I think one of the big complaints that you get from school kids is like, well, I'm never going to use this stuff, what's the point of it?
It doesn't apply anywhere.
And I think really showing just how dramatically important maths is to virtually every aspect of our modern world, I think that that's something that can really make the subject come alive.
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Today I'm talking with the incredible Hannah Fry, a mathematician, author of Hello World and the Mathematics of Love.
We talk math, how schools can promote better engagement, human behavior, how math can help you date, and we explore what it means to be human in the age of algorithms.
It's time to listen and learn.
Hannah, I'm so happy to have you on the show.
Oh, well I'm very excited that you invited me.
Thanks for having me on, Shane.
What got you interested in maths?
Oh, I like how you said math there for starters.
Thank you for for Anglicizing it.
Appreciate that. I think partly I was born that way.
So okay, actually what happened was when I was about 11 years old, my mum, I think she just didn't know what to do with us over one summer holiday.
So she she bought me this maths textbook and she made me sit down every day and do a page of this textbook before I was allowed to go out to the garden to play.
And then when I went back to school, that's September after after the summer, I was just so much better at the subject, I just understood everything.
I'd seen everything before and I was just really well practiced at it.
And I think that it's inevitable that if you're good at something, you just find it all the more enjoyable and the more enjoyable you find something for less like it feels like hard work.
So I think that's it really.
I think that's just that was sort of before then, I mean, I didn't dislike it at all, but I wouldn't have said it was my thing.
But I think that that was really a stark change.
Like after that, then it became my thing.
And then, you know, the more and more I got into it, the more and more it became part almost of my identity.
I mean, math is such a tricky subject for students.
I mean, they seem to have this very love hate relationship with it, with most people hating it.
What are some of the things that schools could do to promote better engagement with students over maths?
So it's a different concept.
So if you're going to be able to reach the most beautiful elements of the subject, if you're ever really going to be able to properly to put it to use, you can't have your working memory being swamped by remembering all of these rules and remembering these really fundamental basics of the subject.
So it's slightly unfortunate that that inevitably means that when you're starting out, when you're in the early stages, it has to be dominated by essentially learning the subject.
It's not particularly inspiring or, you know, if it's taught in a very straight fashion, it's not particularly inspiring.
So in terms of what schools can do, I mean, I think for me, I've really seen a difference when teachers really put in the effort to demonstrate just how useful this stuff is.
I think one of the big complaints that you get from school kids is like, well, I'm never going to use this stuff.
What's the point of it?
It doesn't apply anywhere.
And I think really showing just how dramatically important maths is to virtually every aspect of our modern world.
I think that that's something that can really make the subject come alive.
Do we see that sort of manifesting itself now with kids' attitudes?
Because they're surrounded by algorithms and machines, and does that change how they perceive math?
Well, yeah, but I think that unfortunately, the math is invisible, right?
Because I mean, for this stuff to work, for a mobile phone to work, it has to be all of the amount of maths involved in getting your mobile phone, or, you know, me speaking to you now, however many thousand miles apart we are, the amount of maths involved is like phenomenal.
I mean, it's easily PhD level stuff.
But for this to work effectively, it has to be invisible.
It has to be hidden completely behind the scenes.
You as the user can't really be aware that any of it is there.
So even though, as you say, with algorithms dominating more and more of the way that we're communicating with each other, how we're accessing information, what we're watching, who we're dating, everything, even so, I think the maths is so behind the scenes that I don't think it's necessarily clear that it's
driving so much of a change.
As you were saying that, I was sort of thinking of a Formula One car.
The driver gets all the attention, but there's this big, huge team of engineering behind them that we don't know their names.
We don't know who they are or what they do.
That's a perfect analogy.
It's a perfect analogy.
I always think so a big fan, actually, of Formula One, and the reason why I like it, if I'm honest with you, is because I think of it as a giant maths competition, just with, you know, a bit of glamour on top.
I have this idea where they should do a driverless version of the cars too, because you have this closed track, right?
So it actually, then the engineers are competing.
There's no human element.
Then you could celebrate the engineers.
I think by celebrating the engineering and the people behind the scenes, you get kids more interested in that work.
Oh, see, I don't know if I agree with you, actually.
Oh, pushback. Yeah, pushback.
I'm sorry. So early on.
Okay, so partly there are examples of that already.
There's a, I think it's called Robo Race, which is the fastest autonomous vehicles in the world.
There's different teams build the cars and it's like Robot Wars, right?
But on a track. And it's all very fun.
It's all very interesting.
But for me, I think that part of the problem with why maths communication is difficult is that really we care a lot about stories and we care a lot about stories of people.
And I think that in many ways, the thing that makes Formula One or other racing so fascinating to watch is because you have it sitting in that gigantic engineered machine with so much science and technology going into it.
You have a person who cares so much about what happens in that race.
You live the whole emotional roller coaster with them as the series progresses.
And I think if you take that out of the situation, then actually I think it dehumanizes it and makes it less interesting in a way.
That's really interesting.
So how do we make a better story around maths then?
So I think it's that for me, it's humanizing it.
I think that really is it for me.
I think one of the, certainly in Britain, I think in the States too, there's this massive book called Fermat's Last Theorem, massive as in in terms of its sales rather than physically big.
It was written by Simon Singh and I read it when I was maybe 16 years old.
And one of the things that really I guess solidified the idea that I wanted to be a mathematician.
And in it, it's just a long story of hardcore maths throughout the centuries.
But what he did was he anchored all of the stories to the people that were involved.
And it's exactly like your race car driver.
Like you care so much about the characters who are involved in this history of math.
The stories of someone like Galois is a great example of a character that Simon Singh tells the story of in the book.
So he was French. He was about 19 years old, I think someone I'm sure will know the facts better than me and I'm sure he'll contact me and correct me.
But he was about 19 or 20.
And he'd been having an affair with a very important person in French society, a woman who was older than he was, and her husband had found out about this affair, and had challenged him to a duel.
Now, of course, in France, this is like I'm going to guess 1700s, 1800s in France at that time, someone challenges challenges you to a duel, you do not back out, you go to the duel.
Except unfortunately, Galois had been working on this incredibly important theory of mathematics now known as Galois theory, and hadn't quite finished the math.
And so he knew that at sunset, he had to go off and fight this duel and probably be killed.
And he was desperate all the way into the night, drinking and cowering over his quill and his paper, desperately trying to write down as much math as he could.
And the papers that he left, they were left on his desk as he went off to his duel.
They're just incredible, like you can see photos of them, or see images of them, they still exist.
And it's loads and loads of equations, loads and loads of scribbling.
And then every now and then he's like, oh my goodness, what's happening?
This lady, why did I do this?
I'm off to my death.
And he's desperately trying to finish everything.
And I think for me, that's what makes the maths come to light.
Because when you realize how important this stuff is to people that they know that they're going to their death and still the only thing they want to do is finish them off.
I think that's the stuff that makes it come alive.
That's a great story.
I hadn't heard that one before.
It is, isn't it? Yeah, it sort of pulls you in.
What does it mean to you to be human in an age of algorithms and machines?
Wow. Goodness. I mean, I could and have write an entire book on subjects.
So I think that actually that whole idea of humanizing maths, I think it sort of works both ways, actually.
I think that you need to humanize maths to make people want to find out more about it.
But I also think that the maths itself needs to be humanized if it's to properly fit in with our society.
Because I think this is something that's happened a lot, actually, in the last decade, certainly.
I think that people have got very, very excited about data and about what data can tell us about ourselves.
And I think that people have sort of rushed ahead and maybe not always thought very carefully about what happens when you build an algorithm or when you build something based on data and just expect humans to fit in around it.
And I think that that actually has had quite catastrophic consequences.
So the most sort of famous examples of this, there's Kathy O 'Neill's book, Weapons of Maths Destruction, which I think honed in on one aspect of this really brilliantly, which is the bias that comes out when you don't think very carefully about taking this algorithm and planting it in the middle of society
and expecting everyone to just fit in around it.
The sort of gender bias that we've seen, the racial bias, all of that stuff, I think that's very well documented and quite well known and understood about.
But I think there are slightly more subtle things as well.
So the example that makes this a really personal story for me is this, and the reason I guess why I started thinking about this very clearly, or very seriously, and the reason why I wrote a book about it, is because of something that happened to me where I think I made that same mistake, where I got
so tunnel vision about the maths that I didn't think about what it meant when you put it in the human world.
So this is back in, as soon as I finished my PhD back in 2011, the first project really that I did was a collaboration with the Metropolitan Police in London.
So we just had in 2011, we had these terrible riots across the country that started off as protests against police brutality, but they evolved into something else.
There's a lot of looting, there was a lot of social unrest really.
The police had been, I think, slightly stunned by how quickly this had taken hold.
I mean, for four days really the city was on lockdown, London certainly was on lockdown.
So we've been working in collaboration with the police just to see if there had been anything they could have done earlier, just to calm things down, I guess, to just see if there were signatures or patterns in the data that would have given them a better grasp on how things were about to spread.
So okay, we wrote up this paper and the academic community were really happy with it, whatever.
And a couple of years later, I went off to this big conference in Berlin and gave a talk.
I had, there was like 1500 people there at this talk, and I was standing on stage giving a talk about this paper, and I think that, I think it was a bit naive really, I think it was a bit foolish at the time because when you're a mathematician, there's no Hippocratic oath for mathematicians, right?
You don't have to worry about the ethics of, I don't know, fluid particles when you're running equations on them.
And so I was standing on stage and I was presenting this paper and I was giving this very enthusiastic presentation.
I was essentially saying how great it was that now with data and algorithms, we were in a world where we could help the police to control an entire city's worth of people.
That was essentially what I'm saying.
And it just hadn't occurred to me that, you know, if there is one city in the entire world where people are probably not going to be that keen on that idea, it's going to be Berlin.
So I just like totally, yeah, I just didn't think it through.
Anyway, so as a result, the Q &A of this session, I mean, they destroyed me.
I quite rightly say they destroyed me.
They didn't destroy the map.
They just destroyed.
They did destroy the map, they just destroyed, yeah.
It was like heckling and everything, it was amazing.
It was amazing. I think for me, that was just this really, really important moment because I think I hadn't, it just hadn't quite twigged with me.
It sounds, I know that it makes me sound really naive, but it hadn't quite twigged in my mind that you can't just build an algorithm, put it on a shelf and decide whether you think it's good or bad, completely in isolation.
You have to think about how that algorithm actually integrates with the world that you're embedding in.
And I think that that's a mistake that sounds like it's really obvious, but actually I've seen lots and lots of people make that mistake repeatedly over the last few years and continue to make it.
Can you give me examples of what comes to mind when you say that?
Just as a silly example, a kind of more trivial example, I think that the way that some sat -navs used to be designed, this is less true now, but certainly the way that some sat -navs used to be designed was that you would just type it in and it would tell you your destination and off you went, right,
tell you where you were going and off you went.
And you could, if you wanted to, go in and interrogate the interface and find out exactly where the thing was sending you.
But most of all, you'd put in the address and it would just tell you where to go.
And that is an example, I think, of not thinking clearly about the interface between the human and the machine, because there are all sorts of stories of how people just blindly following their sat -nav.
So my favorite example is there's a group of Japanese tourists in Brisbane, and this is a few years ago, who wanted to go visit this very popular tourist destination on an island off the coast of Brisbane, got a sat -nav, put it in, didn't look at the map, off they went, didn't realize the sat -nav was essentially
telling them to drive out into the ocean.
Amazingly, amazingly with the story, you think, okay, fine, right, you get to the side, to the ocean and you're like, well, no, it's obviously asking me to drive into the ocean, I'm not going to.
They didn't have that moment, they carried on driving, they really trusted the machine and thought, oh, well, it'll bring us to a path eventually.
Eventually, they had to abandon their vehicle, I think, like 300 meters out into the ocean, this is amazing.
It's like half an hour later as the tide came in, a ferry sailed past their abandoned path.
That's crazy. It sort of calls to mind though, what role do algorithms play then in abdicating thinking and authority?
Well, that's it. That's it.
I think the shift in design that we've seen recently, and this is only very recently, is where you type in the Google Maps in ways certainly, and perhaps others, is that you type in the address and then up pops a map which gives you three options.
It's not saying, I've made the decision for you, off you go.
It's saying, here is the calculations I've made, now it's down to you, but it's giving you just that last step where you can overrule it, where you can kind of sanity check it if you like.
I mean, maybe I'm giving them a bit too much credit, they did drive out into the ocean, but I sort of think that these theorists had seen a map for showing that they were getting into the ocean, maybe they would have done it.
How does that work as algorithms become more and more?
Is that the goal then?
I'm thinking about the integration between algorithms and medicine, where you're scanning.
Is it always a human overruling?
Are there edge cases?
Is there a certain, how do you think about that?
Yeah, so that I think is an incredibly, incredibly tough example.
Okay, the first algorithms that came through, the machine earning algorithms that were designed to just tell you whether there was cancerous cells within an image or not, right?
Yes or no. That's all very well, that's good.
They proved themselves that they were good, that they could perform well in that.
They're problematic.
There were examples where they'd go into a hospital, they've been performing incredibly well on a certain set of images, and then suddenly they're performing incredibly badly.
These algorithms are so sensitive that they were picking up on things like the type of scanner that was used, was making a difference to the decision process of the algorithm.
Or actually, the best example of that is there was a skin cancer diagnosis algorithm that was picking up on lesions on people's skin.
Photographs taken by dermatologists was the training set.
It turned out that the algorithm wasn't really looking at the lesion itself at all.
It was deciding whether or not it was cancerous based on whether there was a ruler photographed next to it or not.
This stuff makes stupid mistakes.
I think that was phase one of these algorithms within medicine.
I think phase two is about making them much more able to be interrogated.
For instance, a deep mind who I spent a long time working with on public outreach projects, one of their big systems is, rather than just having an algorithm that tells you what the answer is, is having two separate AIs, two separate agents.
One of them that highlights areas of interest within the image itself.
The second algorithm that goes in and labels them, but it's just opening out the box a little bit more so that it's possible for a pathologist or a radiologist to interrogate that image.
I think that's stage two.
That's the difference between old type of sat -navs and new type of sat -navs.
I think that there's a stage three in medicine that we're only just beginning to go into, which is I think an even harder one of all.
Most cancerous cells in people's bodies actually are nothing to worry about, which sounds like a mad idea.
There was a study a few years ago, you have to forgive me slightly because I don't have all the numbers on the tip of my tongue, but there was a study a few years ago where a group of scientists performed autopsies on people who had died from a whole host of different causes.
Everything from heart attacks, car crashes, all these different kinds of things.
They looked deliberately to see whether they had cancerous cells in the body.
Even though none of these patients had died from cancer, a huge percentage of them had cancerous cells within their body.
The reason for this, it's not that they all had really serious cancer that needed to be detected and treated, it's that actually this happens a lot.
It's not if you have breast cancer for example, it's not a case of you don't have cancer or you do have cancer.
There's a whole spectrum in between that and in between totally fine and really, really nasty cancerous cells.
There are tumors that may turn out to be something bad and may just make the body made to deal with them, or they may just stay there untouched well into, for essentially all of your life and be nothing to worry about.
The real danger of relying too much on algorithms to detect those cancerous cells is that if you are too good at detecting them, you're not just good at detecting the ones that then go on to be a problem, you're also going to be good at detecting the ones that are nothing to worry about.
Hence, potentially causing huge numbers of people to have very serious and very invasive techniques like double mastectomies for instance, life -changing treatments that actually they never needed to have.
That I think is something that's another thing about that boundary between how much do we trust our machines that I think is not resolved yet and a tricky one for the next few years I think.
That's fascinating.
I hadn't really thought of it in that way before, but I like the way you put it.
I think one of the interesting things going into the future is also going to be on if algorithms are involved in the decision.
Is there an obligation to make them open source and then that would be stage one where you can critique and see the actual algorithm working but stage two would be maybe it's a machine learning algorithm and then each iteration that it runs is actually slightly different.
Do we have to keep a copy of each algorithm and would we be able to detect how it actually worked?
I know. It's so hard because I think it's very easy to say there are definitely problems with algorithms that are not open source.
It's very easy to say there are huge problems with transparency but finding the way around it, finding the solutions is a lot harder.
I mean because I think I sort of am of the opinion that open source algorithms, at least the ones that are proprietary, at least the ones that have some sort of intellectual property attached to them, I think that that is both too much and too little.
So what I mean by that is I think it's too little because if you publish the code, if you publish the source code of something, the level of technical knowledge and time actually that it would take to interrogate that as an outsider enough that you have a really good understanding of how it works enough
to be able to say, okay, you know what, just sort of sanity check it if you like.
It's just fast and I just don't think it's realistic that actually you can ask the community at large really to be able to take on that load.
But then simultaneously I think it's by doing so, by releasing and making everything open source, then I think that you are going to stifle innovation.
Because I think that part of the really good thing and part of the reason why we've seen such acceleration of these ideas is because it's possible to make them commercially viable.
And I think that if you publish things as open source, then there's a problem with that that you risk slowing down innovation I think, which I don't think you'd want to do either.
The workaround though, okay, so what do you do instead?
Because I think that everybody sort of agrees that transparency is really important here.
I think particularly when it comes to the more scientific end of algorithms.
I mean I think to be totally blunt, I think that unless you're doing science openly, you're not doing science.
But yeah, so some of the suggestions have been, and I think this is one that I broadly support, some of the suggestions have been to copy the pharmaceutical industries model.
So where you have a separate board like the FDA who have the ability to really interrogate these algorithms properly, and can give a sort of rubber stamp of approval as to whether they are appropriate to be used or not.
But that's different from just open source because I mean, a sort of FDA style thing would be able to go in and stress test them and test them for robustness and check them for bias and all of those type of things instead.
But I mean, there's no easy, there's no silver bullets to sort of, yeah, addressing some of the many problems that algorithms raise.
Do you think like we would rather on general, like when do we want algorithms making decisions and when do we want humans making those decisions?
Well, so there's certainly some occasions where actually the further away humans are from us, the better.
Humans are not very good at making decisions at all.
We're not very good at being consistent.
We're not very good at being clear, you know, with nuclear power stations, for instance, as much as possible, you want to leave that to the algorithms, you want to leave that to the machines.
Likewise, in flying airplanes, I think you want to leave that to autopilot as much as you possibly can.
In fact, actually, there's that really nice joke to fly a plane, you need three things, a computer, a pilot, a human and a dog.
And the computer is there to fly the plane.
The human is there to feed the dog, and the dog is there to bite the human if ever it touches the computer.
There's definitely some situations where you want the humans as far away from it as possible.
But I also think that actually, these machines, especially the ones that are getting much more involved in more social decisions, they really are capable of making quite catastrophic mistakes.
And I think that if you take the human out of the decision, even if on average, you might have a slightly better, more consistent framework, if you take the human out of that decision process altogether, then I think that you risk real disasters.
We've certainly seen plenty of those in the judicial system, you know, where algorithms have made decisions, judges have followed it blindly, and it's been really the wrong thing.
Just to give you an example, there was a young man called Christopher Drew Brooks.
This is actually a few years ago, but he was 19 years old and from Virginia.
And he was arrested for the statutory rape of a 14 year old girl.
So they had been having a consensual relationship, but she was under age.
And so he was, which is his chance of going on to commit another crime in future.
These are the sort of very controversial, yeah, exactly algorithms that do so, but actually have been around for quite a long time.
And this algorithm, it went through all of his data.
And it determined that because he was a very young man, he was only 19 years old, and he was already committing sexual offenses, then he had a long life ahead of him.
And the chances of him committing another one in that long life were high.
So it said that he was high risk.
And it recommended that he'd be given 18 months jail time, which I mean, I think you can argue that one way or the other, depending on your view.
But I think what this case really does do is it highlights just how illogical these algorithms can sometimes be.
Because in that particular case, if instead, the young man had been, I think 36 years old, that would have been enough.
This algorithm had put so much weight on his age, that if he'd been 36, it would have been enough to tip the balance.
Even though that put him at 22 years older than the girl, which I think surely by any possible metric makes this crime much worse.
But that would have been enough just to tip the balance, and for the algorithm to believe that he was low risk and to recommend that he escaped jail entirely, which I think is just an extraordinary example of how wrong these decisions can go if you hand them over to the algorithm.
But I think for me, the scary thing about that story is that the judge was still in the loop, right?
The judge was still in the loop of that decision making process.
And I think that you would hope in that kind of situation that they would notice that the algorithm had made this terrible mistake, and step in and overrule it.
Well, turns out that you know, those Japanese tourists we were talking about earlier, I think that judges are a lot more like them than we might want them to be, because so in that case, and lots of other cases like it, actually, the judge just sort of blindly followed what the algorithm had to say
and increased the jail centers of this individual.
So I mean, you've got to be really careful, right?
You've got to be careful about putting too much faith in the algorithm.
But just on the flip side of that judge's example, I also don't agree with the people who say, well, let's get rid of these things altogether in the judicial system.
Because I think there is a reason for them being there, which is that humans are terrible decision makers, right?
Like, there's so much luck involved in the judicial system.
There's studies that show that if you take the same case to different judges, you get a different response.
But even if you take the same case to the same judge, and just on a different day, you get different responses, or judges who have daughters tend to be much stricter in cases that involve violence against women.
Or my favorite one actually, is that judges tend to be a lot stricter in towns where the local sports team has lost recently, which is kind of shows you what you're dealing with, right?
Like, there's just so much inconsistency and luck that's involved in the judicial system.
And I think if you do it right and carefully, I think there is a place for algorithms to support those decisions being made.
Do you think in a way, we get to advocate ourselves from responsibility if we defer to an algorithm?
So if you're a judge and you defer to an algorithm, it's not like you're going to be fired for deferring to the algorithm that everybody agreed was supposed to input or make the decision.
Exactly that, especially if people vote you in.
And here's a way that you can absorb yourself from responsibility.
I completely agree.
I think all of us do it.
And that's the problem is that this is a really, really easy thing to happen.
It's very easy for us to just, I don't know, take a cognitive shortcut and do what the machine tells us to do, which is why you have to be so careful about thinking about this interface, thinking about the kind of mistakes that people are going to make and how you mitigate against them by designing
stuff to prevent that from happening.
Can you talk to me a little bit about what we can learn about making better decisions from mass?
I'm going to do a pertinent example because I think the example of what's going on right now with the pandemic is a tragic and chilling example of how important mass can be when it comes to making clear decisions.
Because I think that this is just one situation where in many ways, mass is really the biggest weapon that we have on our side.
We don't have pharmaceutical interventions yet.
We don't have people listening to 2020.
Yeah, exactly. So we're still at the stage where things are ramping up.
Who knows how bad it's going to get from here, but certainly in the last month, they're the first ones really, the epidemiologists and the mathematical modellers are the ones who've been raising the alarm and driving the decision making and driving the strategy and driving government policies.
Because at the moment, if you looked only at the numbers of where we are, I think there's been maybe 150 deaths or so in the UK.
I haven't got the exact numbers to my fingertips, but something of that order, around 100 deaths in the UK, which is every single one of those is a real tragedy, but it's not a huge, huge, huge number.
But the reason why we know that that's a bad, why we're in a bad situation, and the reason why we know we need to take these extreme measures to essentially shut down our borders, to shut down our country, is because the maths is telling us what is coming next.
We don't have a crystal ball to look into the future, but really, maths is the only thing that's there guiding us.
It's really fascinating to me.
Can you talk to me a little bit more about the pandemic and how you think about it through the lens of math?
Yeah, totally. So I actually, in 2018, I did a big project with BBC, because we knew that a pandemic was coming.
So we teamed up with some epidemiologists from the London School of Hygiene and Tropical Medicine and the University of Cambridge to collect the best possible data so that we could be prepared for when something like this did happen.
The big problem at that point, so this is a couple of years ago.
The big problem was that if you want to know how an epidemic or flu -like virus will spread through a population, then you need to have really good data on how far people travel and how often people come into contact with one another, and crucially, who they come into contact with, the different age
groups, the settings they come into contact with other people and so on.
Up until a couple of years ago, it sounds mad to say it, given that everyone's carrying mobile phones, but up until a couple of years ago, the best possible data that we had, within the UK at least, for how people did that, how people moved and how people mixed with one another, was a paper survey from 2006
where a thousand people said, oh yeah, I reckon I did this, I reckon I went about that before, I reckon I came into contact with these people.
So what we did with this, with the help of the BBC, because you know they have such amazing reach, is we created this mobile app that would essentially track people, people would volunteer and sign up by watching the programme and so on, and let us track them around for 24 hours and track who they came
into contact with and also get loads of things about their demographics and their age and so on and so on.
Now, two years later, or less than two years later, we have this, you know, incredibly detailed data set that's feeding right into the models that our government are using, making this enormous difference in terms of the accuracy of how well we can predict things, and I just think it's like, it's just
the most pertinent and chilling example I've ever been part of, which just demonstrates how important the maths is.
If you're going to try and win a war with nature, essentially.
It seemed to me, I mean there was two different types of people, just to broadly generalise going into this pandemic, there was people who understood non -linear and exponential functions and people who maybe had a harder time with that and the people who did seem to understand or grasp those concepts
better, seemed to take it a lot more seriously than the people that didn't, and I would love to find a way to help people think better in terms of exponentiality.
Yeah, of course. Part of the problem is that the word exponential just gets thrown around.
Like, you know, people say, this project's exponentially more difficult or, you know, exponentially more dangerous.
And it's like, well, no, it's not.
It's not what the word means.
And it is really counterintuitive because the thing about exponential growth, it doesn't just mean big.
It doesn't just mean lots.
It means something very specific.
It means that it's where something is changing by a fixed fraction in a fixed period.
So this virus, for instance, is doubling every five days.
So doubling fixed fraction every five days is a fixed period.
And I think that it's just, yeah, I mean, it's just not something that's counterintuitive at all.
Like, there's the really classic example of the rice on the chessboard.
So this is this idea.
It's like a classic story about an Indian king who was really impressed with the chessboards when it was when it was shown to him.
And so he said, OK, I'll tell you what, I will I'll give you a grain of rice for the first square and then we'll double the grains of rice every subsequent square.
Right. Which sounds like, oh, that's not very much at the beginning.
And it's like one grain and two grains and then four grains like, OK, you know, this is not going to cost me very much.
The thing is, is that by the end of the the end of the chessboard, you need like a lot of rice.
Essentially, you need 18 quintillion grains of rice, which is essentially I work this out.
If you take Liverpool, the area of Liverpool, which I know for American listeners isn't easy to imagine, but it's essentially like a whole city.
It's that an area that size stacks three kilometers high with rice.
That's how much rice it is.
So I mean, exponential growth is just beyond imagining.
It's just completely counterintuitive.
One of the stories I loved about in your book Switching Gears a Little Here to Hello World, you had the story of Kasparov and playing Deep Blue.
And everybody's told that story, but you had a unique angle to it that I hadn't heard anywhere else, which is that the machine was also playing with Kasparov.
Yeah. So this goes exactly back to what I was saying earlier about it's not just about building a machine.
It's about thinking about how that machine fits in with humans and fits in with human weaknesses.
Because the thing is, is that Kasparov, I mean, he's an incredible player.
So I had a chat when I was researching my book, I spoke to lots of different chess grandmasters.
And one of them described him like a tornado.
So when he would walk into the room, he would essentially pin people to the sides of the room.
They would kind of clear a path for him because he was just so respected.
And what he used to do had this trick, if he was playing you, he would take off his watch.
And he would place it down on the table next to him, and then carry on playing.
And then when he decided that he just had enough toying with you, he would pick up his watch, and he would put it back on as if to say, that's time now I'm done.
I'm like, I'm not playing you anymore.
And essentially, everyone in the room knew that was your cue to resign the game, which is just like so intimidating, and just really like terrifying.
The thing is, is that those tricks that Kasparov has, I mean, they're not going to work on a machine, right?
You've got the IBM guy sitting in the seat.
But I mean, he's not he's not the one making the moves.
He's not the one playing.
So you know, it's not going to affect him at all.
So none of that stuff worked into Kasparov's favor.
And yet, the other way around, the IBM machine could still use tricks on him.
So there's a few reports, the IBM team deliberately coded their machine so that the way that it works, right, would sort of search for solutions.
And depending on how long that search would take, it would be how quickly the answer came back, but they deliberately coded it so that sometimes, in certain positions, the machine might find the answer very quickly.
But rather than just come back with the response, they added in a random amount of time where it looked like the machine was just ticking over thinking very carefully about about what the move was, when in reality, it was just sitting there in a sort of holding pattern.
And Kasparov himself, so in his latest book, and in several interviews, had said that he you know, was sitting there, and was trying to second guess what the machine was doing at all times.
So he was trying to work out why this machine was stuck grunting through very difficult calculations, and essentially got psyched out by the machine.
Because I think all of the chess grandmasters are pretty much uniformly in agreement that at that moment in time, when the machine beat Kasparov, Kasparov was still the better player.
But it was the fact that he was a human, it was the fact that he had those human failings that meant that he was outsmarted by the machine.
That's such an amazing and incredible story.
Thanks for sharing that your first book, The Mathematics of Love, explained the math, underlying human relationships.
How can applying math math's concepts to romantic situations be helpful to people?
Well, so this was, this is a, it was sort of a kind of private joke that got terribly out of that book, where I, you know, when I was sort of, you know, in the dating game, or like, you know, designing my table plan for my wedding, or like any of those things, I mean, I just like generally apply math
to everything. And we're just trying to calculate as much as possible, I'm trying to like game it as much as possible.
And so in the end, I like wrote these up into a book and it's all very tongue in cheek.
But the thing is, is that while I totally believe that you cannot write down an equation for real romance, you can't write down an equation for that sort of, that spark of delight that you get when you meet someone who you know you really like them.
There's kind of, there's no real math in that.
But there's still loads of maths in lots of aspects of your love life, right?
So there's maths in, you know, how many people you date before you decide to settle down.
Watch, there's maths in the data of what photographs work well on online dating, or, you know, apps or websites.
There's loads of maths in designing your table plan for your wedding to make sure that people that don't like each other don't have to sit together instantly.
My code's available if anyone wants it.
And there's, there's even actually my favorite, favorite one is there's even maths in the way that arguments between couples in long term relationships, the dynamics of those arguments.
So there's lots of little places that you can, you can find a place to kind of latch on and use the maths.
How many people should we date before we settle down?
This is the one that got me the most in trouble.
So okay, so here's the problem, right?
Is that what you don't want to do, I guess, in an ideal world is you don't want to just decide to latch onto and settle down with the very, very first person who shows you any interest at all, because actually, they might not be that well suited to you.
And if you hold out a little bit longer, maybe you'll find someone who's better suited to you.
But equally, you don't want to wait for ever and ever and ever and ever, because you may end up missing the person who was right for you, turning them down because you think someone betters around the corner and then finding out that actually they were always the right person.
So what you could do is you can you can set this up as though it's like a mathematical problem.
So you've got a number of opportunities lined up in a row, sort of chronologically lined up.
And your task is you want to stop at the perfect time, you want to stop at the moment that you're with your perfect partner.
So it's good, it's essentially a problem in optimal stopping theory, it's called.
So the rules are that once you reject someone, you can't go back and say, actually, I wanted you out at all, because you know, people don't tend to like that.
And the other rule is that once you decide that you've settled down, you can't look ahead to see who you could have had, you know, going on later in life.
So if you frame it like that with those assumptions, then it turns out that the mathematically best strategy is if you spend the first 37 % of your dating life just having a nice time and playing the field, so it's one over E, right?
So there's 7%, yeah, spend the first 7 % of your life just playing field, having a nice time, getting to know people, but not taking anything too seriously.
And then after that period has passed, you then settle down with the next person who comes along that is better than everyone you've seen before.
So yeah, that's what the math says.
But I should tell you, right?
I should tell you that there's quite a lot of risks involved in this.
Is that what you tell your husband?
You're the best after the 37 %?
Yeah, yeah, yeah, marginally better.
Yeah, that's exactly right.
How can we use, I don't want to say argue better, but I'll use your language.
Like, how can we use math to argue better in our relationship?
Oh, this is my favorite, favorite one.
So this is some work that was done by the psychologist, John Gottman.
He's done some amazing work with couples and long -term relationships.
And he's worked out a way that he, what he essentially does is he gets couples in a room together, and he videotapes them.
And he gets them to effectively to have an argument with one another, right?
So officially they say that it's, they asked them to have a conversation about the most contentious issue in their relationship.
But basically, they lock up a couple in a room and make them have an argument.
But what they've done is they've worked out a way to score everything that happens during that conversation.
So every time that someone's positive, they get a positive score.
Every time someone sort of laughs and, you know, gives way to the partner and, you know, but even gestures, right?
So if you roll your eyes, you get negative score.
If you stonewall your partner, you get negative score, that kind of thing.
Anyway, the thing that's kind of neat about this is that it then means that you can look at a graph of how an argument evolves over time.
So the really nice thing about this is that John Gottman then teamed up with a mathematician called James Murray, who came up with a set of equations for how these arguments ebb and flow, the dynamics of these equations, essentially.
And hidden inside those equations, there's something called the negativity threshold.
So essentially, this is how annoying someone has to be for they provoke an extreme response in their partner, right?
So my guess would have been, I mean, they've got the data on, you know, hundreds, if not thousands of couples here.
My guess always would have been, all right, negativity threshold, surely the people who've got the best chance at long term success, the people who end up staying together, surely those are going to be the ones where they've got a really high negativity threshold.
That would have always been my guess.
You know, like the couples where you're leaving room for the other person to be themselves, you're not sort of picking on anything on every single little thing and you're compromising, that would have been my guess.
Turns out, though, when you actually look in the data, the exact opposite is true.
So the chances, the people who have the best chance at long term success are actually the people who've got really low negativity thresholds.
So these instead, they're the people where if something annoys them, they speak up about it really quickly, immediately, essentially, and address that situation right there and then.
But they do it in a way where the problem is dealt with.
And then then actually you go back to being, you know, go back to normality.
So this is the it's couples where you're continually repairing and resolving very, very tiny issues in your relationship.
Because otherwise, you risk bottling things up and then not saying anything and then one day coming home, being totally angry about a towel that's left on the floor or something.
And it just being totally at odds with what the incident itself is, you know, bottling things up and then exploding.
Yeah, I think that's really fascinating, right?
Because if you look at what it takes to bring things up in a relationship when they happen or pretty close to the time they happen, it means you have a lot of security and comfort and you know that bringing this hard thing up and it might make somebody angry or hurt them, but it's not going to be the end
of the relationship.
And then not letting it faster actually makes the relationship stronger long -term.
Exactly. Exactly. Now, of course, the language that you use is really important as well, right?
So you can't just be like, you know, you can't just launch it and be a nightmare about it.
But I think that's, I really love, I love those stories.
I love those stories where there's something about humans that is just written completely in the numbers.
I think that's really wonderful.
Hannah, this has been an amazing conversation.
I want to thank you for your time.
Thank you. Thank you very much.
Hey, one more thing before we say goodbye.
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