Coincidences may seem like random occurrences to many of us – but not to a mathematician. Sarah Hart is professor of geometry at Gresham College and professor emerita of mathematics at Birkbeck, University of London. She joins host Krys Boyd to discuss why we so often look for coincidences in our lives — and why that’s a mathematically futile endeavor — why the blind luck behind lottery wins might not be so blind after all, and why revealing this magic with numbers makes the phenomenon all the more interesting. Her article, “The surprising maths that explains why coincidences are so common,” was published in New Scientist.
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Transcript
Krys Boyd [00:00:00] We like to believe everything happens for a reason. Maybe because it gives us a sense of control in a world that can feel chaotic and unpredictable. So when really weird things take place, we often can’t believe it’s just a coincidence. We say, What are the odds of, say, being in a room with just two dozen people and discovering two of them have the exact same birthday? As if determining those odds is impossible. From Kera in Dallas, this is Think. I’m Krys Boyd. Of course, it is not impossible to calculate those chances or the likelihood of a lot of other weird and fascinating co occurrences. And if you open your mind to it, the hard numbers that prove these things are not magical and take nothing away from how cool and interesting they are. Sarah Hart is professor emerita of Geometry at Gresham College and professor emerita of mathematics at Birkbeck University of London. She’s author of the book “Once Upon a Prime” and of the New Scientist article “The surprising maths that explains why coincidences are so common.” Sarah, welcome to Think.
Sarah Hart [00:01:03] Thank you so much. Thank you for having me.
Krys Boyd [00:01:05] I know your article is actually maths, but I have such a hard time with that word that I just Americanized it and I hope you’ll excuse that. That’s fine. So you start your piece in The New Scientist with this weird experience you had. Will you share that with us?
Sarah Hart [00:01:19] Yes. So this was a little while ago I was visiting the beautiful English city of York with my daughter, and we stopped off at a cafe for a snack. And when I went up to order, I also asked, can I have the access to the bathroom to take my little girl? And they said, Yeah, sure. And then when I came to pay, I had to type in my PIN number, you know, to to pay. And just after that, the young lady at the counter handed me a piece of paper, and on it was my pin number. And this made me just be slightly anxious for a moment. Then I realized, no, this is a coincidence. The pin number happens to be the key code for the bathroom in this cafeteria. So after the look of slight shock on my face past, I started to think, Well, okay, it’s a coincidence. It startled me. But what are the odds of this happening? And then that led me to thinking more about coincidences in general, because actually, to have a four digit number randomly be the same as my pen, you know, it’s not some big conspiracy. There’s a small chance of that happening. The chance we can work out exactly, because it’s a four digit number. So the first digit is a 1 in 10 chance of that matching. And then there’s a 1 in 10 chance of the second digit matching and the same for the third and for the fourth. If you multiply all those 1 and 10s together, you got a 1 in 10,000 chance that my PIN number would exactly match the key code for the bathroom in this cafe.
Krys Boyd [00:02:48] The funny thing about this coincidence, Sarah, is what you can’t do is what I think most of us want to do is immediately say, That’s my PIN number. You have to keep that to yourself.
Sarah Hart [00:02:59] Exactly. Yeah, precisely that. So I had to sort of I wanted well, luckily I could go and tell my daughter that this thing had happened, but I obviously couldn’t say that to the barista. So I was able to vent my excitement at this brilliant coincidence to someone safe.
Krys Boyd [00:03:15] So momentarily, some part of you, a professional mathematician, you did find it a little jarring, right? Emotionally, if not rationally.
Sarah Hart [00:03:24] Yes, exactly. That was this shock of what? But I just put that number into this machine and what’s happening here. You know, this this slight the world is strange feeling that in this instance, of course, you know, it clearly must have been a coincidence. And very quickly my rational brain intervened. But in other kinds of examples, it’s really it can be really enjoyable to experience those coincidences. And we’re really tempted often to think something more is going on. Sometimes it is, sometimes it’s not. And that’s where mathematics can help us to tell the difference.
Krys Boyd [00:03:57] Well, you know, one thing that is so interesting is that, you know, it might sound like this show is all about debunking every coincidence, but sometimes important things happen because people notice patterns that stand out. Like, I talk a little bit about that.
Sarah Hart [00:04:12] Yes. So I think as human beings, one of the reasons that we have been so successful as a species is our ability to spot patterns and to work things out from them. So, you know, early, early peoples who were starting with agriculture, they spotted that, you know, the River Nile at the same time every year it will flood and that leads to very fertile soil. And then you start to be able to plan, you know, when to plant things and and how to make your crops grow better. So those kinds of observations, it’s not a coincidence that the river floods the same time each year, right? It’s there are various scientific causes for it. And spotting those patterns, whether at the time, you know, they thought, well, it’s, you know, a particular Egyptian god is doing this. Now, we may think the causes are different, but the fact of those patterns and that those are really do mean there’s something underneath this that we can rely on this pattern that helps us and you know, leading on from that thousands of years later when we start to really develop scientific method spotting things that look like they may be coincidences or they may not, and working out what’s happening underneath it and whether it really is a coincidence is really very important. And I’ll give you one example. And it’s to do with with preventing and curing diseases. So a few centuries ago, there was this terrible disease, smallpox, that was making people’s lives misery. Lots of people were dying from it and getting very sick. And there was a curious fact that a guy called Edward Jenner noticed that milkmaids and dairy farmers seemed to be much less susceptible to smallpox. Now, that’s seems a weird it’s a strange coincidence that all these people that he knew in this kind of area of agricultural work were not really getting smallpox. And instead of just saying, That’s a weird coincidence, what are the odds? He investigated it and he discovered that people who had had a similar disease called cowpox, which you can catch if you’re in close contact with with cows as milkmaids, of course, would have been. That disease gives you partial immunity to smallpox. And it was that discovery in investigating this. Is it a coincidence or not, which led to the very first vaccine, and that was for smallpox. And of course, now with modern science, we’ve we’ve completely eradicated smallpox. So that’s, you know, a huge, huge thing coming from looking at whether something is a coincidence or not.
Krys Boyd [00:06:46] This paradox is so fascinating to me. We have to somehow find the balance between exploring whether things that happen in connection with one another really do have some significance and also letting go of coincidences that really are just accidental.
Sarah Hart [00:07:02] That’s right. I mean, and there are some examples, say, in astronomy where there are coincidences that if you’re not careful, you can be really kind of led into a path of maybe superstition or thinking there’s more going on than there really is. So one example is my favorite coincidence, in fact, in all of astronomy is the reason that we have these fabulous solar eclipses every few years. A total eclipse of the sun. Now, that is only possible because when when an eclipse happens, eclipse at the sun, it’s when the moon gets between the sun and the earth and just exactly fits over the sun. Right? And so blocks out the sun almost completely apart from this beautiful corona that can appear just at the edges. Now that when you first hear about eclipses, we may not think too much about why that’s possible. But the moon is a lot smaller than the sun, right? So how is it that the moon appears to cover the sun? It’s because, by a lovely coincidence, the moon is 400 times smaller than the sun, but it’s also 400 times closer to the earth than the sun. So those two things cancel each other out and they look the same size from Earth, which is a fabulous coincidence. And if we didn’t have that, you know, we wouldn’t get total eclipse of the sun. We’d probably be able to know a lot less about the Sun because Eclipse observations have taught us a lot about the sun and about the astronomy of our solar system. So that’s just a beautiful bit of coincidence. But, you know, it is a coincidence. And in the universe, the reason we get coincidences is because there are an awful lot of stars. There are an awful lot of astronomical bodies, comets, asteroids. With so many of these things available to potentially have commonalities or not, you’re just very likely to get coincidental similarities here and there. And and the one with the sun and the moon is just one example of that. But it’s my favorite.
Krys Boyd [00:09:06] And lucky for us. Right. Eclipses are pretty amazing.
Sarah Hart [00:09:09] That’s totally amazing. Yes, absolutely. So I feel very lucky. And I think, you know, just because we’re talking about the mathematics that might explain apparent coincidences, that doesn’t mean that I I’m bored by them or that I think they’re not worth thinking about. They are some of the most delightful things and they enrich our lives. So I’m a huge fan of enjoying the coincidences that we that we happen across in our everyday lives. And I think they, they, they bring happiness, right? So let’s enjoy them. And we may be able to explain some of them, but that doesn’t mean we’re not going to enjoy them as well.
Krys Boyd [00:09:41] Can math always help us draw a line between correlation and causation?
Sarah Hart [00:09:46] It can help. I mean, it certainly there there can be gray areas and sometimes we can think that that things are related when they’re not. And sometimes there’s an issue around events that we may think are happening independently, like, you know, the toss of a coin, heads or tails. If you toss a coin, it comes up heads, then you toss it again. It’s not going to come up heads just because the last time it was heads, you know, we expect those throws to be independent or rolling advisable, you know, shuffling cards, all of those things we can think of as being independent events that don’t affect each other. But actually in real life, in reality, events tend to be more in connect interconnected than we might give them credit for. And there would have been very serious situations in in courts of law where the perception of how probabilities work and whether things are. Independent. All coincidences have led to really unfortunate outcomes. So there’s a famous example in the UK about 20 years ago. It was really a tragic case because there was a young woman called Sally Clarke who who very sadly her first baby died of sudden Infant Death syndrome, often called Cot death. And it was a terrible tragedy. And then just over a year later, she had another baby and then that baby died as well. And she was accused of murdering them. She hadn’t heard of them. She hadn’t led them. But unfortunately, in court, there was a witness who was there. He was a doctor, but he wasn’t a mathematician or statistician. And he said, look, she definitely did it because the odds of a child dying of this terrible thing are about 1 in 8 thousands roughly like that. So the odds of two children dying in the same family of this of this cause are and he multiplied the odds together and he said it’s like 1 in 73,000,000. So that’s just impossibly unlikely. So she must have done this terrible thing and she went to prison. But luckily. Well, it’s a tragic there’s no way around it. But fortunately, there was an outcry against this. And lots of statisticians about Titian said, no, this is this is not the right way to calculate this. Yes, it’s very unlikely for this thing to happen. But what we need to compare is the odds of this thing happening by chance, which are small but not as small as as the witnesses said. Compare that to the odds of a mother, actual children. And that’s so, so, so unlikely and rare that, in fact, it’s nine times more likely for this awful thing to have happened by chance. So those statistics were completely misleading and they were used in the wrong way because this this this witness for the prosecution just multiplied the probabilities together when in fact, very sadly, those events are actually not independent. We don’t quite know why it is. But in a family where very sadly a baby has died of of sudden infant death syndrome, unfortunately there is a slightly raised chance that it will happen again in that family. So the calculation that this witness did was wrong. But also the comparison wasn’t right as well. Isn’t is this 1 in 73,000,000 chance more likely than the thing not happening? It’s is it more likely than the alternative, which is, you know, a mother ending the lives of her children?
Krys Boyd [00:13:19] Sarah, we are not wired to easily understand probability. This seems like a huge flaw in human brains. I suppose that too is just a coincidence.
Sarah Hart [00:13:30] I think you’re right. And actually, even mathematicians really struggle with intuition around these things. I suspect that the underlying cause of this is that. If you are if you think of sort of, you know, our human ancestors spotting patterns and being able to survive because of that, if you see like a little waving in the grass nearby and you jump to the conclusion that it’s a predator out to get you and run away. If it isn’t a predator, no harm done if it is great. But on the other hand, if you if you look at this little pattern that you’re saying and dismiss it as nothing interesting, maybe then occasionally you get eaten by a sabertooth tiger. So for me, I think it’s part of the way we’re built to see patterns. And that’s why you robotics is so fascinating and interesting to us. We enjoy patterns. But it does mean that we overestimate the significance of of these kind of coincidental events. We want to make connections. And you see this all the time. You know, we enjoy if we meet someone, say we’re sitting next to someone on a on an airplane, we get chatting. We really love it. If we can find a connection between us, a coincidence, say, you know, my my brother went to the same university as your cousin. You know, we love those those connection points. We are social beings and we enjoy finding those those little things in common. So I think we enjoy them. We look for them and we’re pleased when we find them.
Krys Boyd [00:15:02] And they can be sort of socially valuable. Right? On my first day with my husband, we discovered that we both drove the same kind of car, which means nothing. It is not so unusual, but it felt like something else special, in addition to the fact that we really liked each other.
Sarah Hart [00:15:19] Yes, absolutely. And that moment, you know, when you’re talking with someone, you make a bond with them over something like that. And, you know, it’s like, well, I like pizza as well. What are the odds of that? Everybody likes pizza. Yeah. Is something that that chimes with us. We we want to form communities. And luckily for us, in fact, if you look at the mathematics behind it, it’s really quite likely that we will be able to make links with people, even strangers that we meet. There’s been some fascinating mathematical research into social networks which kind of the ways in which we’re all linked with each other. So I might I may know lots of different people. I may have friends, acquaintances, you know, work colleagues, work connections. I’ve got children. So I know, you know, their friends, their friends, parents, the teachers and all of us has this web of people that we know, whether it’s friends, acquaintances and our other contacts that we have and everybody has one of these sets of connections and building up, it forms a whole network, a social network of, you know, everybody in the world. And then when we meet someone randomly. It actually turns out to be not too hard statistically to find a link most of the time. And when I say most of the time there are back of the envelope calculations, you can do that say if two people in the US meet each other, you know, strangers, there’s a high chance, like better than 99%, that maybe they don’t know each other, but they’ll either have a mutual friend or acquaintance or they’ll each have a friend. Those are mutually acquainted. So kind of a chain of about three people will very likely get you between any two individuals in America, which is really, really cool.
Krys Boyd [00:17:08] So now that we have social media, we can see some of these links. I mean, I’ve had the experience of discovering that two friends that I thought had nothing to do with one another from separate aspects of my life are connected online. Are we are we down well below the six degrees of separation rule?
Sarah Hart [00:17:26] Yeah. I think we all nowadays and social media and all that connectivity that we have probably that I would say it’s more like five degrees of separation. It’s very hard to be absolutely certain so we can make these mathematical models. There were two mathematicians called Duncan Watts and Steve Strogatz, who were investigating social networks because social networks are not absolutely random, of course. We tend to know people. We’re more likely to know people who live in the same city or who have the same line of work or from, you know, similar socioeconomic backgrounds. So it’s not just that we just randomly each know, I don’t know, 1000 contacts. There is this clumping in this network. So it’s quite difficult to think about it mathematically if you don’t know the exact structure. And of course, you can’t test every person in the world who they know and draw the picture. But what Watson Strogatz discovered was that actually social networks, which are very nonrandom, they have this property, which is that as we all know, there are hubs, there are social hubs, there are very well connected individuals. And many of us will have someone in our group of friends who just seems to know loads and loads of people. They know everybody and then they connect different groups. So there are a few people who perhaps don’t have huge numbers of connections, but they’ll probably know one of these very well connected people, these these social hubs, as I call them, and they provide kind of shortcuts in the in the network. So even if a particular individual doesn’t know a huge number of people, but they will very, very likely know one of these highly connected people and then that gets them into the rest of the network. And so the what Strogatz model, which which deals with these small world networks, as they called them, found that we can we can approximate these very nonrandom networks like the Social Network by thinking about what we know about random random networks. And those are very easy to understand mathematically, as though you could analyze them quite easily just using basic probability. And they found that, in fact, you can estimate everybody in the world, you take the entire world population of 8 billion people. And even if everyone only knows or is connected to a hundred people, an average, which is really, really small and way less than most of us know in our networks, then it would mean that there’s this path between them. Kind of the six degrees of separation phenomenon actually is only five degrees of separation. So, you know, you can do this mathematical analysis and that’s not an absolute cast iron guarantee. Of course, you know, if someone goes and becomes a hermit and lives in the desert, doesn’t talk to anyone. Yes. Okay. They’ve excluded themselves. But, you know, statistically, the probability is that any two people in the world, there’s a chain of five connecting them at most five. And it’s probably less than that for the kind of nonrandom situations we find ourselves in, where we’re meeting friends of friends, social events. We’re moving in particular circles. So it’s it’s really fascinating.
Krys Boyd [00:20:30] You share in the piece the example, hypothetical example of somebody in Birmingham, England, dreaming the next day’s news. Will you walk us through this?
Sarah Hart [00:20:39] Yes. So this is one of the things that, you know, occasionally will happen, that you’re talking to someone or you yourself will have a strange dream. And then. This dream seems to tell you what’s going to happen. And every so often, maybe it does happen. So you have a dream and it appears to predict the future. And of course, if that happens to you, it would be very unsettling. And you might even start to think maybe I have special powers. However, you know, of course, it’s very difficult to say. What are the odds of randomly dreaming the next day’s news? But if we say a very, very unlikely event like that, if we say it is a 1 in 1,000,000 chance of it happening and this would work for any 1 in 1,000,000 kind of event, a really, really rare, freakishly unlikely coincidence. Now, there’s a bit of a calculation you can do that says if you got a 1 in 1,000,000 event, then if you look over a population of 700,000 people or more, that is a big enough threshold to say that it’s more likely than not that event will happen to someone in that population. So I took Birmingham in England because that’s the population is over a million. But so any city where the population is more than about 700,000 people. If dreaming tomorrow’s news is a 1 in 1,000,000 event, it’s more likely than not that every morning someone wakes up and thinks they must be psychic because they’ve had that dream. So it’s just that that point seventh thing, I call it the point seven rule. If you’ve got an event, it’s like a 1 in 1,000,000 chance. If you multiply that one in, whatever it is, chance by by the number 0.7, that’s the number of people you need or the number of opportunities you need for that thing to have a better than even chance of happening. So the other example I sometimes give is that we as individuals in our lives, we have lots of opportunities, let’s say, to experience a 1 in 1,000,000 event. For instance, you know, you’re thinking about someone you haven’t thought of for a while and then suddenly you get a text from them or you you do something that appears to predict the future. Or you have some astonishing coincidence where you are reading a book about a particular thing, and then there’s a knock on the door and someone with exactly that same name is there. And you’ve never met the before. All of these kinds of very, very unusual coincidences. So I estimated that perhaps every hour of your life you have a chance, an opportunity for 1 in 1,000,000. Coincidence. Whether that’s while you’re dreaming of something or, you know, you’re you’re you’re looking at your phone and it suddenly rings or whatever it is. And then I worked out the average human life expectancy is about 710,000 hours. Right. So we’re over that 700,000 threshold. That means for each one of us, there’s a better than even chance that we’ll have a 1 in 1,000,000 coincidence at some point in our lives. So we can all look out for that.
Krys Boyd [00:23:39] Sometimes it’s just hard to believe that coincidences could possibly be so random. What happened with the Bulgarian National Lottery in 2009?
Sarah Hart [00:23:50] Yeah, I mean, this genuinely, even though it was, there was nothing weird going on. But when this event happened that I’m going to tell you. Yeah, you can really not blame people for thinking there was something a bit strange. So this was in 2009, in the Bulgarian National Lottery. The same numbers, exact same six numbers. You draw six numbers in this lottery. The same numbers came up in two consecutive draws. So the exact same numbers were drawn on September the 6th, I think it was and then four days later, on the 10th, exactly the same numbers came up. And of course, immediately many, many people said, well, this this can’t possibly happen by chance. You know, the odds of that are many million to one against. There’s no way this could happen by chance. We must have a public inquiry. And, you know, this just seems impossible. And indeed, it is extremely unlikely. So unlikely. But that, you know, you really do. Even as a mathematician, I feel a kind of frisson of my goodness, that’s a strange thing. However, when you look at actually the fact that there are lots and lots of lotteries all around the world happening and that there are many lottery draws going on within the same lottery, it starts to become likelier and likely over time that this will happen somewhere in the world. You will get the same numbers coming out twice. The Bulgarian lottery by that point had been running for 52 years. And so actually, if you think about all the draws that have happened in that in those 52 years, it’s about a hundred a year, over 50 years. So many, many draws the chances of at some point the same numbers coming up actually increase an increase because there’s so many ways for it to happen. There’s so many different ways for it to happen that it becomes more likely than not. There was a statistician called David Hand in the UK who calculated around this time that after 43 years of a lottery like like the one in Bulgaria, actually you would start to expect that the same numbers would come up at least once, same numbers as had occurred previously. And in fact, this isn’t the only time this has happened in the Israeli state lottery. The same thing happen now. They weren’t separated by only four days. I think it was about two months apart, but the same numbers came up. So it happened a couple of months earlier. And so, again, you know, you get these things and yes, we can we can say that mathematically this will happen with enough lotteries taking time over the well, you know, across the world, enough lotteries are happening for enough length of time to make it start to be likely that these extremely rare events will occur. And actually, lotteries are a good example of a case where we can see that very, very unlikely things do happen if there are enough opportunities because, you know, someone will win the jackpot in the lottery on a regular basis, that is extremely unlikely. You know, it’s one in many millions chance of that happening, but it does happen regularly to two individuals that somebody will win the lottery. And we don’t say, well, there must be something fishy going on because we know that there are many, many millions of tickets bought every week. And so it’s highly likely someone will have those winning numbers. So that’s an example of the fact that with coincidences, you know, the more chances you have for it to happen, the likelier it is that will get one of these rare events.
Krys Boyd [00:27:20] I don’t actually play the lottery, Sarah, but if I did, I know there are people who like to do different numbers every time and there are people who play the same numbers every single time they buy a ticket. Does one or the other have any better shot at winning?
Sarah Hart [00:27:35] Well, the answer is no. If you add any I mean, if you’re picking six numbers, all have many is if you do the same number every week or you change it up a little bit, it won’t make any difference because it’s random and lottery balls, you know, do not have a memory. They don’t remember what came up last week. However, having said that, there are some some ways that you can improve your chances of not having to share the jackpot because, of course, you want to win huge amounts of money naturally, but you don’t have to share it. So there are some things you could do. For instance, there are lots of people who know that actually any numbers are equally likely to come up. So to sort of prove that they’re not superstitious, they might choose the numbers one, two, three, four, five and six. Right. Just to say, I know that this is just as likely as any other combination. The only problem with that is that tens of thousands of people also do that every week to prove to prove their kind of rationality. And so if those numbers were to come up. Which is just as likely as any other set of numbers. However, if you pick those numbers and the numbers come up, you’re going to have to share your jackpot with all of those other tens of thousands of people. So while you claim that there’s no way of, you know, no numbers, more likely than any other to come up. So you can’t change the odds in that way. It’s it’s always worth thinking about, perhaps not choosing very, very popular numbers that others are going to pick because what you do in the jackpot, you don’t have to share it. I’ll just mention one other thing about the lottery, which is you can be very lucky in the lottery and win the jackpot, but there’s also some cases of of bad luck. And my most kind of dear moment is having is reading about the case of Maureen Wilcox, who spent 25 years ago I think in the same week she bought a ticket for the Massachusetts lottery and she bought a ticket for the Rhode Island lottery. And she got the winning numbers for both lotteries, but on the wrong tickets. Wow. So, yeah.
Krys Boyd [00:29:41] It’s hard not to read some kind of meaning into that. But she was not meant to win.
Sarah Hart [00:29:46] Yeah, exactly. I mean, you have to be philosophical about these things and say, okay, it’s maybe a sign for the universe that maybe I shouldn’t gamble, you know?
Krys Boyd [00:29:56] Sarah, sometimes coincidences fall apart when we realize not everybody actually has the same odds. For example, you share this story of a park ranger in Virginia who was struck by lightning seven times over the course of his career. What made him more likely to experience this bizarre set of coincidences than, say, his brother in law who maybe worked at a grocery store somewhere?
Sarah Hart [00:30:23] So this is a really good illustration of the fact that while life may be a lottery, we are not lottery tickets, right? Our odds of individual events definitely vary. So if we think about lightning striking, actually it’s quite a common thing. Lightning strikes somewhere on Earth. It’s estimated a hundred times a second. Of course, it does not necessarily hit everyone or hit somebody in those 100 times. So we have to think about, well, how often does lightning actually strike a person? And the the US National Weather Service did a calculation and an estimated that on average a person’s lifetime risk of being struck by lightning is about 1 in 15,300, something like that. So that’s pretty unlikely. And it might be tempting to say, well, okay, the odds of then being struck twice might be 1 in 15,000 times 1 in 15,000. And that’s something like 1 in 200,000,000 seems very, very implausible that anyone could be struck twice, let alone seven times, which, as you say, happened to poor old Roy Sullivan, who was nicknamed the human lightning rod. Poor thing. But that is to misunderstand the probabilities, because these are not independent events. People’s individual risk of being struck by lightning varies hugely according to where they live, what their job is, the climate, the time of year, the time of day. So Roy Sullivan, as you say, he was a park ranger in Virginia. Now, being a park ranger means you’re outside an awful lot. So you’re going to be out in bad weather. You want to be out in thunderstorms much more than, you know, a librarian somewhere in Alaska, for example, as well. The climate in Virginia, it’s it’s a kind of warmer, wetter, slightly more in the southeast and coastal state. And so that climate is more conducive to thunderstorms and lightning. You get more of those in that part of the world than in some other places. So it’s where he was. It’s what his job was. And I have to also mention that of all the people who get struck by lightning, 84% of them are men and 16% of them are women. Now, we would speculate on why that might be a big part of it will, of course, be that that those jobs which involve outdoor work are probably more often done by men than by women. But, you know, if your hobby is flying kites and thunderstorms like Benjamin Franklin, you know, your risk is going to go up. So so individuals will have vastly different risks of being struck by lightning now. Roy Sullivan, he was obviously had a very high, high risk factor compared to other members of the population because of his outdoor job, because of where he lived. But, you know, when he kept getting struck by lightning, he did start to feel that, yeah, that the fates were not in his favor. He after the third time he got struck by lightning, he started carrying a kind of water around with him at all times. Because if he was going to be struck, he wanted to be, you know, in case his hair caught fire. He wanted to be able to put it out with the water. So he began to be understandably kind of superstitious that he was in some way disliked by the I don’t know, by the thunder gods or something. But, you know, of course, that’s totally understandable that you would feel like that. However, you know, his his chances of being struck by lightning were were much higher than than, say, mine, who mostly spends a lifetime sitting in a nice quiet room surrounded by books. So, yeah, that this is this is another case where we might think something is just absolutely implausibly impossible. Very, very low chance. And so there must be some kind of other thing making it happen. But really, it’s just that our individual odds vary so much.
Krys Boyd [00:34:13] I won’t put you on the spot here, but the bonus question would be what are the chances of surviving seven lightning strikes?
Sarah Hart [00:34:20] Well, that’s an excellent point. I mean, I suppose. Yes. If you’re going to be struck by lightning, then a priori, you’ve survived the first six of them. But yeah, I mean that’s that’s also you could say he was unlucky, but you could also say he was very lucky to have survived all of those lightning strikes.
Krys Boyd [00:34:37] Okay. I want to talk about psychic predictions, which some people see as nonsense and some people believe in quite steadfastly. The fact remains, psychics have occasionally made predictions that appear to come true. What was the prognostication that made Jean Dixon, who was a professional psychic, such a star in the latter half of the 20th century?
Sarah Hart [00:34:58] Yes. So she very famously predicted the Kennedy assassination. What she actually predicted was that the 1960 presidential election would be won by a Democrat who would be assassinated or would die in office. So, obviously, at Kennedy with that, we all know what happened after that. And that, of course, in isolation, that seems. Absolutely mind blowing. How could anyone have predicted that unless they genuinely had the power of clairvoyance? However, if you dig into it a little bit more, then things start to become slightly less impressive. Now, this is, you know, not we’re not going to discuss like, is there any true psychic or anyone who could truly do this ever will have their different opinions. However, Jean Dixon, she did predict the Kennedy assassination, or at least that that the president would die in office. However, she later, before it before the actual election happened, she changed her mind and predicted that Nixon would win. She also predicted that Russia would be the first to put a man on the moon, and she predicted that the next World War, after the Second World War, the next World War would start in 1958. So those other predictions are less well remembered. And and so, you know, if you if you cherry pick the things that come true, you know, then we could all tell the future. I could write down 100 predictions now and and likely that that some of them would come true. And the other thing that is often done, you know, if you read your horoscope or something like this, you will notice that there’s quite a lot of vagueness in the predictions of of fortune tellers. You know, if you predict something like something lucky will happen to you this month, that’s pretty likely to happen, especially if you’re on the lookout for something lucky and you want to believe that it’s right. Or maybe you say during 2025, a politician will be embroiled in scandal. You know, there are lots of politicians in the country, and it’s quite likely the least one of them will have some sort of scandal attached. And so you can find something that meets those those predictions and say it was successful. So what we find a lot is that people who, you know, say that they can tell the future. They are making lots and lots of predictions and they can be quite vague or open to interpretation, ambiguous. And then after the fact, you know, they’ll point out the the 1 or 2 that were true. But what we don’t tend to remember is the ones that didn’t come true. And, you know, this is a very beguiling and tempting thing to want to believe that that that individuals can have these powers. And I remember when my sister and I were young, we used to be really, really desperate to be telepathically connected. We wanted to we wanted to feel that we had a special connection, you know, And so we’d try and predict what the other one was thinking. Or we’d try and guess what, you know, picture the other one was, was imagining and we’d get it wrong almost all the time, of course. But every so often we we’d make a correct guess and then we’d be absolutely excited and convinced that, yes, our all our work on our telepathy was finally coming to bear fruit and we were really going to improve on our telepathic powers. Sadly, I don’t think we are telepathic, but, you know, it’s a very beguiling thing.
Krys Boyd [00:38:22] So when we talk about big math, I mean, big data obviously comes into play here. Now we have artificial intelligence that might help us work some of these things out. Will A.I. software solve the problem of plagiarism, demonstrating whether somebody accidentally sort of, you know, had the same language as someone else or the same song or whatever? Or will it just complicate the process?
Sarah Hart [00:38:48] So this is a really, really difficult and challenging issue increasingly at the moment, because I can be a great tool and increasingly, you know, it’s tempting to use A.I. in our in our writing. And students have been exploring what is possible here. And occasionally, yes, there will be students who. Who will get to write their essay. However, however, there is a real issue around accusations of plagiarism using A.I. that. Are really difficult to fight against. There are plagiarism checkers that that are used by educational institutions. One of the big ones has said that it has an error rate of only 1%. So it looks at your work that you’ve submitted and it compares it to other things that are online. And it also tries to work out if if you’ve perhaps used AI by again, it’s sort of statistical analysis, all that correlations between between sources or between ways in which machines can can write and then it reaches a conclusion and it says, you know, this is or is not likely plagiarized. The problem is that error rate of only 1% feels low. But, you know, if there are a thousand students, that means ten of them are going to be accused incorrectly of plagiarism. And then how do you prove that you didn’t plagiarize? If you’ve written a sentence that is kind of accidentally very like one that’s online that you haven’t seen? It’s very, very hard to show that you didn’t copy that sentence. You know, this is troubling because traditionally, you know, you’re innocent until proven guilty. But there seems to be a little bit going the other way around. And there was a an interesting report about a student at the University of California, Davis, who she was accused and she she fought against it because she she was innocent. But what she had to do and the only way she managed to convince the authorities, let’s say, of her innocence, was by showing them, you know, time stamped drafts of her work. So the essay, you know, version one, version two, version three and so on showed her work being developed. And that’s one way to fight against it. But, you know, with so much online, I mean, think about all of the sentences that there are online and all of the all of the ways that these sentences and paragraphs can be rewritten and reshaped and all of the sources that we could possibly consult, the chances of accidentally producing a sentence looks like something that’s already been written or just only going to increase an eye, which can produce, you know, an entire essay in a second, I think is the moment. It’s a challenge to see how we can work out how to ensure that the students who are doing, you know, genuinely independent work on their own are not going to be caught up in any unfortunate accusations related to that. You know, there’s there’s such a lot of music being produced nowadays on Spotify and other streaming services. There are thousands and thousands of songs being uploaded every day. And there was a famous court case where a. A musician accused Ed Sheeran of plagiarism. So Ed Sheeran and a multi billion selling artist, he had a a hit shape of you and he was accused by a musician of having plagiarized a sequence of four notes in that song. But actually. Four notes. There’s only so many ways you could make a four note sequence. There are kind of 12 different notes in the in the Western scale. The number of possible four note phrases that you could you could construct is only about 20,000. And with 22 million songs a year being produced and uploaded to Spotify, you’re just guaranteed that there are going to be some overlaps quite innocently. Now, I’m not saying nobody ever copies anyone else’s work, but we have to be really careful before making these kinds of accusations. And actually yet it went to court this thing and Ed Sheeran was completely vindicated in the court case. He won the lawsuit.
Krys Boyd [00:43:03] Did you see the recent headline that said some mathematician, I think in the UK worked out that if you gave a monkey a typewriter, it in fact would not be able to generate collected works of Shakespeare because the age of the universe is not long enough. Yes.
Sarah Hart [00:43:21] I think I did see that article. Yes. Well, I mean, we’re just going to need more monkeys and more typewriters. I think that’s the only answer. That one.
Krys Boyd [00:43:28] Can we train ourselves to be just as delighted by the math behind coincidences as by the idea that they are magical or meaningful in some way?
Sarah Hart [00:43:36] Well, I think understanding a thing only adds to the pleasure of it. I don’t need that kind of unknowable mystery to still find pleasure to thing. So for me, understanding why patterns happen and how things are put together is so fascinating. And these famous sort of parlor games, like if you put 23 people in a room together, it’s more likely than not that two of them will share a birthday. For me, understanding why that’s true is part of the joy of that really surprising fact. And so, yeah, I think having that curiosity to understand what’s going on behind these events, firstly, it’s just fun in its own to explore these ideas, but also it helps us because it can help us to understand when there’s more than coincidence going on and that’s when science starts to happen, and we can really make progress in understanding the world around us.
Krys Boyd [00:44:40] Sarah Hart is professor emerita of geometry at Gresham College and professor emerita of mathematics at Birkbeck University of London. She’s the author of the book “Once Upon a Prime” and of the New Scientist article “The surprising math that explains why coincidences are so common.” Sarah, this has been delightful. Thank you for the conversation.
Sarah Hart [00:44:58] Thank you so much.
Krys Boyd [00:44:59] Think is distributed by PRX the Public Radio Exchange. Again, I’m Krys Boyd. Thanks for listening. Have a great day.
