

678
00:36:06,280 --> 00:36:09,320
Speaker 1: which is that the universe isn't just described by calculus.

679
00:36:09,400 --> 00:36:12,319
Speaker 1: The universe actually runs on calculus. I really do, in

680
00:36:12,360 --> 00:36:14,840
Speaker 1: my heart of hearts, think that, and I don't know

681
00:36:14,920 --> 00:36:17,640
Speaker 1: why that would be true. I think the answer could be, again,

682
00:36:17,760 --> 00:36:20,600
Speaker 1: some kind of anthropic argument that that a universe that

683
00:36:20,640 --> 00:36:24,560
Speaker 1: doesn't run on math in some way is such a disorganized,

684
00:36:24,560 --> 00:36:28,160
Speaker 1: tiggle dy piggledy universe that it can't support life intelligent

685
00:36:28,280 --> 00:36:31,080
Speaker 1: enough to ask questions. So I sort of think just

686
00:36:31,120 --> 00:36:33,480
Speaker 1: the fact that we exist and we're here pondering it

687
00:36:33,520 --> 00:36:36,000
Speaker 1: tells you the universe has to obey a certain amount

688
00:36:36,040 --> 00:36:39,000
Speaker 1: of orderliness, and calculus is going to come up in

689
00:36:39,080 --> 00:36:42,600
Speaker 1: such universes. So it's not the most convincing argument. I

690
00:36:42,600 --> 00:36:44,759
Speaker 1: don't like that argument, but that's the best I can do.

691
00:36:44,800 --> 00:36:47,160
Speaker 1: I mean, obviously you could give a theological argument that

692
00:36:47,280 --> 00:36:50,239
Speaker 1: God knew calculus better than anybody and chose to make

693
00:36:50,239 --> 00:36:53,799
Speaker 1: a universe that runs on calculus. Okay, if that satisfies you,

694
00:36:53,880 --> 00:36:56,520
Speaker 1: then that's you could use that argument. But to me,

695
00:36:56,600 --> 00:36:58,839
Speaker 1: that just raises a lot more questions. But I don't

696
00:36:58,840 --> 00:37:01,040
Speaker 1: have the answers to why was it designed this way

697
00:37:01,120 --> 00:37:03,520
Speaker 1: or built this way, or why did it evolved to

698
00:37:03,560 --> 00:37:05,560
Speaker 1: be this way. I don't have any idea, But yeah,

699
00:37:05,640 --> 00:37:08,040
Speaker 1: that's interesting. I mean that ten digit example you give

700
00:37:08,080 --> 00:37:11,440
Speaker 1: from quantum field theory, from quantum electrodynamics, that's really the

701
00:37:11,520 --> 00:37:15,600
Speaker 1: poster child for the claim that the universe is running

702
00:37:15,719 --> 00:37:18,240
Speaker 1: on math, and that we happen to have stumbled across

703
00:37:18,320 --> 00:37:20,960
Speaker 1: that math. That's also fun to think about that. Just

704
00:37:21,040 --> 00:37:24,840
Speaker 1: think of the story. There's Archimedes in Syracuse pondering circles

705
00:37:24,840 --> 00:37:28,560
Speaker 1: and spheres to fifty b C and he's stumbling across

706
00:37:28,640 --> 00:37:33,200
Speaker 1: the math that turns out to describe sub atomic particles

707
00:37:33,239 --> 00:37:36,640
Speaker 1: like nuance. Ultimately, a few thousand years later, it's that

708
00:37:36,760 --> 00:37:39,880
Speaker 1: same math and he wasn't thinking about that. It's really

709
00:37:39,920 --> 00:37:42,960
Speaker 1: spooky that that should work, but it did. It is

710
00:37:43,000 --> 00:37:45,560
Speaker 1: pretty amazing. All right, I'm really excited about these topics.

711
00:37:45,560 --> 00:38:01,040
Speaker 1: But let's take another quick break. Okay, we are here

712
00:38:01,080 --> 00:38:04,720
Speaker 1: talking with Professor Steve's drogats about why math and physics

713
00:38:04,719 --> 00:38:08,399
Speaker 1: are so closely intertwined. In your episode of The Joy

714
00:38:08,440 --> 00:38:11,400
Speaker 1: of Y, you interviewed Kevin Buzzard, and mathematician, and he

715
00:38:11,520 --> 00:38:15,680
Speaker 1: described math as a single player puzzle game. And I

716
00:38:15,760 --> 00:38:17,920
Speaker 1: was actually expecting you to object a little bit because

717
00:38:17,920 --> 00:38:20,640
Speaker 1: it makes it sound like math is just this game

718
00:38:20,719 --> 00:38:23,480
Speaker 1: we play. It's fun to use to describe the universe,

719
00:38:23,680 --> 00:38:26,319
Speaker 1: but not actually fundamentally important. It makes it sound like

720
00:38:26,440 --> 00:38:28,279
Speaker 1: checkers or chess, you know, just a game that we

721
00:38:28,320 --> 00:38:32,759
Speaker 1: invented rather than something physical and true. Uh, well, that

722
00:38:32,840 --> 00:38:35,759
Speaker 1: might be me As a podcast host. I probably ought

723
00:38:35,840 --> 00:38:38,080
Speaker 1: to push back more, and maybe it would make for

724
00:38:38,080 --> 00:38:41,080
Speaker 1: a lively or discussion. I try to be even handed,

725
00:38:41,120 --> 00:38:43,200
Speaker 1: unfair to the guest. And there is an aspect of

726
00:38:43,280 --> 00:38:47,200
Speaker 1: math that is game playing, especially in pure math, and

727
00:38:47,280 --> 00:38:50,600
Speaker 1: that's not to be sneezed at. Just playing games for

728
00:38:50,760 --> 00:38:53,880
Speaker 1: the intellectual pleasure of playing games and the fun and

729
00:38:53,880 --> 00:38:56,279
Speaker 1: the curiosity of how does the game turn out or

730
00:38:56,400 --> 00:38:58,399
Speaker 1: what happens if I change the rules in this way

731
00:38:58,480 --> 00:39:01,640
Speaker 1: or that way. That's all part of the scientific enterprise

732
00:39:01,880 --> 00:39:04,360
Speaker 1: as well as the mathematical enterprise, and it's a healthy

733
00:39:04,400 --> 00:39:06,000
Speaker 1: one for one thing, I mean, if you want to

734
00:39:06,000 --> 00:39:08,920
Speaker 1: be utilitarian about it. A lot of great discoveries in

735
00:39:09,040 --> 00:39:11,640
Speaker 1: science have come from playing games like that. You know.

736
00:39:11,760 --> 00:39:14,000
Speaker 1: You could think about all those centuries that we thought

737
00:39:14,040 --> 00:39:17,680
Speaker 1: Euclidean geometry was the one true geometry, and then people

738
00:39:17,719 --> 00:39:19,799
Speaker 1: started playing games and ask, well, what if we don't

739
00:39:19,800 --> 00:39:22,239
Speaker 1: have the parallel postulate. What if we allow you know,

740
00:39:22,400 --> 00:39:25,279
Speaker 1: infinitely many parallel lines to a given line, or what

741
00:39:25,320 --> 00:39:27,160
Speaker 1: if we say there are no parallel lines to a

742
00:39:27,160 --> 00:39:29,719
Speaker 1: given line, you know, through a specific point. Well, then

743
00:39:29,760 --> 00:39:34,279
Speaker 1: you invent hyperbolic geometry and curved spherical or elliptic geometry.

744
00:39:34,400 --> 00:39:37,200
Speaker 1: Those are games for a few hundred years until it

745
00:39:37,239 --> 00:39:40,319
Speaker 1: turns out the universe uses them. In Einstein's work, so

746
00:39:40,440 --> 00:39:43,160
Speaker 1: you could say, let the people play the games, because

747
00:39:43,200 --> 00:39:45,040
Speaker 1: it's going to turn out that the universe is going

748
00:39:45,080 --> 00:39:47,160
Speaker 1: to use them and they'll be very practical, you know.

749
00:39:47,239 --> 00:39:50,200
Speaker 1: Or similarly, games about prime numbers have led to the

750
00:39:50,200 --> 00:39:52,279
Speaker 1: way that we can do encryption on the internet for

751
00:39:52,320 --> 00:39:55,440
Speaker 1: all of our financial transactions or for keeping secrets. So

752
00:39:55,520 --> 00:39:58,840
Speaker 1: game playing is not to be sneezed out on utilitarian grounds.

753
00:39:58,880 --> 00:40:01,919
Speaker 1: It turns out it's often very practical and useful maybe

754
00:40:01,960 --> 00:40:04,480
Speaker 1: a few centuries later, but I I wouldn't want to

755
00:40:04,520 --> 00:40:07,319
Speaker 1: just make the utilitarian argument. It's also part of the

756
00:40:07,400 --> 00:40:10,319
Speaker 1: human spirit. Just be curious for the sake of curiosity,

757
00:40:10,360 --> 00:40:12,040
Speaker 1: and it may never turn out to be useful, and

758
00:40:12,080 --> 00:40:14,840
Speaker 1: that's okay. That's what makes it good to be alive

759
00:40:15,120 --> 00:40:18,200
Speaker 1: for me. One way to make this question less philosophical

760
00:40:18,320 --> 00:40:21,759
Speaker 1: and more concrete is to think about aliens. I know

761
00:40:21,800 --> 00:40:24,160
Speaker 1: it makes people snicker to talk about aliens, but instead

762
00:40:24,200 --> 00:40:27,360
Speaker 1: of asking, you know, is math universal or is it cultural,

763
00:40:27,400 --> 00:40:29,640
Speaker 1: which is a question philosophers have been chewing on for

764
00:40:29,800 --> 00:40:33,120
Speaker 1: millennia without making that much progress. I wonder like, if

765
00:40:33,200 --> 00:40:37,560
Speaker 1: technological scientific aliens arrive, it's a question we're actually going

766
00:40:37,640 --> 00:40:40,560
Speaker 1: to have to face whether they do math. We asked

767
00:40:40,640 --> 00:40:43,000
Speaker 1: Noam Chomsky about it on the podcast recently, you know,

768
00:40:43,000 --> 00:40:45,800
Speaker 1: how do you get started talking to aliens in that scenario?

769
00:40:45,920 --> 00:40:48,200
Speaker 1: And he went with the math. He said we should

770
00:40:48,239 --> 00:40:52,120
Speaker 1: start with arithmetic because one plus one equals to everywhere,

771
00:40:52,600 --> 00:40:55,719
Speaker 1: and he was suggesting that any intelligent being in the

772
00:40:55,840 --> 00:40:58,640
Speaker 1: universe is going to end up being mathematical, which is

773
00:40:58,719 --> 00:41:01,799
Speaker 1: essentially making the argument that math is not just human right,

774
00:41:01,840 --> 00:41:04,120
Speaker 1: that it's part of the universe itself. So, I don't

775
00:41:04,120 --> 00:41:05,799
Speaker 1: know if you've given this question any thought. What do

776
00:41:05,840 --> 00:41:08,560
Speaker 1: you think if aliens arrive? Are you volunteering to be

777
00:41:09,040 --> 00:41:11,680
Speaker 1: one of the envoys? Should we send our mathematicians to

778
00:41:11,719 --> 00:41:15,720
Speaker 1: talk to the aliens? I've seen too many Twilight Zone episodes.

779
00:41:15,760 --> 00:41:20,120
Speaker 1: I know how this turns out, but I've seen the

780
00:41:20,200 --> 00:41:23,000
Speaker 1: ending of that one. Well, it's probably the best suggestion

781
00:41:23,040 --> 00:41:25,399
Speaker 1: there is to that that math would be the most

782
00:41:25,480 --> 00:41:30,400
Speaker 1: universal possible language in this scenario. I'm not totally convinced

783
00:41:30,400 --> 00:41:32,400
Speaker 1: that they would know about one plus one, because you

784
00:41:32,440 --> 00:41:35,799
Speaker 1: could make up stories about intelligent life based on plasma

785
00:41:35,920 --> 00:41:39,040
Speaker 1: or fluid dynamics where they don't have discrete particles, so

786
00:41:39,080 --> 00:41:41,319
Speaker 1: they don't really have one plus one. Maybe it's all

787
00:41:41,320 --> 00:41:44,520
Speaker 1: continuum for them and they would rather talk about calculus

788
00:41:44,600 --> 00:41:48,160
Speaker 1: rather than I'm hammering again on the discreete stuff, but no,

789
00:41:48,360 --> 00:41:50,160
Speaker 1: I mean, basically, if the point is that we would

790
00:41:50,160 --> 00:41:54,080
Speaker 1: could communicate through math better than any other way, yeah, maybe,

791
00:41:54,120 --> 00:41:55,920
Speaker 1: so I tend to think they would have to have

792
00:41:56,000 --> 00:41:58,200
Speaker 1: some version of math, or they couldn't have built their

793
00:41:58,280 --> 00:42:01,560
Speaker 1: rocket ships or teleportation and devices, or however they got here.

794
00:42:01,600 --> 00:42:03,399
Speaker 1: I think they have to have math. I do think

795
00:42:03,600 --> 00:42:05,960
Speaker 1: the math is inherent in the universe. I like the

796
00:42:06,040 --> 00:42:09,279
Speaker 1: quote you gave earlier. There's a psychological dimension to this

797
00:42:09,320 --> 00:42:11,000
Speaker 1: that I want to bring up, which is that there's

798
00:42:11,040 --> 00:42:14,239
Speaker 1: what philosophers talk about, and I like philosophy, but there's

799
00:42:14,239 --> 00:42:17,479
Speaker 1: also what working physicists and mathematicians feel when they're doing

800
00:42:17,520 --> 00:42:21,080
Speaker 1: math or making discoveries. It really feels like the results

801
00:42:21,080 --> 00:42:23,239
Speaker 1: are out there waiting for you. I mean, maybe it's

802
00:42:23,239 --> 00:42:27,120
Speaker 1: a fiction, maybe it's a psychological self deception, but it's

803
00:42:27,239 --> 00:42:29,960
Speaker 1: very profound and it goes way back. Archimedes says it

804
00:42:30,080 --> 00:42:32,359
Speaker 1: two thousand years ago. He says that the things he

805
00:42:32,400 --> 00:42:35,640
Speaker 1: discovers about the sphere are not his inventions, they're inherent

806
00:42:35,680 --> 00:42:39,840
Speaker 1: in the figures themselves. So he expresses very clearly a

807
00:42:39,920 --> 00:42:42,759
Speaker 1: philosophy of math, which I find kind of heartwarming because

808
00:42:42,760 --> 00:42:44,759
Speaker 1: it makes me feel like I'm having a conversation with

809
00:42:44,800 --> 00:42:47,480
Speaker 1: this person thousands of years ago, and that he's feeling

810
00:42:47,680 --> 00:42:50,560
Speaker 1: some of the same things I'm feeling as a mathematician today.

811
00:42:50,640 --> 00:42:52,840
Speaker 1: And also that he's very humble that he doesn't know

812
00:42:52,880 --> 00:42:55,000
Speaker 1: how to solve certain problems, and he just says he

813
00:42:55,040 --> 00:42:58,560
Speaker 1: hopes his methods will help future generations solve the things

814
00:42:58,560 --> 00:43:00,239
Speaker 1: that he cannot figure out. I think it is an

815
00:43:00,239 --> 00:43:02,359
Speaker 1: important lesson there. I mean, we can talk about math

816
00:43:02,520 --> 00:43:05,880
Speaker 1: is inherent to the universe, but also there's a human

817
00:43:05,920 --> 00:43:09,160
Speaker 1: aspect to it. I mean, we really appreciate the beauty

818
00:43:09,280 --> 00:43:11,719
Speaker 1: of math the way we appreciate the beauty of a

819
00:43:11,719 --> 00:43:13,880
Speaker 1: gorgeous view from the top of a mountain. Some of

820
00:43:13,920 --> 00:43:15,839
Speaker 1: my favorite bits in your book are when you write

821
00:43:15,920 --> 00:43:20,400
Speaker 1: very elegantly about your appreciation for understanding something and seeing

822
00:43:20,440 --> 00:43:23,719
Speaker 1: things come together, and making these connections with ancient mathematicians

823
00:43:23,719 --> 00:43:26,640
Speaker 1: and knowing that you have this joy in common with them.

824
00:43:26,719 --> 00:43:28,840
Speaker 1: I mean, I think a lot of people often see

825
00:43:28,880 --> 00:43:32,000
Speaker 1: math portrayed is like cold and crisp and rigorous, But

826
00:43:32,040 --> 00:43:34,759
Speaker 1: in your book you write about the creativity necessary to

827
00:43:34,800 --> 00:43:38,600
Speaker 1: play this game. You said, quote rigor comes second. Math

828
00:43:38,840 --> 00:43:41,359
Speaker 1: is creative. Why do you think that is that we

829
00:43:41,440 --> 00:43:44,160
Speaker 1: find beauty in math? Is it the same reason we

830
00:43:44,239 --> 00:43:47,319
Speaker 1: find beauty in nature? Is it necessary that we would

831
00:43:47,320 --> 00:43:49,600
Speaker 1: have found math to be beautiful? Is it possible we

832
00:43:49,640 --> 00:43:51,600
Speaker 1: could have evolved and all found math to be like

833
00:43:51,719 --> 00:43:55,719
Speaker 1: a horrible chore, even if it is useful. Well, this

834
00:43:55,960 --> 00:43:58,759
Speaker 1: sensation of beauty is not universal. There are people who

835
00:43:58,800 --> 00:44:00,799
Speaker 1: don't have much patience for the kind of talk who

836
00:44:00,800 --> 00:44:03,200
Speaker 1: are still good mathematicians. There are a lot of reasons

837
00:44:03,239 --> 00:44:06,719
Speaker 1: to love math. Some people do love the beauty of it. Some,

838
00:44:06,960 --> 00:44:09,880
Speaker 1: you know, like the human struggle. Some like the social

839
00:44:09,960 --> 00:44:12,520
Speaker 1: aspect that you get to do it with your friends

840
00:44:12,640 --> 00:44:14,960
Speaker 1: and think about it together and you can surprise each other.

841
00:44:15,000 --> 00:44:17,840
Speaker 1: Some people like the competitive aspect. I'm smarter than the

842
00:44:17,840 --> 00:44:20,600
Speaker 1: other person because I figured out. Beauty is one side.

843
00:44:21,280 --> 00:44:23,279
Speaker 1: I think there's a tendency to go on a little

844
00:44:23,320 --> 00:44:27,000
Speaker 1: too much about beauty, especially because it can be very exclusionary.

845
00:44:27,080 --> 00:44:30,359
Speaker 1: People who aren't seeing math as beautiful are even more

846
00:44:30,400 --> 00:44:33,440
Speaker 1: excluded when they don't get what's beautiful about it. You

847
00:44:33,440 --> 00:44:35,840
Speaker 1: know that it can be um a kind of cudgel

848
00:44:36,080 --> 00:44:38,719
Speaker 1: or a gate keeping a bit of language. So I

849
00:44:38,719 --> 00:44:41,640
Speaker 1: know that when we harp on about beauty or trying

850
00:44:41,640 --> 00:44:44,160
Speaker 1: to make the subject appealing to people and say, hey,

851
00:44:44,160 --> 00:44:46,120
Speaker 1: it's just like music. You like music, you should like

852
00:44:46,200 --> 00:44:49,360
Speaker 1: math maybe, but you have to be very sensitive to

853
00:44:49,480 --> 00:44:53,160
Speaker 1: helping a person appreciate the beauty. I'm reminded of like opera,

854
00:44:53,719 --> 00:44:56,719
Speaker 1: where I don't get opera. When I hear opera, it

855
00:44:56,719 --> 00:45:00,200
Speaker 1: sounds like a lot of hysterical carrying on, and I

856
00:45:00,280 --> 00:45:02,600
Speaker 1: just think, you know, get over yourself. But I see

857
00:45:02,600 --> 00:45:05,759
Speaker 1: other people weeping from it, and they understand it, so

858
00:45:05,800 --> 00:45:08,560
Speaker 1: it's beautiful to them. It's very profound and emotional, and

859
00:45:08,600 --> 00:45:11,160
Speaker 1: I feel like I'm missing something but I'm not getting it,

860
00:45:11,320 --> 00:45:13,440
Speaker 1: so you know, I actually there is this one commercial

861
00:45:13,480 --> 00:45:15,840
Speaker 1: for wine. I think it was Ernest and Julio Galla

862
00:45:15,920 --> 00:45:19,480
Speaker 1: where they're seeing somebody singing Omeo Bambino Carro and it's

863
00:45:19,520 --> 00:45:22,759
Speaker 1: so beautiful even I got it, okay, But other than that,

864
00:45:22,840 --> 00:45:25,600
Speaker 1: I mostly don't get opera. But anyway, my point here,

865
00:45:26,200 --> 00:45:30,280
Speaker 1: silly point is um, you know, as educators or as communicators,

866
00:45:30,280 --> 00:45:32,319
Speaker 1: like through your podcast or the one that I try

867
00:45:32,360 --> 00:45:34,319
Speaker 1: to do, or when I write books, I want to

868
00:45:34,360 --> 00:45:37,200
Speaker 1: be careful about this beauty argument. There there are a

869
00:45:37,200 --> 00:45:39,880
Speaker 1: lot of ways into our subjects. Like I'm trying to

870
00:45:39,920 --> 00:45:43,160
Speaker 1: press every possible button, so I might hit somebody's button

871
00:45:43,440 --> 00:45:45,279
Speaker 1: at a given time. Well, let's talk a little bit

872
00:45:45,320 --> 00:45:49,520
Speaker 1: about the button of creativity. Some folks feel like math

873
00:45:49,640 --> 00:45:52,800
Speaker 1: and science and physics are a different kind of intellectual

874
00:45:53,040 --> 00:45:56,840
Speaker 1: venture than things like music or art. But there's a

875
00:45:56,840 --> 00:46:00,320
Speaker 1: creative side to science where and to math and to tellect.

876
00:46:00,480 --> 00:46:02,520
Speaker 1: We do sometimes feel like you're playing a game. You

877
00:46:02,600 --> 00:46:05,720
Speaker 1: wrote in your book. Mathematicians don't come up with proofs.

878
00:46:06,000 --> 00:46:09,239
Speaker 1: First comes intuition, and rigor comes later. Can you talk

879
00:46:09,280 --> 00:46:11,960
Speaker 1: a little bit about the element of creativity that's involved

880
00:46:12,000 --> 00:46:15,320
Speaker 1: in your work specifically? Oh, well, before I say anything

881
00:46:15,360 --> 00:46:18,839
Speaker 1: about my work specifically, I do appreciate you bringing up

882
00:46:18,880 --> 00:46:22,480
Speaker 1: that point, because in math, especially in high school geometry,

883
00:46:22,480 --> 00:46:24,759
Speaker 1: we're taught the proof has to be rigorous, it has

884
00:46:24,800 --> 00:46:27,840
Speaker 1: to follow logic. You're sometimes teachers will even have students

885
00:46:27,920 --> 00:46:31,120
Speaker 1: right out statements in the left column and reasons in

886
00:46:31,160 --> 00:46:33,399
Speaker 1: the right column. There's a point to that to help

887
00:46:33,520 --> 00:46:36,040
Speaker 1: young students learn how to get organized in their thinking

888
00:46:36,080 --> 00:46:39,719
Speaker 1: and construct logical arguments. And so that is definitely a

889
00:46:39,760 --> 00:46:43,040
Speaker 1: part of math. Mathematicians are very proud of being able

890
00:46:43,040 --> 00:46:46,880
Speaker 1: to have absolute proof in a way that scientists cannot. Right,

891
00:46:46,960 --> 00:46:50,520
Speaker 1: sciences get revised as more information comes in, But in math,

892
00:46:50,640 --> 00:46:53,000
Speaker 1: the theorems that were proven thousands of years ago are

893
00:46:53,040 --> 00:46:55,480
Speaker 1: still true, and the proofs if they were correct back then,

894
00:46:55,520 --> 00:46:58,520
Speaker 1: they're still correct. Some of us like this absolute nature

895
00:46:58,680 --> 00:47:02,160
Speaker 1: of the subject, but that's only half of the story.

896
00:47:02,360 --> 00:47:04,120
Speaker 1: And how do you come up with the proof in

897
00:47:04,160 --> 00:47:06,160
Speaker 1: the first place, or how do you dream up what

898
00:47:06,239 --> 00:47:09,720
Speaker 1: theorem you're even trying to prove? Those things are more

899
00:47:09,760 --> 00:47:14,080
Speaker 1: akin to music and poetry and art and other creative

900
00:47:14,520 --> 00:47:18,799
Speaker 1: parts of of human activity. I mean, you have to

901
00:47:18,840 --> 00:47:21,560
Speaker 1: have imagination, and you have to dream, and you have

902
00:47:21,640 --> 00:47:25,040
Speaker 1: to have wishful hopes. All that kind of stuff is

903
00:47:25,040 --> 00:47:27,520
Speaker 1: a big part of math, and anyone who does math

904
00:47:27,680 --> 00:47:30,239
Speaker 1: or physics or any other part of science knows all

905
00:47:30,280 --> 00:47:32,359
Speaker 1: of that. I mean, when you're doing it, you're still

906
00:47:32,360 --> 00:47:35,480
Speaker 1: a person. You still have dreams and hopes. So I

907
00:47:35,520 --> 00:47:38,000
Speaker 1: don't know why we don't teach that more. I mean

908
00:47:38,160 --> 00:47:40,359
Speaker 1: you learn it when you're in as an apprentice, as

909
00:47:40,360 --> 00:47:42,920
Speaker 1: a young scientist or mathematician, and you're in the lab.

910
00:47:43,400 --> 00:47:46,239
Speaker 1: You feel it. You all want something, But we don't

911
00:47:46,280 --> 00:47:48,880
Speaker 1: do a great job in our textbooks or are lecturing

912
00:47:49,360 --> 00:47:51,239
Speaker 1: and conveying that. And I think that's why a lot

913
00:47:51,280 --> 00:47:53,040
Speaker 1: of people, you know, they might think it's a cold

914
00:47:53,280 --> 00:47:55,680
Speaker 1: subject that wouldn't hold any appeal to them, But once

915
00:47:55,719 --> 00:47:58,080
Speaker 1: they get in the lab or actually do some math,

916
00:47:58,280 --> 00:48:00,840
Speaker 1: they'll see it's just like anything else, that it's really

917
00:48:00,880 --> 00:48:03,799
Speaker 1: fun and occupies your whole human spirit. I want to

918
00:48:03,800 --> 00:48:06,600
Speaker 1: talk a little bit about accessibility of math. You tell

919
00:48:06,640 --> 00:48:09,400
Speaker 1: a story in your book about a novelist who received

920
00:48:09,400 --> 00:48:11,600
Speaker 1: the advis city he wanted to write about physics. He

921
00:48:11,640 --> 00:48:14,520
Speaker 1: needed to understand calculus, but as a non technical person,

922
00:48:14,600 --> 00:48:16,879
Speaker 1: he was unable to find his way in, even going

923
00:48:16,920 --> 00:48:19,080
Speaker 1: so far as to audit a high school class. And

924
00:48:19,160 --> 00:48:20,960
Speaker 1: you say that your book is for people like him

925
00:48:21,000 --> 00:48:23,560
Speaker 1: who want to understand the ideas and the beauty of

926
00:48:23,600 --> 00:48:26,200
Speaker 1: math but can't otherwise find their way in. Do you

927
00:48:26,200 --> 00:48:28,120
Speaker 1: think there's a wide bread appetite for this? Do you

928
00:48:28,120 --> 00:48:31,200
Speaker 1: think if we taught math differently, it might have more

929
00:48:31,239 --> 00:48:34,200
Speaker 1: supporters and you might less often find people on airplanes

930
00:48:34,200 --> 00:48:37,759
Speaker 1: who go I hated math in high school. Yes, unequivocal

931
00:48:37,840 --> 00:48:40,319
Speaker 1: yes to that question. There is a hunger for it.

932
00:48:40,400 --> 00:48:42,799
Speaker 1: I know it as a fact. I've done the experiment.

933
00:48:43,000 --> 00:48:46,959
Speaker 1: The New York Times back in opinion page of all things,

934
00:48:46,960 --> 00:48:50,080
Speaker 1: not the science page, but the opinion page. Editor David

935
00:48:50,120 --> 00:48:53,040
Speaker 1: Shipley asked me to write a series of columns about math,

936
00:48:53,160 --> 00:48:56,960
Speaker 1: starting with preschool math about numbers and going as far

937
00:48:57,000 --> 00:48:59,719
Speaker 1: as I could up to grad school level topics for

938
00:49:00,080 --> 00:49:03,239
Speaker 1: his readers, for a curious person who like the kind

939
00:49:03,280 --> 00:49:06,000
Speaker 1: of person who would read the opinion page, but who

940
00:49:06,880 --> 00:49:09,840
Speaker 1: like him, fell off the math train somewhere, you know,

941
00:49:10,000 --> 00:49:12,560
Speaker 1: just didn't see the point of it, didn't like it anymore,

942
00:49:13,560 --> 00:49:17,360
Speaker 1: or found it hard or repelling in some way, repulsive anyway.

943
00:49:17,440 --> 00:49:20,640
Speaker 1: So I tried to write for that audience. And there

944
00:49:20,719 --> 00:49:22,719
Speaker 1: was a big audience, and they liked it, and they

945
00:49:22,760 --> 00:49:26,840
Speaker 1: were very grateful and appreciative, and I their comments, you know,

946
00:49:26,840 --> 00:49:30,080
Speaker 1: because on the Internet people can talk back, and they did.

947
00:49:30,400 --> 00:49:32,359
Speaker 1: And of course there were some people who talked back

948
00:49:32,400 --> 00:49:34,759
Speaker 1: saying they had a better explanation or they think I

949
00:49:34,800 --> 00:49:37,400
Speaker 1: got it wrong. But for the most part, there was

950
00:49:37,440 --> 00:49:40,200
Speaker 1: a big audience that was very grateful and said things like,

951
00:49:40,320 --> 00:49:41,960
Speaker 1: you know, I wish you were my high school teacher.

952
00:49:42,080 --> 00:49:44,320
Speaker 1: I wish math was taught this way. Why wasn't it

953
00:49:44,360 --> 00:49:46,960
Speaker 1: taught this way? And that's a good question. Why isn't

954
00:49:47,000 --> 00:49:50,160
Speaker 1: it taught in a way that engages people more? You know,

955
00:49:50,200 --> 00:49:53,880
Speaker 1: it's complicated about the story of education in the United States.

956
00:49:54,480 --> 00:49:58,000
Speaker 1: There's a lot of demands on teachers to get their

957
00:49:58,040 --> 00:50:01,400
Speaker 1: students to learn certain things that the government requires or

958
00:50:01,480 --> 00:50:04,000
Speaker 1: wants people to learn by a certain age. There's all

959
00:50:04,000 --> 00:50:06,680
Speaker 1: the pressure of getting into college. I mean, there's a

960
00:50:06,719 --> 00:50:09,840
Speaker 1: million things. Also. You think of the position of teachers

961
00:50:09,880 --> 00:50:13,040
Speaker 1: in our society. How much reverence is or is not

962
00:50:13,160 --> 00:50:16,480
Speaker 1: accorded to the profession of teaching at the elementary or

963
00:50:16,560 --> 00:50:19,799
Speaker 1: high school level, So what people are attracted to it,

964
00:50:20,040 --> 00:50:22,040
Speaker 1: how much teachers are paid. I mean, there's a million

965
00:50:22,080 --> 00:50:23,960
Speaker 1: things we could talk about that we don't have time

966
00:50:24,000 --> 00:50:26,839
Speaker 1: to talk about, but for all kinds of reasons, we

967
00:50:26,880 --> 00:50:30,160
Speaker 1: aren't teaching math in the optimal way. Well, I certainly

968
00:50:30,160 --> 00:50:33,360
Speaker 1: appreciate your efforts to translate some of these d ideas

969
00:50:33,400 --> 00:50:36,360
Speaker 1: and the historical stories of mathematics. Even as a physicist

970
00:50:36,360 --> 00:50:38,640
Speaker 1: who thinks about math all day long, I certainly gain

971
00:50:38,840 --> 00:50:41,080
Speaker 1: and benefit from your efforts, and I think a very

972
00:50:41,120 --> 00:50:42,879
Speaker 1: wide group of people do as well. And I want

973
00:50:42,920 --> 00:50:45,960
Speaker 1: to ask you a personal question about why you're a

974
00:50:46,040 --> 00:50:48,720
Speaker 1: little bit unusual. I mean, there are people who write

975
00:50:48,760 --> 00:50:52,120
Speaker 1: for the public about science and math, but you're also

976
00:50:52,160 --> 00:50:56,040
Speaker 1: somebody who's doing that. You're actively researching, you're publishing papers.

977
00:50:56,080 --> 00:50:59,000
Speaker 1: You're an academic and you're participating in these studies yourself.

978
00:50:59,040 --> 00:51:01,320
Speaker 1: What is that like for you, sort of living in

979
00:51:01,360 --> 00:51:06,799
Speaker 1: both worlds. Is your academic intellectual professorial community supportive of

980
00:51:06,840 --> 00:51:08,680
Speaker 1: this or do you have to sort of push back

981
00:51:08,760 --> 00:51:11,799
Speaker 1: against trends that encourage you not to spend your time

982
00:51:11,840 --> 00:51:14,800
Speaker 1: doing this kind of outreach. That's a happy story. Actually,

983
00:51:14,840 --> 00:51:17,239
Speaker 1: the community is pretty supportive, I would say, And I'd

984
00:51:17,239 --> 00:51:19,799
Speaker 1: be curious your own take on this too, because you

985
00:51:19,800 --> 00:51:22,160
Speaker 1: you must be encountering it. A lot of us fear

986
00:51:22,440 --> 00:51:25,759
Speaker 1: that if we go into public communication of physics or math,

987
00:51:25,840 --> 00:51:28,120
Speaker 1: that some of our colleagues would think we're getting soft,

988
00:51:28,239 --> 00:51:31,200
Speaker 1: or we're selling out, or we're pandering or dumbing it

989
00:51:31,239 --> 00:51:35,360
Speaker 1: down or whatever. And that seems to be mostly a

990
00:51:35,360 --> 00:51:38,600
Speaker 1: misplaced fear. If colleagues do feel that way, they've been

991
00:51:38,640 --> 00:51:41,440
Speaker 1: polite enough to not tell me so that I appreciate that.

992
00:51:42,600 --> 00:51:45,640
Speaker 1: But but mostly people seem to take it in in

993
00:51:45,680 --> 00:51:48,000
Speaker 1: a good spirit, like, you know, thanks for trying to

994
00:51:48,040 --> 00:51:50,759
Speaker 1: do this. It's difficult and it's worth trying to do,

995
00:51:50,960 --> 00:51:53,600
Speaker 1: and the public certainly seems to appreciate it. But no,

996
00:51:53,719 --> 00:51:58,120
Speaker 1: I haven't found much resistance or even antagonism from colleagues

997
00:51:58,160 --> 00:52:01,799
Speaker 1: about it. It's also very much fun for me as

998
00:52:01,800 --> 00:52:05,600
Speaker 1: a perpetual student. I learn a lot from interviewing guests

999
00:52:05,640 --> 00:52:08,040
Speaker 1: on the podcast in fields I don't know anything about.

1000
00:52:08,160 --> 00:52:11,080
Speaker 1: I talked to people about inflammation or the origin of

1001
00:52:11,160 --> 00:52:14,200
Speaker 1: life or whatever on this joy of Y podcast. So

1002
00:52:14,239 --> 00:52:17,000
Speaker 1: I'm constantly in school. You know, for anyone out there

1003
00:52:17,000 --> 00:52:19,680
Speaker 1: who's had this feeling like, now that I know so

1004
00:52:19,800 --> 00:52:21,680
Speaker 1: much more, I wish I could be a student at

1005
00:52:21,719 --> 00:52:24,439
Speaker 1: this age. I was so busy. I was so young

1006
00:52:24,520 --> 00:52:26,480
Speaker 1: and had all those hormones raging, and I had so

1007
00:52:26,520 --> 00:52:28,600
Speaker 1: many things on my mind. Now that I'm old and

1008
00:52:29,960 --> 00:52:33,719
Speaker 1: I can think straight anyway, I'm just saying that it's

1009
00:52:33,719 --> 00:52:36,080
Speaker 1: fun for me as a student to be able to

1010
00:52:36,120 --> 00:52:38,560
Speaker 1: do this, and I think it actually helps my research too.

1011
00:52:38,840 --> 00:52:42,320
Speaker 1: It's giving me a broader perspective. I'm thinking about questions

1012
00:52:42,320 --> 00:52:44,040
Speaker 1: that never occurred to me before. So no, I think

1013
00:52:44,040 --> 00:52:46,160
Speaker 1: it's all to the good. I had the same feeling.

1014
00:52:46,320 --> 00:52:49,920
Speaker 1: I really appreciate the license to explore topics I wouldn't

1015
00:52:49,960 --> 00:52:52,719
Speaker 1: otherwise feel like I had time to dig into and

1016
00:52:52,760 --> 00:52:54,960
Speaker 1: to educate myself about them to a level where I

1017
00:52:54,960 --> 00:52:57,759
Speaker 1: feel comfortable explaining them in intuitive terms. It's a lot

1018
00:52:57,800 --> 00:53:00,319
Speaker 1: of fun. I really feel like it's broadened my understand ending.

1019
00:53:00,440 --> 00:53:02,080
Speaker 1: But let me ask you one more, maybe even more

1020
00:53:02,200 --> 00:53:04,799
Speaker 1: pointed question. What would be your advice to a young

1021
00:53:04,920 --> 00:53:08,759
Speaker 1: person whose career isn't as well established as yours but

1022
00:53:08,960 --> 00:53:11,520
Speaker 1: is excited about outreach, you know, maybe a postdoc or

1023
00:53:11,560 --> 00:53:14,759
Speaker 1: a graduate student. Would you recommend that they not participate

1024
00:53:14,800 --> 00:53:18,160
Speaker 1: in that and focus on their academics until they're better established,

1025
00:53:18,239 --> 00:53:20,000
Speaker 1: or is this something you think we should be encouraging

1026
00:53:20,080 --> 00:53:24,080
Speaker 1: in young people as well. That's a hard one because realistically,

1027
00:53:24,280 --> 00:53:26,919
Speaker 1: I don't think it will really help a person's chance

1028
00:53:26,960 --> 00:53:29,640
Speaker 1: in the academic life at a young stage. It's not

1029
00:53:29,920 --> 00:53:31,840
Speaker 1: the answer I want to give, but I think it

1030
00:53:31,960 --> 00:53:35,279
Speaker 1: is the honest answer. That the culture of the academic

1031
00:53:35,320 --> 00:53:37,440
Speaker 1: world for a person who wants to become a professor

1032
00:53:37,880 --> 00:53:40,480
Speaker 1: is such that you have to focus on research, depending

1033
00:53:40,480 --> 00:53:42,279
Speaker 1: what kind of place you want to work at. So

1034
00:53:42,360 --> 00:53:44,560
Speaker 1: if you're working at a place that considers itself a

1035
00:53:44,600 --> 00:53:47,839
Speaker 1: research powerhouse or aspires to be one, then you've got

1036
00:53:47,840 --> 00:53:50,919
Speaker 1: to focus on your research and there wouldn't be much

1037
00:53:50,960 --> 00:53:55,239
Speaker 1: benefit to doing outreach work. Honestly, I mean the priorities

1038
00:53:55,280 --> 00:54:00,400
Speaker 1: are first research, second teaching, third service, of which outreachesnsidered

1039
00:54:00,440 --> 00:54:03,600
Speaker 1: one of aspect of service. So yeah, don't do it

1040
00:54:03,640 --> 00:54:05,960
Speaker 1: for that reason. Now that's not to say you shouldn't

1041
00:54:05,960 --> 00:54:08,279
Speaker 1: do it. There are people who decide why should I

1042
00:54:08,280 --> 00:54:11,319
Speaker 1: be a professor? I can make money supporting myself on

1043
00:54:11,360 --> 00:54:16,399
Speaker 1: YouTube um, and there are fantastic streamers on YouTube. I mean,

1044
00:54:16,440 --> 00:54:19,560
Speaker 1: think of Grant Anderson on three Blue One Brown, who's

1045
00:54:19,600 --> 00:54:23,280
Speaker 1: producing some of the best math explanations on the planet

1046
00:54:23,480 --> 00:54:27,880
Speaker 1: through his wizardly use of of computer graphics and his

1047
00:54:27,960 --> 00:54:30,439
Speaker 1: brilliant pedagogy. I mean, that guy would be the best

1048
00:54:30,480 --> 00:54:33,239
Speaker 1: teacher at any university where he was a professor. But

1049
00:54:33,640 --> 00:54:36,040
Speaker 1: he's chosen not to be a professor, at least not yet.

1050
00:54:36,080 --> 00:54:38,600
Speaker 1: And he's reaching millions or tens of millions of people.

1051
00:54:38,800 --> 00:54:41,759
Speaker 1: So I'm not sure someone with those aspirations needs to

1052
00:54:41,760 --> 00:54:44,640
Speaker 1: be an academic. You know, there is an ecosystem only

1053
00:54:44,680 --> 00:54:47,440
Speaker 1: in recent years where you can actually thrive and do

1054
00:54:47,520 --> 00:54:49,879
Speaker 1: really good work for humanity, as he and a bunch

1055
00:54:49,920 --> 00:54:52,080
Speaker 1: of other people are doing so. I guess I would

1056
00:54:52,120 --> 00:54:53,960
Speaker 1: say for a person who wants to do that, if

1057
00:54:53,960 --> 00:54:56,200
Speaker 1: you're going to do it in the academic setting, get

1058
00:54:56,280 --> 00:54:59,680
Speaker 1: tenure first, do your research, and then you know, go wild.

1059
00:55:00,280 --> 00:55:02,840
Speaker 1: But if you're doing it outside of the academic world,

1060
00:55:02,920 --> 00:55:05,360
Speaker 1: you could make money creating companies that do it. You

1061
00:55:05,400 --> 00:55:09,040
Speaker 1: may have to get lucky, like say con Academy teaching

1062
00:55:09,080 --> 00:55:11,600
Speaker 1: math and science to the world. But what a great

1063
00:55:11,640 --> 00:55:15,560
Speaker 1: service Salman Khan has provided too. So there's there's a

1064
00:55:15,600 --> 00:55:18,200
Speaker 1: lot of possibilities today. All right, great, Well, thanks very

1065
00:55:18,239 --> 00:55:20,640
Speaker 1: much for coming on the podcast and talking with us

1066
00:55:20,960 --> 00:55:24,040
Speaker 1: about an incredible breath of topics, from the beauty of

1067
00:55:24,080 --> 00:55:27,480
Speaker 1: math to communicating with aliens to advice for young researchers.

1068
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Speaker 1: Really appreciate your frank and open conversation. Well, thank you, Daniel.

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Speaker 1: This is a really great pleasure for me and I'm

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Speaker 1: very grateful to you for having me on the show.

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Speaker 1: So you see that the question of why math is

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Speaker 1: so important for physics is a difficult one to answer,

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Speaker 1: even for a physicist and a mathematician talking about it

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Speaker 1: for almost an hour. Hope you enjoyed that conversation. Tune

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Speaker 1: in next time. Thanks for listening, and remember that Daniel

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Speaker 1: and Jorge explained The Universe is a reduction of I

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Speaker 1: Heart Radio or More podcast from my heart Radio, visit

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Speaker 1: the i heart Radio app, Apple podcasts, or wherever you

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Speaker 1: listen to your favorite shows. H