The Infinite Monkey Cage - The Science of Coincidence

Episode Date: November 14, 2023

Are some people just lucky? Is there any scientific formula behind coincidences? Is randomness the norm? Brian and Robin team up with comedian Sophie Duker, mathematician Marcus Du Sautoy and statistician David Spiegelhalter to uncover the reality and the maths behind seemingly incredible coincidences. How many people do you need in a room to find two with the same birthday? What is the weirdest coincidence that the panel have ever encountered? Is there a mathematical formula to being lucky? How good are we at judging how likely something is to happen? The answer is not very, as Brian and Robin unluckily discover.New episodes released Wednesdays. If you're in the UK, listen to the newest episodes of The Infinite Monkey Cage first on BBC Sounds: bbc.in/3K3JzyFExecutive Producer: Alexandra Feachem.

This is the first radio ad you can smell. The new Cinnabon pull-apart only at Wendy's. It's ooey, gooey and just five bucks for the small coffee all day long. Taxes extra at participating Wendy's until May 5th. Terms and conditions apply. BBC Sounds. Music, radio, podcasts. Hello, I'm Robin Ince. And I'm Brian Cox. You're about to listen to The Infinite Monkey Cage. Episodes will be released on Wednesdays, wherever you get your podcasts.

But if you're in the UK, the full series is available right now, first on BBC Sounds. Hello, I'm Brian Cox. And I'm Robin Ince, and this is The Infinite Monkey Cage. Now, in a probabilistic universe, is there anything that we can truly be sure of? Well, I'm just going to interrupt you there there because the statement that we live in a probabilistic universe is non-trivial, I would say, because it contains assumptions about the foundations of quantum theory. For example, in many worlds' interpretation of quantum theory, that's Everettian.

You don't know. Then, whilst observing a particular branch of the wave function might conclude that quantum mechanics is inherently probabilistic, the evolution of the wave function of the universe as a whole is unitary. Good night. That's not the end of the wave function of the universe as a whole is unitary good night that's not that's not the end of the show it's just i'm leaving this has definitely gone way above my pay grade that in fact when we were working on how to start the show our producer said if brian starts by saying that we will lose 97 of our order but i corrected it because i said

it's 97 plus or minus the square root of the size of the audience of the first order estimate. What our producer said after Brian said that was if you then say that immediately after the previous thing you said, then you'll lose 99% of your audience. So the main thing is, well done those of you who've made it this far. You are almost unique. But in today's show, we're talking about the science of coincidence and luck. Why are we so bad at estimating the probability that something will happen? What is a coincidence and is there any such thing as good and bad luck? To discuss a show that is probably about probability we are joined by a statistician and emeritus professor of statistics in the statistical laboratory at the University of

Cambridge. Are you sure that we're joined by an emeritus professor of statistics in the statistical laboratory at the University of Cambridge? Yes, I am sure that he's an emeritus professor of statistics in the statistical laboratory at the University of Cambridge, in the very model of a modern normal distribution. And also a mathematician and a professor for the public understanding of science, and probably the most prestigious of all, and I mean even more prestigious than the Emeritus Professor of Statistics in the Statistical Laboratory at the University of Cambridge, a comedian and winner of Celebrity Mastermind and winner of Taskmaster.

And they are? I'm David Spiegelhalter. I am the Emeritus Professor, blah, blah, blah, blah. And my biggest coincidence has happened to me was when I was making a radio programme about coincidences. And I was telling a story that involved a birthday and I had just made one up January the 27th. And there was this pause. There were three people on the line listening to me. And one of them said, well, I'm the producer and my birthday is January the 27th. And then the sound engineer said, my birthday is January the 27th. So that's the one big coincidence that's happened to me.

Because they never happen to me because I never talk to anybody and I never notice anything. I'm Marcus de Sautoy. I'm a mathematician and also author of a new book called Around the World in 80 Games, in which chance plays a big role. In fact, the coincidence I had, I used to be a big bridge player when I was a sixth former. And there was one time when we dealt out a hand and we almost all had one suit in our hand. It wasn't quite perfect, but I had like 12 hearts and one other card. And somebody else had all the diamonds except for one other card.

But I did see that about 10 years ago, some people in Warwickshire, a kind of group of retirees, But I did see that about 10 years ago, some people in Warwickshire, a kind of group of retirees, actually did get dealt such a hand where everyone had 13 of one suit. So what are the chances of that, David? It's all right, David. We wait till the end for the correct answer. We can calculate it, though, can't we? It's not too hard, is it? No, it isn't, because what's happening is that people take a new set of cards, they shuffle them twice with a riffle shuffle, and that actually interleaves the cards in exactly the way such as when they're dealt out, so it's actually much more likely than you'd expect. So actually, it probably wasn't a big coincidence after all. adorable comedian and reluctant Aquarius. And my strangest coincidence was when I was traveling in the country of Ghana, completely lost. I spontaneously, despite having been previously

very well adjusted, spontaneously had a four hour vision of my late grandmother and then later realized that the waterfall I had been wandering around was actually a waterfall next to which she had grown up and I coincidentally had also taken some psychedelics. And this is our panel. David we're going to be talking about luck, chance and coincidences and I thought we should start with a definition. So what is your definition of a coincidence? Okay the one that's been provided by some really good statisticians is a surprising concurrence of events perceived to be meaningfully related with no apparent connection. Which I quite like because it means it's got this element of surprise, it's got this element of its emotional

impact that it has people feel something about it, and yet there doesn't seem to be any reasoning behind it. So that's a very important part, isn't it? The emotional impact. That bit where, again, we always hear the normal thing, I was thinking about, and then they rang. And it's that sense that whatever your yearning has been for perhaps a conversation is then fulfilled.

So that's part of the narrative of making that a coincidence. Well, it's things that make something a story. People are interested. Oh, did you know what happened to me? So it's had an impact on people. They don't just sort of ignore it. And people remember them, like Marcus did. For their whole life, people remember these things that happened to them.

It's a very powerful stimulus. And do you find, Sophie, I mean, you've just mentioned an incredible coincidence. Are you someone who's quite good at kind of being a little bit logical in terms of, do you know what, I think this coincidence is just actually happened because, or are you someone who thinks, oh, do you know what, I might elevate this to a kind of synchronicity moment? Oh, I love serendipity. I love things happening for a reason.

In my world, nothing happens just because it happens. It has to have happened because I'm special and important. I just think it's nicer to look at life that way. I think the thing about coincidences is that colloquially people talk about coincidences and it's so obvious why the thing has happened. Like people get excited when they see people they know on holiday. They're like, oh my God, we ran into Flopsy Mopsy and Areola in Cambodia. Can you believe? I love the idea you're actually going to bump into some rabbits and they're like oh my god we ran into flopsy mopsy and areola in cambodia can you believe i love the idea you're actually going to bump into some rabbits and they're

but you know people are like oh my god like what are the chances that they were also at this exclusive resort it's just kind of like people just moving in the same circles just in a different side of the world and thinking it's a coincidence rather than very likely but anything actually surprising i'm like it's fate. And I think very often that it's a coincidence because we really don't appreciate probability very well. So, you know, I think David's one about the birthdays is a perfect example because, you know,

if you ask how many people do you need to be in a room for there to be a more than even chance that two people have the same birthday, most people will say, oh, maybe 150 because they're thinking about their own personal birthday. But the way that the network can happen or pairing people up means you only need 23 people in the room and there's more and even right we're gonna have to stop you on this one right this is a statistic that we have been given over and over again how many times have we attempted this on this show how many times have we found out that a group of 23 people there are two people now this

is one of those ones which is beautiful to hear because I've seen people go, no, no, we've got to go on them. Right. Yeah. Is this going to be anecdotal evidence? This is real evidence. I've done it with the Women's World Cup. There are 32 countries. Each squad has got 23 people in it, which is perfect. So all you have to do is take all the 700 and something things, look at all their birthdays. perfect. So all you have to do is take all the 700 and something, look at all their birthdays and you find out out of the 32 teams 15 teams

have got two people in the squad with the same birthday. That'll be astrology won't it? Because that's because they've got the star sign to make them good footballers. And Nigeria. Actually Robin's got a point here because actually more footballers. He hasn't got a point, don't say that. Nigeria has got two players both both born on Christmas Day,

and they're called Glory and Christy. Isn't that lovely? But, Marcus, could you step through the reasoning? How would you go about calculating that number? Oh, that's really interesting, because you shouldn't approach it directly. Actually, what you should do is to calculate the opposite. So what's the chance of having 23 people

that don't have the same birthday? And this means this means you know that you bring somebody up on stage they've got to have one of the 364 dates which are not the one that's on stage so that's 364 over 365 chance that they miss that birthday then you bring the next person up they've got 363 days and so you build up these fractions which which you multiply together. 23 of them, as they decrease, actually get you below 50%. And therefore, the chances that two will have the same birthday are above. Yeah, I mean, if I was in a classroom, you know, I would then start doing some experiments. As you say, they never work out. But I know, you know, the front row of the audience here, there's 16 people.

If they look to the last two digits of their mobile phone numbers, there's a 72% chance that at least two of you have got the same last two digits. But I'm not going to ask you to try, because it won't work. It never does. That was very precise. Again, so you said 16 people. There is a 72% chance. Yeah.

Did you do that in your head? No, I looked it up. So have you got a look-up table? If there are 18 people or 20 people or 15 people, did you count the seats earlier? It's in my book. I had someone try and do this to me. I had a chugger come up to me on the street

and be like, I'm going to guess your sort code. And he did. And it turns out that they are not unique to individuals. They are very, very common between other people. But I was really impressed. But this coincidence, it sounds like a bit of fun. We have birthdays and how many people's phone numbers will match. But I suppose in everyday life, David,

we make important decisions based on our understanding of chance and statistics and coincidence. So, for example a topical one which is the reliability of trains or otherwise so for example let's say that you london's and manchester let's say there are two train companies running the trains and one month 10 trains break down they're all from the same company so there are two ways you could approach that couldn't you is it a coincidence or does it mean there's something wrong with that company and their maintenance?

So how are we to make rational judgments and not just jump to conclusions about things that feel right? OK, you've got half an hour for a lecture on p-values, I hope? Yeah, that's what statistics does. You look at, if it were just chance, how likely it is to get such a an extreme difference between the companies if one company's got 10 times as many trains running as another or something that could explain it so you work that out and you and if it's a really tiny number you know that well

there's something other than just chance that's happening and then you look for another reason why it might be so quite a lot of statistics is working out, well, how surprising things are, how compatible is the data with just, you know, bad luck, or how extreme of the events you think, oh, no, this, you wouldn't expect this to come up under the play of chance. It is quite strange how much that is referred to in our daily lives, because it's just chance, it's just luck, or something like that. And we live with this all the time. And it's basically things we can't explain. I think there's some interesting examples like the Bulgarian lottery where six numbers came up and then the following week the same six numbers came up.

And you think, God, that sounds so suspicious. But actually when mathematicians analysed that, they saw that the number of lotteries that have been run around the world over the years, there should have been one moment when that happened. But course it spikes we notice that we haven't noticed all the other times when it didn't happen well that's the thing yeah a day without coincidences is somehow more unlikely than again it's that emotional reaction we of course we we notice the thing when it's weird but not all the millions of other times when something unweird happened i want I want to just go back to the trains. As someone who's a regular user of our crumbling infrastructure,

can we work out when we hear an alibi from a train company for their reason, say there's camels on the line or something like that, when it's a third occasion of camels being on the line near Chessont, is there a way that we can look at the likelihood of the camel escape? I don't know why I'm using camels, but I just am, okay? You know, that kind of thing. So when you hear certain things go, that's statistically now unlikely for this to have happened three times in a month. Yeah, well, camels do come in clusters, I think. So we'd have to take that into account. But when you hear the excuse for why your train is yet again not running, can you start to go, do you know what? This particular alibi has occurred too often.

Yeah, yeah. Well, you've got a basic scepticism of people wanting a story. Sophie was saying. I love the camels. I believe in the camels. Yeah, but you'd like a reason for everything to happen. And everyone loves a reason for things to happen. Whereas people just don't like saying, well, just that's bad luck.

Certainly in the trains. I don't think that's bad luck certainly in the trains i don't i don't think that's bad luck i just think someone's screwed up when we say there's a chance that something is going to happen what do we actually mean okay we could argue about that for ages because it depends whether you think that the world is basically probabilistic and stochastic and there is some essential absolutely irreducible uncertainty about things happening at core or whether you just think the world is incredibly complicated and we can't grasp it all for me i don't care either of those it could all be the will of god it could be anything all i know well thank you then good night it doesn't care the panel i

personally for me there's unavoidable unpredictability, and I call that chance. That's interesting. So you don't care whether the world is absolutely, in principle, predictable, because in practice it never will be. And so the origin of the chance doesn't matter to you at all. It's such a relief.

I don't have to care about, you know, is the world basically deterministic or is it basically probabilistic? Who cares? You know, it makes no difference to me. Businesses care. Zero difference to my life. I can see why you didn't do that philosophy degree now. I mean, what about you? Because really what we're hearing there from David

is that free will's an illusion, these things are just going to happen. No, you said he doesn't care what the free will's an illusion is. Well, no, he's saying it just doesn't matter. I mean, he doesn't care with the free wills and illusion saying it just doesn't matter i mean he might as well be saying free wills and illusion as far as i'm concerned from an existential point of view how do you feel at this particular time i feel infinitely challenged by that idea i don't think things are just going to happen i think that you have to be able to make things happen otherwise what am i manifesting for yes things are random and cruel and hard to explain like chaos and disaster and certain world leaders haircuts but i do think that you could increase the likelihood of things to happen marcus what

your view is because to me the the origin of apparent chance even if it's absolutely unavoidable, as you said. The origin of it, to me, is an important question. Yeah, I think, for me, I think this is one of the most interesting questions of science, whether there is anything genuinely random happening in our universe. I mean, quantum physics, one interpretation of it is that that's about the only place where something is random is happening. Pre-quantum physics, of course, we talked about Laplace's demon, the fact that if you knew all the equations, you knew the setup thing, you can just run the equations

and know exactly everything that's going to happen in the future. But of course, then we discovered chaos theory, which said actually, even if we knew everything up to incredible detail, but not exactly, still doesn't mean we can make predictions because it might be the

50th decimal place which actually takes the equations off in a completely other direction and so actually the ideas of probability and chance are to deal with both of those situations the deterministic and the perhaps genuinely random. I think one of the most stunning things is you know for centuries we just regarded as this something that was genuinely unknowable, something which was outside the control or understanding of humanity. And then along come these two guys, Fermat and Pascal, who mathematize chance and actually say, no, we can make predictions based on the roll of a dice. And I think that was one of the most exciting moments in the history of mathematics is that suddenly, you know, a subject which doesn't look like it's got anything to do with maths because it's random and chance, suddenly we introduce maths to be able to help us

to navigate. And there's a lovely story when Peeps contacts Newton and says, look, I've got this bet I've been challenged with. What are the chances? Is it more likely that I'm going to see a six if I roll six dice, or two sixes if I roll 12 dice? And, you know, my intuition just doesn't help me at all. I don't know what the answer is. But Newton applies the ideas of Pascal and Fermat and comes up with, I think, the quite counterintuitive answer, is you're more likely to see a six in six dice than two sixes in 12 dice. But's only using mathematics i think that you can overcome your intuition being rubbish when it comes to chance it is interesting isn't it that we seem to have a a real difficulty in understanding chance events understanding probability we said several times these results are counterintuitive our intuition is not working i think that's

because we're not very good at big numbers so you know evolutionary wise we've been used to just a tribe which has a couple of hundred people in it and that's our data set for working out you know what the chances are something but actually when we're dealing with chance we have to take huge data sets to get a real sense of it and our intuition just isn't built for that we're still stuck in the jungle with just a hundred data points sophie i was thinking that this is, again, talking about the intuition, etc., which is one of the problems we have is people like to believe that we have common sense. But actually, it turns out that common sense is very often not very useful at all, that it is based on all manner, sometimes, of bias hunches,

which are connected to a story but not connected to a reality. I feel like the intuition, the inner gut feeling I have is very rarely mathematical and logical. I feel like I was really messed up by a problem that other people might have encountered, probably quite basic for you lot, but the Monty Hall problem which appeared in The Curious Incident of the Dog in the Night Time and it's about say you're on a game show and behind two doors is something terrible like the herb parsley. And behind one is something delicious like the herb coriander. Don't fight me.

You're trying to find the coriander. You pick a door and they open another door that you haven't selected and show you some parsley. I shouldn't have picked these two things that look almost identical. And so then they give you the option of using a different door or sticking with the door that you have and the theory at least that the protagonist in the night time said is that you should always switch because the likelihood is that you have chosen the wrong door in the first place does that feel good to you does that feel intuitive i find it tremendously counter-instinctual but i love the fact you turned it into the herb pasty and the herb coriander.

Because when there's the jeopardy of whether it's a goat or a sports car, I can really see people being very angry when they've made a mistake. When they go, look at this parsley goading me. I could have owned coriander. Who would like to... Yeah, I think the best way... For me, I also found this totally counter counterintuitive when I first met you. I was like, why are you doubling your chances?

There are two doors now, just 50-50. But the way that somebody explained it to me that really convinced me is, okay, what if there are a million doors? You choose one, then the game show host opens all of the other doors, revealing Parsley, and just release one left and the door that you've chosen. Now you're going to swap, because the game show host has the information about where the coriander is,

and so they've opened all of the other doors, there's just one left. What are the chances that you chose the coriander at the first? The coriander is behind the door which is left, and so you'll swap then. What I love is that everyone at home who's currently cooking their tea and using coriander is thinking, what an incredible coincidence.

We've dealt with coincidence and wandered a little bit. Oh, can I ask, though, about the joke? Because we had this argument, didn't we? I mean, we've had many, obviously. We don't get on. We do. I think we do. You're more common-wise at times. He always makes me sleep on the left. I don't like it. Anyway, so I thought this was about coincidence,

and Brian said it's not, and I think he may well be right on this, just on this, which is we're talking about the assassination of Archduke Ferdinand, where the person who went to assassinate him, balled up, didn't manage to assassinate Archduke Ferdinand, just goes and sits like, oh, another failed assassination attempt,

goes to sit in a cafe then archduke ferdinand's car happens to take a different turn into the one it was meant to take and he's sitting in the cafe and goes that's handy and then does successfully assassinate archduke ferdinand now i thought that that involved a level of coincidence the coincidence of the cafe chosen and the coincidence of the roadworks or whatever it might have been that led to archduke ferdinand going down a different street. Brian feels that that wasn't a coincidence. I think, David, it was one of your definitions of chance.

I consider that luck because he was lucky. I mean, not only the cars, he stopped in front of the cafe. He didn't just drive past. And there he was with this. This is the first radio ad you can smell. The new Cinnabon pull apart only at Wendy's. It's ooey gooey and just five bucks for the small coffee all day long. Taxes extra at participating Wendy's until May 5th. Terms and conditions apply. in it as a force but I really do believe in it as a good label for how things turn out so the definition I quite like is it's the operation of chance taken personally which I like again it's like everything I was saying about chance probability and uncertainty regardless of the

personal relationship to the world these are things with a big emotional impact and I love luck I think luck is an absolutely fascinating thing. It's subdivided luck. Yeah, yeah. The philosophers have done this under the idea of moral luck. And I find this really useful. Basically, there are three types of luck, outcome or resultant luck, which is just how things happen to turn out at that moment. Circumstantial luck, which is where you happen to find yourself. And I think the most important one of all is constitutive luck, which is the circumstances in which you have been born. Your parents, which country, whether era and everything like that.

And that's incredible. And I believe that is the most important luck you can have. It's the privileged life that you're born into, which influences absolutely everything in the future. And you may think, oh, I've done everything myself. No, most of what happens to us is generated by how we were born, over which we had no control whatsoever. My grandfather, Cecil Sp everything myself. No, most of what happens to us is generated by how we were born, over which we had no control whatsoever. My grandfather, Cecil Spiegelholt, who was in the Lancashire Fusiliers in the First World War. So he had, I would consider, quite bad constitutive luck in being born in late 1880s, just in time to be there as a soldier for the First World War, which is, you know, that's bad luck to be born in that particular period. And then he had really bad circumstantial luck, is that he was posted on the

Western Front, and he ended up as brigade gas officer on the Ypres salient, just after Passchendaele, which the life expectancy must have been weeks. Anyway, he lasted three weeks in the job. And so he was inspecting the trenches on January 29th, 1918. Shell came over and blew him up. But it didn't kill him. He got shell shock. He was invalided out and spent the rest of the war behind the lines. Meanwhile, his battalion was sent to a quiet section, which was then the Somme,

just in time to meet the Kaiser's offensive in March 1918, when they were completely overrun. And he missed it. So he had a staggeringly lucky resultant luck, in terms of being blown up at just the right time. He might not have felt that at the time, as he heard the shell approaching. He might not have thought, how lucky I am. But it turned out that he was.

And I suppose that extends to your personal existence. Oh wouldn't be here otherwise yeah of course yeah and if we really want to get into philosophical so what's the probability we exist because the chance of us all existing is absolutely microscopic I've I've worked out I was conceived in November 1952 and I've looked at the temperature records for North Devon at that time they were it was going through as a really cold snap in November 1952 and I know my parents were living in this sort of pretty unheated stonewalled cottage and I suppose there's nothing else to do so and so here I am I think the the fact that life formed a tool on our planet, the likelihood of that, I think, is being analysed. And it's the same chance as throwing 36 dice

and them all arriving on a six. You know, you think, it's a miracle. There must be a God because we've got life on Earth. But again, it comes back to this fact that we have a real big difficulty with big numbers. So here it's about time, deep time, that we have been throwing dice for a long long time and the chances of those 36 dice turning up a six actually you know we might expect life to evolve somewhere in the universe even if it is that rare is there a

way that you think we can educate all of us to have a greater grasp on on big numbers because obviously in the past when we've talked about things like evolution by natural selection that's I think one of the reasons that some people are very negative towards it is again the enormity of the expanse of time that we're talking about for each modification to occur for the variety of life to then be what it is now and not having that understanding of the big numbers seems to be... Yeah, we just need more shows with parsley and coriander on and we'll get it sorted, I think.

But I think, like, when I close my eyes and I imagine a million sheep... Sorry, I'm just... I'm worried you're going to fall asleep now if they start jumping. And then I close my eyes and I imagine a billion sheep. It's exactly the same number. That's why when you say, oh, it's a one in a million chance that something happens, you know, there are 10 million people in London. So, you know, one in a million means there are 10 people that might be experiencing that.

So suddenly it becomes less, you know, one in a million sounds like it's impossible. But actually it isn't. David, I remember you're one of your previous titles, one of your many titles, Professor of the Public understanding of risk can you give us some examples of where this this misperception was very natural because these are very counterintuitive ideas where they really matter when we're trying to deal with i suppose our own behavior but also our behavior as a society it really matters that we understand i have some handle on these large numbers it It really helps if we've got some idea of magnitudes. It doesn't have to be very precise at all.

You know, just what is important and what isn't. And we're very bad at it. Our discussion is always about the power of story, the power of narrative, the power of individual experience, which we find overwhelming. We're humans. That's what attracts us. And just looking at numbers can seem very dull

compared with that so i'm really interested in how you know can we tell in a way reliable stories about risks about you know things we're exposed to that actually engage people sufficiently so they can get an image of what's going on what's the recent one uh everyone's making a fuss about artificial sweetener and diet coke and they you know, no quantifiable risk whatsoever, and yet there will already be people who will be starting court cases about that. And there will probably be people getting anxious about it. You kind of think, oh, in an ideal, rational world,

our anxiety would be directly proportional to the threat. But that's not how we are, you know, because we're humans, and some things, for a start, will say, well, I'll just take the hit because i'm having fun and so you'll do things that perhaps are risky and other things you you avoid not particularly because it's a big risk but because you don't like the thought of being exposed to it and you don't like who's doing it to you sophie i wonder that interesting thing about stories may well shrivel with accuracy because it's like you know we both work on stage we both

do like that bit sometimes when we're telling stories on stage this is predominantly true yes so that that juggling between truth and you know the embroider yeah I think it's because it's so we're so drawn in terms of the story to the unlikely like we always want the rarer thing to be the special thing like I have more teeth in my head than the average human, and I genuinely believe that makes me... Your eyes widened so much. I genuinely believe that makes me a witch. But that's like people with different physical characteristics,

whenever it feels like the odds have been statistically low, then we want to attach a huge amount of importance to that. Sorry, no, no, no, but how many teeth? Is it 32? Is it 32 is that is it 32 teeth normally or come on marcus you do numbers four times eight or something isn't it yeah i'm wary to say this on the radio because i don't want to be experimented on like an x-man well marcus is also worried he was willing to say four times eight but he wouldn't say what the answer is i know there's a true mathematician on the panel. Pure mathematician. That number of order one.

I can't remember. Just two more. OK. Two more teeth. Two more. Two more teeth. It's computer... I'm going to be third at the stake.

These are my favourite moments, because Brian doesn't know how to react to kind of dental... Dental revelations, always throat does not compute. 30, 40 teeth. I do not understand this thing called love. I was just moving the discussion back onto the subject. I want to say this idea of probabilities is inherently confusing.

So, for example, toss a coin, it comes up heads, and toss it again, it comes up heads, again it comes up heads. Most people would then be likely to say, well, surely if I toss it again it comes up heads again it comes up heads most people would then be likely to say well surely if i toss it again it's going to come up tails isn't it because i've tossed it like three heads and so so analyzing even very simple problems it's a skill isn't it yeah it is and people kind of you would think it's not true of course if you toss three heads then and i toss well it depends which question you ask well yeah it could be a bite it could have heads on both sides you see so you've got to start to question

that if it comes up heads a hundred times i always have a two-headed well i'm going now usually when i'm doing this at schools i have a two-headed coin just to fool people so the point is that your your comment there which is gambler's fallacy or a tale must be due all of that assumes the coin is perfectly balanced it's being you're not being fiddled and no one's playing with you. There's massive assumptions. It's not the truth. There was a very interesting case in Monte Carlo at the casino where black came up 26 times in a row on the roulette wheel and people started betting more and more,

just convinced that red surely has to come up next. But this is just the mistake of independence. There's nothing in the past, which means that unless that roulette wheel is actually bonnest in some way, maybe they should never have been betting red and they should be betting black each. Our intuition is terrible on this

because we can do endless exercises that show that people don't recognize how much things cluster. So for example, hang on, how many times do you have to flip a coin in order to have more than a 50-50 chance of four in a row four heads or four tails so i'm going to flip the coin till i get four in a row and you only have to do it 11 times for there to be a 50 50 chance of getting four heads and that's completely unintuitive totally unintuitive so you know we go back to

this old thing which you're saying before that you my intuition is terrible on this stuff i have to do everything from scratch and do it three times and you know go and sit on the lab and concentrate and come back again and yeah that might be the answer you think why i wouldn't have to do that if this was an algebraic problem or something and i think probability is something different it doesn't't exist. We made it up. So no wonder we find it difficult to deal with because it's fictitious. But it works very well. It works very well. That's why casinos are rich and we're poor.

Exactly. And we know how things will work if it's a proper coin. But I prefer to refer to it as goddess Fortuna, I think is how I like to think about it. That's a real ocado version of lady luck that's interesting though because it's quite a provocative statement probability does not exist

well i think the perfect example and david's said this one to me before you know if you roll a dice and i cover the dice you know it's already landed um it's showing a six but you don't know what it is so for probability for you is this one in six that it's on six but for me i've got complete information i can see it's a six and so what is this number of this one over six the probability that we're assigning to it is different according to a different perspective yeah if i flip a coin and cover it up you know what's the problem your probability this is heads and what's your probability this is 50 50 50 50 and you're wrong is heads? 50-50. 50-50. And you're wrong.

You lost. So that's why mine is different. Now, what that probability is, it's nothing to do with chance anymore. This is what's called epistemic uncertainty. It's an expression of your lack of knowledge. And that depends on the observer. It's an expression of your relationship

between you, an observer, and the world. It's not a property of the coin anymore. And you could say that actually that holds to all probabilities. It goes back to something you said right at the start, actually, about feeling that there is randomness. Yes. And you said that feeling that there really is chance in life is important.

Yeah, I think it's important to feel like there are things that are likely to happen, but they might never happen. So happen so like I can see you getting enraged at this but even though it feels very very probable that something might happen that's not necessarily going to be the case there's no way that you could ensure it that's kind of hope isn't it you you know well I suppose our own death is one example it's something that's definitely going to happen but we keep hoping that it's not going to happen. Not quite, yeah. I mean, for a lot of my life, I didn't really feel like I could die. I didn't feel like I think that was me.

For you guys, it's fine, but for me, it felt wrong. And now I'm sort of slowly reconciling that that could be a thing, but it's very hard to believe. You know, if I was flipping a coin coin I was going to win some money or something good was going to happen if it came up as a certain way you may think oh this is pure chance there's nothing I can do it's just play of luck or whatever but you are emotionally engaged always you know you cannot I think stop feeling that engaging with it with something you've got no control over at all and yet you're really interested in what happens it's part of being human you know people have had to live with this you know forever the fact

they cannot predict or control so much of what's in their life i mean it's very it's very hard to be detached like i have an energy provider that every month it asks me to spin a wheel of fortune to see whether i get my energy off that month. And I know that the wheel is rigged and it's never going to happen. Every time I go to do that wheel of fortune, I'm like, maybe because he lives for me will be easier this month. But that's why I don't like playing games where I know it's just about the numbers and things outside my control. Like I'd like playing poker because I feel like I can bluff in poker, not because I can wish the cards into my hand. Yeah, I think there is some...

By the way, if you're an energy provider, actually the way they generate energy is by getting loads of individuals just to spin a wheel. So they don't even realise that they're part of the whole scam. Sorry, Marcus. No, I think in games where there is chance involved, you can still give yourself an edge if you understand what the chances are.

So for something like Monopoly, that's a game where you're just throwing dice. But actually, if you analyse the dice, the most likely throw of two dice is seven. Six, seven and eight are very likely. Two and 12 aren't. So how can you use that? Well, actually, the most visited square on the Monopoly board is the jail square. So actually, people visit jail three times more likely than any other square. You can't buy jail. But after jail, they're more likely to throw six, seven or eight, which gets them into the orange region of property.

So if you buy that property, the chance is that other people are going to be landing on it and you're going to cash in and win the game. My God. There you go. That's incredible. So just to analyse that a bit, so the mid-dice range, it's because there are more ways of the dice adding up to those numbers.

Yeah, you can get a seven in a one and a six, a two and a five, a three and a four, a four and a three, and so on. But to get 12, you've got to get two sixes, so there's only one way out of 36 ways the dice could land. So that kind of knowledge is really helpful in playing games because it gives you kind of edge over your... Over your family at Christmas.

Yeah, exactly. My family never play games with me anymore because... I mean, do you think there is a useful way to be more mathematically consistent in the way that we travel through the world without at the same time removing too much of the joy of the world to look at certain problems of our existence and go do you know what this one i can start working out the probability and the chance and you know all of these different ideas and this one is best to left the illusion perhaps the illusion of not

being a deterministic universe yeah i like it right it. So it takes away, for me, let's say that you say, should I fly from London to Glasgow, or should I get the train, or should I take a car? And maybe you don't like flying very much, or maybe you don't like it. So I find it removes all responsibility for me. I just say, what is the probability, based on the data, that I successfully make it from London to Glasgow,

whatever it is, by these three modes of transport, and I take the one that the data tells me to take. And it just removes all responsibility and emotional crap from my decision-making. Yeah, but you own a helicopter. Which is the most dangerous. No, I don't. It's probably the most dangerous way to get there.

Or a motorbike, maybe. I think it's impossible for individuals to be rational because what about the joy? Most individuals. What about fun and all those things? Quite difficult to put numbers on. But I would like my society to be rational and consistent and work out magnitudes and work out risks.

And insurance companies and things like that to be based on a real basis so that they're going to remain solvent so i think that is difference between an individual and organizations which really should i think try to get a really good grasp on risks and magnitude and expected gains and losses are you saying that public policy should be evidence-based. Oh, sure. Oh, I know. Yeah. I know it's a hopeless ambition, but... I like your crazy dreamer moments, Brian.

And so, at the end of this, how do you feel about things like your good fortune or luck? Are you someone who views yourself, you know, where? Good luck, bad luck, where do you find yourself? I feel like I'm going to keep trying to wrangle luck, trying to like massage the situation to get myself the best possible outcome. Because even though life is random and chaotic and maybe nothing is predictable, there are some things that I think I can predict with absolute certainty. and you have to go with me on this, that sometime in the next ten seconds there will be an absolutely thunderous applause break

from everyone in the room. An absolutely thunderous applause break! APPLAUSE You are a witch. It's the scene. We've also asked our audience a question And obviously we have... You are a witch. You are a witch. It's the tea. It's the tea. Got there first.

We've also asked our audience a question, and the question is, who do you think is the luckiest person in the world and why? Brian? Well, this says Robin Ince forgetting to work with Professor Brian Cox. No, it doesn't. Do you know what? I actually predicted, I knew that was going to happen.

Oh, imagine what it's like to sit next to Brian Cox. Yeah, imagine what it's like to sit next to something made out of coat hangers with a wig that's just pointing at a thing. Doesn't it? Anyway, so... I got one of those as well, Brian Cox, because he gets to work with Robin, but they're all in the same handwriting. Yeah, I don't know why you do it, Brian, but it's very sweet of you.

Isn't that your handwriting? Yeah, Robin. OK. Myself, as in my wife's D-ream, it didn't get better. OK, this is me, because you are about to read... So this is me. You are about to read my name out and pronounce it correctly. Oh, no, why did we give that one to him?

This is OK. Meryl Goulbourne. Is that correct? Meryl? Close enough. Which is a lovely way of saying no. How should I have said it? Meryl Goulbourne.

OK. The last person to get into this show, Brian Cox, because he gets to sit next to robin intz uh lucky lucky brian cox sitting next to robin intz uh i always think brian cox must feel so happy to always be working with robin intz thank you to our panel david spiegel dalter sophie duker and Marcus de Sautoy. Next week, we'll discover if Robin and I are likely to be replaced in the foreseeable future by an artificial intelligence. You see, I think it's going to be very easy to replace Brian

because he's reasonably linear, and as long as they just put in some scientific information, whereas I think my overly lengthy, frequently incomprehensible questions will be far harder for artificial intelligence to regenerate. So you've made a fool of yourself by merely being a man of simple and deep understanding. And I am chaos.

Yeah. Hear me roar. I am chaos. Goodbye. Goodbye. APPLAUSE In the infinite monkey cage The naughty monkeys In the infinite monkey cage

Without your trousers In the infinite monkey cage Turned out nice again. What do you see when you look at the numbers on a graph? Imagine if they could help you reveal the guilt of a serial killer. It's the most chilling graph I've ever seen. Or prove that global climate change is not a hoax. It was such a visceral indicator of the profound impact that we were having on the planet.

I'm Hannah Fry, and in this series for BBC Radio 4, Uncharted will reveal how the humble graph has changed your life. I will be your guide through a collection of extraordinary discoveries which shifted the world with a single line on a page. From BBC Radio 4, this is Uncharted. Subscribe on BBC Sounds. phones.