The Science of Coincidence

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Hello, I'm Robin Ins.

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 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 a many worlds' interpretation of quantum theory, that's Everettian.

Yeah.

You don't know.

Then, whilst an observer in 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 show, it's just I'm leaving.

This has definitely gone way above my pay grade.

In fact, when we were working out how to start the show, our producer said, if Brian starts by saying that, we will lose 97% of our audience.

Yeah, but I corrected it because I said it's 97% plus or minus the square root of the size of the audience, 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 and 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 Spiegeler.

I am the Emeritus Professor, blah, blah, blah, blah.

And my biggest coincidence has happened to me was when I was making a radio program 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.

said, My birthday is January the 27th.

So that's the one big coincidence that's happened to me because they never happened to me because I never talk to anybody and I never notice anything.

I'm Marcus de Sotoy.

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, actually did get dealt such a hand where everyone had 13 of one suit.

So what are the chances of that, David?

Not this.

It's all right, David.

We wait until the end for the correct question.

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 calves in exactly the way such that when they're dealt out, it's actually much more lightly than you'd expect.

So actually it probably wasn't a big coincidence after all.

Hello, I am Sophie Duca, 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 realised 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'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 that 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.

You know, 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, it 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.

Like, 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 your closest friends.

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 evens 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 of pairing people up means you only need 23 people in the room and there's more than evens.

Right, Marx, we're going to 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, yeah.

Is this going to be anecdotal evidence?

No, no, 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 you think, 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.

So that would be astrology, won't it?

Because that's because they've got the star sign to make them good football.

And Nigeria.

And Robin's got a point here because actually more football is...

He hasn't got a point.

Don't say that.

Nigeria has got two players both born on Christmas Day and they're called Glory and Christie.

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 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 you multiply together.

23 of them, as they decrease, actually get you below 50%.

And therefore, the chance is that two will have the same birthday or 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 that, you know, the front row of the audience here, there's 16 people.

If they looked at 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, or 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.

individuals they are very very common between other people but I was really impressed.

But this coincidence it sounds like a bit of fun with 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 a Manchester let's say there are two train companies running the trains and one month ten 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?

Okay, you've got some half an hour for the lecture on p-values, I hope.

Yeah, that's what statistics does.

You know, you look at, if it were just chance, how likely it is to get such an extreme difference between the companies.

Well, if one company's 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 are the events that you think, oh no, 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.

People say, oh, 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.

There is 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 analyzed 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 of course, 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 a day.

Well, again, it's that emotional reaction.

Of course, we notice the thing when it's weird, but not all the millions of other times when something unweird happened.

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 the third occasion of camels being on the line near Chesant, 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 a 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, or you've got a basic scepticism of people wanting a story, as 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.

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 is

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.

So,

the origin of the chance doesn't matter.

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.

Physicists can make zero difference to my life.

I can see why you didn't do that philosophy degree now.

But that is, I mean, what about you, you know, Because really what we're hearing there from David is that free will is an illusion, these things are just going to happen.

No, he said he doesn't care what the free will is and illusions.

Well, no, he's 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, I don't know what your view is, because to me, 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, physics, one interpretation of it is that that's about the only place where something is random is happening.

Pre-quantum physics, of course, you know, we talked about Laplace's demon, the fact that if you knew all the equations and 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, you know, 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 Pepys 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 is 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 counter-intuitive answer:

you're more likely to see a six in six dice than two sixes in twelve dice.

But it'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.

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 and such, 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 Bonte Hall problem, which appeared in The Curious Incident of The Dog in the Nighttime.

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 fix 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 Nighttime 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 parsy 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 who would like to who would like yeah I think the best way for me I also found this totally counterintuitive when I first met it I was like why are you doubling your chances is 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

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.

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.

And

I think we do.

And I think we do.

Yeah, no, we do.

More common-wise at times.

He always makes me sleep on the left.

I don't like it.

Anyway, so the Archdeacon is on the left 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, ball started, didn't manage to assassinate Archduke Ferdinand, just goes and sits like the another failed assassination attempt, goes to sit in a cafe.

Then Archduke Ferdinand's car happens to take a different turning to 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 it's David it was one of your definitions of chance I consider that luck because he was lucky.

I mean, not only the car actually stopped in front of the cafe, it didn't just drive past.

And there he was with this with still.

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With the pistol.

I mean, luck is a strange thing, and I don't believe in it as a force, but I really do believe in it as a good label for how things turn out.

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.

I regarded this as a 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.

You subdivided luck.

Yeah, yeah.

The philosophers have done this under the idea of moral luck.

And I found this really useful.

Basically, you know, 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, where the 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 Spiegelholter, 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 Passchendae, 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 the 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 result on 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, I wouldn't be here otherwise.

Yeah.

Of course.

Yeah.

And if we really want to get into philosophical stuff, what's the probability we exist?

Because the chance of us all existing is absolutely microscopic.

I've worked out, I was conceived in November 1952, and I've looked at the temperature records for North Devon at that time.

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 stone-walled cottage.

And I suppose there was nothing else to do.

And so here I am.

I think the fact that life formed at all on our planet is, you know, the likelihood of that, I think, has been analyzed.

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 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 Parson Coriander on, and we'll get it sorted, I think.

So, but I think, like, when I close my eyes and I imagine a million sheep,

sorry, I'm just

having a moment

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 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 one of your previous titles, one of your many titles, was Professor of the Public Understanding of Risk.

Can you give us some examples of where this misperception, which is 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 or have some handle on these large numbers.

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 can we tell, in a way, reliable stories about risks, about 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?

Everyone was making a fuss about artificial sweetener and diet coke.

And there, you know, no quantifiable risk whatsoever, and yet there will already be people 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, we'll say, well, 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 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 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.

So that that juggling between truth and you know the embroidered 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 well.

I genuinely believe that makes me a witch.

But that's like what we 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 teeth normally?

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 to say four times eight, but he wouldn't say.

Well, the answer is

a true mathematician on the street.

That number of order ones.

Just two more.

Okay.

Two more teeth.

Two more.

Two more teeth.

It's confusing.

Probably thug at the stake.

These are my favourite moments because Brian doesn't know how to react to kind of dental demand.

It's like dental revelations always throw does not compute 34 teeth.

I do not understand this thing called love.

I was just moving the discussion back onto the subject.

I won't 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's going to come up tails, isn't it?

Because I've tossed it like three heads.

And so, analysing 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 toss.

Well, it depends which question you ask, I think.

Well, yeah,

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've got one now, usually when I'm doing this at school, I have a two-headed coin just to fool people.

So the point is, your comment there, which is a gambler's fallacy, or a tail must be due.

All of that assumes the coin is perfectly balanced,

you're not being fiddled, and no one's playing with you and things like 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.

You know, like there's nothing in the past which means that unless that roulette wheel is actually bonused in some way, maybe they should never have been betting red and they should be in betting black each year.

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, hey, now how many times do you have to flip a coin in order to have more than a 50-50 chance of getting four in a row, four heads or four tails?

So I'm going to flip the coin until 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 were saying before.

My intuition is terrible on this stuff.

I have to do everything from scratch and do it three times and go and sit on the lab and concentrate and come back again.

And yeah, that might be the answer.

And 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 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.

But I prefer to refer to it.

That's why casinos are rich and weird.

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, it's showing a six, but you don't know what it is.

So for probability for you, it's 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, this one over six, the probability that we're assigning to it?

It's different according to a different perspective.

Yeah, if I flip a coin and cover it up, you know, what's your probability this is heads?

And what's your probability this is heads?

50-50.

50-50.

And you're wrong.

You lost.

So that's right.

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.

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, like, I can 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?

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 yet.

Yeah, well, I don't, I mean, like, for a lot of my life, I didn't really feel like I could die.

Like, 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, I was going to win some money, or something good was going to happen if it came up 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 is part of being human.

You know, people have had to live with this, you know, forever, the fact that they cannot predict or control so much of what's in their life.

I mean, 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 I'd like playing poker because I feel like I can bluff in poker, not because I could wish the the cards into my hand.

Yeah, I think there is a way, 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 realize that they're part of the whole scam.

Sorry, Marcus.

No, I think uh 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, you know, that's a game where you're just throwing dice.

But actually if you analyze the dice, the most likely throw of two dice is seven.

Six, seven, and eight are very likely.

Two and twelve 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.

That's incredible!

So, just to analyse that a bit, so the mid-dice range is because there are more ways of dice.

You get a 7 and a 1 and a 6, a 2 and a 5, a 3 and a 4, a 4 and a 3, 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

family at Christmas.

Yeah, exactly.

Yeah, yeah.

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 to the illusion, perhaps the illusion of not being a deterministic university.

I like it, right?

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.

But so I find it removes all responsibility from 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, so I like.

Which is the most dangerous

road.

It's probably the most dangerous way to go.

Or a motorbike, maybe.

I think, you know, it's impossible for individuals to be rational because what about the joy?

What about the people?

Most individuals.

What about fun and all those things?

Quite difficult to put numbers on.

But I would like my societies 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 there's a 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?

Surely not.

Oh, I know.

Yeah.

I know, I know, 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.

I predict, and you have to go with me on this, that sometime in the next 10 seconds, there will be an absolutely thunderous applause break from everyone in the room.

An absolutely thunderous applause break.

And obviously, we have a lot of people.

You are a witch.

You are a witch.

Oh my gosh.

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 is Robin Ins forgetting to work with Professor Brian Cox.

No, he 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.

Anyway, so

I've got one of those as well, Brian Cox, because he gets to work with Romania, but they're all in the same handwriting.

Yeah,

I've done a way to do it Brian, but it's supposed to be.

Isn't that your handwriting, yeah, Robin?

Okay.

Myself, as in my wife's D-Reem, it didn't get better.

Okay, 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 okay.

Meryl Goulborn.

Is that correct?

Merrill?

Close enough.

Which is a lovely way of saying no.

How should I have said it?

Merrill?

Goulborn.

The last person to get into this show, Brian Cox, because he gets to sit next to Robin Ince.

Lucky, lucky Brian Cox sitting next to Robin Ince.

I always think Brian Cox must feel so happy to always be working with Robin Ince.

Thank you to our panel, David Spiegel-Halter, Sophie Duka, and Marcus DeSotoi.

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.

Hear me roar.

Hi.

Chaos.

Goodbye.

In the infinite monkey cage.

In the infinite monkey cage.

What do you see when you look at the numbers on a graph?

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