David J. Hand, emeritus professor of mathematics at Imperial College London, talks about his new book The Improbability Principle: Why Coincidences, Miracles and Rare Events Happen Every Day
Podcast Transcription
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Welcome to the Scientific American podcast, Science Talk, hosted on April 30, 2014. I’m Steve Mirsky. On this episode—
David Hand: So it’s just chance, and you would expect that truly large numbers of opportunists for this sort of thing to happen, sooner or later it’s going to happen.
Steve Mirsky: That’s David J. Hand. He is Senior Research Investigator and Emirates Professor of Mathematics at Imperial College, London, where he was the chair in statistics. He is also a fellow of the British Academy and an honorary fellow of the Institute of Actuaries. He has served twice as president of the Royal Statistical Society. In 2002 he was awarded the Guy Medal of the Royal Statistical Society. He is good with numbers.
David J. Hand is also the author of the new book for a general audience called The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day. He was visiting New York recently, not coincidentally, and we got together to talk about the book.
I was nine years old. It was July of 1967. I know this ‘cause I just double-checked it. And I took some spoken word records out of the library. One was Carl Sandburg reading his own poetry and one was Basil Rathbone reading Sherlock Holmes. A couple days after I took the records out Basil Rathbone died. The next day Carl Sandburg died.
David Hand: Yeah. Yeah.
Steve Mirsky: So I was nine years old and I was a little concerned about my special ability.
David Hand: What else could you do?
[laughter]
Steve Mirsky: But what was really going on there?
David Hand: Yeah, it was just one of those very unfortunate events. There would be doubtless similar sort of situations at other times, many other times in your life. You read a particular author, particular column written by somebody or something and they didn’t die, so you didn’t notice.
Steve Mirsky: Right.
David Hand: You know, these happen too, and it naturally focused your attention on it. And yes, led you to think you had superpowers, yes.
Steve Mirsky: Yes, unfortunate superpowers. I was a little concerned about taking any more records out of the library, but I gradually got over it. So The Improbability Principle, this is a very readable, entertaining, and engrossing book.
David Hand: Thank you.
Steve Mirsky: And why don’t we go through it a little bit and talk about some of the ways in which events that just seem to be too unbelievable to believe they could’ve just happened without some higher purpose or direction to the events of the world, how these things just happen willy-nilly. So you have various laws in the book that you discuss, for example, the Law of Inevitability.
David Hand:Yes, indeed. So there are five laws. The Law of Inevitability is the first one, and in a way it’s the sort of most elementary. And when I tell you what it is you’ll think, “Well, that’s obvious, isn’t it? That’s not very profound. How can that have any implications?” But as we’ll see, it does. The Law of Inevitability just basically says that something must happen, many of all of the possible outcomes must occur; it’s guaranteed. So I can guarantee you that a flipped coin will come up heads or tails or something else; it will fall down a crack in the floor or a passing bird will take it or something like that. So we have three possibilities, heads or tails or other, all these other strange things might happen. They’re guaranteed; one or the other of those three things is certain to happen. I can’t tell you beforehand which one it will be, but one of those is certain to happen.
Steve Mirsky: Now this appears to be trivial, but it’s not.
David Hand: Exactly. It appears to be trivial, but you can in fact take advantage of it. And there’s a story in the book, a story about people who took advantage, tried to, and in fact succeeded in taking advantage of the Law of Inevitability to win the lottery. And it’s not the only group who – it was a group of people.
Steve Mirsky: This is where there was 7 million possible-
David Hand: Exactly. Exactly.
Steve Mirsky: -possible combinations.
David Hand: That’s right. But other groups have done the same. This is a particularly well-known classic story. 1992 Virginia State Lottery, the Virginia State Lottery is a 644 lottery, you have to choose 6 numbers out of 44, which means exactly as you say, there’s a 1 in 7 million chance that a particular ticket will be the jackpot-winning ticket. Seven million. So if you bought all the tickets it would only cost you $7 million. They waited, and they’d obviously planned this, as we’ll see it takes a lot of planning, they planned this well in advance. They waited until the rollover jackpot had built up to – hadn’t been won, so it built up over several weeks to $27 million. So there was a window there between the jackpot rolling over and a jackpot of $27 million being paid at the next draw. If you manage to spend $7 million and buy all the $7 million tickets you are guaranteed to hold the jackpot winning ticket.
Steve Mirsky: For a $20-million profit.
David Hand: Exactly.
Steve Mirsky: Assuming no one else had the same exact numbers and you’d have to split it. But even if you did have to split it, you’d still be ahead $6.5 million.
David Hand: That’s right. If you split it two ways that’s fine. If you split it-
Steve Mirsky: Right, three ways, you still, but now it’s not so worth – anyway.
David Hand: Yeah. Yeah. But there’s a lot of organization involved in this. In fact, what happened was they put together a consortium of 2,500 people, Australians, Americans, and other nationalities as well, so a lot of organization, each of whom paid $3,000.00 or thereabouts, so they had $7 million. And then in the few days’ window they had available they ran around buying – trying to buy all the 7 million tickets. Unfortunately, they only managed to buy 5 million of them.
Steve Mirsky: Right.
David Hand:Imagine the sinking feeling in their stomachs when they-
Steve Mirsky: White knuckle-
David Hand: Yes. Yeah. Yeah.
Steve Mirsky: -on the drawing, although now their chances are excellent of winning their 5 out of 7.
David Hand: Yeah, and they have over a quarter of a chance of not winning.
Steve Mirsky: Right.
David Hand: Previously with the Law of Inevitability they were certain to win, but because of their failure of their organization they had a good chance of losing now. As it happened, however, they did have the winning ticket, so they were guaranteed winning the jackpot. Except for the fact that the lottery operators pointed out a clause in the regulations which said that they had to buy the tickets, receive the tickets at the same place they paid for them, and they hadn’t done this; they had paid bulk, you know, check for $100,000.00 in one place and then printed the tickets out in other places.
Steve Mirsky: But eventually it – this settled _______-
David Hand: Yeah, this then went into a sort of legal argument and eventually the lottery operators realized it was getting too complicated and no guaranteed outcome, they gave them the money.
Steve Mirsky: Right.
David Hand: But the organization beforehand, the logistics of running around trying to buy these tickets, the nail-biting, looking through the tickets, it’s easier just to get a job.
[laughter]
Steve Mirsky: Some friends and I, when I was in high school, tried a very modest version of this. We were at the track and we, you know, you can do the bets where you have two horses.
David Hand: Yeah. Yeah.
Steve Mirsky: And we, I think it’s called “boxing.” We boxed the entire field, figuring that if a long shot comes in we’ll make a profit, and if favorites come in we’ll lose, but not too much.
David Hand: Yeah. Yeah. Yeah.
Steve Mirsky: So we tried that for a few of the races during that evening’s events and what we wound up with was basically breaking even.
David Hand: Yeah. Yeah. Yeah. I mean I think you always have to remember in these circumstances that bookmakers, betting operators, as I say, you don’t see them riding bicycles.
Steve Mirsky: Right. I had to think about that and then I realized what it meant was they can afford limousines.
David Hand: Exactly.
Steve Mirsky: So after the Law of Inevitability we start to get into the big number business.
David Hand: Yes, the Law of Truly Large Numbers. Okay, so there are two of the five laws which are fairly straightforward, and I think the Law of Inevitability is one and the Law of Truly Large Numbers is also fairly straightforward. This is different from the Law of Large Numbers which you’re taught about in college, which just says that things get closer to the average the larger the sample you take is really what it says. The Law of Truly Large Numbers says if you take enough opportunities you’re guaranteed the most extraordinary results. So if I flip a coin and keep flipping it long enough, maybe millions and millions of times, I’m guaranteed to get 20 heads in a row, or as happened in roulette, 26-
Steve Mirsky: Twenty-six black-
David Hand: -coming up in a row, yeah.
Steve Mirsky: -roulette numbers in a row.
David Hand: Yeah. Yeah.
Steve Mirsky: You know, if you were there when that happened you would say-
David Hand: Absolutely.
Steve Mirsky: -the fix is in, something is wrong with this wheel. But when you look at all the roulette wheels in the world being spun every day-
David Hand: Time and time again, night after night-
Steve Mirsky: -thousands of times.
David Hand: Yeah, exactly.
Steve Mirsky: It becomes inevitable that you’re going to get 26 blacks in a row.
David Hand: That’s right, yeah. And the key thing there are a truly large number of spins of these roulette wheels.
Steve Mirsky: Right.
David Hand: Yeah. Exactly. So that’s an illustration of that law and it manifests itself in all sorts of ways. You know-
Steve Mirsky: You have the Bulgarian Lottery example, which is amazing.
David Hand: I do. That’s right.
Steve Mirsky: It’s really amazing when you work out the math and you see that it’s inevitable.
David Hand: Yeah. Yeah. 16th of September 2009, on the sixth – so six numbers came up on the Bulgarian Lottery and four days later exactly the same numbers came up, which caused a media storm, around the world in fact. The Bulgarian minister ordered an investigation, you know, clearly this is fraud.
Steve Mirsky: ______ fraud _______.
David Hand: Yeah, exactly.
Steve Mirsky: But when you work out the math, even in just the Bulgarian Lottery case the chances become greater than 50/50 that you’ll repeat the numbers every 43 years.
David Hand: Exactly. Maybe not consecutively.
Steve Mirsky: Right.
David Hand: But some numbers will be the same. Yeah, the two sets of six numbers will be the same somewhere in that 43 years. And because of the probability of getting some matches so great you would expect it to happen. You know, we realize now that, okay, it’s not so unusual given the huge number, truly large numbers of lotteries around the world being drawn again and again and again. And it’s not just happened in Bulgaria; it’s also happened in Israel and it also happened in the-
Steve Mirsky: [inaudible cross-talk]
David Hand:Carolina Cash 5 Lottery, same sort of thing happened, and I think that was consecutive draws.
Steve Mirsky: Wow.
David Hand: So, you know-
Steve Mirsky: And you have the poor woman in Massachusetts.
David Hand: Maureen Wilcox.
Steve Mirsky: Right. I’m not sure, was she in Massachusetts or Rhode Island, it’s not clear?
David Hand: Yes, either.
Steve Mirsky: But she bought the lottery tickets for both states.
David Hand: That’s right, she bought the lottery – and she bought the winning numbers for both states. Unfortunately for her, the winning numbers she bought in one state were for the lottery in the other state and vice versa.
Steve Mirsky:And I mean that’s the real amazing thing, she had them both, but switched to the wrong states.
David Hand: Yeah. Now if anyone is going to think somebody up there has got it in for me, that poor woman must’ve thought so.
Steve Mirsky: Right.
David Hand: So it’s just chance. And, you know, you would expect that truly large numbers of opportunities for this sort of thing to happen, sooner or later it’s going to happen, so it’s not really surprising at all.
Steve Mirsky: Yeah. Yeah, the case in the book of the park ranger, now this is a little different because he’s a park ranger, so he’s outdoors a lot. But he’s been hit by lightning seven different times.
David Hand: He has indeed. Yeah.
Steve Mirsky: At least seven. And possibly he was also hit as a youngster, but we’re not including that in the official count.
David Hand: That’s right. That’s right. Yeah, and I use him to illustrate the Law of the Probability Lever, which basically says that if you change the conditions or circumstances a little you can dramatically change the probabilities. So for instance in the U.S. the chance of being killed by a lightning strike is about 1 in 3 million; there are about 100 people in the U.S.
Steve Mirsky: Per year.
David Hand: Per year, yes. So about 100 people in the U.S. killed per year by lightning strikes, which pro rata is far fewer than you would expect if you look at things around the world. And the reason is because America is a safer place to live in; you tend to live in buildings, work in offices. There are lightning conductors down the sides of the buildings and so on, the insulation is better, earthing is better. So the circumstances changed.
Now Roy Sullivan, this park ranger that you mentioned, well, clearly he didn’t work in an office; he worked in an environment which predisposed him, made him more vulnerable, more likely to be struck by lightning. The circumstances, the conditions had changed, and so his probability – you know, so in retrospect, looking at it, well, not too surprising that he’s been hit more than once.
Steve Mirsky: Seven times is pushing it a little bit.
[laughter]
David Hand: Well, yes. You know, you do wonder why he didn’t think, “Hmm, this is getting a bit much and next time might be the last time. Maybe I should make the last time the last time and stop.”
Steve Mirsky: Right. Get a desk job.
Yeah, you have the other case of, what was it, Major Summerfield?
David Hand: Oh yes.
Steve Mirsky: Hit by lightning a few times and after he died, not from lightning, his gravestone-
David Hand: Absolutely.
Steve Mirsky: -was hit by lightning.
David Hand: Yes. Yes. That’s right. As if, you know, God had said, “I haven’t forgotten you.”
[laughter]
Steve Mirsky: So that’s the probability lever, where we can really increase the chance of something happening without really – without necessarily realizing you’re doing it. What’s another example of something like that?
David Hand: Another example of the Law of the Probability Lever, oh, I suppose one of the examples I give – there are many examples. One is financial crashes, where people use the wrong model. Financial mathematicians really understand this, but a lot of the calculations for simplicity are based on what’s called a normal distribution, which is not appropriate, so you end up with figures saying we should’ve experienced such a movement in the market only once in a billion years, but we seem to experience them once every 10 years or 20 years. And that’s because the wrong model is being used.
But let me give you another example. The Titanic. The Titanic was well-known to have been thought to be unsinkable. It was unsinkable because it was a double-hull ship and it had lots of separate compartments, 20 separate compartments, which could be separated from each other by watertight bulkheads, doors. And it was built such that if one or indeed, one or a few more of these compartments got ruptured and flooded it wouldn’t sink, so it was unsinkable. That calculation, though, was basically based on the assumption that any one of these compartments being flooded, the probability of that, the chance of that happening was independent of any of the others being flooded. And what actually happened was that the ship was hit on the side by an iceberg, which then scraped all along the side and ruptured five consecutive compartments, which all flooded. The flooding of the compartments wasn’t independent; it was related. The wrong probability model was being used, with clearly in that case incredibly dramatic effects on the outcome. Now the chance of it sinking was much greater than was thought when you use the right model.
Steve Mirsky: Based on the actual runs of that experience, the odds of it sinking are-
David Hand: Much higher.
Steve Mirsky: -much higher.
David Hand: Yes. Exactly. Yes.
Steve Mirsky: So those are a few of the laws. What’s another law that you discuss in the book? There’s the Law of Inevitability, Truly Large Numbers, Probability Lever.
David Hand: And then the Law of Selection and the Law of Near Enough.
Steve Mirsky: Ah, selection is very interesting, especially from a point of view many of the people who will listen to this are obviously very interested in science or are scientists. You know, Law of Selection really comes into play in a lot of research, publication of medical studies.
David Hand: Yes, it does. Law of Selection manifests itself in all sorts of curious ways. I mean one way is in science is through publication bias, where naturally papers which produce exciting results with potential implications are more likely to be published. The authors want to get them out there, editors want to have their journal to have an impact, so if you produce a paper like that it’s more likely to be accepted and published. If you produce a paper which says there was no effect editors are less likely to publish it. So this produces a natural bias in the nature of the papers which are published. And there’s also something going on at a more fundamental probabilistic level; any scientific result has got a random component, just by chance the patients who are allocated to one group or the other group were more likely to get better or whatever. So there’s always a random component. Now if that random component happens to push you over some sort of threshold so it appears to have an effect, the drug or treatment or whatever it is appears to be effective then because of the publication bias I’ve just described you’re more likely to get it published.
So amongst a lot of the papers which have appeared in journals, there is likely to be an overabundance of papers which really show an effect, which will then vanish when they’re repeated. And it’s just the selection process.
Steve Mirsky: There’s a point where selection and regression to the mean come up. You discuss in the book the placement of speeding cameras.
David Hand: Oh yes.
Steve Mirsky: And this was – I love this part; this was so fascinating.
David Hand: Yeah.
Steve Mirsky: How public policy officials can look at numbers and have no idea what’s really going on.
David Hand: Yeah, that’s exactly right. I like this example as well, because at the time it wasn’t very clear what was happening, how it should be analyzed, but in retrospect it’s very clear. Of course that’s at the time, but in retrospect is a key aspect of the improbability principle in general. But in this particular case if you’re investigating the effectiveness of speed cameras what you would do is you will clearly site your speed cameras at accident black spots to see if they have an effect in reducing the number of accidents or rate of accidents at those places.
Steve Mirsky: Right. So we have these places here in New York, you know, you go to Queens Boulevard, famous for terrible traffic accidents, a lot of speeding cars. So that’s a prime place where you would put a camera.
David Hand: Exactly. Yeah.
Steve Mirsky: The idea is that when the motorists know that the camera is there they’ll behave better.
David Hand: Exactly. That sums it up very nicely. But the fact is, of course, that accident black spots like that one, the high rate of accidents is a product of two things; first it’s perhaps a naturally dangerous place which is does encourage poor behavior, like driving, behaving like this. But also, in any particular year the fact that there’s a higher rate of accidents will be also partly due to chance because it will fluctuate over the course of time; sometimes it will be less, sometimes it will be high.
Now if we look back at last year and identify the places which have particularly high rates of accidents, the high rate of those places will be due to a sum of two things, the natural degree of dangerousness of those places, plus the fact that that particular year just happens to be a bad year, there were more accidents than normal at that year. But because it is a high rate of accidents we’re now going to put a camera there.
Now what happens next year? What happens next year? The natural dangerousness of the place hasn’t changed, it’s still the same corner or intersection or whatever, but the chance bit of the number of accidents there, well, it could be just – it could be low just as easy as high next year. On average it will be lower than the high rate we saw. So next year the rate will come down. It won’t be because of the camera, it will just be because of natural fluctuation, removing that sort of chance part. But it will look as if putting the cameras there has improved things.
Steve Mirsky: When you look at the entire array of let’s say 100 cameras you’re going to see – almost inevitably we’re going to see a decrease in the accidents that occurred at those 100 sites together.
David Hand: Exactly. So it seems that when people analyze the data, taking this into account, it seems – and I want to make this clear, because I don’t know about in the U.S., but in the U.K. speed cameras are a bit controversial; there is a group of people who thinks they’re just ways to raise revenue for the authorities. The fact is, however, the speed cameras do work. There is no question that they do reduce the rate of accidents, but not as much as a superficial analysis failing to take into account the Law of Selection and Regression to the Mean makes it look like.
Steve Mirsky: Right. I forget the actual numbers, but let’s say there’s a 50-percent reduction. Maybe only 60-percent of the 50-percent is due to the camera and the other 40-percent is just due to fluctuation in your rate of accidents at any particular spot in a year.
David Hand: That’s right. Yeah. That’s exactly right.
Steve Mirsky: That’s really fascinating. But of course the city councilman who put that camera there are going to take credit for the full decrease.
David Hand: Absolutely, yes.
Steve Mirsky: So near the end of the book you talk about how – well, let’s talk about the Law of Near Enough.
David Hand: Yeah. Yeah. Okay, so the sort of statement of this law is that events which are sufficiently similar are regarded as identical. And what this means is that we look for, as we discussed earlier, we notice things which appear to match or which strike us as the same or whatever, we notice these coincidences. And I’ll just give you an example of the Law of Near Enough. A couple of people, a man and woman, were both involved in train accidents which killed a number of people. Bill Short was involved in one in 1986, killed 13 people, I think. And then 15 years later his wife was involved in another train accident which also killed a number of people. And you think rail travel in the U.K. is extremely safe; if you look at the figures it’s very, very low fatality rates, so they were very unfortunate. What a coincidence that a husband and wife should both be involved in fatal quite serious train crashes.
But then you think it wasn’t Bill being involved in both; it was Bill and Ginny, his wife. And they weren’t at the same time; they were 15 years apart. We would also regard it as coincidence if it had been 20 or maybe 30 years apart. And it hadn’t been Bill and his wife, well, Bill and his cousin or brother or somebody with the same name, for instance. So what we’re doing here is enlarging the scope of things which we would nevertheless had said, “Wow, what a coincidence.” And if you do that sufficiently, of course, sooner or later you end up with something which is quite likely, not so improbable at all.
Steve Mirsky: There are an infinitude of things that go on every day that we don’t pay any attention to.
David Hand: Yeah.
Steve Mirsky: Just off the top of my head, the number of strokes I use when shaving my face, that’s going to fluctuate around some mean.
David Hand: Yeah. Yeah.
Steve Mirsky: But if I were to count them up exactly, I would find, isn’t this amazing, I used exactly the same number on, you know, January 14th as I did seven years later on January 14th. And it would look like something.
David Hand: Yeah. Yeah. I think that’s right. I mean I sometimes say that, you know, we go through the world surrounded by events, there’s a buzzing, boiling confusion of countless trillions, an infinitely large number of things going on all the time. But when two happen to come together in some way ‘cause the same numbers come up then we notice and we say, “What a coincidence.” But if you take all these things into account then you would expect these things to happen. That’s the improbability principle.
Steve Mirsky: I’ll give you – I realize you’re not a big baseball fan, coming from the other side of the Atlantic, but there’s something in American baseball called a perfect game, when the pitcher gives up no base runners at all. So a Yankee pitcher did this in 1956 in the World Series. Then in 1998 a Yankee pitcher did it in the regular season. And it turned out that they had both attended the same high school in San Diego.
David Hand: Yeah. Yeah.
Steve Mirsky: So naturally everybody went crazy, “This is unbelievable. How could they have gone to the same high school?” And I was saying to people, “But if you lay out their biographies and go through them with a fine-tooth comb you will find, you know, they both have the same wedding anniversary. Something like that is going to come up.”
David Hand: Yes, that’s right. And there are many countless things that they differ in, but you don’t care about those; you only care about the high school, all the things that they happen to match on, yeah.
Steve Mirsky: Right. Exactly. Like one had a terrific career over a 25-year span and the other one really just had that one moment of ________. But anyway, so near the end of the book you talk about how understanding these laws can actually help you in your day-to-day.
David Hand: Yeah. I mean the book is really intended to be a book about, as it were, the nature of the universe, about science. But I thought it was also useful to actually then turn things around and say, “Well, how can we apply these things in our everyday life?” And I talk about things which I think will be familiar to people who know statistics or some statistics, although they may not have thought of them in this particular sorts of ways, for instance. So for instance, the Law of Likelihood, where you balance the chance of getting an observed phenomenon in the world or a set of data or an incident or something under two possible explanations, is it very unlikely under this one and very likely under this one, and then you decide which one you prefer. So you’re balancing improbabilities – well, probabilities in that sort of example. And there are various other sort of ways I’ve tried to illustrate how they could be used.
Steve Mirsky: What was the case in the book about, it might’ve been Pascal, talking about the lesser of the two miracles?
David Hand: No, that’s absolutely right. And that’s a very early example of this likelihood principle; you look at the evidence and you say, “Well, what’s the chance of” – or, you know, a man comes to you and said, “I have just seen something amazing. I have seen someone float into the air, do a loop-de-loop and then fly off into the distance,” and you say to yourself, “Well, one explanation is he saw this happen, another explanation is he’s been drinking.” Now which do you think is the most, you know, most likely to have led to that result? That’s really what he’s talking about, balancing probabilities, balancing improbabilities, yeah.
Steve Mirsky: It reminds me of a parable, I think it’s a parable, and I think it’s Saint Francis, who was considered to be so earnest that the other monks would even make fun of him, how honest and simple he was. And one of the monks – one of the other monks came up to him and said, “Francis, you have to come look out the window, there’s a mule and he’s flying.” And so Saint Francis runs to the window and he looks out, and of course there is no flying mule. And the monk starts to laugh at him and Saint Francis says – the monk says, “You actually ran to the window to see – you thought a mule could fly?” And he said, “I believed a mule could fly before I believed that a monk could lie.”
David Hand: Ah, that’s tremendous. Yes. Yeah. Yeah.
Steve Mirsky: Anyway, I really enjoyed this book. There’s so much fun stuff in it, even if you’re not a fan of reading about people getting hit by lightning. And I think it can only help people make somewhat better sense of the swirling morass of things that go on in their day-to-day lives. Did you enjoy writing it?
David Hand: Oh, it was tremendous fun, yes. People sometimes ask me how long it takes to write a book, and I say, “There are two answers. One is 20 years sort of collecting ideas, evidence, formulating it in your mind, and the other is six months, just sitting down and actually putting pen to paper.” So two answers. I think this one took about ten years of accumulating the sort of ideas and evidence, and it was driven by, you know, probability really is intriguing and often counterintuitive; it’s just fascinating stuff. And people often find it very difficult to contend with the sort of – with uncertainty, which in some sense is another name for probability. So it’s fascinating stuff which does pervade life; it affects us all. So yeah, it was great fun to write.
Steve Mirsky: And you’re a professor of emeritus, professional statistician. You know, you’re immersed and well-versed in all this information. But in the course of writing it did you learn anything new?
David Hand: I’ve learned all sorts of new things, yes. I’ve certainly got a much better grasp of the ideas behind it, ‘cause I have to – the point about writing – science writing in general, writing scientific papers or even a book, sort of popular book like this, is that you’re forced to make sure your ideas are clear. It’s very easy when you’re just thinking about things to think, “Oh, I’ve got that. That’s no problem.” But putting it down on paper, explaining it to someone, they say the best way to learn something is to teach it, and this is rather like that. So I learned all sorts of new things.
Steve Mirsky: Remember the Audible special offer you heard about at the beginning of this episode? You can take advantage of it to get the full unabridged 8 hour and 32 minute recording of David J. Hand’s The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day. Just go to Audible.com/sciam.
That’s it for this episode. Get your science news at our website, www.ScientifiicAmerican.com. You can check out the collection of Scientific American e-books; the latest volume in the series is called Designing the Urban Future: Smart Cities. All the e-books are less than $4.00 there at Books.ScientificAmerican.com/sa-ebooks, or just go to the Scientific American homepage and look around till you find them; they’re on the right side of the page. And follow us on Twitter, where you’ll get a tweet whenever a new item hits the website. Our Twitter name is @SciAm. For Scientific American Science Talk, I’m Steve Mirsky. Thanks for clicking on us.
[End of Audio]
David J. Hand, emeritus professor of mathematics at Imperial College London, talks about his new book The Improbability Principle: Why Coincidences, Miracles and Rare Events Happen Every Day.
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