Marcus_mixdown.mp3

Marcus: [00:00:00] Well, I think, first of all, you know, one has to learn the power of the short cut in statistics, which, you know, I tell the story about the we had this advert when I was a kid which which stated eight out of ten cats prefer a particular type of cat food. And, and we had a cat and I never remember anybody asking our cat what cat food it likes. So it was very striking that when I got to university, I learned about the power of sampling and the fact that, you know, to be able to there are 7 million cats here in the UK. How many cats would you have to ask to be confident enough to make that statement about?

Harpreet: [00:00:36] But everybody, welcome to the Artists of Data Science podcast, the only self-development podcast for data scientists you're going to learn from and be inspired by the people, ideas and conversations that will encourage creativity and innovation in yourself so that you can do the same for others. I also host Open Office Hours. You can register to attend by going to Bitly.com/adsoh forward slash ads0h. I look forward to seeing you all there. Let's ride this beat out into another awesome episode and don't forget to subscribe to the show and leave a five star review. Our guest today is a professor of mathematics who's the author of numerous academic articles and books, as well as a radio and TV personality. His research focuses on number theory, utilizing a wide range of topics such as model theory, algebraic geometry and analytic methods. Over the course of his career, he's received numerous awards and honors, including having been elected a fellow of the Royal Society in 2016 and the prestigious [00:02:00] Berwick Prize by the London Mathematical Society in 2001. He's widely known for his work aimed at educating and popularizing science and mathematics and having written a number of extremely popular books making mathematics accessible to everyone, including the Music of the Primes, What We Cannot Know The Creativity Code, and his latest book, Thinking Better The Art of the Shortcut in Math and Life. But you might recognize him as the host of numerous documentaries for the BBC, including some of my favorites, such as the Code Algorithms, The Secret Rules of Modern Living and the Story of Math. So please help me in welcoming our guest today, the Charles Simonyi, professor for the public understanding of science at the University of Oxford, Professor Marcus du Sautoy. Professor, thank you so much for taking time out of your schedule to come on to the show today. I really appreciate having you here.

Marcus: [00:03:02] Absolute pleasure to be joining you and talking mathematics, science and data and a bit of art hopefully, too.

Harpreet: [00:03:08] Yes, definitely. You know, I definitely want to get into to some of your getting some philosophical questions and things like that. But before we get into your books that we're going to particularly talk about thinking better and then the creativity code. Let's get to know you a little bit more. Talk to us about where you grew up and what it was like there.

Marcus: [00:03:26] Yeah. I grew up just outside London, actually, quite near Oxford, which is where I'm now a professor. I just went to a very normal state school here, but I was very lucky at school to have a teacher who math teacher who kind of opened up this amazing world of mathematics to me. He kind of told me that what we're doing in the classroom is not really what matters about. It's the very technical side of mathematics. And a bit like learning a musical instrument, you're only allowed to do scales and arpeggios and and [00:04:00] he said, no, there's actually really wonderful kind of music out there. And he recommended a few books to me to read, including one which are really recommend your listeners to check out. It's called A Mathematician's Apology by G.H. Hardy, and it's a beautiful description of what it's like to be a mathematician. And he describes it in a very creative manner and sort of code himself as a creative artists rather than a useful scientist. Yeah, sure. Math is useful for describing the world building bridges for science, but there's also a very creative, artistic side, and I think that really appealed to me. So I really credit that teacher, Mr. Billson, when I was about 12 or 13 for kind of giving me this key to this secret garden. That's for some strange reason we don't tell all our kids about. I mean, I don't know quite why we don't tell our kids about Fibonacci numbers, prime numbers, multi dimensional geometry, fractals, infinity.

Marcus: [00:04:54] You know, these are the things I started to experience and it really made me want to be a mathematician. And so I from that point on, my kind of trajectory was, okay, I want to make my own stories in this language. So so I went to up to Oxford actually as an undergraduate. I stayed on there to do my PhD, and I've visited many universities around the world as a professor, but somehow Oxford is my home and that's where I am now doing my mathematical research, creating new mathematical stories. But also, as you said in the introduction, I'm professor for the public understanding of science as well. So not just a professor of math, but I also had this role which I took over from Richard Dawkins. And this professorship is a bit I call it a bit like being an ambassador for the world of science, that science is this massive superpower now, which has a massive impact on everybody around the world. And every kind of major superpower needs ambassadors to try and build bridges to other, other societies. So so my [00:06:00] role is kind of communicating the sort of importance of science to the public so they can engage in debate. And in a way, you know, it's kind of playing back for inspiring me that I hope that the all the TV programs you mentioned and the books and things, maybe they will inspire the next generation of mathematicians that perhaps can prove all the things that I'm stuck on at the moment.

Harpreet: [00:06:21] I absolutely love that. I love that kind of viewpoint. It reminds me of reading a The Bed of Orestes by Nicholas Nassim Taleb. He's got he's got this quote in there. If you are approaching mathematics as if it's purely mechanical and not mystical, then you're approaching it wrong. And I feel like that kind of parallels what you're seeing there.

Marcus: [00:06:40] Yes. I mean, it does have a mechanical side, but that's sort of not the most interesting part, I think, you know. Whenever I tell kids, for example, that nature is doing mathematics, that you find math everywhere, that bumblebees are making sorry, honeybees are making their their hives in hexagonal shapes. Why are they choosing hexagons? Well, there's a reason. It's a kind of the the shape which has uses a least amount of wax to enclose that. You know, the the honeybee is a mathematician at heart. It it tells its other fellow bees where sustenance is using this waggle dance, which is basically a little bit of trigonometry turned into dance form. So I think, you know, when you show people that, well, gosh, mathematics is everywhere in nature and that is the kind of mystical side, you know, wow. Why why is nature why is the universe so mathematical? And, you know, I love the Galileo quote which says, you know, if you want to understand the universe, you have to understand the language it's written in and it's written in mathematical language. And the words are circles, triangles and other geometric figures and without, which means you cannot understand a single world word, your light wandering around, as he says, in a dark labyrinth. So this mathematical language is really our key to to to sort of understanding how the universe works. And that is kind of amazing [00:08:00] and slightly mystical. I mean, why is the universe so mathematical? That's kind of an interesting philosophical question.

Harpreet: [00:08:09] Yeah, absolutely. So so so in your in your kind of thinking in the stance that you take. So is is mathematics something that is that we've invented or is it something that's always been out there and it's just something that we've discovered? But, you know, math is kind of just the language we use to describe it. What are your thoughts?

Marcus: [00:08:25] Well, that's a really deep philosophical question. And there's been so much discussion on whether, you know, is mathematics a human creation? Is it are we creating it or are we discovering it? Is it somehow got a platonic existence out there and we're just chipping away and revealing things? I mean. Personally, I am a platonist at heart, so I am a believer in mathematics existing sort of outside the need for humans to sort of bring it alive. So 17 is a prime number, whether regardless of whether you've got conscious beings to to recognize that fact. But I mean, I think there is this kind of platonic world out there, but the stories that we then tell about that that that mathematics, you know, we've got these prime numbers, we're trying to understand them. But the way that we're understanding them, I think that is often a reflection of our human psyche and our and our ways of looking at things. So so I think that's why it's such an interesting debate, this one about creation, discovery. Does this thing exist or not? Or are we sort of bring it? Bringing it to life is because of that tension, of the fact that we are making choices as mathematicians about the theorems that we get excited by.

Marcus: [00:09:40] And that's why many people probably think a mathematician is just like a bit of a computer churning out proofs of true statements about numbers and geometry. And and actually, we're doing something slightly different. We're making choices about the things that we think are interesting. And so that must reflect our kind of human psyche. So [00:10:00] I often compare this a wonderful short story that I love by Borges called the Library of Babel, and it's about a library which contains every single book it's possible to write. And so you think, Wow, that's amazing. That library contains everything. But of course, actually, as the story goes on, you realize the library contains nothing because nobody has made choices about which things are worth writing or reading. And and I think a mathematician is a little bit similar that most people think, well, surely you're trying to create the mathematical library, which contains proofs of all the true statements about numbers. But no, most of them are boring, just like most of the books in the Library of Babel are just meaningless. So that side, I think there is a a human side to what actually becomes the mathematics that we celebrate in the journals and in our seminars and things.

Harpreet: [00:10:49] So from your viewpoint then, do you think math is an art? Is it a science? Is a combination of art and science. How do you how do you view this?

Marcus: [00:10:57] Well, I think that I chose mathematics because I feel it's almost where those two rivers join, that it has very much a scientific side there. There are true statements. You can't make a false statement. True. It's got a robustness about it that, you know, you just cannot push it around how you want it to be. It is how it is. It is the language which describes the universe. We know about the fundamental particles which make up the universe because of the mathematics which describes these quarks and electrons and things. On the other hand, there's a highly creative side to mathematics, which relates the fact that sometimes we create consistent worlds in mathematics which have no relationship to our own physical universe. Now in science, if you come up with a theory, might be a wonderful theory, but if it doesn't match the data, you throw the theory out. It's not interesting anymore. And that's why we now have a potential [00:12:00] theory of supersymmetry. Maybe there are these other particles, but if we don't find those particles and we even find evidence that they're not there, as beautiful as that theory is, it will have to be thrown away. It's just not interesting to the scientist. But for a mathematician, we're quite happy to have independent kind of mathematical universes, which internally consistent, and we're sort of more happy with the multiverse in a way, the mathematical multiverse that we'd be very happy with all of the different sorts of worlds.

Marcus: [00:12:31] I mean, for example, in the 19th century, mathematicians came up with new sorts of geometries, spherical geometries, negatively curved geometries, which were different to the Greek Euclidean geometries. Now, only one of these geometries describes our universe, but we're interested in all of these geometries, and they're wonderful to play with and explore. And I think that's that's the kind of creative side of a mathematician. It's almost like you can write a novel and it doesn't have to be true. But if you're writing nonfiction, it has to be, you know, you can't write something which isn't true. So there's a sort of freedom in mathematics, which I think my other fellow colleagues in science don't have that freedom so much because they're just not. If their theory does not fit experiment, it's just thrown out. I don't care about the experiments. I just have to make sure that my my universe is that I create a consistent and they're all equally exciting.

Harpreet: [00:13:33] Speaking about different geometries. I remember when I first heard about read about, learn about topology, it just blew my mind. Like, it's just the weirdest thing ever. And a little bit of synchronicity. I was watching at this YouTube video about that Gaussian curvature yesterday. And Gauss is.

Marcus: [00:13:50] One of you, as you do.

Harpreet: [00:13:52] Well. Well, you know, I'm a mathematician at heart. I guess I didn't finish my PhD, but still have a love for mathematics. And you're [00:14:00] kind of love of mathematics. Started with with Gauss. So what was it about Gauss? He plays kind of like the hero of our story in thinking better. What was it about Gauss that kind of, you know.

Marcus: [00:14:09] Absolutely. Yeah, he is. I mean thinking better is it's describes all of the different ways we come up with mathematics to think of clever ways to solving problems. And I wanted some way to sort of have some glue which connected all of these stories together. And I actually found that one of my heroes, Carl Friedrich Gauss, just seemed to play a part in all of these different ways of thinking. So he became a natural sort of partner in the journey through that book, and he really is the beginning of the book as well, because I try and give the reader sort of a sense of what I mean by when I talk about a shortcut. You know, this is a book celebrating mathematics as an incredible suite of shortcuts to to kind of avoid you having to do hard work, boring, laborious work. And so I tell the story of the young Carl Friedrich Gauss, who's in his classroom about nine or ten, but younger than I was when I got excited about math. But already it was clear that he was quite an amazing sort of thinker. But the. Teacher in the class would ask the pupils to add up the numbers from 1 to 100. And I think the teacher thought, Oh great, that'll take them forever because they've got to add one plus do three, probably make lots of mistakes on the way.

Marcus: [00:15:26] So I think he was trying to get a little bit of shut eye, a bit of sleep. But before he even finished posing the problem, Gauss had written down a number on his little slate board and put it down in front of the desk or in front of the teacher. I think the teacher thought he was being impudent, but when he looked at the number on the chalkboard there, it was the correct answer. And so he said, How did you get that so quickly? And GAO said, Well, you know, all my fellow students are beginning at the beginning of the journey and just trying to go through all the way to 100. That's not the way to do this. There's a clever shortcut, which is [00:16:00] you go from the beginning and the end of the journey. So you start at one end, 101 plus 100 is 101. Two plus 99 is 101, three plus 98 is 101. So he very quickly seen you've got 50 pairs of numbers adding up to 101, so that's 50 times 101. And he'd written very quickly down 5050. So I think that for me captures in a beautiful little story and perhaps it's apocryphal and not true.

Marcus: [00:16:27] I think Gauss kind of liked to tell his story later in life, show how precocious he was. But I think it really shows the essence of a mathematical way of thinking, sort of stepping back from a problem, not just going through the hard labor of adding up numbers one after another. For a start, you'll make a mistake. But this beautiful symmetry that he saw in the problem just gave him an access to solve it. Not only that, it has the beauty that if the teacher said, Oh, okay, Gauss, I'm going to give you a problem, 1 to 1000000. Well, the same trick still works. And that's what's so powerful about these mathematical shortcuts. Often it doesn't matter if the numbers get bigger and bigger. The shortcut still does its work and finds you a quick way to get to the solution. So. So I really thought that story captured what all the shortcuts are trying to do, which is, no, you don't want to do that hard labor of just doing the sort of laborious, boring work which can often lead to error. Step back and try and find the clever way, the shortcuts. And this is kind of celebration of an extraordinary range of mathematical shortcuts. We've come up with over 2000 years of creating mathematics.

Harpreet: [00:17:38] The thing that we do best at finding patterns. I feel like that's the ultimate shortcut, right?

Marcus: [00:17:42] Yes. And that's the the shortcut I start with. And it's actually often when people say, well, how do you define a mathematician? I think most people think that. As a research mathematician, am I doing long division to a lot of decimal places in my office? And if I am, surely hasn't a computer [00:18:00] put you out of a job? And I say, No, that's arithmetic. And actually most mathematicians are rubbish at arithmetic, you ask. I often get asked on radio stations. Okay, you multiply 723 by 462 and I haven't a clue, you know. And actually, I describe a mathematician. It's about patterns, a pattern searcher. That's what a mathematician is. And somehow mathematics is the science of patterns. And I think you're right that humans have become very good at spotting patterns because it gives given us an evolutionary advantage, because patterns are our access to what might happen in the future if we have data and we can spot some sort of pattern in that data and then we can read that data into the future, we have a good chance of predicting what's going to happen next. So so I think that that's partly why we've all evolved to be able to spot those patterns, because they they are the key to our evolutionary survival very often.

Harpreet: [00:19:02] So it seems like patterns are kind of or rather shortcuts, I guess. Shortcuts kind of hint at the laziness of humans. Is there. Is there any virtue in human laziness?

Marcus: [00:19:13] Yeah, actually, I think there is. And you know what? I sort of wrote this book as a companion book to my previous book, which you mentioned The Creativity Code, which is all about the extraordinary power of modern artificial intelligence. Machine learning has just given A.I., you know, an incredible push at the moment. I mean, we talked about A.I. winters for decades. You know, we're in an AI heat wave at the moment with the power of code to to learn from data and to evolve change. And it seems incredible what this code can do. And that book is all about the fact that code even can be creative. It can learn to do new things. And so I did an interview with a journalist about that book, and by the end he was so depressed he said, Well, what [00:20:00] what's there left for humanity? You know, I can even write novels and poetry and things. And I had to try and cheer him up because he was so depressed. So I actually thought, well, actually, I think our laziness actually might be our saving grace because you see, an AI on a computer just doesn't get tired. It can keep on working on a problem. It doesn't need to be lazy. But if we're faced with adding up numbers from 1 to 1000000, most of us, if we're going to do it the boring way, the computer doesn't mind doing that the hard way. But, you know, I think that we're so lazy that we go, Oh, I can't be bothered to do that work.

Marcus: [00:20:38] And we step back and it's that laziness that then pushes us to find some cleverer way to do this, which can mean that I can go and do something I really want to enjoy doing. And that's why I actually make a really important distinction at the beginning of the book, which is, you know, most of us actually get value from our work. It's not like I want to replace all our work because I enjoy my work as a mathematician. So but Aristotle had a very nice description of two different sorts of work. So he talks about praxis, which is work for its own sake, work you enjoy doing, and then paresis, which is work to get to a goal. And very often it's the goal that we're interested in and we're not interested in in the work getting to the goal and the shortcuts are trying to get you to your goal quickly enough that you can then do the work that you really enjoy. So, so I think that, you know, I'm looking for the yeah. So I think idleness is important because it often says I don't want to do this boring work, I want to do the work I really enjoy. So, so my shortcuts are trying to, to give you those techniques say, okay, oh, I can avoid doing all this hard work and get on with what I really love doing.

Harpreet: [00:21:52] Yeah, I think Aristotle calls it that that not necessarily idleness, but noble leisure I think is what he.

Marcus: [00:21:57] Noble leisure. I like that. Yes. Yes.

Harpreet: [00:21:59] Speaking [00:22:00] of creativity and putting you out of a job, apparently, apparently some of your book was written by GPT three. Has anybody figured out which paragraph that was yet?

Marcus: [00:22:10] Is absolutely sure. It wasn't actually GPT three because I think and I think GPT three is actually incredibly impressive. I mean, I actually wrote a review for a book that has been co-written between an artist and GPT three and it's, it's quite an extraordinary sort of stream of consciousness both by the artists, but also in a way trying to understand the subconscious of GPT three. But I used another piece of software and it's extraordinary because not even my editor who edited she still hasn't identified the passage that wasn't written by me. And I've had one person who's written to me because I offered a bottle of wine from my college in Oxford as a prize. And I have I've only had in all of this time I've had a lot of people suggesting bits. Only one has identified the passage. Actually, I find deeply depressing because I think it's so obvious, it's so badly written, it's slightly incoherent. And and if this means that, does that mean that all my writing is. So it's interesting. You know, I gave it a very specific story that there was a lot of data on the Internet that it could plunder to tell the story. And it did tell the story in its own particular way. And the other thing was I had to be very strict with my copy editor not to correct all the slightly strange punctuation and grammar, because I thought that was important to keep in as well. So so it it is also slightly weirdly the grammar slightly weird as well, but it is extraordinary how but there is there was a restriction in this because it was only 350 words. And I think that's a really important point because I think GPT three, for example, which is kind of the gold standard now of text generation, is very good short form prose and it can really have [00:24:00] quite.

Marcus: [00:24:01] Sort of stimulating ideas. And but what it isn't able to is is the long term kind of narrative. So this book that I reviewed, it's very interesting from sort of page to page, but by the end of a chapter or end of the the actual the whole book, you really feel like it's just meandering. It isn't going anywhere. And I think that's that's the issue at the moment. The AI is very good at locally generating things. So for example in music as well, it's very good at improvising jazz where it listens to a human playing and then can respond to that. But you know, after about 5 minutes of a jazz improviser, everything just gets really boring because you just don't feel there's an overarching narrative. So I think I at the moment is having a little bit of difficulty sort of with the concept of time, interestingly. So it doesn't understand a sort of global structure. It can do things locally. That said, of course. It was very successful in playing the game of Go Against Lee Sedol, and that required a kind of making moves which had implications deep in the game. So it's not like it can't connect things early on to things later. So the reason that the kind of moves that it made that we now call a very creative move 37 game to everyone celebrates as this extraordinary move that it made in this match against Lee Sedol. That move was very early on in the game. It had big implications later, so it can think ahead. But in the creative side, I'm not seeing that really happening.

Harpreet: [00:25:35] Yeah. It's interesting. Having trouble with time, I guess, for. Entity, for lack of a better word, that's not really counting any age. What would time really mean to it.

Marcus: [00:25:43] That's yeah and that's I mean, I think this relates of course to, you know, very deep philosophical problems about consciousness because I think one of the qualities of consciousness that we have is our ability to see ourselves in the [00:26:00] future, where we can do mental time travel because of our conscious minds. And that means that we can actually see that we will die sometime in the future. And I think a lot of art is about then creativity is a reaction to that. And and I think that's right at the moment. I think my, my iPhone doesn't realize that it's got a very short lifespan and will be dead in two years time. So I think that at the moment, one of the things which is sort of we're not seeing is a response to a consciousness yet because I don't think it is conscious. But and I think that's actually when I talk in the Creativity Code book, I do talk about creativity being our tool that we developed as a species to explore our inner worlds and to explore other people's inner worlds. Is your pain anything like my pain? Are you seeing the world like I do? So I think that we will start to see really interesting creativity emerging when I think air becomes conscious and you know, that's going to be a key moment. When will we know that this is not just simulation anymore, but there's something really going on and I think its creative output will probably be the key to, hey, I think something new is happening inside this.

Harpreet: [00:27:18] So yeah, it's a fascinating question to ponder and think about, but we can go down the rabbit hole for that one. But yes, speaking of creativity, you took time in this pandemic to write a play. How is that coming along?

Marcus: [00:27:32] Oh, it's going terrifically, actually. I've been working on the play today. I mean, I've worked a lot with theater companies, so one of my big passions is theater. So I worked with Complicity, a theater company here in England, and I met an actress there, and we did a play together, which we put on a couple of years ago at the Barbican. But so I love using theater as a way of exploring kind of scientific and philosophical ideas. So yeah, during the lockdown I finished [00:28:00] my book thinking better early because my diary just got gutted of all my commitments. And so I handed it in to my editor and my editor said, Oh my gosh, you writers are loving lockdown because you're all becoming so productive. I've got novels I haven't even commissioned. So so she's not going to be able to read your book for another couple of months. So I thought, okay, I had this idea for a play. It's about a mathematician, one of my heroes of the 20th century, a mathematician called Andre, a French mathematician who worked in number theory and did amazing things about things called Elliptic Curves proved a Riemann hypothesis for Elliptic Curves rather than for the prime numbers.

Marcus: [00:28:40] He was hoping for the primes one, but he had a really fascinating life. And so the play is exploring his life. But it's also a play exploring whether whether we have any choices in our lives. You know, the idea of free will, do we really have free will or is everything actually determined as Laplace daemon basically says, Well, if I know how everything is set up, everything else is just follows from the equations. Maybe quantum physics says that that's not true. So that does seem to be indeterminacy. But is that true at a kind of all life level? So. So the play is sort of exploring the kind of choices that this mathematician made in his life and why he made them so. And yeah, so I've actually got a group of actors together, four actors, a director and a producer, and we're going to put it on in London in February at a festival here, which is kind of a theater festival in London. So. So yeah, it's really going well and very exciting, I hope maybe bring it over to America at once once we get it up and running.

Harpreet: [00:29:44] It definitely sounds like a play that I would very, very much be interested in watching, so I'm excited for that to come over to. We have this annual festival here in my city, Winnipeg, called the Fringe Festival. I know there's a equivalent of that in the UK somewhere.

Marcus: [00:29:59] Yeah, in Edinburgh, [00:30:00] exactly. And actually this festival in London is our London fringe, so. Yeah, great. Well, Winnipeg, here we come.

Harpreet: [00:30:07] It. Well, if you need a place to stay, Professor, my house is open for you. Speaking of, of, like, I guess fictional characters at the time of this recording, Halloween Is Upon US. So you shared a story in the book about how we can use math to fight off of vampires. I love it. I'd love it if you could recount that story.

Marcus: [00:30:26] Oh, I like what you did there. Very good. Yes. Well, actually, I. I always have two characters that I dress up for in Halloween. It's my favorite festival of the year. And I'm either because I. Now got no hair on my head. I can cover myself in orange paint. And so I either become a pumpkinhead or I become a vampire because vampires, they they have an interesting kind of condition, which is called erythema mania. And this, you know, everyone knows the kind of classic ways to kind of fend off a vampire crosses garlic mirrors and things. But what people might not know is that one strategy is to throw a lot of rice or poppy seeds down on the ground because vampires just have this addiction to counting. So they just see all of these these grains of rice and they just cannot stop counting the grains of rice. And then you've got a chance to to kind of escape. And this is a well known condition. And it's a Tesla, for example, was meant to suffer from arrhythmia mania and just had this obsession with counting things. And so people might have grown up on Sesame Street and remember the vampire that is responsible for teaching kids to count. And he's called Count von Count. And that is absolutely picking up on this idea that vampires seem to love counting. But there's also a very interesting mathematical explanation for why actually there can't be any vampires. And this is actually a little story I used during the pandemic [00:32:00] to try and explain to kids about exponential growth and the impact of a virus and how it can explode very quickly just from a small number of people.

Marcus: [00:32:09] So, you know, a vampire has to feed on on human flesh every month. So but once the vampire bites, the human the human becomes a vampire. So by the second month, you've got two vampires which need to feed again, so they double up to four. So each month you're doubling the number of vampires on the planet. And a little puzzle for people, you know, how many months or years would it take for the whole planet to become vampires? So, I mean, it's quite unexpectedly small number. It's like in the order of 35 months or something. This is the power of doubling that. It looks very innocent to start with. 248 16. Well, you know, it's going to take ages to get to the whole planet, but then you suddenly see this exponential nation kicking in. And that's what we've seen with these graphs of the pandemic. And I think still we see the same mistakes being made by politicians that they don't understand that the early part of the graph is also exponential. And they, they say, oh, it's going to become exponential. They don't understand that it's already climbing. It's yeah, small numbers again in this new phase, but it's going to go the same way. I mean, how many times do you need to see this pattern before you understand exponential growth? So, you know, if it only takes like 35 months for the whole planet to become vampires, either we are all vampires already or there wasn't an initial one.

Harpreet: [00:33:33] I mean, just get a checkerboard bag of rice and double each square. Right.

Marcus: [00:33:37] That's pretty much that's the beautiful story of this, the reward that the king gave for the guy who invented chess. Is the the rice on the chessboard? Exactly.

Harpreet: [00:33:47] So I appreciate that so much. That story is awesome. Thank you very much, Professor. So I want to get back to your book, Thinking Better, which is a great book. I urge you guys to pick it up. I think it comes out in just a couple of days, at least here in Canada, comes out on the 29th. [00:34:00] And I think some topics that would be really relevant to to my audiences is talking about shortcuts with probability statistics and with data. So, you know, shortcuts aren't always really pathways to knowledge. Sometimes they could lead us astray, right? So what are some dangers of using statistical shortcuts that we should be on high alert for?

Marcus: [00:34:22] Well, I think, first of all, one has to learn the power of the short cut in statistics, which, you know, I tell the story about the we had this advert when I was a kid which which stated eight out of ten cats prefer a particular type of cat food. And, and we had a cat and I never remember anybody asking our cat what cat food it lives. So it was very striking that when I got to university, I learned about the power of sampling and the fact that, you know, to to be able to there are 7 million cats here in the UK. How many cats would you have to ask to be confident enough to make that statement? About eight out of ten cats prefer this particular type of food, and it's really small. I mean, it's very surprising. It's in the order of like 250 cats will 19 out of 20 times that sample will give you within 5% of the true value in that 7 million cats. That's amazing. So that's an extraordinary shortcut, which gives you access to understanding a large dataset from a small sample. The danger, of course, is are you sure that you're sampling this truly randomly and this is something, you know, probably all your listeners know already. But, you know, there's the classic story of the the poll trying to ask people what they're going to vote in the US election in the fifties or something like that.

Marcus: [00:35:41] And they, they did a telephone poll. Now they bias their sample because only rich people could afford telephones in those days. And so they didn't realize they weren't getting a good representative sample of the whole population. So I think this is the real danger with, you know, there's a [00:36:00] real power to sampling to be able to get access to what's happening in a big data set. But how do you make sure that you're really randomly sampling it? And there's a very interesting example about this because I talk about the wisdom of the crowd, you know, the power of tapping into the crowd to help you solve a problem. I mean, that's a really powerful shortcut when we use quite a lot now in science because we have a thing called citizen science. So so I think that's really interesting to to be able to tap into using the crowd to do that. But again, you want to make sure that your crowd is not somehow specially chosen for that. In order to get wisdom, you sort of need a multiplicity of kind of backgrounds and things like that. So there's a very interesting thing which has emerged called participatory budgeting. So governments, some governments have tried and I think actually the government in Canada, a region in Canada tried this, but they said, okay, we're not just going to let our politicians decide this.

Marcus: [00:36:59] Let's let the public try and help us make decisions. So we're going to use the wisdom of the crowd to try and help us make decisions and that the diversity of the crowd should help us. But in some places, so in Iceland, they tried this and they invited people to come and take part. But of course they got a very biased crowd that came in that had very specific political views. They weren't representative of the general public. And so I think the place in Canada which tried this said, actually, we're going to change this, we're going to make this like being a juror. We're going to send out letters which demand that you come. And so we randomly sent out letters, and it's your civic obligation to take part. And this then enabled the crowd that gathered to to take part in the participatory budgeting, actually to be much more diverse because it wasn't self selecting. And then you got a crowd which was wise and made very interesting kind of new political decisions. So, so I think that's the big issue with all of this [00:38:00] use of data is have you got a bias in there? And that is absolutely the big problem with artificial intelligence at the moment, that quite often bad data in, bad decisions out. And there's lots of examples.

Marcus: [00:38:14] And in the AI book I talk about one in particular, a woman that I did an event with who's at MIT Media Lab and she was had some some robots which had some vision recognition software that she was interested to use. But when she got these robots out and started trying to interact with them, they just didn't recognize that she was in front of them. And then she got some other people in the lab to come in and the robots responded to them. And then she suddenly realized, Oh my gosh, I'm the only black woman in this lab. And the. And then when she lifted up the bonnet and looked at the data that had been given to the vision recognition software, it was all white men. I mean, no women. Even. So, this is really important in going forward because we are training our eye on data, because we are using sort of statistical sampling all the time. We need to introduce measures which make sure that we know there's no bias in it, which is difficult because we have our own biases. So the interesting thing is that we're now beginning to see AI being used to. Help us to understand that there are biases in the data that often they can pick up their strange kind of anomalies that we're missing because we're kind of slightly blind to these biases.

Harpreet: [00:39:34] It's interesting you make that the point in thinking better as well, that data science can be dangerous if it's not combined with a deep understanding of where the data comes from.

Marcus: [00:39:45] Yes. And I think, you know, there's been such a surge of big data as a way of doing science that I think what I'm slightly nervous of is that we might find ourselves just being wooed by the data so much that we don't we [00:40:00] forget to ask what will why is there this interesting connection which the data seems to have emerged? You know, the correlation may not be causation. So maybe there's a third thing that we don't understand. So I think we're big data has become so powerful and it has given us amazing new insights. I'm not saying it's some really important things which it's revealed, but I think we we need to combine that still with that kind of analytic way of thinking and asking. Yeah. So why is that connection? Not just being satisfied with having found a connection? Now ask why it's there.

Harpreet: [00:40:33] So yeah, it seems like probabilistic kind of statistical. Statistical intuition is something that we don't come equipped with right out of the womb. So I guess why is it that our that our brains aren't very good at assessing probabilities?

Marcus: [00:40:47] I think because actually we don't have a very good evolutionary experience of large numbers. So beyond 100, everything is sort of infinite in a way. I mean, we we're able to, you know, we have 100 probably close friends or something, but I don't think we just have an evolutionary experience of numbers in the order of a million. I mean, for most people, a million is is infinite. So if you say a one in a million chance, that's that for most people means a certainty. But, you know, if you take, for example, a legal case and you've got somebody who's a suspect and it comes back that their DNA is a one in a million chance, that their DNA matches the DNA at the crime scene. Well, for most people, one in a million means that person has done it. But if you think London, we have 10 million people here. So actually that means there are ten people in London whose DNA match the DNA at the crime scene. So now this one is one out of ten. Well, that's a very different statistic. And so I just don't think people really understand large numbers, which [00:42:00] is what means that we that that we just don't have a probabilistic instinct and we don't we find identifying risk really, really difficult. And that's why we do need these tools of mathematics to to to replace the fact that we don't have an intuition for these things.

Marcus: [00:42:23] So so that's the amazing thing. Mathematics has been able to to give us a way of assessing what will happen in the long run if you do an experiment so many times and and it reveals very counterintuitive things. That's the other I think important point is that probability is the results are very counterintuitive. But here's a little question for your listeners. You know, if I how many people do I need to have in a room for it to be more than likely that two people in that room have the same birthday? Now, first of all, what people do is think, well, gosh, it must be you must need a lot. Maybe you need 180 because, you know, then I might have. But of course, they're already thinking, what's the probability somebody has my birthday? So you personalize the thing and you don't understand that. Actually, the question is, well, yeah, but there are there are other ways of pairing it up with the number of pairs you can make in that room means that very quickly you actually get a good chance of there being two people with the same birthdays. So rather unexpectedly, only 23 people are needed in the room for four, more than likely to have two people the same birthday. And that for most people got 23. And I've done this experiment. It's quite fun. What's your birthday, by the way? Maybe we have the same birthday.

Harpreet: [00:43:45] May 17th.

Marcus: [00:43:47] May 17. You see, there's a one in 365 chance that we two have the same birthday. But if we actually invite more of your listeners on Be Amazing, that by 23 will probably more than likely have two people [00:44:00] with the same birthday. That's very counterintuitive. Yeah.

Harpreet: [00:44:03] I do. This thing every Friday is called a data happy hour where a bunch of people just come into a zoom call just like this and we talk about things. I think that might be something to test out during that.

Marcus: [00:44:13] Absolutely.

Harpreet: [00:44:14] Happy hour. So kind of implicit in the example that you're talking about with the with the DNA testing and one in a million chance and ten people, implicit in that I think is based there. So why is it that that some people find that shortcut that Reverend Bayes discovered so controversial?

Marcus: [00:44:33] Yes. It's it's very interesting because I mean, again, I suppose it's because it's very counterintuitive for a start. I mean, there is a whole philosophy about what we mean by probability. So this is this is part of the discussion. When you went in, you get into sort of discussions of the kind of Bayesian philosophy of probability. I mean, if I if I toss a coin now and I, you know, I have it on my hand and I look at the coin and I can see it's ahead. But so for me, I've got certainty about the way this is landed. But for you, you will you've got uncertainty and you will assign a number to that, even though the thing is one thing or the other. But we are assigning a probability to that. Now, some people find that sort of controversial even from the outset, because we're not talking about something in the future. It's now happened. It is either heads or it's tails. But you assign a number to this, which is just a measure of your lack of knowledge about what the situation is. But so it's more data comes in. You can really assess those values that you're giving to the data. And that is a sense what Bayes Theorem is about. It's a it's a little formula which you calculate in order to to re establish what the value will be or are going to give to a particular outcome given this new information about the data.

Marcus: [00:45:58] So I don't think it's particularly [00:46:00] controversial when you look at actually just the mathematical formula, it totally makes sense. But often what it is, is it's counterintuitive because it's the sort of thing which helps you to understand these false positive results, which people find very difficult to understand. You know, among 1000 people, you know, one in 1000 will have cancer, but there's a negative result in 9 to 10% of the time. If you get a negative results, then then you think you might have a positive result, you think you might have cancer. But when you look at the data and you realize that the probabilities, although you think, oh, my gosh, I'm 90% certain to have cancer, but the the numbers, you kind of forget the base rate that, oh, actually, it's very unlikely I have cancer because only one in 1000 have cancer. These kind of formulas just help you to kind of undo all of this complexity of these kind of false positives and things. And and I think once you look at the formulas, it becomes less controversial really.

Harpreet: [00:47:02] When in doubt, just put it into a confusion matrix and try to convince yourself. Right, and see what happens. So I'm curious, you talked about that philosophical view of probability. Is it is it frequentist approach, the Bayesian approach? Like I'm curious, how do you view probability? What's your take on that?

Marcus: [00:47:18] Well, I mean, I, I go back to right at the beginning. I mean, I think Fermat and Pascal, I think started us on our journey to say, you know, we do have tools to be able to assess likelihood of what might happen in the future. And I think that's the beginning of probability for me is, yeah, you look at all the different possibilities and then you look at the subset of those that you're interested in, and that gives you a very good number, a way of mathematically using uncertainty. And so that for me is really the basis of this whole thing. And then the interesting thing is when you come to something then has happened. Yeah, [00:48:00] I think there's something slightly controversial about, well, why are we still assigning a kind of fraction to this? You know, it's either, you know, is that still a valid way? Yeah. Fermat and Pascal were interested in some games of dice and things where you don't know what's going to happen next and how to decide what your best wager will be. And in that case, yeah, you do want to know each individual role. I can't predict, but in the long term, a casino will take advantage of the fact that they know that 52% of the time they're going to be winning and that's enough for them to make money out of that.

Marcus: [00:48:38] So so I think it's not my area of expertize. So I think there are there are definitely, you know, really interesting philosophical discussions to be had around that. And actually, I do recommend a colleague of mine, David Spiegelhalter, who's he's sort of my sort of partner. You know, I'm the professor for the public understanding of science in Oxford. He's the professor for the public understanding of risk in Cambridge. And I think this is both of them are really important roles. Science is having a big impact on society and being able to just assess risk is obviously important. And he's he's the person that I've listened to most on probability and really respect his kind of opinions. And I think he is. Well, I let him speak for himself if you have him on. But I think he's a Bayesian at heart. But he'll probably be able to justify what that whether he's.

Harpreet: [00:49:32] That's through definitely evasion through and through as well. I mean, I might have to tap you for an introduction to a Dr. Spiegelhalter because.

Marcus: [00:49:40] Pleasure. Yeah, we'll do.

Harpreet: [00:49:41] It'll be a pleasure to speak to him. So let's get into some some topics in your penultimate book here, I guess is not the right word. I don't know the creativity. So in the book you talk about so a lot of us in machine learning field, we all kind of familiar with like the Turing test, right? But you talk about something here called the Lovelace test. [00:50:00] So talk to us about this. What is the Lovelace test and in what ways is it different from the Turing test?

Marcus: [00:50:07] Yeah, so people probably know Ada Lovelace because we celebrate her as the first computer coder. And we we celebrate Lovelace Day every October, I think it is. And she very interestingly, when she went to see this analytic engine that Charles Babbage had made to do, calculations began to speculate that, well, this thing can do more interesting things and just calculating. And she started writing instructions for it to to do more interesting things. And those notes that she made is what we celebrate as kind of first idea of code. But already in those notes, she was speculating that, well, maybe this machine could do really interesting things like compose music of a kind of scientific nature. But she has a word of caution. She says, Yeah, but we won't really call the the machine the creative one, because it's the human who wrote the code, which we should really credit as having been the creator. The the machine just implemented the ideas of the human, but it led to this idea of, okay, yeah. So most of the time it will be the human who's sort of really the creative one. The machine is just implementing the ideas, but maybe we'll get to a point where somebody will write some code.

Marcus: [00:51:19] And this is the point about machine learning. The code starts to change and mutate, and so it becomes something different from the original code that the human wrote. Could we get to a stage where the code is actually now producing results, which the the code, the original code of human code, it doesn't understand how it's making those decisions. And so, for example, if it starts to make music and the human can't explain where the kind of music came from in the code, then do we need to call the code now the creator of this music, rather than the human who kind of started it off on its journey? And so the Lovelace test is a challenge, [00:52:00] which is kind of computer create a piece of work and creative piece of work which the original human coder cannot explain how it made it. And another important point, you know, a lot of creativity projects in coding sort of tap into using random number generators to try and trick people into thinking there's some agency in the code. And it's really important in the Lovelace test that you don't resort to something external, like a random number generator or what the state of the weather or the stock market is because that is something equally the code can't explain as it needs to be a product of the code.

Marcus: [00:52:42] So not a randomness from outside. And so that's why actually, rather than, you know, I think creative projects in the past would often tap into randomness to try and give the code some agent seeming agency. But what is now being tapped into is ideas of chaos theory, actually, that we can write code which becomes so complex that very small changes can send it in in new directions. So the output of the code is a product of the code is deterministic, but it's because of this sensitivity to small changes. It means that it's very hard to predict what it's going to do and and actually reverse engineer what it's going to do. So that Lovelace challenge is machine learning is now giving us a chance to to have code which mutates so much that it starts to make decisions that the human can't really explain quite why it's making those decisions. And so that's why we're getting, I think, output, which really is passing that Lovelace test of the creativity is now the creativity of the code, not the original human who coded it. And I think.

Harpreet: [00:53:50] Fascinating.

Marcus: [00:53:51] So fascinating. So I think an interesting thing to compare this with is what about our own human creativity? We are a product of the DNA [00:54:00] of our parents. That fusion of code, the two DNA of our parents produces our code, but we're like a little machine learning thing. We then have the impact of our environment and we change and mutate and epigenetics turn on various things and turn other things down. And so Picasso's output, we would never say, is the the creativity of the parents of Picasso. Yeah, it's a contributing factor, but actually very small compared to the environmental effects of Picasso's experience of. Being an artist in the world. And I think we'll get to the stage where machine learning is producing code that really needs to to be credited as a creator in its own right and have really had less and less to do with the the original code that was written from from which it started learning.

Harpreet: [00:54:51] Yeah. These generative models are really, really fascinating. So a couple of colleagues that I work with brilliant, brilliant, deep learning researchers, and they've we've implemented something where it's called clip draw, where you just type in a prompt and it'll draw the picture. And then my other colleague is working on generative jazz and doing all this crazy stuff. It's really fascinating stuff.

Marcus: [00:55:10] I mean, for me, that that is the most interesting bit of this whole story is these generative adversarial networks which, you know, sort of tap into the kind of gaming quality that AI is so good at, give it a game to play, and and it does it very well. So the game here is each algorithm plays against the other one, trying to trick it into producing something new or, or something within the. Yeah. So these artistic things, I think they're the ones for me that are genuinely pushing the output into something interestingly new rather than just being copies of things we've seen already. You know, AI's very good at producing Rembrandts or Bach's suites, but what we really want is it to take us into the new. And I think the generative adversarial networks for me are actually [00:56:00] mimicking what the human brain does. I mean, the human brain has this kind of bubbly, creative side, but also a discriminator side, and it's the kind of fusion of the two which keeps us in check. So we're not we're not going wild and doing crazy things, but still is creative enough to to take us somewhere new. So so I think for me, these generative, adversarial networks are the most exciting thing I've seen.

Harpreet: [00:56:25] Absolutely. And, you know, and I'm interested to see kind of the the interplay between, I guess, just the ability for for Gans to augment human creativity. But I guess, you know, what is creativity in the first place? Like how how would you define that? You talk about a few different types of creativity in your book as well. Yeah.

Marcus: [00:56:42] Well, I like this definition that sort of starts the book because it's quite user friendly, which is it's got to be new, surprising and have value, and that will define something as creative. And that's fairly simplistic, but I think it sort of captures that creativity needs to engage the emotions. So that surprise surprising. So it's not just creating something new that's very boring, but it's also it can't be just surprise for shock's sake, you know, it has to have some sort of value. So it sort of feeds back and, and pushes humanity on in some way. But I actually yeah. And then I talk about three different sorts of creativity, which are actually an idea that Margaret Boden, a cognitive scientist, came up with. And, and I think this is quite interesting because it helps us to understand what I might be good at creatively and what it might have trouble with. And so these three types are exploratory creativity, which is pushing the rules of the game to the absolute extreme. So something like Bach being the ultimate of composer of the Baroque period, just explore exploring the potential of Baroque music to its absolute limits. I think that's something a computer does very well, pushing things to its limits. Then you've got combination of creativity, which is a kind of fusion of two different styles. [00:58:00] So for example, fusion cooking might be an example where you take the ingredients of Japan, but you cook it in a French way or or maybe actually I did a project just recently with a composer where we wrote a string quartet together.

Marcus: [00:58:15] It's called for musical proofs and a Conjecture. So that was the kind of fusion of I explained some proofs to her and then she interpreted those proofs musically. So it was kind of fusion. So actually I is quite good at that because often it can take, say, a visual and make it into music because once it takes it into digital language, it doesn't really know whether this was a picture or a piece of music. So it's actually able to be much more fluid between seemingly very different genres. The third creativity is the real challenging one for AI, because this is transformational creativity, where you see something new appear almost from nothing, and it's the game changer, the phase change and and the breaking of a system. So for example, Picasso breaking the way art was done with cubism or or Schoenberg throwing away harmonic structure and working within 12 tone scale. These I think these are the exciting moments because they're the really rare ones. And I think many people thought, well, how could I ever be transformational like that? Because it's stuck within a system. How can it break the system and come out of itself? But I think even that one, because if you think about it, well, there is a rule there which is break the rules and see what happens.

Marcus: [00:59:38] And, you know, we do that in mathematics a lot. We might be interested in structure, but what I'll actually remove one of the conditions and see whether anything new emerges out of that. And that's the way it's imaginary numbers came from some. Somebody said, hey, you know, I know all numbers when you when you square them a positive. But wouldn't it be amazing if there was one which when you square [01:00:00] it was negative and most people say, well, that's breaking the rule, you know, we're not allowed to do that. But eventually somebody said, I think this is really going to unleash a new idea. And sure enough, you know, we couldn't do quantum physics without imaginary numbers. So so I think that's the challenge. Can can I break out of the system and break the rules? And in a way, the generative adversarial networks? I think you'll have a little bit of that quality because the the sort of creator algorithm is tasked with trying very often to break style. You know, it's trying to show make something which does not fit into a category that we've seen before. And the discriminator is either saying, Yeah, no, I recognize you haven't moved far enough or you've gone too far. So so I think even transformational creativity is something that I can do.

Harpreet: [01:00:49] Speaking of music, you guys should check out the YouTube video with Professor du Toit and then the Philharmonic Orchestra, I believe it was in at Oxford University, explored baroque. And math is very, very beautiful and well put together. So I'll link to that in the show notes. Excellent. So I guess it's creativity, something that can be taught then if we're teaching, let's say Gans and things, you know, machines to be creative. Like how about for us humans? It's, there's something that we can teach.

Marcus: [01:01:17] Yeah, in a way. I think that's partly why I enjoyed writing that book, because I was trying to understand my own creative process as a mathematician and what, what the tools that I use to kind of make new things. And I have that very often with my PhD students that they come along, they're having to go into the unknown for the first time. What are the skill sets I can equip them with to be able to to come up with something. Genuinely new, which is what they have to do to get their PhD. And I do recognize, for example, that combination or creativity is one that I use a lot in mathematics. So for example, I go along to a lot of talks in areas not related to my own, because what I find is that [01:02:00] I suddenly see a way of looking at the world that they have, which is helping them to understand their structures. But I can adapt it and bring it into my own field and suddenly see a new way of doing things. So in your introduction, you you mentioned the different kind of skills I use and that that's very much part of my creativity is saying, okay, I'm going to take I'm interested in understanding symmetry, but I'm going to take this tool from number theory, which was used to understand prime numbers. And actually, I can I can use that perspective to to not look at primes, but look at symmetries instead. And suddenly I got new insights. So so that kind of combination of creativity is one that I encourage my students to just go out and expose yourself to different ways of thinking, because that will bleed into a new way of thinking for you.

Harpreet: [01:02:50] Actually love that. Like combinatorial creativity is kind of my, my go to method for creativity. I've been like learning and thinking a lot about creativity. Some book that you might enjoy is this one. I'm not sure if you've read it. Chase, Chance and Creativity. It's quite an old book by James Austin, MD. And in this book he just talks about the various types of luck as well as what creativity looks like in research. So yeah, definitely one I would highly recommend.

Marcus: [01:03:15] I think it's very interesting that you know the role of luck, but I think, you know, it does seem time and again that people seem to be very lucky when they stumble on a structure. But actually I think that often covers up a huge amount of groundwork that they've done to give themselves a chance of having that luck. It's a bit like, Yeah, if you only buy one lottery ticket, your chances are very low of winning. But if you if you buy many and have then then you're upping your chances. So, you know, that's why hard work is a lot of the work that you do as a researcher goes nowhere, but you have to put that in. But nobody ever talks about that because it's not, you know, that's never mentioned in the journal papers or in the talk you give. But I think we need to sometimes be a bit more honest about [01:04:00] the amount of failure that we go through in order to make the breakthroughs.

Harpreet: [01:04:04] Yeah, that's something he talks about in the book. The Four Types of Luck. There's type one like which is Dumb Luck, Blind Luck, Type two. Luck is the luck that you get just from, you know, just persistence, hard work, hustle, motion type three. Luck is the type of luck you get just by going really deep into a field that you're able to see things on the horizon that other people may not recognize. And then Type four luck is the luck where you just become really well known for something and and develop some type of a brand type of reputation. So that luck finds you.

Marcus: [01:04:38] Luck finds you. That's nice. Yeah. Yeah. But I think that's right. I like that third type, which is, I think why in immersing yourself in a world such as you start to get an intuition for it. And that's, you know, as a mathematician, I spend a lot of time immersed in my world because it's very alien. It's I work in symmetrical spaces which are, you know, very high dimensional. But the more time I spend there, the more I get a feel for where something is and how to get there. And and that you and that's interesting when we come to A.I., because actually, I think that one of the reasons mathematics is done sometimes very by very young people is that they can get a maturity in mathematics because they, you know, they're nerds and spend all their time doing math. Actually, they can actually get a maturity, which means that they get these insights, become able to navigate the mathematical world. And I think in a way, I, I mean, I talk about the potential for AI to do mathematics in the creativity code book. And at the moment, I don't think it's doing interesting math, but I think very soon it will have immersed itself in enough of mathematics to be able to start to get a feel for for where to look for the next thing, because mathematics is quite a young subject. We've only really been doing it for 2000 years. But if you think about music or visual art now, that's very ancient. [01:06:00] We've been doing that for as a species, really for hundreds of thousands of years. So so I think that it's possible that an AI could get a maturity and get that kind of third sort of luck and start sort of feeling what what might be going on in this world.

Harpreet: [01:06:17] Yeah, absolutely nothing. I think we take for granted how new some of the stuff that we have conjured up really is in the grand scheme of our history as humans. So the first statement you made in the book about how moving from deterministic, foolproof algorithms to probabilistic ones is like a significant psychological shift that is like moving from a mathematician's mindset to an engineer's mindset. I spent some time reflecting on that, just trying to understand what it was that you meant by that. What's the. Can you elaborate on the statement? What is it about a mathematician's mindset that is, you know, deterministic and foolproof and engineers? That's the other way?

Marcus: [01:06:54] Well, I think one of the things that we have really going for us in mathematics is the power of mathematical proof to to get certainty. And that is a very rare, I don't think, any other subject. I mean, I don't think any other science can really be confident that their theory will not be overturned at some point by new evidence. But the you know, the mathematics that was discovered by the ancient Greeks 2000 years ago is as true today as it was when Euclid proved these theorems or Pythagoras. The science is is very different. So the way you do science is, you know, I think a whole different process of building up evidence to support your theory experiment's replicability. But you will never know that there isn't a bax black swan on the other side of the world, which means you have to rewrite your theory. And so so I think the mathematicians mindset is, is very addicted to the power of proof because it means that once the theorem is in the literature, we can build on that. So everybody is sort of building on, as Newton said, [01:08:00] on the shoulders of giants. We are building this edifice of mathematics and we can be confident that the layer that we're putting in will be secure because of the proofs in the past.

Marcus: [01:08:10] So now there's the kind of challenge of, oh, okay, but what if we introduce a kind of more style of mathematics, which with less certainty to it? So for example, if you're using AI and AI is making suggestions and so you might actually have part of the proof done by AI, but you're not quite sure whether the you know, are there bugs in the code. But, you know, should we perhaps be changing the style of the way we do mathematics to sort of accommodate these new tools? And I think many mathematicians are very loathe to give up the the security of mathematical proof in exchange for a sort of more probabilistic, experimental, evidential approach to to the subject. Because, you know, we've valued our certainty so much up to this point. But maybe we're reaching a point where the complexity of the subject is such that we may have to to change the way we do things. So I think we're at a challenging point where maybe we've got as far as we can with this kind of addiction to certainty and maybe we have to to change the way we do math. I don't know. I think it's challenging the role that machine learning will play as a collaborator in this process.

Harpreet: [01:09:34] Obviously love that. And while you're talking, it just makes me want to get into some some some incompleteness theorem topics. But but we are we're running short on time. I want to be respectful over time. I know it is quite late there. So let's begin to wrap it up. Do you have an extra 5 minutes to get into a random round? Okay, awesome. Cool. So so the question I love to ask right before we get into the random round is that it is 100 years in the future. What do you want to be remembered for? [01:10:00]

Marcus: [01:10:02] Yes. Well. I have. Discovered a new symmetrical object in kind of high dimensional space, which has connections to a completely different area of mathematics called Elliptic Curves. And for me, I'm already so proud of that new discovery. I've already talked about fantasizing about having it on my gravestone or maybe a to do with this. And I think it it it completely changed the way we looked at these particular bit of mathematics. So for me, I the lovely thing is that mathematical proof will mean that that's true 100 years from now, it won't be superseded by a new kind of way of doing things. So so I think I have the chance that that will be the thing that I will be remembered for in 100 years time.

Harpreet: [01:10:46] I actually love that. I did want to talk to you about that, the fascination with prime numbers and symmetry. But we'll have to save that for another time. For another time. So let's go ahead and jump right into the random round where we go to a random question generator. We'll do just a couple of questions out of here. First question is, what was your best birthday?

Marcus: [01:11:04] I went when I was about 12 years old to a Chinese restaurant, so with my parents and some American friends of my parents. And there was a band at the Chinese restaurant and they played Happy Birthday to Me. And that was just like so amazing that the whole restaurant heard me playing. The new is my birthday and I think I actually planned from that point. This is the best birthday ever. What's my next birthday going to be? So I sort of started planning what all the other birthdays were going to be, but I think that one, I just still remember that amazing experience of the band playing Happy Birthday to me.

Harpreet: [01:11:37] How old were you at that birthday?

Marcus: [01:11:39] I think about 12 or something, yeah.

Harpreet: [01:11:42] What's the worst movie you've ever seen?

Marcus: [01:11:45] I really. What's the worst movie I've ever seen? Gosh, I couldn't imagine the movie. And I can't remember what it's called. It's Austin Powers. That's it. I just cannot stay. Just This doesn't do it for me.

Harpreet: [01:11:59] Austin Powers [01:12:00] Yes, he did. He did mention that Austin Powers in one of these two books that you just absolutely hated that movie.

Marcus: [01:12:06] Exactly.

Harpreet: [01:12:06] Yeah. Yeah. Okay. Last one here. What would you do on a free afternoon in the middle of the week?

Marcus: [01:12:14] I would practice my cello. I'm trying to learn the cello at the moment. And if I've got a sneaky free afternoon, I will get my cello out and do a bit of practice. And in fact, just before I came on air with you, I had my string quartet rounds that I formed called the first B Quartet. So so I've just been playing the cello, which has put me in a very good mood to talk to you.

Harpreet: [01:12:35] And as you talk about in your book, thinking better, there really is no shortcut to learning to play the cello. Right.

Marcus: [01:12:41] You just know you've got to just got to put it in there. Yeah. Interesting, because you've got to change your body. It's that muscle memory and that that just takes time.

Harpreet: [01:12:51] How can people connect with you? Where can they find you online?

Marcus: [01:12:53] I'm very active on Twitter so people can follow me there. I'm Marcos de Soto. I have a website in Oxford. It's Simone Oxford, UK, and I try and put all of my projects up there. So I think those are the two best ways to interact with what I'm doing.

Harpreet: [01:13:11] I'll definitely be sure to link to those in the show notes. Thank you so much for taking time at your schedule to be on the show today. I appreciate you having me here.

Marcus: [01:13:17] Yeah, it was really fun talking with you.

Harpreet: [01:13:20] And my friends. Remember, you've got one life on this planet. Why not try to do something big? Cheers, everyone.