Instant Genius - Mental Shortcuts, with Prof Marcus du Sautoy

Episode Date: October 10, 2021

Professor of mathematics Marcus du Sautoy reveals how thinking like a mathematician can help you make better decisions in all aspects of life. Once you’ve mastered the basics with Instant Genius, dive deeper with Instant Genius Extra, where you’ll find longer, richer discussions about the most exciting ideas in the world of science and technology. Only available on Apple Podcasts. Produced by the team behind BBC Science Focus Magazine. Visit our website: sciencefocus.com Hosted on Acast. See acast.com/privacy for more information. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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All eight episodes now streaming, only on Disney Plus. This podcast is sponsored by name, audio and focal. Streaming has made music more accessible than ever, but true listening is about more than ease. It's about quality. British audio experts name audio, alongside French acoustic specialist focal, combine handcrafted tradition with cutting-edge innovation and high-end materials,

delivering digital precision with analogue warmth. So you can experience exceptional sound at home. Music just as the artist intended. visit name audio.com to learn more. Hello and welcome to Instant Genius, a bite-sized masterclass in podcast form. I'm Daniel Bennett, the editor of BBC Science Focus magazine. In this episode, I'm joined by Marcus de Sotoi,

a professor of mathematics and the Charles Simoni Professor for the Public Understanding of Science at Oxford University. Marcus is also a prolific presenter of brilliant science TV and radio programs. and if you search for him on BBC Sounds or IPlayer, you're sure to find a show that explores maths in a way you might not have considered before. Today, Marcus joins us on the eve of the publication of his new book, Think Better, The Art of the Shortcut,

which explores how thinking like a mathematician can give you an edge in life. In your book, you've kind of turned the shortcut into a kind of whole philosophy of life, a kind of way of thinking. So to get things off, to you, what's our shortcuts and how do they help you think better? Well, I think that a shortcut is trying to get me to my destination in the quickest and most efficient way. Essentially, actually, you can look at Aristotle's division of two sorts of types of work. He talks about praxis work that you love doing just for the sake of doing the work. for example, going for a walk in nature, you don't really want to shortcut that because you're

kind of enjoying your time in nature. What I'm after is kind of shortcuts to what Aristotle calls poesis, which is work for trying to get to a destination, a sort of an end game. And very often there, you just want to get to the destination so you can begin the thing you want to do. So I'm after shortcuts, which avoid just plodding away, having to do. do lots of hard work and can get you to where you want to be. For example, if you're going on holiday, you don't want to have to walk to your destination on holiday. You want to use a shortcut so you can start doing the things you really want to do.

What I really enjoy about the book is you set this out at the start that part of it comes from laziness, a desire to sort of not put more effort than is needed into something, but also that it's actually not just about being lazy, it's about finding simple route. So was that your thinking behind writing a whole book on shortcuts to sort of prove that you weren't lazy? Well, actually, the book was partly inspired by my previous book, which was the Creativity Code, which is all about artificial intelligence and human creativity. And I remember talking to a journalist who, by the end of our interview, was so depressed at the thought that, well, gosh, it looks like AI is going to be able to do everything,

including matching human creativity. And so he was looking for some sort of glimmer of hope. And I actually settled on this idea that, no, a computer doesn't get tired. It isn't lazy. It doesn't mind doing lots of boring hard work. But actually, our human laziness, our desire to avoid doing hard work, sometimes is the inspiration for us coming up with really clever ways at looking at problems, where a computer might not go down that route.

So the book is really kind of like a celebration of just one of, I think, our wonderful human traits is that we are lazy, but that actually ends up with us coming up with all these incredibly clever ways of thinking. So often actually you have to do quite a lot of hard work to come up with the shortcuts. But once it's there, it's ready for the rest of humanity to take advantage of. in a way, kind of this book is your shortcut to all the shortcuts that it's taken us a long time to come up with. I like that idea, a shortcut to all the shortcuts.

And you make this point really well that actually this shortcut is something innate within us, our own brain is making shortcuts all the time. Yeah, it's kind of interesting that there's a neuroscientist that I talked to in the book who was actually hoping to become a, grandmaster at chess and was very frustrated that even putting in the 10,000 hours and talking to all the experts, he just couldn't achieve anything other than, I think, expert or something. And so he turned to neuroscience to see, is there something about the way his brain is working that is stopping him becoming a grandmaster at chess? And what do you discover is a kind of signature,

kind of behavior of a brain which is kind of inflow working at its best? And often it's of doing less work. He actually took my brain and we scanned it as I was playing chess. And he said, look, I can see that you're almost using too much of your brain because you're overthinking things and it's kind of getting in the way. And he saw that the signature of grandmasters are that they sort of shortcut activity in the brain. And I suppose that's kind of like intuition and flow. So it seems that our brain when it's working best is kind of getting the neurons going from one place to another in the most efficient way. And essentially, I talk about network shortcuts in the book.

And one of the things we've discovered that if you want to get from one place to the network to another very quickly, there is a kind of way to do that, which is to, you have lots of local connections in your network, and then a few global ones which connect sort of one side of the network to the other. And that actually means that you get these networks which have something that people may have heard of, kind of six-degree. of separation that you can get from one point in the network to the other with just kind of six moves. And that seems to describe our kind of social network where we know a lot of people

on our local environment. We know a few people across the world. And that seems to create a network where you can get from one place to another incredibly efficiently. But knowing that's quite useful because if you're creating a network and you want that kind of property, then we know these what they're called small world networks. What you need to do is just add a few global connections and you'll be able to make a network which has this fast way to get through it. We even believe the human brain is actually constructed like that. A lot of local neuronal connections and a few global connections means we can very efficiently get from one neuron to the other by, say, six synapses of separation.

It's funny because, so psychology is my sort of, I suppose, pet subject on the magazine. And, you know, just describing that. It also makes me think of something I'm also quite interesting in right now, which is a little game that I suggest you play as a mathematician called Mini Motorways. I don't know if you've ever heard of it. No, I'm intrigued. You have the job of a city planner trying to connect little homes to their workplaces as they pop up around a little grid. And you do just that to win the game. You create little clusters, little branch-like structures of local networks.

and then you try and join up key points with longer highways to sort of join up the furthest points of the map. Very interesting. So there's your shortcut to playing that game efficiently. Well, exactly. And that brings me really nice. So you talk there about sort of shortcuts that help us understand networks of things

and as cities can be simplified into just a network. And in the book, I came across this fascinating idea that it was to do 15% is the sort of bonus you get from a city. And I was just hoping you could explain that idea to our listeners. Yes, because this is a wonderful shortcut, actually, if you want to get an extra 15% on your salary by doing nothing but the same work that you're doing already. Because it transpires that, I mean, one of the shortcuts I talk about in the book is the power of looking for patterns because if you can spot a pattern in your data, then that enables you to shortcut looking into the future and sort of manipulating that data. So one thing that was discovered is if you look at data associated with cities, for example,

the number of restaurants in the city or the number of libraries or the amount of creativity of people in that city, then if you double the population, Very often you think you should just double whatever number of restaurants or double creative output. But it seems like there's this pattern that's emerged where you get a kind of extra 15% on top of that. So, for example, if you look at the number of patents filed in a city of 1 million residents, then when you move to a city of 2 million residents, you don't double a number of

patents, you actually get another 15% more, which is kind of curious. and it seems to be a quality of the network of a city that means that somehow by doubling, you're getting this kind of extra connectivity, which is creating this kind of bonus 15%. And in particular, it transpires that if you live in a city of 1 million people and you compare yourself to somebody doing the same job as you in the city with 2 million residents, they're earning 15% more than you are. So this could well be your shortcut to getting a little bit more for doing the same amount of work. I think the other part that I found really interesting about that is, and you make this point,

is that it's a kind of looking at it in this, I suppose, abstracted way, it solves to remove the distraction of comparing London and Tokyo based on their cultural or geography. Yes, I think this is one of the very powerful shortcuts. that mathematics offers the power of abstraction and throwing away extraneous information, which turns out not to be important. And so it was a surprise that the actual way the city is constructed, whether it's on a small bit of area and very tall like Manhattan or sprawling like L.A., that it doesn't seem to make a difference. And it's really just the number of an inhabitants of that city, not the actual kind of geography of it. So I think time and again,

in mathematics, you see that one of the powerful shortcuts is being able to know what isn't important and throwing that away and sort of abstracting what is important. And very often, another shortcut that emerges is that therefore this model that you have, it might be describing a city or it might be describing, for example, the physiology of different animal bodies. And you can actually apply the same theory to sort of show how. the different animals behave differently according to their increase in size and weight and things like this. So that's often the power of mathematics as a shortcut is to abstract things and then you actually have a shortcut that can be applied in many varying different situations.

Yes, so that kind of idea that you can use these shortcuts when you take them in an abstraction and apply them to other problems, that fits really nicely with how you look at startups in the book. And I think for many of us, we kind of, you know, if I'm being honest, I look at, sometimes look at startup culture where they have loads of pool table, ping pong tables, that's the current one, isn't it? And serial bars. And I jealously, jealously, scoff at them. But actually, there is a kind of method to their thinking beyond, you know, we want to look friendly and nice. Yes, I think it's about encouraging an atmosphere of play. because play allows you to do experimentation and often something kind of new can appear out of that.

And it's kind of related to that idea that we're celebrating laziness that actually during lazy periods when you don't seem to be doing anything, actually your mind is working on its subconscious. And I think your subconscious often is able to kind of try lots of different possibilities until it latches onto one that seems to really be new and works. And then that's when you get the aha moment and it kind of flashes up into your conscious world. So I think sort of encouraging downtime play is really important. And actually sometimes I think that mathematics,

I spend a lot of time at my desk sort of thinking on a hard problem. But actually the breakthroughs very often come when I'm not looking at the problem. I'm running by the river near where I live. and suddenly something appears. So I think startups have gotten onto that. And I think math departments as well, we have a lot of games in common rooms. We have a lot of areas where you can just doodle on boards.

And I think that helps to encourage these kind of flashes. So if you just occupy yourself with just boreous work, then that just doesn't give your minds the opportunity to wander and come up with something innovative and new. So in a way, this suite of shortcuts. that I put together in the book, is really trying to help you avoid the kind of laborious slog that can often just shut down innovation and allow you to sort of be fleet of foot and find kind of cunning ways to get something new coming up.

And so one thing I definitely regret is that I didn't do more maths at school and university, which I bet you probably hear a lot. Well, sometimes people say I was quite happy to give it up. But I think, yeah, my books really celebrates mathematics as the art of the shortcut. And what I want to try and show people is that, you know, there's so much more to mathematics than kind of the boring long division and signs and cosines that it's actually something really exciting. And I think I was very lucky with my teacher at my comprehensive school. He kind of opened up this well for me and made me realize very early on how beautiful, creative,

but also just how extremely powerful it can be in solving problems that we're faced with. Yeah, I mean, there's always a great teacher, isn't there? Somewhere lurking behind every sort of... It does seem to be, yeah, exactly. There's always this school teacher, so I blame mine for not getting rid of the best. But there is... So I regret not doing more. And so one of the concepts I regret not really fully understanding it in my time in college was calculus.

Yes. So within mathematics, it's an exceptionally powerful tool. And I just wondered if you could try and, you know, get across to our listeners how valuable and important it is. And I suppose trying to explain it in as late terms as you can. Yeah, no, I think this probably is the most extraordinary shortcut that we've come up with over the last 2,000 years of doing mathematics. And actually, it's trying to match nature's ability to find shortcuts, because nature, there's a kind of old adage in science that nature is really very lazy at heart. So it, like human species, and that it tries to find the most efficient fast solution, low energy solution to something. So, you know, a ball falls down into the valley because it's trying to find a low energy solution.

bubble, for example, creates a spherical shape because that's the shape with the lowest energy on the surface. And light as well, light finds the shortest path from one part of space to the other. And that's what we saw when we saw light bending in the geometry of space post-Einstein. But we see that even with a more mundane example of lights going through water and air. So when we're in a swimming pool, we see ourselves kind of shortened. But how does Light know how to find that fast path? So it gets through the medium where it's slowest more quickly and then goes into the medium where it's faster. But there's a kind of sweet spot where it doesn't want to spend too long in the fast area either.

So it seems to use quantum physics where it tries all possibilities and then collapses into the place where the fastest route. But actually, we as mathematicians, we will look at, analyze all of those paths. and calculate the time it takes to get from one place to another. Actually, an interesting kind of example would be, you know, you've got a lifeguard who's got to run across sand, which is quite slow. Well, I don't know, maybe you're faster on sand. Let's say you're faster on sand, then you're swimming where it's a bit slower. So where's the optimal point to dive into the water?

And so you'll set up an equation which will give a random point along the shoreline, to enter, how long would it take me to get to the drowning person? But then calculus is able to tell you, well, the optimal place where it will minimize the amount of time to get to the person drowning, this is an incredible tool which will give you that point. So it's sort of our tool to explain how nature finds all of these shortcuts kind of more naturally. So it was Newton and Leibniz's great insight that a world in flux where everything is changing, very hard to navigate, drop an apple from that apple tree in Walththorpe Manor

where Newton came up with all of these ideas, actually during a pandemic, that, you know, to say what the speed of that apple is, it's changing all the time, but calculus is able to sort of make sense of an instantaneous moment and what its velocity is. And it's hard,

actually, it's making sense to the kind of curious mathematical challenge if I divide by zero, what should the answer be? And so calculus kind of makes sense of taking a time interval which gets smaller and smaller and smaller until you want a snapshot of what's going on. And so, you know, distance divided by time, that speed. But if the time is zero, I want to know exactly at that point. So calculus is a kind of amazing tool to tell you that. But it's used, you know, by every engineer to kind of find or somebody

in commerce as well. If you're trying to find the sweet spot to price your goods, to maximize profits, then in an equation in economics, you will want to use the calculus to find that sweet spot to maximize your profits, for example. So what you're saying is I instinctively understand calculus because of the way I'm interesting you say that. Absolutely. In some sense, nature and including animals and including humans, we sort of by kind of, I suppose almost like trial and error and evolution, we have developed an ability to sort of roughly know the kind of often these optimal solutions. But the point is we're now in a much more complex world where our intuition often fails us.

And I suppose in a way this book, it's called Thinking Better. It's almost meant to be a companion book, to Carneman's book, Thinking Fast and Slow, because thinking fast is our kind of intuition, what I feel for things, very quick. It's very often based on heuristics, but often it's very faulty, as Kahneman illustrates. You've got to think slow and kind of analytically bring your mind to see sometimes the counterintuitive things, ways things happen. And I suppose my book is, yeah, you can think analytically, but you don't have to be slow. these shortcuts find you, like calculus, get you to the solutions quickly, but securely, as it were. Yeah, I mean, I suppose it's important to say that you're not sort of advocating that every problem or everything that you want to achieve has a shortcut that will get you to the right answer.

it's essentially about, you know, finding heuristics or set of rules that help you approach a very, you know, the world and a lot of problems that we face are very complicated problems now with lots of moving parts. Yes, exactly. And I think, you know, what you need to know is, you know, have this suite of shortcuts at your fingertips because sometimes it will be calculus that will get you your shortcut, but not everyone knows calculus. Maybe that means your shortcut is going and talking to a mathematician to help you with the shortcut. But sometimes it might be the power of a very good diagram, which throws away extraneous information that is just clouding your view of the problem.

And then with a diagram, suddenly you can see very clearly what's going on. So one of the shortcuts I talk about is the power of throwing away. information that is clouding things and, you know, getting that diagram which just crystallizes and helps you to solve the problem. I think, you know, for example, if you go into any particle physicist's office, their Blackboard is covered in those Feynman diagrams, which describe particle interactions. But those Feynman diagrams, which actually Feynman's way of trying to navigate hugely complex mathematical calculations that he was just having a real difficulty with these path integrals that describes what possible things might happen with these interactions

of the particles. And he just needed some clever way to see the problem. And now it's become an incredibly powerful tool to explain the complex mathematics that is hiding behind there. So using a good diagram is very often a clever way. And you mentioned actually psychology that you're interested in psychology. And one of the pit stops I make is to talk to therapists. it's interesting that sometimes you're trying to change the way the brain works.

And that often doesn't have a shortcut because it takes years of therapy sometimes to really change brain structure so you don't sort of fall down the same kind of patterns of thought. Actually, Susie Orbach described it. It's like trying to unlearn a language. If you think about, you know, you speak English, but imagine trying to unlearn English is going to take you sort of a long time. However, you know, there are therapists who use amazing shortcuts, including kind of diagrams during therapy, and CBT has really been celebrated

as a very powerful way in eight weeks, for example, of really helping to change behavior in certain particular problems that, yeah, you can actually help people to see the faulty algorithm that's at work in your thought process and to be able to intervene before you, start going in depression. So there's a couple of things I wanted to pick up on there. One, I think perhaps you need another chapter, the first chapter to be a friend of mathematician. And then, also I just, I still wanted to pick up actually on the idea about diagrams and, and that's, you know, that is one of the, the stops in your books. And, you know, I, I think, I think it's, It's quite interesting because I suppose we all know someone who explains something with a diagram.

If you need something conveyed, they'll always get out of pencil and a piece of paper and sit on a desk and start scribbling. And I suppose I didn't really consider the power of that until I was actually looking at it was, was it Kate. Raworth. Raworth, yes. Her work. And actually her work kind of using a diagram to reinterpret how we should. be thinking about economic growth. And that really struck me as a really powerful demonstration. I wonder if you could just sort of tell the list there about that.

Yes. I mean, during the kind of pit stop, which are these moments between the shortcuts that I present throughout the book and I talk to people from other professions, I was really keen to go and talk to Kate Raworth because she has this wonderful new diagram, which is part of her idea, something called Donut Economics. And actually, her diagram is sort of a counter to the, sometimes diagrams can almost lead you astray as well. So they're very powerful kind of tools and you need to use them very carefully. So she realized that any talk on economics always seem to use the same sort of diagrams. You'd have exponential growth. That's what you're after in sort of profits or the supply and demand diagram, this little X that you see

where you're trying to again, you use calculus to find a sweet spot. And she said, well, this is just actually economics sort of promoting a very sort of capitalist view of the world. And actually, we need to put in some other considerations about climate, about humans having a basic level of living, the sort of kind of more human side of and ecological side of economics. And so she started introducing new diagrams. So this diagram of a donut, or what I call mathematically a torus, one of my favorite shapes in mathematics, is basically, I mean, her picture is two circles,

and the inner circle represents, kind of if you fall inside the inner circle, then it means that the human species is kind of, you know, either poverty hitting or not enough water. It's about the kind of more personal protection of people, whilst the outer circle represents our planet, and going outside there is a threat to the planet,

at the sort of a more global view of economic kind of considerations. And so she's trying to say, yeah, we might work in a capitalist model, but we need to be in this safe zone in the middle part. And so she's using this diagram to always question economic decisions to see, well, does that mean that you're actually outside the outer circle and therefore a threat to the planet or inside the, inner circle and therefore people individually are suffering because of your economic decisions. So it was a powerful illustration how a diagram can really help to change people's perspectives

on kind of views of the world. Yeah, absolutely. It was a study second. Yeah, I mean, it's a wonderful book. Kate Raworth's book, Don't It, Economics, was one of my favorite books, I think, of the last few years. Yeah, I'll definitely check it out. So there's plenty of shortcuts we could talk about, but one particular area that you look at is finding shortcuts in patterns. And there you talk about music, which is another thing I'm fascinated by. Is kind of music and art one area where you struggle to find shortcuts that could help you get better at cello? Yeah, exactly. So I'm learning the cello at the moment. And I was, really hoping to talk to an international cellist and find there were shortcuts to being able to

play the Bach suites. I talked to Natalie Klein, who's a wonderful cellist. And she was very interesting because on the one side, she said, look, it's very difficult to avoid those 10,000 hours that Gladwell talks about in order to become an expert, because you are sort of changing your body. You're having to get your fingers moving. It's always that motor memory to be able to play a sequence of notes very quickly. That just requires hours and hours of practice. So on the one side, she kind of hinted that, no, you're not going to be able to get away with this, because a bit like when I was talking about psychology, that you've got to change brain structure, you're changing body structure. So I think becoming a performer of a musical instrument, or for example,

in sport as well. It's very hard to shortcut even if you were using drugs to become a 100-meter sprinter at such the top level. However, she did have shortcuts, and I think that's connected to why music and mathematics seem to be so intimately related, because in a way music is the art of patterns, whilst mathematics I often call the science of patterns. And so those sequences of notes quite often have a sort of rationale to them. And often you'll see a sequence of notes kind of repeated throughout a piece of music, maybe altering in pitch. So often if you spot those patterns, it can help you to shortcut sort of learning a piece of music or playing it, for example, at sight. So one of the reasons that you spend so long doing your scales and arpeggios when you're

learning an instrument is these will be amazing shortcuts when you then come to play a piece, because very often there'll be a kind of run of notes, which is basically a little scale. And so it sort of enables you to read the music, almost like reading a book where what you don't want to do is to read every letter individually. You start to see words, and that speeds up your reading. And so spotting those patterns actually helps you to speed up reading the music and being able to kind of play it much more efficiently. Yeah, you build up a feel of where the music is going and so that, I suppose, in a way, puts blinders on because you know where your finger's probably going to be.

Yeah, so you can concentrate on other things. And actually even bigger structure. So she and Natalie talked to me about kind of Schencanian analysis, which kind of uses something called an ersatz, kind of the structure of the piece. and that often is very mathematical. I mean, just simply, you know, often a sonata form is ABA, so you'll see the thing you've played at the beginning

kind of repeated, maybe with some, or theme and variations as well as kind of has kind of often mathematical structure. And if you actually can see this and spot it, it can really help you to navigate a piece of music more intelligently and kind of allows your brain to concentrate on a, other things like the actual kind of quality of the performance. I just wondered that so the book is

it's a great history of maths and it's really good at kind of showing the different ways we mathematicians use shortcuts. And it just did leave me wondering whether you have kind of used to day life, if there are tough decisions that you make. I just, yeah, I just wondered how it's influenced you when you're choosing a queue at the supermarket or those kinds of decisions. Yes, I guess it does inform them. I mean, for example, I have a very bad memory. And so I often use kind of idea of patterns as a way of helping me to memorize something.

If I could see a pattern, it's almost like a little algorithm. which helps me to kind of resurrect the thing I'm trying to memorize. So I find that very helpful. Also just things like, you know, I discovered that if you're in a tunnel with lots of people and you're trying to get to the exit as quickly as possible, you know, where's the best place? Is it in the middle or is it on the edge? And you might think if you, well, this is like a fluid. So maybe the middle is best because the edge is kind of producing a friction.

But if you mathematically analyze it, it turns out the shortcut is actually going, hugging yourself to the wall, because that turns out to be a much faster part of that flow. So often that's the power of these mathematical shortcuts, because it's often counterintuitive. And so it gives you a kind of edge in that crowd to be able to get to the exit first. That was Marcus DeSotoi there, talking about how a bit of maths can help you solve problems big and. small. If you'd like to hear Marcus and I dig a little deeper and discuss the creativity of maths and debate whether maths is an art, check out Instant Genius Extra, a bonus podcast available via subscription on Apple's podcast app. And of course, if you want to learn more about the art of the

shortcut, check out Marcus's book, Thinking Better, which is on sale now and published by Fourth Estate books. Thank you for listening. The Instant Genius podcast is brought to you by the team behind BBC Science Focus magazine, which you can find on sale in supermarkets and newsagents, as well as your preferred app store. Alternatively, do come find us online at sciencefocus.com. See you next time. This podcast is sponsored by name, audio and focal. The texture and emotional depth of music can be lost through digital sources or poor signal. Name Audio believes you can have digital precision with analog warmth. Alongside French acoustic specialist vocal, Name creates high-end audio systems, combining innovation with craftsmanship, so you can listen to music, just as the artist intended.

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