Into the Impossible With Brian Keating - Steven Strogatz: The Infinite Power of Calculus (#158)

Episode Date: June 18, 2021

Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. Early in his career, he worked on a variety of problems in mathematical biology, including the geometry of supercoiled DNA, the dynamics of the human sleep-wake cycle, the topology of three-dimensional chemical waves, and the collective behavior of biological oscillators, such as swarms of synchronously flashing fireflies. In the 1990s, his work focused on nonlinear dynamics and chaos applied to physics, engineering, and biology. Several of these projects dealt with coupled oscillators, such as lasers, superconducting Josephson junctions, and crickets that chirp in unison. In the past few years, this has led him into such topics as the role of crowd synchronization in the wobbling of London’s Millennium Bridge on its opening day, and the dynamics of structural balance in social systems. His best-known research contribution is his 1998 Nature paper on "small-world" networks, co-authored with his former student Duncan Watts. It's the sixth most highly cited paper—on any topic—in physics. Strogatz's writing includes five books. His book Sync was chosen as a Best Book of 2003 by Discover Magazine. His 2009 book The Calculus of Friendship was called "a genuine tearjerker" and "part biography, part autobiography and part off-the-beaten-path guide to calculus". His 2012 book, The Joy of x, won the 2014 Euler Book Prize. His latest book is Infinite Powers. http://www.stevenstrogatz.com/ Thanks to our sponsors! https://magbreakthrough.com/impossible http://betterhelp.com/impossible 00:00:00 Intro 00:03:20 Who was Herman Wouk and why do you start you book with him? 00:08:38 Should we train mathematicians to be good communicators? 00:16:19 On the significance of time, and the entropy of happiness. Is time the emotional dimension? 00:17:51 Small world theory, and one of the most cited papers of all time. 00:21:30 The thermodynamics of happiness and family size. 00:30:10 Can anyone understand infinity? 00:46:33 Are we becoming too connected? 00:53:44 What do you think about the idea that God in science? 00:57:03 The history of science! Carefully. 01:08:22 Intuition first, rigor later. 01:13:21 Is string theory to beautiful to be wrong? 01:17:12 Final Thrilling Three: Ethical Will, Billion Year Monument, Advice to your younger self. Join this channel to get access to perks: https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join Support the podcast: https://www.patreon.com/drbriankeating And please join my mailing list to get resources and enter giveaways to win a FREE copy of my book (and more) http://briankeating.com/mailing_list.php 📝 🎥 🎥 Watch my most popular videos🎥 🎥 Frank Wilczek https://youtu.be/3z8RqKMQHe0?sub_confirmation=1 Weinstein and Wolfram https://www.youtube.com/watch?v=OI0AZ4Y4Ip4?sub_confirmation=1 Sheldon Glashow: https://youtu.be/a0_iaWgxQtA?sub_confirmation=1 Michael Saylor The Physics of Bitcoin https://youtu.be/CaN_CDKqXOg?sub_confirmation=1 Sir Roger Penrose, Nobel Prize winner: https://www.youtube.com/watch?v=AMuqyAvX7Wo?sub_confirmation=1 🏄‍♂️ Find me on Twitter at https://twitter.com/DrBrianKeating 🔥 Find me on Instagram at https://instagram.com/DrBrianKeating 📖 Buy my book LOSING THE NOBEL PRIZE: http://amzn.to/2sa5UpA 🔔 Subscribe for more great content https://www.youtube.com/DrBrianKeating?sub_confirmation=1 ✍️Detailed Blog posts here: https://briankeating.com/blog.php 📧Join my mailing list: http://briankeating.com/mailing_list.php 👪Join my Facebook Group: https://facebook.com/losingthenobelprize 🎙️Please subscribe, rate, and review the INTO THE IMPOSSIBLE Podcast on iTunes: https://itunes.apple.com/us/podcast/into-the-impossible/id1169885840?mt=2 🎙️Listen on all other platforms: https://wavve.link/into A production of http://imagination.ucsd.edu/ Support the podcast: https://www.patreon.com/drbriankeating Learn more about your ad choices. Visit megaphone.fm/adchoices

Any sufficiently advanced technology is indistinguishable from magic. And I am joined with someone I've never met, but is probably the person I'd most like to meet of all the guests that have graced my presence, or grace me with their presence, rather, on the end of the Impossible Podcast. And it's a friend of mine who's a dear human being. It's Stephen Stroggatz, one of the simultaneously most humble but most accomplished people that I've ever known. He got his PhD in Applied Mathematics from Harvard, and he's currently the Jacob Gould-Scherman, Professor of Applied Mathematics at Cornell, which almost would have been my alma mater, Steve, had you guys accepted me the two times I applied. So, you know, well, had nothing to do with me.

Oh, thank you. Wow, Brian, that's a very nice introduction. I feel the same way. I can't wait to meet you in person. It's going to be great. We were supposed to meet about a year ago. when I was supposed to come to Cornell to give a colloquium for the astronomy department, many good friends over there, and something came up.

There was some cancellation of most world travel. But I am hoping that the invitation will remain good, and that someday I will be able to meet you in person there, and I'm actually secretly hoping to get you here maybe by proffering an invitation during next January. Perfect. I think I think I think it is a travel destination, but usually not in January. Well, nothing compares to San Diego. You start off this wonderful book, which we're going to talk about, although not exclusively,

I'm going to try out a whole bunch of crackpot theories. I'm going to talk about the art of podcasting because you are also a raconteur and a podcast host, extraordinaire from whom I've learned much. But I want to start off with Infinite Powers, your delightful latest book, in addition to Sink and The Joy of X, some of your most famous. books. The latest book was also New York Times bestseller, and it's just such a beautiful book, but it starts off with someone that I regret, Steve, that I never met, and it's Herman Woke. Whoke wrote The Winds of War, the Cain Mutiny, and I actually had a chance to meet him because

he is the namesake of the Woke chair of, and it's Woke, not W-K-O-K-E, like some people can be hearing it. We won't talk about politics today, but W-O-U-K-E, And he lived in Palm Springs, and he had the chair called the Herman Woke Chair of Judaic Studies here at UC San Diego. It still exists. And I never met him. And I was, oh, he's hung out. I'll meet him. You know, I'll take the time.

It's a couple hour drive. But he's always so vivacious and vibrant. I never thought it would be a limitation to my being able to visit. And that shows you how the truism, Steve, that no one is as dumb as an intellectual. because I never met him and he passed away about three years ago at the age of 103. But you opened this book with a recollection or a statement about him and how he spoke to Richard Feynman. I wonder if you could recount that and then tell us.

Why was that sort of the impetus for this book? Sure. Well, yeah. So Herman Woke was really one of the greatest, most popular American novelists of my parents' generation. So the World War II generation needed someone to tell their story. And he had been a sailor. He was in the Navy, and he wanted to write something like War and Peace for Americans. But hopefully, you know, something that'd be popular and readable.

So he was researching this big book about World War II, and he thought he should include something about the Manhattan Project, right? I mean, the building of the atomic bomb did end the war, at least in Japan. And so he wasn't sure who to talk to about this, but people told him, well, you've got to go to Caltech. And while you're there, you have to talk to this guy named Feynman. So Woke, who came from the background in, you know, literature, history, philosophy, the humanities, goes to see this tremendous physicist, Richard Feynman. And as they talk, they start to realize they have a lot in common. They're both Jewish guys. They both grew up in New York.

You know, they both love to tell stories, have good senses of humor. And of course, Feynman had also served in the war. He was a very young guy working on the Manhattan Project, like in his early 20s. But they also have some big differences that woke was devout, orthodox, whereas Feynman was extremely atheistic. So anyway, they're kibitzing and they're having a good time talking about everything. But on his way out, as woke is walking out the door, Feynman stops him and says, hey, I just have to ask you one thing. Have you ever, do you know calculus? And Woke said, well, no, he never studied it.

And so Fine and said, well, you better learn it. It's the language God talks. And that then became the title of a book that Herman Woke wrote about his conversations about science and religion with a variety of scientists over the years and philosophers and other people. So anyway, why did I tell that story at the beginning of the book? because it does a couple of things for the book, I feel. One is it sets up this really uncanny idea that there is a language of the universe and that that language is written in mathematics and specifically a particular dialect of mathematics calculus

and even more specifically the sub-dialect of differential equations. So I wanted to tell the story of how we as a species have come to understand the workings of anything that changes smoothly in time or space by learning this weird language of calculus that, you know, as Feynman said, Feynman doesn't really explain what he means about the language God talks, but I think any working physicist or mathematician understands that, you know, the laws of fluid dynamics, the laws of gravity, even quantum mechanics, all these laws are written as differential equations. And so he urged woke, you know, if you're going to write about the atomic bomb, you better learn calculus. But the other thing I like about Woke is that he stands in for the general reader in my mind. Woke goes on to tell that he tried to learn calculus. He took Feynman seriously, and he had a real heck of a time learning it.

He could not, you know, he tried reading books with titles like Calculus made easy. It didn't work. He went to a high school class. He started falling behind. I mean, he really tried. And so I felt like the reader I have in mind is someone who would like to know what calculus is about or they're curious. Or maybe they even took calculus but never saw the point of it. That's who I'm writing for, someone who is open-hearted and wants to learn,

but who is really mystified by every exposure to calculus they've had so far. Yeah, that meshes nicely with my mission on the Into the Impossible Podcast. I always say it's to deconstruct the tactics of the taciturn. Because the old joke, Steve, this holds doubly true for applied mathematicians, is that how do you know an applied mathematician? is outgoing because he looks at your shoelaces when he talks to you. But actually, I've had on his nine Nobel Prize winners. I had on Jim Simons, who's a renowned mathematician and philanthropist, obviously,

but also, you know, even Pulitzer Prize winners, astronauts, and very few of them are able to communicate these ideas to the lay public. And I feel like, you know, I've kind of gotten maybe a little bit off the deep end, Steve. You should, you know, step in and intervene as you see Ness. But I see, I keep saying it's a moral obligation. We get paid by the taxpayer, by, you know, my case, the state of California as well as a public servant to study and do things that we do for fun. The joy of what you do is evident not only the title of your books, but in your exuberance and your irrepressibility, which is so infectious. But you would do it for free.

Of course. Right. Sure. Is that you studied how to be like I hadn't yield to Grass Tyson on last week. He was talking about how much he studies the craft of storytelling. Should we make it a requirement along with partial differential equations? Mathematicians and scientists have to learn how, if nothing else, to communicate to the people who pay their salaries. That's a very interesting thought.

We never even consider that, do we? And yet, you know, I am actually doing that, not as a requirement, but we're offering a seminar that we call them the mathematical communication seminar. and I've got grad students and faculty and postdocs coming to it. It's a small group, maybe 15, 20 people. But we are trying everything to get better at this. We watch videos on YouTube of people giving Fields Medal addresses or Nobel acceptance speeches or just ordinary colloquium. You know, like in other words, we try to analyze what's working or not.

We read some of the best writers. We think about going on TV or radio. How do you get your message across crafting the so-called elevator pitch in one or two minutes? Anyway, so we're trying to think about all aspects of written and spoken communication, and we don't really know what we're doing because there's no textbook for this. I mean, we're all just winging it using our instincts and using the best role models we can find to try to imitate. But yes, the short answer is yes. I don't know about requirement, but I totally agree with you that it's a moral obligation.

It's also good strategy. If you want to be a successful scientist, if you can communicate well, I mean, of course you have to have the chops. You have to be able to do the good work, have creative ideas, have the technique to solve the problems that you're trying to solve, have some luck. Even with all of that, if you can't communicate, you're not going to get the grants. You're not going to get your papers in the best journals. Your colleagues aren't going to understand or appreciate what you're doing as much as if you could really get your point across. Right. I feel like it's a baseball, you know, it's like Major League Baseball where, you know, we're just teaching them how to hit home runs or run around the bases, you know, when you hit a home run.

But we're not teaching all the soft skills, all the, you know, kind of just blocking and tackling to mix metaphors. But now you're also a pot. We're going to get into some serious red meat, I hope, for my, or some tofu. Don't worry. Stay tuned because I have some real-time calculus, which is always very dangerous to do. But I have some actual real-time, nonlinear dynamical questions to ask the world's most foremost expert, Stephen Strogetz, is my guest today on Into the Impossible. Before I do that, you've interviewed a lot of the most brilliant people around the world for your Joy of X podcast for Quanta. Can you talk a little bit about Quanta?

I was a guest. I was honored to be on it. Yeah, wonderful. Thank you for being part of it. I think your standards have certainly risen since that time. Tell me, what is that like? And have you noticed this, too, with the... these brilliant intellects that, you know, you have to do a lot of coaching and kind of get them out

of their shells and really make interesting. What is fascinating in these interviews that you do and you do it so well. First of all, you had no training in that, right? It wasn't. Of course, no. No, well, thanks. I'm glad you feel that it's working. We would love to have more listeners. Yeah. So if any of your listeners would give us a try, that would be great. But it's really hard for podcasts to be discovered or to be noticed. There's a lot of people trying hard out there. And there's a lot of fantastic, you know, things to choose from. Big investment of time for people. So we understand why it's difficult. But as far as how to get people to open up, I don't know. I mean, I like to talk to people about their lives. Often if you get someone talking about their

mentors, you know, their beloved teachers or even their parents, it softens people up. They will get out of lecture mode, which is the default mode for all of us, professors. and researchers, and into just warm human connection mode. So I usually like to start with something soft like that. And then I also don't prepare very much. I don't know about you, but I have found that when I prepared a lot, that I wasn't listening as well. If I didn't know what was coming, like for instance,

I had Frank Wilcheck, who I think you also may be interviewed recently. Is that right? Yeah, I did. I was going to ask you about that specific podcast. That and Robert DiGraph. when you had him on two days. Yes. Well, so, I mean, Frank has done such magnificent work in physics and cosmology,

or at least with implications for cosmology, some of his stuff, potentially, if he's right, about dark matter and axiants. But, I mean, when I was talking to him, I just wanted to stroll down memory lane about his work on asymptotic freedom. What is the nature of the force that's holding quarks together inside the nucleus? And, you know, why don't the protons in the nucleus just repel each other? I mean, they are. They're trying with their electromagnetic repulsion, but the strong force is holding them together even more tightly. So anyway, and I have never studied nuclear physics, not really. And so I didn't know anything much about quarks and jets and asymptotic freedom.

So I went in as a beginner, just knowing the words, and Frank explained it all very clearly to me. But along the way, he talked about his father in very affectionate terms, his father who hadn't gone to, you know, really, certainly not college. I'm not even sure if his father finished high school. So it was a really warm, nice discussion. But then by the end, at some point after Frank had finished explaining work he did as like about a 21 or two-year-old graduate student, you know, and he's now probably 70 or so. He's like, well, you want to hear anything I've been doing since then? And I did. And then he'd knocked my socks off by telling me in a very slow burn kind of way, I didn't see where he was going.

but anyway, it ended up that something he thought of might explain dark matter in a very natural way that would grow right out of the standard model. And I didn't see that coming. And you can hear if you listen to that podcast, you'll hear my audible surprise. Like, oh my God, what? You know, like you saved the best for the last, I said to him, because I had no idea we were going to be talking about dark matter. So I don't know.

I mean, what I'm saying is by not preparing, it gives a genuine connection, if you really listen to the guest. But of course, it also makes it kind of meandery, which might be a deficit in our show. I mean, maybe if I had more structure, it would be better. I don't know. Well, I find them really delightful. And what's so great is that sometimes you'll just, like, the interview with DiGraph, who is the director, I think, of the IAS, an Institute for Advanced Study. And then all of a sudden he starts talking about art and why visual art is not as deep or effective or emotional as music. And you guys start going into this discussion of why

you can get moved to tears by music, by some notes of music, a score. He talks about classical music, but it can hold for anything. But you never start crying, oh, the Mona Lisa. I mean, you might have it. It's interesting, isn't it? It is. I mean, that's an interesting point. It's going off on it. And it made me think, and I want to get your opinion, you know, really, really on this as well. But like, if that's true, then

by dimensionality. In other words, music is one-dimensional. That was kind of the thing that that you guys came to the, like, you have to get it revealed at the pace that the author wishes you to experience it because it's a musical one-dimensional format. Art, painted art, like this thing over here is two-dimensional. But then maybe I was thinking, like, is three-dimensional sculpture, like less moving or more moving? Like, how do you think about that? And then I started to think, what would a four-dimensional creature, what kind of art would they produce? But I found it so interesting. You don't have to react to that.

I mean, I do have a little reaction. I don't even really remember, especially what Robert and I said. But to me, the thing about music is time. The music unfolds in time. You said this place was steps from the water. We just haven't found the steps yet. How much did we save? Enough.

Enough to get lost. Or you could book a stay with Hilton. Welcome to your oceanfront room. Just steps from the water. The Hilton sale is on now. Book on Hilton.com. the Hilton app and save up to 20% to get the stay you expected. When you want savings, not surprises.

It matters where you stay. Hilton for the stay. And our, well, of course, film can unfold in time cinema, literally meaning something about motion. But snapshots or pictures on the wall really are at a disadvantage in terms of emotional power because time is that, I mean, Robert and I did start talking about this, that the time is the emotional dimension, much more so than space. And I think because of memory, because of loss, because of dreams of the future,

these are all things that have to do with time as a dimension. And also our mortality, you know, that we get to live for a certain amount of time. But we can move through any part of space. Yeah, I wanted to talk about that and keep on this theme because I've had, you know, Carla Rebelly on the podcast, and he has a book, The Order of Time, I had on many people. I have some folks kind of a brief history of time.

I had on not Stephen Hawking, although I would have loved to, but I had on his closest collaborator, Leonard Milan now, and they talked about their writing and Stephen, etc. And now I've got a lot of folks coming up like Julian Barbor and others.

And a lot of these thoughts that people are thinking about have to do with time. And I think of it in terms of course, entropy. And this is where I'm going to tap into your expertise. So Stephen is perhaps, is perhaps known for, I mean, you're known for so many things. I mean, you're the father of, you know, along with Duncan Watts, your student, the, you know, small network, small world theories and,

and network analysis, network science, I think it's called now with a paper that has over 45,000 citations at last check. I think it's, it's growing exponentially as we speak, but, but I started to think all of these, all these interviews, I've done interviews with stand-up comedians. And I start to think, like, it's interesting because time, according to Carlo, And Frank, Frank will check on, as you mentioned. You know, Frank's basically, his thesis is that, you know, time is what we call things that clocks measure and measure things changing. And of course, that's related to the second law of thermodynamics. And if there was no change or you were at absolute zero, you'd experience no time change.

And so I asked a comedian once I said, is it easier to make people sad or angry or to make them laugh? because there are actually many more ways I could make you sad right now, Steve. Please. How can I make you happy? Like the state of ways I can make you. I mean, you're already very happy. You're at top university in the world. You've gotten all this acclaim.

You know, like, it's very hard to make you. You could win the Nobel Prize. You could win the lottery or stuff. But those are very few compared to all the ways life could get worse for us. I see where you're going. I see. And so I'm wondering. Interesting.

When we think about these things, like, how firmly rooted is that experience? The emotion, is it intimately connected with entropy? In other words, who experienced time is so painful or melancholic because it's associated with entropy? Jeez, this is a really deep and interesting question. Yeah, whoa.

Okay. I mean, I see where you're a really interesting analogy you're making because we're taught in physics that when we think of a state that's highly, ordered. It's sort of like there are very few ways it can be in macroscopically. Like from the outside, there's only a few ways that you could arrange the small parts, the microscopic configurations. I'm just using a lot of jargon. It's like in short, it's not plain language. Well, okay, but I mean, plainer language, it's like you're almost saying there's nowhere to go but down, right? If you're too

successful or if things have worked out well for you in your life or you've had a lot of luck, you get a natural feeling of concern like my luck is going to run out. And that's because you're in this highly negative entropy type state, right? I mean, you're in a very abnormally ordered or lucky state. And so eventually the laws of chance will catch up with you and your luck will run out. And you're going to get sad as a result. So it's a really interesting analogy. But you're saying somehow the wistfulness or the melancholy of time is a direct, like,

emotional response to the second law that things tend toward greater entropy. And I don't know. I mean, certainly aging is a kind of entropy or, you know, or is, I'm just sputtering. You caught me not really knowing what to say. You want to help me out? Do you have some thoughts you want to give me some of your thinking on it? I've got a couple of follow-ups. Actually, yeah, because of this notion of small world networks that you and Duncan, your student,

and worked on a couple decades ago, it got me thinking a lot about networks and for good and bad. And where I'm eventually going to go with this is the relationship between entropy and networks. And I'm just not clear if such a notion exists. But here's what I was thinking. Along the lines of what I just said,

you know, I have a big family, a bunch of kids, have been married. But there's sort of, I was making this argument, you know, to a friend of mine who's single, he's a perpetual bachelor. He's scared to commit. He doesn't want to have kids.

You know, he's having fun with his girlfriend. I said, you know, you should not only get married, but you should have as many kids as possible while you can't. Yeah. There's some biological limits on it, if you don't know. But also, I said, I made the argument from network theory. So if you have a family of size N people, then there are exactly N choose two pairs of relationships.

of dynamics. There are all these like sayings, and I was trying to like figure out, can we construct the thermodynamics of happiness, the entropy, you know, reduction that occurs when families have a lot of kids. And I've noticed that happy family, like big families, they can be unhappy, of course, but like I come from my adopted family was family of 10 brothers and sisters, you know, and they were the happiest people that I knew, the Keating side. And I started thinking, like, how many pairs of relate?

So I went through it and you can do the math very easily. And it comes out, you know, for that many networks, it grows, it grows basically quadratically, right? With the number of. So, but the cost of having N kids, you know, probably grows linearly at the number of kids, right? Probably. Although in terms of interactions between the kids that can cause it, cause it to be difficult to deal with them. Right, right. Because sometimes they have their own.

So there might be a little bit of quadratic or even cubic. terms in there. But yes, okay, I'll take, let's first stipulate that, yeah, probably the cost is proportional to the number of kids, roughly. So you only need one minivan, you only need one house, you know, whatever. That's true. And some of them are independent of the number of kids, like the minivan, it doesn't matter if there's four or five kids, right? They all, yeah. So sort of the benefit, because there's a saying, Steve, I'm sure you've heard it, like, you're only as happy as your least happy kid. Yes. You have two daughters, and you always talk so nicely about them. But like if one of my kids is unhappy, yeah, it's true. But is the converse true?

Are you, you know, can you be as happy as your most happy kid? Maybe. And if so, would the happiness function bro, what I'm getting at is you should have more kids because the benefit grows is n squared, but the cost grows is n. So net benefit leads as n. What do you think about this crack? Well, when you say, so the n squared benefit is because there's all these relationships. So you're sort of implying that individual kids because they have more possible partners to goof around with or have fun with or have heart-to-heart talk with or whatever they need to do. And by the way, they're going to spend half their lives without us, right? I mean, the average parent, you know, dies at a certain age, and then the kids are left with themselves. Their parents aren't around half their lives.

Well, it's an interesting argument. It doesn't occur to me because, you know, there are also other costs that you put on sustainability. by having too many kids, though you could decide you don't care about that and it's every family for themselves. I don't know. I, you know, I mean, we made the decision to have two kids and stop because we thought it was nice for them to have each other, which it has turned out to be. You know, being in an ecosystem, a family with two people your own age approximately to grow with and to fight with and to just, you know, all the things that make life interesting, seemed to us more desirable than just having one child or zero.

I kind of grew up effectively by myself. I did have a brother and I do have a sister who's still alive. My brother passed away. But they were much older than me. My mother had been married before and then her first husband died and she had these two little kids and then my father married her and then they tried for a long time and eventually had me. So my brother and sister were 12 and 10 years older than me. So effectively I was psychologically an only child, you know, in the house, nobody picking on me, nobody doing

irrational stuff. It was a very, speaking of entropy, I mean, everything was clean and well-ordered and well-regulated. So what it meant was like in relationships later in life, people would yell at me or get mad at me or have fights with me, I was always pretty terrified of that because I never had anybody picking on me or being crazy. So, I mean, I think it sort of set me back in a way. Like having brothers and sisters around, I think it's very developmentally healthy for people to learn how to deal with conflict and other stuff. I didn't really have that. Yeah. No, it's sort of the same argument I hear, you know, where people shouldn't homeschool their kids, you know, because then they're only getting exposed to, you know, this very small, small network

and they're not getting diversity of opinion or backgrounds or what have you. But, yeah, that was just something interesting I wanted to run by you. If you thought it was totally crazy, I'd stop thinking about it. But I wanted to turn now back. There's also a linear cost to the person bearing the children. Yes, of course. I mean, maybe more than linear because what is it like to have four kids versus five physically? Right.

I don't know. So this might be a very male-centric thing we're expressing here. How does your wife feel about the idea of a large family? Well, I keep saying, you know, we're at least halfway done, you know, once we hit the magic numbers that we... So maybe turning away from families now, back to calculus. Okay. Wonderful book.

Although, actually, before we leave that, is there a notion of, like, this entropy come into play at all in, like, network theory or network science? Is there, like, with clustering, I mean, is it beyond just, like, a counting of states? Is there some way to character a classify a network? It's a good question, and I haven't seen people talking about entropy. There are ideas of curvature. I mean, like you can have discrete versions of curvature,

just like we have continuous curvature. But does entropy generalize to network? I mean, we have entropy in dynamical systems we certainly talk about, aside from thermodynamics and classical physics. I mean, even in nonlinear dynamical systems, there are people that calculate things about information and entropy and all of that. So those ideas do. work outside of statistical physics.

But I haven't seen anyone use them in networks that I can remember, but it seems so natural. It's such a powerful idea. So there must be, I'm just not up enough on the literature to give you a good answer on that. Getting back to calculus,

so again, part of your mission was to evoke Herman Woke, who was like a very educated, I think of him as a Renaissance man in our century. You know, he was someone who was incredibly curious. He actually ended up writing a book, as you know, called The Language God Talks. You wrote a book about the superconducting supercollider cancellation.

He's a very brilliant and peripatetic intellect. But I forwarded, you know, I gave a copy of your book. I bought many copies. One I gave to one of my guests, his name is Kamal Ravakhan. He wants to learn quantum mechanics. And so I said, well, the only way to learn quantum mechanics is to learn calculus. And the only way to learn calculus from now on is going to be me giving out copies of your book, infinite powers. So I want to thank you for that.

Your book is based on, and I gave it to my father-in-law who knew Herman personally, and he said that this, that his, the eventual book that he wrote combined Herman's curiosity about physics and mathematics with his traditional Jewish beliefs, beliefs about faith and God. Maybe later if we have time, I'll talk about the proliferation of books and things about God, the God particle, the God equation, the mind of God, all these God references by, by atheist scientist mostly. I gave my father-in-law your book and he said

I was surprised by the reference to Herman Woke and as I have gotten farther into the book, I am overwhelmed by the author Stephen Struggouts' skill as a writer and a storyteller. The description of Archimedes' work and humility is so amazing. Now my head is full of triangles.

And this is, you know, he's not a young man and he's very brilliant but he's not inclined to mathematics whatsoever. He goes, also there is a spiritual quality about Stephen's book that brings together mathematical discovery, music, art, and the idea of infinity. I wish that all mathematics could be taught this way. Many of us who hit the wall with calculus, those half steps, would have made it through if we had Stephen. So I want to commend you on that, and I want to highlight this infinity principle. First up,

I'm going to ask you a rapid-fire question. Can any entity, any mind known to exist, comprehend the concept of infinity? Even a computer. Can a computer comprehend infinity? Well, I'm sort of stuck on the word comprehend there. I mean, we can certainly define it in various ways mathematically and work with it. I guess I'm thinking in terms of like visceral understanding versus intellectual understanding. You know, I mean, I can operate in a consistent way with various types of infinity. So to that extent, I think a pretty ordinary mind can comprehend it in an operational way. But can you really absorb it in your bones? Well, I don't know.

It's through the ages. This has been something that has inspired all kinds of feelings in people. Dread, you know, the fear of bottomless pits and the abyss. I mean, some people say that you can go crazy thinking about infinity, you know, like that you really shouldn't go there. So I don't know. I mean, it's tempting to say, no, no human finite mind. can really comprehend infinity, but I don't really know what that means.

Mathematically, it feels like we know how to operate with it. My claim is that, you know, I'm not really that worried about, you know, Alpha Zero, alpha infinity, whatever. I'm not worried if computers can beat human beings at chess. That actually doesn't concern me or I don't think about that as an important question because it's true. But I wonder, can a computer create chess? Can a computer create the game of Go?

In other words, can it come up with the idea of infinity? I don't think it can. I think it's something unique about human beings, and that's why, to me, Stephen, calculus is a uniquely human, you know, as the old, someone once said, some mathematician, you'll correct me, that, you know, God made the integers and all the rest is mentioned, Verk. But I think, but only humans could come up with calculus. Just like I think only humans could come up with general relativity.

Only humans can come up with things that are derivatives of calculus. No computer can't. Do you agree? Doesn't sound right to me. Yeah, I doubt that's true. Just on principle, because I don't believe there's anything fundamentally mysterious about us. When I say here the word fundamentally is doing a lot of the work. So, in other words, I'm a completely materialist person when it comes to this sort of thing.

To me, we're not that different from the machines. We're made of atoms that came from stars. you know, we're organized much more brilliantly and in a sophisticated way than any computer for now. So, of course, we pat ourselves on the back that we're much, you know, no computer could ever do what we do. But we've been saying this for a long time and we keep moving the goalposts. You know, it used to be no computer would ever beat us at chess. Now that they've done that, we regard that as a trivial activity. You know, so now we say no computer can recognize a woman pushing a baby carriage across the

street. They're still terrible at pattern recognition, but they're going to solve that too pretty soon. I mean, I'm, I guess, well, like an optimist. Of course, it could be real trouble, but I sort of think that computers in principle should be able to do everything we do because we're made of the same stuff, and I don't think there's anything extra in us. They're faster. They have better memories. You know, they're just not there yet. So, but if I'm wrong about that, which of course is quite possible, if there's something like soul, or, you know, a fundamental thing that makes us human, like some spirit of God in us. Like if you're a Christian, I don't know if the Holy Spirit would come into play here,

but something that's ineffable beyond pure, beyond physics, then, sure, then computers will not be able to do it because presumably they don't have what we have. But I don't believe any of that. I think we're made of star stuff like everything else. It's interesting. I wasn't thinking to go there, at least. not this soon in the podcast. Because, yeah, talk about God and all these.

I love that you do and that you did. I was thinking more practically because you say something so brilliant in this book. You say when you see like an infinite, like when you see pie, I used to think of it as geometry, but you say, no, it's calculus. No, it is. And I used to think natural logarithm. You say, no, think calculus. And I think just in a practical standpoint, you know, one third, you can't represent that unless you had an infinite computer, right?

So the five-third is perfectly fine if you work with fractions. Right. But if you want to start converting into decimals, that's the thing. Because of being ten-fingered creatures, we like to massage our representations of numbers into this decimal format. Yeah, one-third doesn't play that well with decimals because it forces you to take infinitely many threes after the decimal point. But, you know, you get used to that. And also, in the spirit of physics, if you just want to go. good approximation to one-third. You take as many threes after the decimal point as you need and say

good enough. And actually, it doesn't take that many to get an approximation better than, you know, the scale of the plonk length or whatever we think the smallest amount of space or time will be in physics. So for all practical purposes, you could compute very well with, I mean, I make that little calculation in the book that if you measure the length of the biggest thing we know, say the diameter of the known universe, something you've thought about, I know, and you taught me about, actually. I was surprised, actually, when you told me it's more than two times the, you know, it's not just the age of the universe, times the speed of light, times two. Because what? Because inflation was going so fast at the beginning? Or even if there was an inflation, just the expansion

of space itself is taking place independently of time or can take place. I guess because no signals are getting sent. There's no speed limit or. That's right. But anyway, we're off in a different place there. But anyway, the basic point was, I think, still correct, that if you measure this whole size of the universe, its diameter in terms of the smallest distance we know, the Planck scale of quantum

gravity, you need something like 60 digits. So, in other words, talking about pie that's now computed to 50 trillion digits, you know, is big overkill if you just want practical things. But on the other end, if you just want to think about,

that's why real numbers are so unreal. There's nothing in reality that corresponds to real numbers, but yet they're mathematically very beautiful. You can't really do calculus without them. Right. So you would think that, I'm surprised in some ways that you would think that a computer, I think of things, maybe it's because of your, you know, just profound expertise in applied mathematics,

but in the pure mathematical sense, and again, just because you're not a pure mathematician, doesn't mean that you don't know infinitely more than I do about pure mathematics. And I guess I'm thinking of things again with regard to entropy. In other words, there are many, many more unprovable things than are provable things. And especially given Girdle in the language of, it seems to me that Gertl's theorem combined with Turing's proof of what is and what is not computable would suggest that there's really a tiny number of things that are computable and by computational standards, And then layered on top of that as an even greater filter,

the paucity of things that are mathematically self-consistent via girdle would mean that there's almost like a very small number of things that are mathematically true and computable. So therefore, how could a computer come up with calculus like ab initio? How could an artificial Galileo, a Galileo I-O, come up with Galilean relativity, or how could an artificial Einstein come up with the general theory relativity. It seems like there is something different. It's not, it can't be purely computational, thanks to Turing. It can't be purely mathematical, maybe thanks to Gertl. So how can you say,

sorry to sound like I'm on 60 minutes, but no, it's good. That you think that, that, you know, a computer could, you know, comprehend infinity or could, you know, whatever comprehend means, or actually invent the concept of infinity. Like just given to, I don't, I mean, for me, these questions are always easy to, because I can retreat to saying that, well, a computer has done it. I mean, we've done it. In this belief that we're nothing special, with regard to this question, that

we're made of a particular kind of wetware, the biologists would say, we happen to use carbon and water and all that in our cells instead of silicon. And we have our neurons running at you know, kilohertz or something

instead of gigahertz. Speak for yourself. You know, speak for yourself. I'm one of really hurts. Miller's here. Anyway, I just don't see any real particular obstacle that computers have, human computers have done these things over the core. Now, okay, here's the, if I were going to push back against my own argument, I think the big, the big deficit that computers have is they don't have bodies yet, right? They don't get to move around in the world and sense the world the way. That's our big advantage. We have bodies with interfaces. We have ear drums that vibrate when sounds. Sound waves hit them. We have fingertips that, you know, we have all kinds of things. We have eyes, everything else. There is computer vision now. I suppose computers can hear. I mean, my microphone right now is hearing me. So once computers get better at censoring, sensing the world and get

to move around and have, the other thing is emotions, right? That's interesting, too. Computers at the moment have been, have not, as far as we know, been imbued with emotions. And we have desires, including the desire to understand, to think, to create. They don't have any of that. So they're really missing a lot of important stuff. And so, yes, they haven't thought of calculus yet. They have proven theorems in very creative and even elegant ways. They've been told to do it. They haven't been taught how to do it. I mean, they've actually invented. See, this is why I get emotional about computers because I am a very active and interested chess player. And when you see the games of the best chess programs now, they don't play like machines anymore, even though they are

machines. They play in this very romantic swashbuckling style, sacrificing material. They look like they're imaginative. Now, you could say that's just stupid. Of course, they're not imaginative. They're just machines. But then what are we? I don't know. I mean, we look, we think we're imaginative too, but we're just using parallel processing or. Anyway, I'm kind of sputtering, but I just, I kind of don't see the argument for anything particularly special about us. You can also go in the other direction when I think about my dog. When I see the emotions on my dog's face, I know I'm not kidding myself.

Some people who don't have animals will say, come on, you're being, you're being soft. It's not true. Your dog doesn't feel anything. Your dog doesn't really love you. Your dog doesn't miss you when you're away. But anyone who has a dog knows that's wrong. That's not true. Of course they do. Wishing you could be there live for the big game,

soaking up the atmosphere in the crowd. But too often, life gets busy. Or the price holds you back. Priceline is here to help you make it happen. With millions of deals on flights, hotels, and rental cars, you can go see the game live. Don't just dream about the trip. Book it with Priceline.

Download the Priceline app or visit Priceline.com. Act. vary, limited time offer. Right. So, anyway, dog makes it into the acknowledgements of your, of infinity. Yes, Murray is in the acknowledgements. Murray was a very good companion for me

when I was walking a lot and thinking about the book and frequently dictating into my iPhone. That's, that's my, I'm under how you wrote your book actually. I mean, when you wrote losing the Nobel Prize, did you type? Did you talk to yourself and record it? What did you do?

A little of each. I did some of each. You know, sometimes in the shower, it's a little inconvenient to, you know, have a have a note pad in there. So I would record on my iPhone or I had a bunch of notes. And yeah, yeah, so that's how I did it. But I didn't have a dog. You know, I only had three kids running around. But actually, that leads me into something I've always wondered about mathematicians. When Feynman used to wonder about this as well. And I wonder how you think about it. When you count, let's say you're counting. to 10. Do you like see numbers moving through the air? Do you are in your mind or do you count like one, two, three? Because I know for me, like I have to sing the alphabet song to get like what letter

comes after. How do you visualize number? How do you count? Just practically speaking. Ask a mathematician about numbers. I'll be like, what's that? Yeah, counting. Why would I count? I think I would do like what you described. For me, it would be sonic. I would hear it. And I, same thing with the alphabet. I can't, if you said, where is L in the alphabet or what? comes after L, I would hear it in my head, L M, N-N-O-P, you know, like that. So, yeah, it goes way back to childhood, and it's very

auditory for me. I don't picture the alphabet on the molding of my first grade classroom. So I don't see it. But the math I do is very visual. So I, just like I like chess, and I like thinking about the pieces moving around on their two-dimensional

checkerboard, my subject is dynamical systems, which is all about things moving around, either in real space like planets in the solar system or imaginary things moving around in an imaginary space that we call state space, where each point represents the state of a hard cell or of a population or whatever,

a bunch of concentrations in a chemical reaction. Basically, the idea is to describe a state of something, you have to give a lot of numbers, saying what's the concentration of this and what's the voltage across that membrane and whatever. You give all these numbers, and each axis represents one of those numbers, and you could have 100 of them, and then you think of that as one point that's an ordered 100-touple. You know, 100 numbers separated by commas, and we picture that as a point in 100-dimensional space that moves around as the state changes as time goes on.

Except we're not really picturing it. I'm taking liberties there. What I'm really picturing is three dimensions, and something's flying around in 3D, like a drone flying around in space. I have my imaginary point moving around in 3D, but I pretend it's kind of a hundred-dimensional. Interesting. So also thinking back, if we can go back to networks and friendship and stuff like that, one of your previous book on calculus was called The Calculus of Friendship, which I haven't read, but I was wondering if we could explore a concept that made me think of at least the title of the book,

but maybe some of the work that you've done as well in networks and so forth. But that was this week's Torah portion, and we should say we have talked about the Torah in the past, but this week's Torah portion revolves around gossip. Oh. And the gossip that is engaged upon can be manifest in a human being back in these days at that time, 3,000 years ago maybe, that you actually have a physical symptom. Like your hand would turn white. It was called leprosy, but they don't really think it was leprosy. They don't know what it was. but it made me think and actually gossip is considered the most one of the most awful sins because

it's basically a sin that's impossible to repent for there's a famous story of a man who told tales about his rabbi and they were truth i mean the whole point about gossip is that it's true if it's false it's a lie and so it's it's sort of less less pernicious but anyway this man is telling a story about his rabbi it gets back to the rabbi then the guy goes to apologize to the rabbi. And the rabbi says, you know, and he says to the rabbi, how can I make amends to you? I feel so sorry for the harm that I've caused your reputation. And the rabbi says, it's very simple. Just go to your house and get a pillow. I thought it was going to be a hard, a hard form of teshuvra of repentance.

And the rabbi says, when he brings over the pillow, the man goes, okay, here's a pillow. I didn't know you needed a pillow, but here you go. And the rabbi goes, no, no, no, just simply, I want you to cut it open and go in the town square and just shake it out. And the man goes, okay, fine, if this will absolve me of my sins. So he does it. And then the rabbi goes, waits a couple of minutes and says, now go pick up all the feathers. And the implication being that it's impossible to redo that. But I wonder, you know, is that one of the perils of networks and small or big is that, you know, there is harm that these things can land at any place. And they're almost irreparable. And you see

that obviously with social media and things that grow. you know, virally, there are perils of these networks as well. And I wonder, you know, are we a victim of these networks? Are they kind of just so ingrained you make the point, you know, brain cells or neural networks act this way, human social networks act this way? Are we, are they like the microbes? You know, there's like more microbes than human cells in the human body. Are we like at their mercy of networks or a network something we can master and subdue as God says? Oh, I worry about it a lot. I've been worrying about it a lot. wrote a little essay some years ago, people could probably find it on the internet easily.

It's called Too Much Coupling. So there was an Edge, John Brockman's group, Edge. He asked scientists, maybe you've written for them too. Yeah, I could think who was your agent, I guess, or my friend and John Brockman. They often ask, they've stopped doing it, but they used to ask at the end of every year, some question and then people would answer the question and they would now frequently be collected into a book. So one year I think the question was, what are you worried about?

Yes. And I worried about too much coupling. Now, what I mean by that is coupling is a word that we use in dynamical systems to describe the influence of one thing on another. I mean, I guess it comes from the old days when you would have two train cars coupled together by, you know, iron that grips one to the other so that they're attached.

We speak of a couple, you know, like people who are a couple, they're connected. So coupling is when two things are connected in such a strong way that they can really affect each other profoundly. And when you have, instead of just individuals, you have a population of individuals that are interacting like people in a social network or like species in an ecosystem or all the different cells in your heart or whatever, these are all coupled dynamical systems. Now, we learn in dynamics that often as you increase the strength of coupling, if you let the individuals hear each other a little bit more or influence each other a little bit more,

there's often a phase transition when something qualitatively, dramatically different happens that you couldn't see coming. I mean, an example is on the Millennium Bridge in London when people were walking across the bridge on opening day. It's a footbridge. If you've been to London, you may have walked across it. It's a beautiful thin footbridge. But on opening day, the crowd was so big that they ended up setting the bridge wobbling side to side in a way that

was very uncomfortable for people, and they had to hold on to the railings. But what was weird is that as the bridge started to wobble, people got in step with the wobble because that's a common human reaction when you're walking on a wobbly surface that's going sideways. like if you stand up on a train that's moving fast and it starts jiggling, you may spread your feet out wide and walk in step with the vibrations of the wobbling train. People walked in step with the wobbling bridge, he inadvertently pumped more energy into the bridge, which made it wobble more, until eventually you had to, like, vast crowds walking in step,

not on purpose, driving the bridge. Anyway, they had to close the bridge, and then repair it, and now it doesn't do that. But the point was that, that the bridge engineers couldn't see this transition to spontaneous synchrony when they did tests of the bridge in their computers simulations that didn't do this. And it's only because later experiments showed it's only when there were enough people on the bridge it suddenly started to do this. Below that, nothing. So when I worried about too much coupling in this essay, what I was talking about is that we're doing a lot of social experiments on ourselves at global scale. And we don't know what the heck is going to happen in terms of phase transitions.

You know, the Internet has done this to us. Now the pandemic is doing it to us through airline networks. You know, I mean, viruses are traveling across the world. Nazis can find each other much more easily than they used to, you know, thanks to the Internet. All kinds of things and things that we can't even anticipate now, I'm sure attacks on the power grid or other things, are all being made possible because of this enhanced connectivity that we are walking right into. So I don't know what's going to happen, but I worry about it a lot. Yeah, I found that essay as you're chatting and I was listening as I work with my millerhertz processor.

And you made this really kind of ridiculous claim, Steve. I have to call you out on it as one of the problems of such coupling, this ludicrous idea that, you know, it could lead to a worldwide pandemic. And I just want to give you the chance to recant that. Well, right. So this essay came out when, 2013 or something like that? Yeah. No, it was obvious. Of course, I wasn't alone in imagining that this could happen, and it will happen again. I mean, these things are just in the nature of the modern world now, and we haven't even yet endured the worst of it. On the other hand, there's been great benefits for this interconnectivity.

Think of all the great stuff you can watch on the Internet now, or even this podcast that we're able to. to do and you can reach people. So education, I think, has improved in certain ways because of it. I love being able to find great performances by some of my old musical heroes, you know. That's all there on YouTube now. So I appreciate some of these. I got a text or a Twitter message from the National Champion of Chess of Nigeria. He wanted to be connected to, you know, he wanted to play like a speed chess game with me.

And I said, well, my rating is probably the logarithm of yours. But I referred him to a Cornell graduate by the name of James Altucher, who is a well-known podcaster as well. And so hopefully they'll play a game and maybe the world will be richer for it. But actually, it comes to pandemics. You know, I was noting to one of my friends at one point, like during the pandemic, that flatten the curve was really a calculus notion. And really that more people learned, you know, learned at least one thing about integral calculus from the pandemic. at least. But yes, in this notion of kind of the unbounded power for good or bad of networks, I think we have to be quite careful. I want to ask you about math as a mathematician.

And this notion that we have, as I mentioned before, I'm having people like Michio Kaku on, I've had on, you know, the colleague of Stephen Hawking, who ends his great book, a brief history of time with an exhortation that if we find the final theory of everything, we will know, know the mind of God. And Michi Okaku's new book is called The God Equation. What do you make of the fact that and of Feynman's, you know, the language God talks? What is this about, you know, this notion of God? Is it just a stand-in or kind of a call-out for authority's sake? What is, why do physicists who are mainly, you know, fellow members of the National Academy or American Academy of yours, those people are mostly secular, right? So what is this notion of God? Why

it come up so often? What do you make of it as a materialist yourself, as you say? Well, I'm not sure why different people do it. I found myself doing it in my writing, and my wife pointed it out to me. She said, there's a lot of God in this book, and she was reading some of the chapters. And I was not really very intentional about it, but a lot of the great scientists have been religious. Certainly Kepler was. I mean, Kepler studied to be a minister, before he became Kepler, the astronomer and mathematician. And Galileo, who often is championed by atheists because of his standing up to the church, or at least trying to for a while before he had to recant, you know, understandably otherwise get killed like Giordano Bruno did.

Galileo was, as far as I can tell, not an atheist. Galileo seemed to want to reveal God's handiwork. He thought he was doing something very devout. out in figuring out what God had created in the laws of motion. So I don't think he found it particularly, I mean, it's true that the church was taking some heat from Galileo, but the church is different from God, I mean, in his mind. Yeah. And similarly, Isaac Newton clearly was very interested in God and did, spent a lot of time writing biblical chronology, trying to figure out when the world was created.

Anyway, so... You know what he claimed was the biggest accomplishment, Steve? Absolutely. His work on the Bible. Well, right. Go ahead. You tell me... Yeah, he died as Christ did, a virgin.

He claimed that was a... I haven't heard this story. Yeah, this, you know. But I've also found a lot of, you know, what is thought about Newton, you know, in particular. Have you heard this story, Steve, that the law of gravity had to be modified, basically, introduced this God of the Gaps, kind of. kind of injected himself into into the laws of gravity to stabilize the solar system against the gravitational instability of resonance phenomena.

So when the planets every so often would come together, their orbital periods would resonate and they'd be, it'll cause a dynamic instability. And apocryphly, Newton injects God. But actually, a guest also by the name Stephen Meyer, who's an intelligent designer, I should say. He pointed out that you can find, and he was a philosophy PhD from Cambridge. He's a very well-respected philosopher. Anyway, he points out that nowhere does Newton ever make that claim. Yeah, I don't believe. I've never heard that either. Yeah, but I have heard that from other, from actually, Mitchie who mentions that in, in the God equation. Neal deGrasse Tyson mentioned it,

you know, it's very... I find both of them pretty unreliable historic historians. I don't, would not listen to Neil or Mitch you on a lot of things, honestly. I think I'd like to have some discussions with both of them. I do. Although I have, and maybe I've used it. I tried to be very careful with the history. I really did. I tried to read the best historians I could find. You see, it's interesting. There's a lot of mythology about our heroes, the scientists. And we tell stories. You'll notice I don't tell the story of Archimedes and the bathtub. I don't tell the story of Archimedes getting stabbed by the Roman soldier and saying,

Biac, after he says, don't disturb my surrogens. So much apocrypha in the stories that we tell of scientists. So you really do want to learn from the historians who have looked carefully at this. And so I did try to do that. But back to your question, why so much God talk from people who don't believe in God? When we're thinking about these awesome topics about the harmony of the universe, it's natural to start to become a deist of, I mean, or something. This feeling that there is profound mystery in the structure of the laws of the universe. that big question, I mean, for me, would be where do the laws come from? You know, there's so much math in the universe. I say calculus is the language of the universe. Well, how can that be? You know, why? Why would it be like that?

And I don't know. That's a big one. You know, I often resort to some kind of multiverse style argument that the universe is that don't have properties that are mathematical enough probably are still born. You know, they can't support structure that's sophisticated enough to allow life. to exist to ask the question. So we just happen to be by luck, whatever that means, in a universe where it's all mathematical. That's not very satisfying, and I don't know if I really believe that. I can see why people want to say, oh, because God made it like this. But I can't really make

peace with that explanation either. So I don't know. It's all very mysterious. We talked about this before, right? The Torah says, maybe you shouldn't ask about the beginning. Yeah, well, the Torah is kind of silent on it, but the rabbis and the Talmud, the second-holing... I should say. I mean, in Barachita is what I was talking about, with the interpretation, the midrash. Right. They said be careful, you know, which is a good thing that we don't follow it at the NSF, you know, under grant proposal renewal. The Talmud for the grant proposal.

But it is true. There are so many myths that you bust so beautifully in this book, including. like this, the hatred of Leibniz and the smallness of Newton, although he was a character, I think. There was a character, but I didn't really spend any time about the, so many calculus books would spend a lot of time on the rivalry or the priority dispute, mainly between Newton and Leibniz's followers. Leibniz had a whole army of people making the case for him. Leibniz himself seems to have been very impressed with Newton, as he should have been. I mean, he tried his best to keep up with Newton and would send him his best work. But it became clear to me as I read their original papers that Newton was really in a different league.

He really was. And that's why we talk about Newton and we don't really talk about Leibniz. They're an order of magnitude apart in mathematical depth. Leibniz was great, but Newton is really unrivaled. Maybe, to me, Archimedes is in the same league as Newton. Einstein, not too many. A lot of people like Gauss as a mathematician. I'm not very partial to Gauss.

I don't like Gauss very much. I like Oiler, though. I would put oiler in the league with these other people. But there are only a few. Interesting. Oh, have you not heard this about Gauss? Mathematicians deify Gauss. I don't like Gowler.

Yeah, I don't like Gauss too much. Because there are stories about Gauss. Now, these might not be true, but the stories are that frequently, Gauss would discover things and then keep them his drawer. And so over and over again, young mathematicians would come up with great things. Oh, look, I've discovered non-Euclidean geometry. Well, no, you haven't because I had it 20 years ago. You know, so Koshi's theorem. Well, Koshy didn't really discover it. Gaus already knew it. So Gaus did this to a number of people, and I don't like that.

I don't appreciate that. Anyway. Yeah, he was kind of a pill that sounds like... Just publish it. You figured it out. Why don't you publish it? And then especially to do that sneaky thing, hiding it, and then ruining it for the next person to discover it. And meanwhile, the world could have been farther advanced.

But, you know, he had this expression, few but ripe. That's what he would say. The results were few, he would wait till they were ripe. Few but ripe. I don't like it. No, that would be great.

That would be another good book. And my fantasy when reading this book was like, what if Newton, what if we did a science fiction, fan fiction book about Newton, if he never was into alchemy or, you know, spent less time, you know, torturing counterfeiters. Although you might not, do you know why coins have ridges? Do you know why, like a quarter has a ridge? No, I don't know.

Why do they have ridges? Have you ever looked at a quarter? So you should look at a quarter because they have ridges, but pennies don't. And so why does one, or a nickel, a nickel doesn't have a ridge, but the dime does. And so you go through it. And those are called flutes or there's another technical name for them. So back in Roman times, what people realized, and actually this goes back even further than that, but Roman times, what people would do is they take a quarter or whatever it was back then,

the Ducotte or whatever they called it, Florin, and they would grind it down. And they would grind down the gold or the silver coin, and they would get off just enough material that they could eventually get enough coins together. They could have a whole new coin. So it's called... There's a form of inflation, and it was a form of counterfeiting and coin clipping. So for thousands of years, this was a big problem. In fact, it was a problem in Middle Evil England in the early part of the second millennium,

so much so that our fellow Jews were accused of being the ones responsible for it, and it led to the Jewish expulsion in the 1200s of all Jews from England. And actually, the problem was solved by Isaac Newton. He realized he could take a coin and put ridges on it, and then it could not be ground down without making it evidentiary to anyone who looked at. So actually, and then soon thereafter, the jury permitted to move back to the land of England. So it's very interesting that he did so many interesting things, but I still would have liked to know what would his life been like if he didn't practice alchemy. And also, you imagine how many things he could have done.

He could have had a real career, Steve. He could have been somebody. He could have been a contender. Here's another thing that I can't help. By the way, I read this book twice, but the first time I read it, it was slow and leisure the second time i read it just recently i read it in like a day it's such an and it's 300 pages it's not like like some lightweight book steve and it's not it's a book with a couple equations but not too many some series some equation um but you know as i'm reading it i'm thinking

well what if steve's wrong you know he's been wrong before about this pandemic now that's for sure what if there's something to calculate that stands in relation to calculus as calculus does to you know algebra or linear whatever. Are we sure we have the final theory of math? Oh yeah, I don't make any claim about that. No, I know you don't. But what if there's even like more than infinity? You call it the infinity principle.

Is there something? Is there a possibility? There's your co-author. No, no. There's your muse. You and your muse. Could there be math that we just can't discover? Or would universes that produce higher order math be still born in the multiverse of

mathematics? Oh, I expect there's a lot more math to be discovered, and probably a lot of it will be beyond us. I do imagine a future where the greatest mathematicians are the machines, and they're discovering fantastic things. Hopefully they'll become good teachers. That's what I'm really hoping, you know, that they will find ways, or maybe we can program to have ways of explaining things comprehensively to us so we can share in the pleasure of their discoveries. But I don't picture us being the greatest mathematicians for much longer. I think we're already seeing it. I mean, there are a lot of examples now of computer-assisted proofs.

There are also theorems being proven by computers for the first time. So, for instance, there's a lot of results now, like the famous four-color map theorem, you know, that you could color any map with just four colors so that no two neighboring countries have the same color. under certain constraints on what's allowed as a map. The best proof of that took a long time to prove it. We finally got a proof, I think, in the 70s. Hocken and Appel, I think, get the credit for that first proof of the four-color theorem. But they found, I mean, other people showed that there was a way to reduce the infinitely many possible maps

to just a finite but large number of possible types of maps. Like there's a certain equivalence classes of maps. And if you could check that the four-color theorem was true for each of those types, you would have proved the theorem for all infinitely many possible maps. And no human being was able to check all those types, but computers did. And so we now know that the four-color theorem is true, as of the 1970s, but it's a big disappointment to mathematicians because we kind of already believed it was true. We wanted to understand why it was true.

Why does it have to be true? And we still, the computers have not explained that to us yet, and maybe they don't know why themselves. They're just calculating and don't have any insight. So that's where I think the interesting future is for math and possibly for science is this question of insight. Like right now, and ever since Newton, we have cherished insight

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