{"version":"1.0.0","segments":[{"startTime":5.225,"endTime":11.308,"body":"Is it more than chance when one person survives multiple lightning strikes and another wins"},{"startTime":11.308,"endTime":12.525,"body":"the lottery jackpot?"},{"startTime":12.545,"endTime":13.645,"body":"Not once, but twice."},{"startTime":14.475,"endTime":19.71,"body":"Mathematics can give us the tools to decide when events really are coincidences and when"},{"startTime":19.71,"endTime":21.805,"body":"other factors might be at play."},{"startTime":22.795,"endTime":28.005,"body":"Getting this right has implications everywhere from the science lab to the law courts."},{"startTime":28.785,"endTime":33.035,"body":"But let's begin with someone who you could think of as being either very lucky"},{"startTime":33.035,"endTime":33.885,"body":"or very unlucky."},{"startTime":35.325,"endTime":39.493,"body":"The Gresham College lecture that you're listening to right now is giving you knowledge and"},{"startTime":39.493,"endTime":43.661,"body":"insight from one of the world's leading academic experts, making it takes a lot of"},{"startTime":43.661,"endTime":47.829,"body":"time, but because we want to encourage a love of learning, we think it's well"},{"startTime":47.829,"endTime":48.385,"body":"worth it."},{"startTime":49.325,"endTime":52.465,"body":"We never make you pay for lectures, although donations are needed."},{"startTime":52.925,"endTime":54.225,"body":"All we ask in return is this."},{"startTime":54.735,"endTime":57.105,"body":"Send a link to this lecture to someone you think would benefit."},{"startTime":57.565,"endTime":61.481,"body":"And if you haven't already, click the follow or subscribe button from wherever you are"},{"startTime":61.481,"endTime":62.265,"body":"listening right now."},{"startTime":63.325,"endTime":64.905,"body":"Now, let's get back to the lecture."},{"startTime":67.775,"endTime":71.36,"body":"Meet Roy Sullivan, and he's bending down to show us the top of his hat,"},{"startTime":71.36,"endTime":74.945,"body":"which has scorch marks in it from where he was struck by lightning, but he"},{"startTime":74.945,"endTime":75.185,"body":"survived."},{"startTime":75.565,"endTime":80.479,"body":"So lucky or unlucky, you decide if we're gonna really understand what the chances of"},{"startTime":80.479,"endTime":85.394,"body":"this kind of event happening and whether we should attribute it to some kind of"},{"startTime":85.394,"endTime":86.705,"body":"divine intervention or not."},{"startTime":87.405,"endTime":90.265,"body":"We need to think a bit about probability."},{"startTime":90.885,"endTime":94.114,"body":"And I want to start by giving you an example of a coincidence that happened"},{"startTime":94.114,"endTime":94.545,"body":"to me."},{"startTime":95.285,"endTime":99.562,"body":"Not as unlikely as a lightning strike, but I mention it because just on this"},{"startTime":99.562,"endTime":102.985,"body":"one occasion, I can tell you the exact probability of it happening."},{"startTime":103.125,"endTime":106.79,"body":"So this is a couple of years ago, my daughter and I, we went to"},{"startTime":106.79,"endTime":108.745,"body":"visit York, lovely city, and we got hungry."},{"startTime":108.845,"endTime":111.38,"body":"We thought, we'll stop in a cafe, have something to eat, and we'll go to"},{"startTime":111.38,"endTime":112.225,"body":"the lou while we're there."},{"startTime":112.465,"endTime":113.865,"body":"I went up to buy the coffee."},{"startTime":114.325,"endTime":118.0,"body":"Um, as I was paying, you know, putting my pin into the machine, I said,"},{"startTime":118.0,"endTime":119.225,"body":"could we use the facilities?"},{"startTime":119.525,"endTime":120.825,"body":"Uh, the lady said yes."},{"startTime":121.085,"endTime":124.647,"body":"And so she handed me a piece of paper, which I thought was my receipt,"},{"startTime":124.647,"endTime":126.785,"body":"but it had my pin number written on it."},{"startTime":127.285,"endTime":132.585,"body":"So, oh, no, by the way, just for the avoidance of doubt, not my opinion."},{"startTime":133.935,"endTime":134.745,"body":"Different number."},{"startTime":135.045,"endTime":139.189,"body":"So anyway, I, I was, oh, startled then I realized, no, this is the key"},{"startTime":139.189,"endTime":143.334,"body":"code to use the facilities, but it was just for a moment, I was a"},{"startTime":143.334,"endTime":145.545,"body":"little bit freaked out, I have to admit."},{"startTime":146.045,"endTime":150.362,"body":"So we can work out the exact probability of this, because here is a four"},{"startTime":150.362,"endTime":152.665,"body":"digit number which matched the four digit number."},{"startTime":152.905,"endTime":155.225,"body":"I knew I had just typed into the, the card reader."},{"startTime":155.965,"endTime":157.905,"body":"So how many four digit numbers are there?"},{"startTime":157.905,"endTime":159.545,"body":"What are the chances of two of them matching?"},{"startTime":160.015,"endTime":162.585,"body":"Well, they've got their key card and I've got my pin."},{"startTime":162.765,"endTime":165.185,"body":"So if my pin's gonna match, it's gotta match the first number."},{"startTime":165.205,"endTime":166.465,"body":"That's a one in 10 chance."},{"startTime":166.565,"endTime":170.185,"body":"And the second number one in 10, and the third and the fourth."},{"startTime":170.645,"endTime":175.239,"body":"So the probability of that happening, uh, is one in 10,000, 10 times 10 times"},{"startTime":175.239,"endTime":176.465,"body":"10 times 10, okay?"},{"startTime":176.685,"endTime":177.905,"body":"So that's the chance of that."},{"startTime":177.965,"endTime":179.025,"body":"So it's pretty unlikely."},{"startTime":179.185,"endTime":183.76,"body":"And, uh, one side, you know, recovered from that mild surprise, I could, uh, drink"},{"startTime":183.76,"endTime":185.285,"body":"my coffee as normal \u003claugh\u003e."},{"startTime":185.305,"endTime":187.125,"body":"So we know the exact probability of that."},{"startTime":187.265,"endTime":188.565,"body":"That's quite unlikely."},{"startTime":188.945,"endTime":193.285,"body":"But actually, for, for it to happen to me, yes, unlikely a surprise."},{"startTime":193.865,"endTime":195.805,"body":"But there are lots of tourists in New York."},{"startTime":196.305,"endTime":202.801,"body":"The year that we went, I looked it up, 8.9 million people visited that beautiful"},{"startTime":202.801,"endTime":209.298,"body":"city and each of them are likely gonna have one, probably several cards, bank cards"},{"startTime":209.298,"endTime":210.165,"body":"with pins."},{"startTime":211.225,"endTime":213.365,"body":"Uh, so I was thinking, well, can we be sure?"},{"startTime":213.365,"endTime":214.165,"body":"How do we know how many?"},{"startTime":214.585,"endTime":217.925,"body":"And I thought, well, adults normally have at least two of these."},{"startTime":218.025,"endTime":220.485,"body":"You probably have a debit card and a credit card, maybe more."},{"startTime":220.785,"endTime":222.565,"body":"And of course, newborn babies don't have any."},{"startTime":222.585,"endTime":225.125,"body":"But let's say that on average, you know, there's one purpose."},{"startTime":225.465,"endTime":229.721,"body":"So there are 8.9 million pins wandering around New York at some point in the"},{"startTime":229.721,"endTime":230.005,"body":"year."},{"startTime":230.505,"endTime":235.611,"body":"Um, so if it's one in 10,000 chance and they are kind of randomly distributed,"},{"startTime":235.611,"endTime":240.718,"body":"which pretty much they are, we would expect 890 people in York during the year"},{"startTime":240.718,"endTime":245.485,"body":"to have the same, uh, pin as the key code in that cafe, right?"},{"startTime":245.815,"endTime":248.165,"body":"890, that's nearly three a day."},{"startTime":248.505,"endTime":250.045,"body":"So I don't feel so special anymore."},{"startTime":251.225,"endTime":254.205,"body":"And that's the first thing we have to observe about probability."},{"startTime":254.865,"endTime":260.047,"body":"But even if it's very unlikely, it's probably gonna happen to someone if you have"},{"startTime":260.047,"endTime":261.084,"body":"enough people involved."},{"startTime":261.665,"endTime":266.073,"body":"So that's sort of a bit of a paradox, but it's not really that even"},{"startTime":266.073,"endTime":270.481,"body":"very unlikely events are likely to occur in a big enough population if you have"},{"startTime":270.481,"endTime":272.245,"body":"enough opportunities for them to occur."},{"startTime":272.865,"endTime":276.405,"body":"So let's get back to poor old slash lucky old Roy Sullivan."},{"startTime":277.305,"endTime":281.701,"body":"Now, we would need to know if we're gonna understand just how unlikely this is,"},{"startTime":281.701,"endTime":284.925,"body":"we'd need to know the probability of being struck by lightning."},{"startTime":285.075,"endTime":287.645,"body":"Happily, the US weather services work this out for us."},{"startTime":287.905,"endTime":292.816,"body":"And they have an estimate that the, uh, probability of being struck by lightning at"},{"startTime":292.816,"endTime":297.727,"body":"least once in your life, at least in in the US probably in other places,"},{"startTime":297.727,"endTime":299.365,"body":"two, is one in 15,300."},{"startTime":299.745,"endTime":303.285,"body":"So it's a bit less likely than my very exciting cafe coincidence."},{"startTime":303.285,"endTime":305.765,"body":"But, you know, it's not incredibly, incredibly unlikely."},{"startTime":306.355,"endTime":310.125,"body":"However, this guy is struck multiple times, seven times."},{"startTime":310.345,"endTime":313.885,"body":"In fact, he was struck by lightning during his life and survived every single time."},{"startTime":315.265,"endTime":319.042,"body":"So, so you could think about how can we work out the chance of being"},{"startTime":319.042,"endTime":320.805,"body":"struck twice by lightning in your life?"},{"startTime":321.545,"endTime":326.32,"body":"Now, when we calculate probabilities with things like tossing coins or rolling dice, we might"},{"startTime":326.32,"endTime":331.096,"body":"say, okay, if I, if I toss a coin, the chance of it coming up"},{"startTime":331.096,"endTime":333.325,"body":"heads is, is a half 50 50."},{"startTime":333.625,"endTime":336.951,"body":"And if I toss two coins, then the chance of both of them coming up"},{"startTime":336.951,"endTime":338.725,"body":"heads is a half times a half, right?"},{"startTime":338.825,"endTime":339.285,"body":"One quarter."},{"startTime":339.985,"endTime":345.646,"body":"So you might say, well, okay, the chance then of being struck by lightning twice"},{"startTime":345.646,"endTime":351.307,"body":"would be one in 15,000 times, one in 15,000, one in 243 ish, 234 ish"},{"startTime":351.307,"endTime":351.685,"body":"million."},{"startTime":352.065,"endTime":354.165,"body":"But that is not the correct calculation."},{"startTime":354.345,"endTime":358.645,"body":"And the reason is we may have noticed human beings are not coins, \u003claugh\u003e."},{"startTime":358.645,"endTime":363.799,"body":"Um, those, the, the chance of us being struck by lightning is gonna vary from"},{"startTime":363.799,"endTime":366.205,"body":"person to person based on different factors."},{"startTime":366.385,"endTime":371.121,"body":"And so being struck once by lightning is not completely independent event from being struck"},{"startTime":371.121,"endTime":375.857,"body":"again by lightning because maybe you are the sort of person who's likely to get"},{"startTime":375.857,"endTime":376.805,"body":"struck by lightning."},{"startTime":376.955,"endTime":377.965,"body":"What do I mean by that?"},{"startTime":378.305,"endTime":383.921,"body":"Not that you are cursed by the gods, hopefully, but so many factors can intervene"},{"startTime":383.921,"endTime":385.045,"body":"your geographical location."},{"startTime":385.185,"endTime":389.994,"body":"So in, in America, uh, states that are on the, the east coast, maybe towards"},{"startTime":389.994,"endTime":394.803,"body":"the south, they have higher rainfall, they have more thunderstorms, and therefore more lightning than"},{"startTime":394.803,"endTime":395.445,"body":"other places."},{"startTime":395.865,"endTime":397.925,"body":"So geographical location matters for you."},{"startTime":398.385,"endTime":403.285,"body":"Um, I, I won't speculate on the causes for the fact that of all the"},{"startTime":403.285,"endTime":407.205,"body":"people struck by lightning, 84% are men and only 16% are women."},{"startTime":407.665,"endTime":411.333,"body":"Um, I don't know, let's not even speculate on my, that might be another factor"},{"startTime":411.333,"endTime":413.045,"body":"though, is the job that you do."},{"startTime":413.465,"endTime":417.593,"body":"Uh, if, if you are working indoors a lot, you're gonna have be less, less"},{"startTime":417.593,"endTime":419.245,"body":"likely to be struck by lightning."},{"startTime":419.345,"endTime":424.509,"body":"So if we gather those kind of factors together, we could say, you know, this"},{"startTime":424.509,"endTime":429.674,"body":"is an average likelihood, but people will have different personal likelihoods, um, in order to"},{"startTime":429.674,"endTime":432.085,"body":"have to have be struck by lightning."},{"startTime":432.225,"endTime":436.08,"body":"So if you are, I dunno, a woman working in a library in Alaska, you"},{"startTime":436.08,"endTime":439.936,"body":"are much less likely to be struck by lightning van, a man working as a"},{"startTime":439.936,"endTime":440.965,"body":"park ranger in Virginia."},{"startTime":441.505,"endTime":444.805,"body":"So no guesses what Roy Sullivan's job was."},{"startTime":445.025,"endTime":446.605,"body":"Yes, he was a park ranger in Virginia."},{"startTime":447.345,"endTime":452.127,"body":"So he's much, much, much more likely than this overall, overall average to get struck"},{"startTime":452.127,"endTime":452.765,"body":"by lightning."},{"startTime":452.965,"endTime":457.165,"body":"I mean, of course it's still really unlikely to be struck seven times."},{"startTime":457.305,"endTime":459.405,"body":"And that's why, you know, we know about him."},{"startTime":459.405,"endTime":461.485,"body":"That's why he's, he's an interesting example."},{"startTime":461.985,"endTime":467.966,"body":"But we have to be careful about using average, uh, likelihoods in those kind of"},{"startTime":467.966,"endTime":468.365,"body":"situations."},{"startTime":468.945,"endTime":473.236,"body":"He, of all the people in America, was really high ranking in his chances to"},{"startTime":473.236,"endTime":475.525,"body":"be someone who would be struck multiple times."},{"startTime":477.025,"endTime":482.531,"body":"But if we think about very unlikely events, sometimes it seems so improbable that, that"},{"startTime":482.531,"endTime":488.037,"body":"they could happen by chance, that we start to wonder is something else going on"},{"startTime":488.037,"endTime":488.405,"body":"here?"},{"startTime":489.065,"endTime":494.415,"body":"And sometimes that happens when there are people who appear to be making amazing predictions"},{"startTime":494.415,"endTime":495.485,"body":"of the future."},{"startTime":495.805,"endTime":501.286,"body":"Premonitions clairvoyance, for instance, uh, there was a woman called Jean Dixon who was, you"},{"startTime":501.286,"endTime":503.845,"body":"know, proclaimed herself to be a psychic."},{"startTime":504.225,"endTime":509.725,"body":"Now she predicted that the 1960 US election would be won by a Democrat."},{"startTime":509.755,"endTime":510.965,"body":"Okay, that's not so impressive."},{"startTime":511.065,"endTime":512.885,"body":"But then who would be assassinated in office?"},{"startTime":513.465,"endTime":516.581,"body":"And for those of you who are history buffs, you may have heard of, uh,"},{"startTime":516.581,"endTime":517.205,"body":"John F. Kennedy."},{"startTime":517.544,"endTime":519.445,"body":"And indeed that's exactly what happened."},{"startTime":519.445,"endTime":523.085,"body":"So this seems really kind of spooky thing to predict."},{"startTime":523.914,"endTime":526.205,"body":"Very, very unlikely that you could predict that by chance."},{"startTime":526.305,"endTime":528.165,"body":"So surely there's something more going on."},{"startTime":529.155,"endTime":535.011,"body":"Well, let's discuss this and lead into this with thinking about really rare, unlikely seeming"},{"startTime":535.011,"endTime":538.525,"body":"events, the one in a million kind of event."},{"startTime":540.625,"endTime":545.021,"body":"Can we ever expect to see things if something that's as unlikely as this happens,"},{"startTime":545.021,"endTime":549.125,"body":"do we, and should we conclude that something more than chance is at play?"},{"startTime":550.475,"endTime":552.485,"body":"Well, let's, again, let's have a little warmup for this."},{"startTime":552.545,"endTime":554.605,"body":"Uh, these are big numbers to work with."},{"startTime":555.055,"endTime":559.952,"body":"Let's think about the kind of event maybe that that would be not dependent on"},{"startTime":559.952,"endTime":562.565,"body":"your geo geographical location or something like that."},{"startTime":562.815,"endTime":565.85,"body":"Let's imagine that all of us tonight, you know, we go to bed and in"},{"startTime":565.85,"endTime":568.885,"body":"the morning we wake up and we write down something that happened in our dream."},{"startTime":569.065,"endTime":571.685,"body":"And then we see if anyone has predicted the future."},{"startTime":572.305,"endTime":574.685,"body":"Did any of those dreams actually come true in real life?"},{"startTime":575.245,"endTime":578.325,"body":"'cause occasionally we hear about things like this, very unlikely to, to happen."},{"startTime":578.985,"endTime":582.325,"body":"So instead of dreams, let's think about a, a much more likely event."},{"startTime":582.535,"endTime":584.165,"body":"Let's say we're all rolling dice."},{"startTime":584.745,"endTime":585.805,"body":"Now there are some dice."},{"startTime":585.825,"endTime":590.277,"body":"So if I roll one die and I'm trying to get a six, the chances"},{"startTime":590.277,"endTime":593.245,"body":"of me doing it is one in six, about 17%."},{"startTime":593.625,"endTime":597.21,"body":"But let's say the group of us are all try, we all are rolling a"},{"startTime":597.21,"endTime":598.645,"body":"die, die together, uh, one each."},{"startTime":598.745,"endTime":601.903,"body":"And we are trying to say, can the group collectively get a six, at least"},{"startTime":601.903,"endTime":602.325,"body":"one six?"},{"startTime":602.595,"endTime":604.245,"body":"Well then things get better for us."},{"startTime":604.465,"endTime":607.456,"body":"So if two of us, if there are two of us now each roll a"},{"startTime":607.456,"endTime":610.448,"body":"die, um, then, and we are hoping to get some, one of us will get"},{"startTime":610.448,"endTime":611.845,"body":"a six, at least one of us."},{"startTime":612.265,"endTime":613.685,"body":"So there's different ways that could happen."},{"startTime":613.965,"endTime":617.005,"body":"I could get one or you could get one or we could both get one."},{"startTime":617.265,"endTime":621.27,"body":"So instead of working all those out separately, it's a much quicker way of doing"},{"startTime":621.27,"endTime":621.805,"body":"that calculation."},{"startTime":622.065,"endTime":627.407,"body":"And it's to notice that the probability of rolling at least one six, um, is"},{"startTime":627.407,"endTime":631.325,"body":"one minus the probability of not rolling any sixes at all."},{"startTime":632.505,"endTime":636.501,"body":"So if the probability of rolling a six with, with one dye is one six,"},{"startTime":636.501,"endTime":639.165,"body":"then the probability of not doing that is five six."},{"startTime":640.065,"endTime":643.915,"body":"So if both the dice do not roll a six, and they are, that's it,"},{"startTime":643.915,"endTime":644.685,"body":"those independent events."},{"startTime":644.685,"endTime":649.16,"body":"So we can multiply the probabilities and we see that the probability of rolling no"},{"startTime":649.16,"endTime":651.845,"body":"sixes at all is five six times five six."},{"startTime":652.345,"endTime":656.234,"body":"And so if we subtract that from one, we get the probability of rolling at"},{"startTime":656.234,"endTime":659.605,"body":"least one, six, maybe both of us get lucky, but at least one."},{"startTime":660.025,"endTime":662.205,"body":"And we see that it's actually about 31%."},{"startTime":662.205,"endTime":663.605,"body":"So we've nearly doubled our chances."},{"startTime":664.505,"endTime":668.61,"body":"And if we have three dice and we want to roll at least one six,"},{"startTime":668.61,"endTime":672.716,"body":"same idea, and you now it's a 42% chance that at least one of us"},{"startTime":672.716,"endTime":674.085,"body":"will will get a six."},{"startTime":674.465,"endTime":678.112,"body":"And if you have four dice or four people rolling a dye, then it goes"},{"startTime":678.112,"endTime":679.085,"body":"up to above 50%."},{"startTime":679.505,"endTime":682.965,"body":"So we could more likely than not that someone's gonna roll a six."},{"startTime":683.785,"endTime":687.13,"body":"Now of course, it's easier to role a six than it is to have a"},{"startTime":687.13,"endTime":688.245,"body":"preliminary dream that comes true."},{"startTime":688.705,"endTime":690.685,"body":"But the same principle is going to apply."},{"startTime":691.065,"endTime":695.38,"body":"If you have a group of people, um, all kind of writing down their dreams"},{"startTime":695.38,"endTime":699.696,"body":"or making a prediction, then we can look at the chances that at least one"},{"startTime":699.696,"endTime":703.725,"body":"of those predictions will be right in exactly the same way, just bigger numbers."},{"startTime":704.345,"endTime":707.657,"body":"So let's, we might think about a one in a million kind of event, but"},{"startTime":707.657,"endTime":709.645,"body":"just for the moment, let's use our favorite number."},{"startTime":709.815,"endTime":711.405,"body":"Think about the one in n event."},{"startTime":711.645,"endTime":712.925,"body":"N is the mathematician's favorite number."},{"startTime":713.385,"endTime":715.645,"body":"So let's imagine n is a very big, big number, right?"},{"startTime":715.645,"endTime":720.097,"body":"So the probability of some event having a predictive dream or something else is one"},{"startTime":720.097,"endTime":721.285,"body":"in n let's say."},{"startTime":722.475,"endTime":727.166,"body":"Then if we have a bunch of people who all have an opportunity to, to"},{"startTime":727.166,"endTime":731.858,"body":"have this occur, like predicting the future in a dream, then the chance that none"},{"startTime":731.858,"endTime":735.925,"body":"of them will experience that is we've got one minus one over n."},{"startTime":735.985,"endTime":739.405,"body":"That's the chance of one person not experiencing that unlikely event."},{"startTime":740.985,"endTime":742.685,"body":"Uh, but there are K people altogether."},{"startTime":742.865,"endTime":746.879,"body":"So we raise that to the power K, that is the chance of none of"},{"startTime":746.879,"endTime":748.485,"body":"those K people experiencing that event."},{"startTime":748.875,"endTime":749.365,"body":"Alright?"},{"startTime":749.745,"endTime":754.292,"body":"Now there's a really cute rule of thumb I'm gonna show you now, if you've"},{"startTime":754.292,"endTime":758.839,"body":"got this event that's unlikely to happen, a one in end chance of it happening,"},{"startTime":758.839,"endTime":763.386,"body":"if we have end people and look at what happens to that expression as end"},{"startTime":763.386,"endTime":765.205,"body":"changes, a really nice thing happens."},{"startTime":765.745,"endTime":766.605,"body":"I'm gonna show you the graph."},{"startTime":767.235,"endTime":771.15,"body":"This is the graph of that strange looking function, one minus one over N race"},{"startTime":771.15,"endTime":774.805,"body":"power n Um, as n gets bigger, I've put it on a logarithmic scale."},{"startTime":774.805,"endTime":777.125,"body":"So you can see n getting bigger on the, on the X axis."},{"startTime":777.625,"endTime":779.085,"body":"And then we are plotting this value."},{"startTime":779.345,"endTime":783.365,"body":"And you can see that it very quickly approaches some constant value."},{"startTime":784.155,"endTime":786.165,"body":"It's never quite reaches it, but it getting really, really close."},{"startTime":786.185,"endTime":790.53,"body":"As soon as n is big enough, and even n you know, around a hundred"},{"startTime":790.53,"endTime":794.876,"body":"bigger than that, we're getting closer and closer to this number, which is sort of"},{"startTime":794.876,"endTime":796.325,"body":"about 0.37 somewhere around there."},{"startTime":797.465,"endTime":801.165,"body":"So if, if you are a mathematician, you might recognize what this number is."},{"startTime":801.785,"endTime":805.685,"body":"Uh, well it's one over EE the famous constant."},{"startTime":806.225,"endTime":810.455,"body":"The natural algorithm doesn't matter if you don't know what that number is, but this"},{"startTime":810.455,"endTime":814.685,"body":"is one over it \u003claugh\u003e and it's roughly 0.3, six, seven and some other stuff."},{"startTime":815.185,"endTime":820.415,"body":"So as n gets bigger, and for the purposes of this talk, uh, a hundred"},{"startTime":820.415,"endTime":825.645,"body":"equals infinity, then we can make this approximation that, that we get this number 0.367."},{"startTime":825.785,"endTime":831.45,"body":"So that means that about 37% of the time in a group of n people"},{"startTime":831.45,"endTime":837.116,"body":"all having the opportunity for this one in n type of event, 37% of the"},{"startTime":837.116,"endTime":839.005,"body":"time nobody will experience it."},{"startTime":839.225,"endTime":844.077,"body":"But that means that 63% of the time, at least one person will experience this"},{"startTime":844.077,"endTime":844.725,"body":"rare event."},{"startTime":845.145,"endTime":849.409,"body":"So if we have a million people, um, who in the morning write down their"},{"startTime":849.409,"endTime":853.673,"body":"dream or write down a prediction, 63% of the time, if it is a one"},{"startTime":853.673,"endTime":857.085,"body":"in a million shot, um, at least one person will experience it."},{"startTime":857.085,"endTime":860.385,"body":"And of course those are the people that phone up the radio station and say,"},{"startTime":860.385,"endTime":861.485,"body":"I can predict the future."},{"startTime":862.145,"endTime":865.205,"body":"So that's, uh, kind of an interesting thing to observe."},{"startTime":865.215,"endTime":867.565,"body":"Again, it's if you've got enough people, it's gonna happen."},{"startTime":869.265,"endTime":875.301,"body":"Now, this is, uh, describing a situation where you've got a big bunch of people"},{"startTime":875.301,"endTime":879.325,"body":"all having one opportunity for a rare event to happen."},{"startTime":879.905,"endTime":883.791,"body":"But we can turn it the other way round and think about one person having"},{"startTime":883.791,"endTime":885.605,"body":"many opportunities for an event to happen."},{"startTime":886.345,"endTime":891.013,"body":"And exactly the same mathematics tells us, if you've got this very rare event, a"},{"startTime":891.013,"endTime":895.682,"body":"one in a million or one in end type of event, um, if you have"},{"startTime":895.682,"endTime":900.351,"body":"n opportunities for it to occur, then again there's a 63% chance that it'll happen"},{"startTime":900.351,"endTime":901.285,"body":"at least once."},{"startTime":903.305,"endTime":906.685,"body":"And okay, what about if you wanna know when it becomes more likely than not?"},{"startTime":906.715,"endTime":908.285,"body":"Well, you have to do a bit more calculated."},{"startTime":908.285,"endTime":912.345,"body":"But it turns out, um, if you have at least this many 0.6, nine, four"},{"startTime":912.345,"endTime":916.405,"body":"ish, uh, n attempts at this thing or opportunities for this thing to happen, then"},{"startTime":916.405,"endTime":919.925,"body":"it becomes more likely than not that it will happen at least once."},{"startTime":920.665,"endTime":925.907,"body":"So if you've got a one in a million shot, incredibly rare freak, spooky coincidence,"},{"startTime":925.907,"endTime":928.005,"body":"I mean choose your favorite thing."},{"startTime":928.125,"endTime":930.77,"body":"You know, you are, you are just thinking about someone you haven't seen for 20"},{"startTime":930.77,"endTime":932.005,"body":"years, the phone rings and it's them."},{"startTime":932.385,"endTime":935.882,"body":"Or you go into a random secondhand bookshop when you're on your, on holiday somewhere"},{"startTime":935.882,"endTime":939.38,"body":"and you pick up a book and you find it used to belong to your"},{"startTime":939.38,"endTime":942.645,"body":"father or, you know, name your freaky coincidence, A one in a million shot."},{"startTime":942.745,"endTime":946.741,"body":"We have a few of these, you know, many of these potentially can happen to"},{"startTime":946.741,"endTime":949.405,"body":"us in the course of a day if we have."},{"startTime":949.465,"endTime":950.925,"body":"So n is a million right now."},{"startTime":951.265,"endTime":956.031,"body":"So that means if we have more than 694,000 opportunities for such a thing to"},{"startTime":956.031,"endTime":959.845,"body":"occur, then it's more likely than not that, that it will occur."},{"startTime":960.265,"endTime":964.805,"body":"So let's think about how many opportunities one would have in one's life for a"},{"startTime":964.805,"endTime":966.925,"body":"really rare event like that to happen."},{"startTime":967.745,"endTime":971.005,"body":"So during the course of our day, lots of chances, you know, you're walking around,"},{"startTime":971.005,"endTime":974.265,"body":"you could bump into people who you haven't seen for 40 years, or you could"},{"startTime":974.265,"endTime":977.525,"body":"get that phone call outta the blue when you had a dream about that person."},{"startTime":977.625,"endTime":981.114,"body":"Or you could, yes, at the night in nighttime, you could have this preliminary dream,"},{"startTime":981.114,"endTime":982.045,"body":"all sorts of things."},{"startTime":982.045,"endTime":987.13,"body":"So I'm gonna guesstimate one opportunity per hour on average for a one in a"},{"startTime":987.13,"endTime":989.165,"body":"million kind of event to happen."},{"startTime":989.325,"endTime":990.605,"body":"A really freaky coincidence."},{"startTime":991.065,"endTime":994.565,"body":"So how many hours are we going to be alive for not starting from now"},{"startTime":994.565,"endTime":995.965,"body":"over the course of our life?"},{"startTime":996.515,"endTime":1001.485,"body":"Well, based on the UK life expectancy, it's about, uh, 720,000."},{"startTime":1002.545,"endTime":1004.965,"body":"So have I fiddled the figures a bit?"},{"startTime":1004.965,"endTime":1009.525,"body":"Maybe, well, you can decide \u003claugh\u003e, but look, that's more than 694,000."},{"startTime":1010.025,"endTime":1014.255,"body":"So I, I suggest that we all have a better than average chart, better than"},{"startTime":1014.255,"endTime":1018.485,"body":"even chance of a one in a million event at some time in our lives."},{"startTime":1019.065,"endTime":1023.407,"body":"So maybe these things, you know, we, we, of course they're surprising and exciting when"},{"startTime":1023.407,"endTime":1025.723,"body":"they happen, but they are going to happen."},{"startTime":1027.385,"endTime":1033.045,"body":"Now, the amazing psychic clairvoyant, Jean Dixon had something else on her side."},{"startTime":1034.105,"endTime":1037.285,"body":"Uh, and I'm gonna you three rules for how to become very successful."},{"startTime":1037.714,"endTime":1039.565,"body":"Clairvoyant psychic."},{"startTime":1040.223,"endTime":1044.649,"body":"Uh, so this is her famous prediction that, that the Kennedy assassination, but here are"},{"startTime":1044.649,"endTime":1046.125,"body":"some of her other predictions."},{"startTime":1046.743,"endTime":1050.455,"body":"Um, she also predicted that \u003claugh\u003e the Now and she changed her mind and said,"},{"startTime":1050.455,"endTime":1051.445,"body":"actually Nixon's gonna win."},{"startTime":1051.705,"endTime":1054.757,"body":"Um, she said that Russia would be the first country to put a man on"},{"startTime":1054.757,"endTime":1055.165,"body":"the moon."},{"startTime":1055.345,"endTime":1060.045,"body":"She said that World War II would be begin in 1958 and where we'll have"},{"startTime":1060.045,"endTime":1063.805,"body":"to see \u003claugh\u003e if, if China actually does invade Russia in 2025."},{"startTime":1063.925,"endTime":1064.405,"body":"I hope not."},{"startTime":1064.665,"endTime":1066.725,"body":"But look at this list of predictions."},{"startTime":1067.505,"endTime":1071.765,"body":"We, uh, remember, remember we hear about the first one 'cause it happened."},{"startTime":1072.905,"endTime":1077.261,"body":"But there are two rules, and I'll give you the third and a second to,"},{"startTime":1077.261,"endTime":1080.165,"body":"to improve your like, ability to boast about successful predictions."},{"startTime":1080.315,"endTime":1082.525,"body":"Make a lot of predictions, and then forget the ones you got wrong."},{"startTime":1082.705,"endTime":1086.442,"body":"So if you are absent-minded fortune teller who's very busy, you're gonna, you're gonna be"},{"startTime":1086.442,"endTime":1088.685,"body":"able to say, oh, I was right about that."},{"startTime":1088.685,"endTime":1089.925,"body":"And just forget about all the others."},{"startTime":1090.705,"endTime":1094.725,"body":"Now Nostradamus here can show us the third rule of successful fortune telling."},{"startTime":1095.035,"endTime":1097.885,"body":"I'll give you an example of a genuine, uh, prediction that he made."},{"startTime":1098.265,"endTime":1101.97,"body":"And it's this in the world, there'll be made a king who will have little"},{"startTime":1101.97,"endTime":1103.205,"body":"peace and a short life."},{"startTime":1103.545,"endTime":1110.295,"body":"So correct, that's definitely happened many times since Nostradamus, but that's so vague, you know,"},{"startTime":1110.295,"endTime":1113.445,"body":"there's nothing we can do with it."},{"startTime":1113.825,"endTime":1117.384,"body":"So if you are very vague, then you can retrospectively say, oh, well I, that's"},{"startTime":1117.384,"endTime":1119.045,"body":"what I meant when I said that."},{"startTime":1119.045,"endTime":1122.125,"body":"You know, there'll be a big apple in in the west."},{"startTime":1122.325,"endTime":1124.805,"body":"I meant that apple computers would \u003claugh\u003e."},{"startTime":1125.795,"endTime":1126.085,"body":"What?"},{"startTime":1126.345,"endTime":1130.165,"body":"So, okay, vague, many predictions be forgetful."},{"startTime":1130.385,"endTime":1135.005,"body":"That's how to be a successful fortune teller, um, without having to rely on even"},{"startTime":1135.005,"endTime":1138.085,"body":"these coincidences that we know will happen in our lifetimes."},{"startTime":1139.625,"endTime":1144.085,"body":"So, okay, she got lucky with that, uh, \u003claugh\u003e prediction that she made Jean Dixon."},{"startTime":1144.665,"endTime":1149.376,"body":"But there are sometimes examples of what seem incredible luck and can we really explain"},{"startTime":1149.376,"endTime":1150.005,"body":"those away?"},{"startTime":1150.555,"endTime":1151.845,"body":"Well, let's see how we get on."},{"startTime":1152.995,"endTime":1154.765,"body":"Here are two very, very lucky people."},{"startTime":1155.105,"endTime":1159.109,"body":"Uh, even Marie Adams won the New Jersey lottery, the jackpot in the New Jersey"},{"startTime":1159.109,"endTime":1161.245,"body":"lottery twice in the space of a year."},{"startTime":1162.385,"endTime":1166.127,"body":"No one's done that in the UK yet, at the time of speaking right now"},{"startTime":1166.127,"endTime":1167.125,"body":"could happen any moment."},{"startTime":1167.545,"endTime":1172.005,"body":"But this, uh, chap Mike McDermott, he won the next best thing."},{"startTime":1172.025,"endTime":1175.645,"body":"He twice managed in, I bet he was obscurely disappointed, right?"},{"startTime":1175.965,"endTime":1179.548,"body":"\u003claugh\u003e, he, he twice match five balls in the bonus ball, which is like the"},{"startTime":1179.548,"endTime":1183.131,"body":"next sort of the second prize level in the national lottery in the uk uh,"},{"startTime":1183.131,"endTime":1184.565,"body":"in the space of a year."},{"startTime":1185.425,"endTime":1188.085,"body":"So these, I mean the odds of that happening are, are tiny."},{"startTime":1188.585,"endTime":1190.645,"body":"Uh, it's really, really unlikely for it to happen."},{"startTime":1191.555,"endTime":1198.114,"body":"However, \u003claugh\u003e, however, we can again, think about the fact that although of course it's"},{"startTime":1198.114,"endTime":1202.925,"body":"extraordinarily unlikely that that particular person will win the lottery twice."},{"startTime":1204.015,"endTime":1207.845,"body":"There are lots of people who win the lottery in, in the world every year."},{"startTime":1208.265,"endTime":1211.005,"body":"So again, we do a little bit of a back of the envelope calculation."},{"startTime":1211.335,"endTime":1215.919,"body":"Let's think about, so every country, pretty much every country has a national lottery and"},{"startTime":1215.919,"endTime":1218.365,"body":"many countries have lots and lots of lotteries."},{"startTime":1218.825,"endTime":1222.565,"body":"Uh, because in America, for example, every state will have a lottery."},{"startTime":1222.625,"endTime":1223.565,"body":"So that's another 50."},{"startTime":1224.025,"endTime":1229.436,"body":"So conservative estimate, let's say there are 200 national or state lotteries around the world,"},{"startTime":1229.436,"endTime":1233.765,"body":"and each one, um, will have on average two draws every week."},{"startTime":1233.865,"endTime":1235.325,"body":"So in Britain we have two draws every week."},{"startTime":1235.325,"endTime":1236.405,"body":"Some places they have three."},{"startTime":1236.825,"endTime":1241.405,"body":"Um, but let's say a hundred draws each year in each of 200 lotteries."},{"startTime":1242.115,"endTime":1246.733,"body":"That means 20,000 lottery draws around the world each year, each of of which can"},{"startTime":1246.733,"endTime":1247.965,"body":"give us a winner."},{"startTime":1248.425,"endTime":1251.285,"body":"Now, some don't give us any winners, you know, then there's a rollover."},{"startTime":1251.785,"endTime":1256.325,"body":"Uh, but others, in other weeks, several people should have to share the jackpot."},{"startTime":1256.485,"endTime":1257.605,"body":"'cause there are several winning tickets."},{"startTime":1257.985,"endTime":1261.797,"body":"So again, let's sort of average it out and say we might expect one winner"},{"startTime":1261.797,"endTime":1264.085,"body":"for each of these 20,000 draws in the year."},{"startTime":1264.305,"endTime":1268.045,"body":"So that gives us 20,000 jackpot winners each year being created."},{"startTime":1269.065,"endTime":1272.415,"body":"Now, it's a weird thing of course to win the lottery twice, you have to"},{"startTime":1272.415,"endTime":1273.085,"body":"enter it twice."},{"startTime":1273.625,"endTime":1277.54,"body":"It does seem to be the case that even people who win the jackpot, they"},{"startTime":1277.54,"endTime":1278.845,"body":"carry on buying lottery tickets."},{"startTime":1278.865,"endTime":1280.165,"body":"You think, well, aren't they Richard off already?"},{"startTime":1280.635,"endTime":1284.376,"body":"Well maybe they think I've done it once, it's working for me so far, \u003claugh\u003e,"},{"startTime":1284.376,"endTime":1285.125,"body":"let's carry on."},{"startTime":1285.185,"endTime":1288.835,"body":"But it does seem as if people do carry on buying lottery tickets even if"},{"startTime":1288.835,"endTime":1289.565,"body":"after they win."},{"startTime":1289.865,"endTime":1294.165,"body":"So you've got these 20,000 people who are potential in the pool to be able"},{"startTime":1294.165,"endTime":1295.885,"body":"to win for a second time."},{"startTime":1296.585,"endTime":1297.805,"body":"Now, what are the odds of winning the lottery?"},{"startTime":1297.875,"endTime":1301.897,"body":"Well, I gave a whole lecture on this last year, so I won't go into"},{"startTime":1301.897,"endTime":1305.92,"body":"a lot of detail, but the most common kind of lottery is the pick six"},{"startTime":1305.92,"endTime":1306.725,"body":"numbers from 49."},{"startTime":1306.985,"endTime":1308.365,"body":"That's the most common one still."},{"startTime":1308.665,"endTime":1311.565,"body":"Um, the odds of that are one in about 14 million."},{"startTime":1311.865,"endTime":1316.629,"body":"So I'm gonna say that that's my average summer, much more likely to win like"},{"startTime":1316.629,"endTime":1319.805,"body":"the Polish lottery, it's one in 850,000 only to win."},{"startTime":1320.065,"endTime":1323.805,"body":"Um, you get a smaller prize, of course in the uk ours is more like"},{"startTime":1323.805,"endTime":1327.546,"body":"one in 45 million, but let's take one in 14 million as a, as a"},{"startTime":1327.546,"endTime":1328.045,"body":"reasonable average."},{"startTime":1328.705,"endTime":1333.925,"body":"So each of these 20,000 ja jackpot winners, they're doing their local lottery every week."},{"startTime":1333.925,"endTime":1335.725,"body":"So they have a hundred, uh, draws every year."},{"startTime":1336.145,"endTime":1340.423,"body":"Um, and and every time they do it, there's a chance that they might become"},{"startTime":1340.423,"endTime":1341.565,"body":"a double lottery winner."},{"startTime":1342.805,"endTime":1343.445,"body":"Probably they won't."},{"startTime":1343.585,"endTime":1345.805,"body":"But let's work out the probabilities."},{"startTime":1346.945,"endTime":1351.882,"body":"Uh, so again, we'll do, like we did for the d and the one in"},{"startTime":1351.882,"endTime":1356.82,"body":"a million shot, the chance of any one of these, uh, people not winning is"},{"startTime":1356.82,"endTime":1359.125,"body":"one minus one in 14 million, right?"},{"startTime":1359.345,"endTime":1363.764,"body":"So the chance that the probability that all of them will not win is that"},{"startTime":1363.764,"endTime":1367.005,"body":"number to the power 20,000 multiplied by, by itself 20,000 times."},{"startTime":1367.545,"endTime":1369.765,"body":"And that's still very likely to be the outcome, right?"},{"startTime":1369.765,"endTime":1376.717,"body":"Point nine nine eight six probability of nobody becoming the, uh, double jackpot winner that,"},{"startTime":1376.717,"endTime":1377.645,"body":"that draw."},{"startTime":1378.265,"endTime":1382.633,"body":"But one minus that is the chance that someone will become, uh, a double lottery"},{"startTime":1382.633,"endTime":1382.925,"body":"winner."},{"startTime":1383.145,"endTime":1385.645,"body":"So one minus that, that's about one in 700."},{"startTime":1386.425,"endTime":1390.525,"body":"So now all we have to do is okay, n equals 700, do my n"},{"startTime":1390.525,"endTime":1392.165,"body":"0.694 n trick rule of thumb."},{"startTime":1392.505,"endTime":1399.091,"body":"And we find that actually after 493 draws, it becomes more likely than not that"},{"startTime":1399.091,"endTime":1402.605,"body":"someone will become, uh, a double lottery winner."},{"startTime":1403.065,"endTime":1406.885,"body":"So every few years we will expect to see this happen somewhere in the world."},{"startTime":1406.905,"endTime":1410.783,"body":"We obviously can't predict that it's gonna be evil and Marie Adams and the New"},{"startTime":1410.783,"endTime":1414.662,"body":"Jersey lottery, but we can expect every few years somewhere in the world someone will"},{"startTime":1414.662,"endTime":1417.765,"body":"have this incredible luck of winning the lottery for a second time."},{"startTime":1418.305,"endTime":1422.648,"body":"So it, it could happen \u003claugh\u003e, it just pretty sure it won't happen to any"},{"startTime":1422.648,"endTime":1424.965,"body":"of us, but nevermind, keep our hopes up."},{"startTime":1425.625,"endTime":1429.019,"body":"Now there's something, other, other thing that can happen in the lottery and it has"},{"startTime":1429.019,"endTime":1429.925,"body":"happened at least once."},{"startTime":1430.345,"endTime":1433.125,"body":"And this is another sort of incredible coincidence."},{"startTime":1433.625,"endTime":1437.87,"body":"I'm gonna show you just a screen grab from the BBC uh, news website of"},{"startTime":1437.87,"endTime":1439.285,"body":"the time of the event."},{"startTime":1440.185,"endTime":1443.525,"body":"The Bulgarian authorities have ordered an investigation."},{"startTime":1443.545,"endTime":1447.903,"body":"It says after the same six numbers were drawn in two consecutive rounds of the"},{"startTime":1447.903,"endTime":1448.485,"body":"national lottery."},{"startTime":1448.665,"endTime":1453.827,"body":"So imagine the shock and panic \u003claugh\u003e in the, in the Bulgarian lottery headquarters when,"},{"startTime":1453.827,"endTime":1458.645,"body":"you know, their, their machine throws up exactly the same numbers as last time."},{"startTime":1458.705,"endTime":1462.221,"body":"And of course everyone will say, oh, the computer must be broken, there's something's going"},{"startTime":1462.221,"endTime":1462.925,"body":"on, it's fraud."},{"startTime":1463.545,"endTime":1464.965,"body":"You know, this, this can't happen."},{"startTime":1464.965,"endTime":1467.525,"body":"This is, you know, there's no way this could have happened by chance."},{"startTime":1468.025,"endTime":1472.335,"body":"Um, I expect, you know what I'm going to conclude, but \u003claugh\u003e, but let's, let's"},{"startTime":1472.335,"endTime":1476.645,"body":"see, was there some awful fraud perpetrated for obscure reasons on the people of Bulgaria?"},{"startTime":1477.115,"endTime":1481.765,"body":"Well, the chance of getting the same numbers as last week, it's the same chance"},{"startTime":1481.765,"endTime":1484.245,"body":"as, you know, choosing the jackpot numbers correctly."},{"startTime":1484.385,"endTime":1485.645,"body":"One in 14 million right?"},{"startTime":1486.345,"endTime":1488.325,"body":"Now that of course is extremely unlikely."},{"startTime":1488.745,"endTime":1492.756,"body":"If you look at, you know, all the lotteries going on in the world, it's"},{"startTime":1492.756,"endTime":1496.767,"body":"still actually pretty unlikely, even if you do that, and you can, I did a"},{"startTime":1496.767,"endTime":1500.778,"body":"quick calculation, I estimate it's about a one in seven chance of that happening of"},{"startTime":1500.778,"endTime":1504.79,"body":"consecutive lottery draws coming up with exactly the same numbers, um, in the, in the"},{"startTime":1504.79,"endTime":1505.325,"body":"21st century."},{"startTime":1505.355,"endTime":1507.885,"body":"Well, which actually already happened this century in the next century."},{"startTime":1508.425,"endTime":1510.965,"body":"Uh, so, okay, that's unlikely."},{"startTime":1511.635,"endTime":1513.405,"body":"It's not impossible, but it's unlikely."},{"startTime":1513.595,"endTime":1518.623,"body":"However, if the same numbers had come up as like the week before or the"},{"startTime":1518.623,"endTime":1523.652,"body":"month before, it would still have been a huge story and a big coincidence and"},{"startTime":1523.652,"endTime":1527.005,"body":"kind of people would say there's something weird going on."},{"startTime":1527.425,"endTime":1532.107,"body":"So perhaps we are looking slightly too specifically at the very precise event that was"},{"startTime":1532.107,"endTime":1534.605,"body":"the same numbers as the immediately proceeding draw."},{"startTime":1535.025,"endTime":1538.005,"body":"If we wind now net a bit, things start to look different."},{"startTime":1538.625,"endTime":1543.266,"body":"So by that point, uh, in, in time the Bulgarian lottery had been running for"},{"startTime":1543.266,"endTime":1543.885,"body":"50 years."},{"startTime":1544.425,"endTime":1547.245,"body":"So that's a hundred draws a year, 5,000 draws."},{"startTime":1547.745,"endTime":1551.883,"body":"Now if you start to think about, uh, in, in any draw, what's the chance"},{"startTime":1551.883,"endTime":1556.021,"body":"of in all those 5,000 draws, two draws out of all of those having the"},{"startTime":1556.021,"endTime":1557.125,"body":"same set of numbers?"},{"startTime":1557.875,"endTime":1560.777,"body":"Well, the first thing you have to work out is how many pairs of draws"},{"startTime":1560.777,"endTime":1561.165,"body":"there are."},{"startTime":1561.465,"endTime":1566.125,"body":"So if you're trying to find a pair, you know, draw A and draw B,"},{"startTime":1566.125,"endTime":1570.165,"body":"well, there's 5,000 possibilities for draw A and then 4,999 for draw B."},{"startTime":1570.305,"endTime":1572.085,"body":"So that gives is our pair A and B."},{"startTime":1572.905,"endTime":1577.69,"body":"But if we just did that, we double count because pair a b is the"},{"startTime":1577.69,"endTime":1579.605,"body":"same pair as pair BA, right?"},{"startTime":1579.625,"endTime":1581.165,"body":"So actually we, we've double counted."},{"startTime":1581.265,"endTime":1582.525,"body":"So we have to halve that number."},{"startTime":1582.985,"endTime":1588.541,"body":"If we do, we still get a really big number, 12 and a half million"},{"startTime":1588.541,"endTime":1592.245,"body":"pairs of draws that could potentially have the same numbers."},{"startTime":1593.025,"endTime":1595.631,"body":"And when you look, you know, the chance for each one is one in 14"},{"startTime":1595.631,"endTime":1595.805,"body":"million."},{"startTime":1595.865,"endTime":1599.707,"body":"But if you're having 12 and a half million opportunities for it to occur, it"},{"startTime":1599.707,"endTime":1601.245,"body":"starts to feel much more probable."},{"startTime":1601.625,"endTime":1605.325,"body":"And in fact, the, the statistician, David Hand did a calculation around this."},{"startTime":1605.425,"endTime":1610.27,"body":"He said after 43 years, uh, you'd expect this to be, it's more likely than"},{"startTime":1610.27,"endTime":1611.885,"body":"not that this would occur."},{"startTime":1612.345,"endTime":1616.149,"body":"So we were within 50 years of the Bulgarian lottery we're well into the time"},{"startTime":1616.149,"endTime":1618.685,"body":"period where actually this is gonna happen at some point."},{"startTime":1619.105,"endTime":1624.133,"body":"So of course it was particularly noticeable because, um, it was consecutive draws, but it's,"},{"startTime":1624.133,"endTime":1627.485,"body":"it's not massively surprising that it happened at some stage."},{"startTime":1627.905,"endTime":1631.172,"body":"And in fact, a similar thing happened in the Israeli lottery a few years later,"},{"startTime":1631.172,"endTime":1634.44,"body":"but it was, I think they were three months apart, but everyone was still kind"},{"startTime":1634.44,"endTime":1635.965,"body":"of a bit bamboozled by this happening."},{"startTime":1637.675,"endTime":1637.965,"body":"Okay?"},{"startTime":1637.965,"endTime":1643.16,"body":"So we've seen that lots of different combinations, those different ways of combining lottery draws"},{"startTime":1643.16,"endTime":1648.355,"body":"and looking at all the ways, uh, you could pair them led to the chances"},{"startTime":1648.355,"endTime":1653.205,"body":"of the, the event happening being much higher than we might otherwise have thought."},{"startTime":1653.945,"endTime":1659.518,"body":"And it's the, the combinations and the number of possible combinations that gives a sound"},{"startTime":1659.518,"endTime":1663.605,"body":"next way into amazing seeming coincidences that may be less amazing."},{"startTime":1664.225,"endTime":1666.005,"body":"And that's when we get networks involved."},{"startTime":1666.825,"endTime":1670.983,"body":"So the network I'm to talk about is, is the social network of human beings"},{"startTime":1670.983,"endTime":1675.141,"body":"and how we, uh, know each other and are related and acquainted because we've all"},{"startTime":1675.141,"endTime":1679.3,"body":"had the experience of you're being, you're in a, a social situation, you're at a"},{"startTime":1679.3,"endTime":1683.458,"body":"party or something, you, you meet someone new and within a few minutes you've discovered,"},{"startTime":1683.458,"endTime":1684.845,"body":"oh, what a small world."},{"startTime":1684.865,"endTime":1688.045,"body":"You know, my sister went to college with your cousin or something."},{"startTime":1688.375,"endTime":1688.925,"body":"Small world."},{"startTime":1688.945,"endTime":1693.284,"body":"We constantly say this to people as we desperately try and seek for links between"},{"startTime":1693.284,"endTime":1697.624,"body":"us \u003claugh\u003e, well, there are going to be links of course, because we all have"},{"startTime":1697.624,"endTime":1701.963,"body":"friends and acquaintances and relationships, but it seems that these things crop up a lot"},{"startTime":1701.963,"endTime":1705.725,"body":"more often than we might in our intuition might lead us to think."},{"startTime":1706.385,"endTime":1708.445,"body":"So let's, let's, let's think about this a bit."},{"startTime":1709.095,"endTime":1710.725,"body":"Let's take the United Kingdom as an example."},{"startTime":1711.135,"endTime":1713.205,"body":"Population, I don't know, let's say 70 million."},{"startTime":1714.345,"endTime":1716.285,"body":"How many connections do you have?"},{"startTime":1716.305,"endTime":1718.165,"body":"How many people does each of us know?"},{"startTime":1718.425,"endTime":1722.795,"body":"So if we think of like, okay, we've got friends, we've got family relations, we"},{"startTime":1722.795,"endTime":1727.166,"body":"might have work colleagues, um, if you're like me, if you have children, you know"},{"startTime":1727.166,"endTime":1731.537,"body":"your children's friends and you know your children's friends' parents, uh, you know, the, you"},{"startTime":1731.537,"endTime":1735.908,"body":"know, the, the barista in your local cafe, you know, the local, uh, neighbors and"},{"startTime":1735.908,"endTime":1739.405,"body":"I, I looked in my phone, I've got 414 phone numbers, okay?"},{"startTime":1739.475,"endTime":1740.605,"body":"It's probably not, I don't know."},{"startTime":1740.745,"endTime":1741.925,"body":"Is that less or more than average?"},{"startTime":1742.235,"endTime":1743.925,"body":"I've got loads of email contacts."},{"startTime":1744.145,"endTime":1745.405,"body":"So lots and lots and lots."},{"startTime":1745.405,"endTime":1748.105,"body":"If you were to try and write it all down, you'd get bored before you"},{"startTime":1748.105,"endTime":1748.285,"body":"finished."},{"startTime":1748.985,"endTime":1751.405,"body":"I'm gonna estimate a thousand people, right?"},{"startTime":1751.635,"endTime":1753.765,"body":"That I know, as in I know who they are."},{"startTime":1753.985,"endTime":1757.656,"body":"And if I were to go to a remote village somewhere and see them, I'd"},{"startTime":1757.656,"endTime":1759.125,"body":"go, I'd have a conversation, right?"},{"startTime":1759.125,"endTime":1760.045,"body":"That's my criteria."},{"startTime":1760.185,"endTime":1762.765,"body":"Oh, I know you, you, you, you live down the road from me."},{"startTime":1763.105,"endTime":1766.685,"body":"So let's say a thousand people that we know in somewhere, acquaintances."},{"startTime":1767.385,"endTime":1772.682,"body":"So that means if you were to pick a random person from the United Kingdom,"},{"startTime":1772.682,"endTime":1777.98,"body":"the chances that that you would know them would be, well, I know a thousand"},{"startTime":1777.98,"endTime":1782.925,"body":"people divided by the total population of 70 million, so one in 70,000, right?"},{"startTime":1783.025,"endTime":1785.005,"body":"That's the chance that you know a particular person."},{"startTime":1786.025,"endTime":1791.096,"body":"But what what we actually do when we talk to, to strangers is we find"},{"startTime":1791.096,"endTime":1793.125,"body":"mutual acquaintances or links between us."},{"startTime":1793.385,"endTime":1795.525,"body":"So what are the chances of having a mutual acquaintance?"},{"startTime":1795.875,"endTime":1801.084,"body":"Well, for that, um, if you think of like, you know, here I am, I've"},{"startTime":1801.084,"endTime":1806.293,"body":"got a thousand acquaintances and I want to know what the chances are that, you"},{"startTime":1806.293,"endTime":1808.725,"body":"know, one of my thousand acquaintances, right?"},{"startTime":1808.785,"endTime":1812.04,"body":"So we can do exactly what we've been doing for the past minutes and say,"},{"startTime":1812.04,"endTime":1815.296,"body":"well, the chance of that happening is one minus the probability that you don't know"},{"startTime":1815.296,"endTime":1816.165,"body":"any of these people."},{"startTime":1816.905,"endTime":1821.718,"body":"And if you work that out, you find actually the chance that we do have"},{"startTime":1821.718,"endTime":1823.965,"body":"a mutual acquaintance is quite respectable, 1.4%."},{"startTime":1825.145,"endTime":1828.711,"body":"But the real magic happens if we allow an extra link in the chain, and"},{"startTime":1828.711,"endTime":1831.565,"body":"we all know we are very keen to find links between it."},{"startTime":1831.565,"endTime":1832.805,"body":"We, we are willing to do this."},{"startTime":1833.025,"endTime":1838.683,"body":"So what we want to know then is the chance that a friend of mine"},{"startTime":1838.683,"endTime":1844.341,"body":"knows a friend of yours, if you do that, it's almost certain to happen greater"},{"startTime":1844.341,"endTime":1849.245,"body":"than 99% probability that one of my friends knows one of your friends."},{"startTime":1849.585,"endTime":1853.524,"body":"Now, the difficulty then is trying to find that connection in the five minutes you"},{"startTime":1853.524,"endTime":1857.463,"body":"have to talk, but it's very, very likely that there will be a link, a"},{"startTime":1857.463,"endTime":1859.565,"body":"path through this network that's really quite short."},{"startTime":1860.385,"endTime":1862.165,"body":"So that's when we say it's a small world."},{"startTime":1862.625,"endTime":1868.569,"body":"But I have highlighted some words on this slide that are very important, a little"},{"startTime":1868.569,"endTime":1873.325,"body":"sneaky assumption I made, uh, which is totally invalid as an assumption."},{"startTime":1874.065,"endTime":1879.752,"body":"And that is if randomly distributed, just assuming that the chance of us knowing people"},{"startTime":1879.752,"endTime":1883.165,"body":"is totally like random when we know it isn't."},{"startTime":1883.385,"endTime":1886.508,"body":"You know, there, if we live in the same town, we're more likely to know"},{"startTime":1886.508,"endTime":1886.925,"body":"each other."},{"startTime":1887.405,"endTime":1890.045,"body":"Probably similar socioeconomic backgrounds, more likely to know each other."},{"startTime":1890.105,"endTime":1892.885,"body":"If you work in the same industry, you're more likely to know each other."},{"startTime":1893.345,"endTime":1898.76,"body":"So we know that human societies are very much not randomly distributed, um, in terms"},{"startTime":1898.76,"endTime":1900.205,"body":"of who knows who."},{"startTime":1901.265,"endTime":1903.805,"body":"So that, that's not a good assumption to make."},{"startTime":1904.105,"endTime":1905.165,"body":"But all is not lost."},{"startTime":1905.545,"endTime":1909.325,"body":"So if, if we take a genuinely random network, right?"},{"startTime":1909.325,"endTime":1912.955,"body":"So network has got nodes, so you can think of it, network or a graph,"},{"startTime":1912.955,"endTime":1916.586,"body":"um, like the map of the London underground, it's got nodes, which in our case"},{"startTime":1916.586,"endTime":1918.765,"body":"every node is person and then it's got edges."},{"startTime":1918.905,"endTime":1923.473,"body":"And those edges for us represent knowing someone in some way being acquainted, if that"},{"startTime":1923.473,"endTime":1925.605,"body":"was completely random in any random network."},{"startTime":1926.265,"endTime":1929.885,"body":"And people's got end nodes, so end people are 70 million or whatever."},{"startTime":1930.305,"endTime":1933.405,"body":"And then how many edges on average are coming out of each node?"},{"startTime":1933.585,"endTime":1936.005,"body":"So that's how many acquaintances we have."},{"startTime":1936.165,"endTime":1937.725,"body":"I took cake was a thousand."},{"startTime":1938.315,"endTime":1942.365,"body":"Then, um, the mathematics tells us that the average path length, which is the number"},{"startTime":1942.365,"endTime":1946.415,"body":"of kind of the length of a chain from that links two people together, um,"},{"startTime":1946.415,"endTime":1947.765,"body":"is given by this formula."},{"startTime":1947.985,"endTime":1949.205,"body":"Log in over long log."},{"startTime":1949.325,"endTime":1951.925,"body":"K, uh, doesn't matter if you dunno what that means."},{"startTime":1951.925,"endTime":1953.685,"body":"There's a formula that tells you what the answer is."},{"startTime":1954.345,"endTime":1955.925,"body":"But we do not live in a random network."},{"startTime":1956.385,"endTime":1959.605,"body":"Social, uh, human social interactions are not, not random."},{"startTime":1960.265,"endTime":1961.725,"body":"So is everything lost?"},{"startTime":1961.745,"endTime":1962.765,"body":"Do we abandon this?"},{"startTime":1963.395,"endTime":1964.445,"body":"Fortunately not."},{"startTime":1964.865,"endTime":1970.749,"body":"Um, there's a brilliant bit of, uh, research and a paper in nature by, uh,"},{"startTime":1970.749,"endTime":1976.633,"body":"Duncan Watson, Steve STRs, um, what's now called the Watts STRs model, which looks specifically"},{"startTime":1976.633,"endTime":1982.125,"body":"at the kind of networks, um, that include human, you know, networks of society."},{"startTime":1982.745,"endTime":1985.805,"body":"Um, they call them small world networks for the obvious reason."},{"startTime":1986.345,"endTime":1988.085,"body":"Now, they are definitely not random."},{"startTime":1988.155,"endTime":1994.396,"body":"They have lots of clustering and very much not random, but they found that as"},{"startTime":1994.396,"endTime":1999.805,"body":"long as you have just a few, uh, circuit breakers they call them."},{"startTime":1999.945,"endTime":2004.07,"body":"So people in our, in our example, people who have lots and lots of links"},{"startTime":2004.07,"endTime":2008.195,"body":"who know people from, you know, all walks of life, social hubs, um, there's one"},{"startTime":2008.195,"endTime":2009.845,"body":"in my circle, she's called Alex."},{"startTime":2009.905,"endTime":2013.005,"body":"She knows everybody from every single walk, walk of life."},{"startTime":2013.005,"endTime":2015.725,"body":"And because I'm her friend, then I'm linked to all of those people."},{"startTime":2015.865,"endTime":2020.659,"body":"So even if I'm a bit shy, you know, I, I have links, I can"},{"startTime":2020.659,"endTime":2025.453,"body":"still be on this, this graph, um, just a few of those circuit breaker people"},{"startTime":2025.453,"endTime":2030.247,"body":"can cause this network, even though it's really not random to behave like and have"},{"startTime":2030.247,"endTime":2032.485,"body":"similar properties to, to genuinely random network."},{"startTime":2033.385,"endTime":2037.942,"body":"And so to a really good level of approximation, we get this same average path"},{"startTime":2037.942,"endTime":2039.765,"body":"length even in this non-random situation."},{"startTime":2040.265,"endTime":2041.205,"body":"So that's really cool."},{"startTime":2041.345,"endTime":2045.663,"body":"And if you put in the numbers that we've got, so in my UK example,"},{"startTime":2045.663,"endTime":2049.982,"body":"if you put in the 70 million and knowing 1000 people, you find that the"},{"startTime":2049.982,"endTime":2053.725,"body":"average path length, so the number of connections you need is just 2.6."},{"startTime":2053.945,"endTime":2058.485,"body":"So it kind of fits in quite well with our rough calculation we did before."},{"startTime":2059.344,"endTime":2063.736,"body":"And even if you take the whole world, so 8 billion people, let's say population,"},{"startTime":2063.736,"endTime":2068.128,"body":"and let's have a really conservative estimate for the average number of, of links that"},{"startTime":2068.128,"endTime":2069.885,"body":"there are average number of acquaintances."},{"startTime":2070.284,"endTime":2073.359,"body":"'cause you know, some people live in remote mountain villages, some people live in big"},{"startTime":2073.359,"endTime":2073.565,"body":"cities."},{"startTime":2073.905,"endTime":2078.122,"body":"Uh, newborn babies are really letting the side down in terms of how many friends"},{"startTime":2078.122,"endTime":2078.685,"body":"they have."},{"startTime":2079.105,"endTime":2083.255,"body":"So let's take an average of 100 that ought to, you know, take account of,"},{"startTime":2083.255,"endTime":2084.085,"body":"of those variations."},{"startTime":2084.275,"endTime":2088.252,"body":"Even if you do that, you still get an average path length of 4.95, less"},{"startTime":2088.252,"endTime":2089.844,"body":"than five links in the chain."},{"startTime":2090.385,"endTime":2095.421,"body":"So the six degrees of separation theory that we've all heard of actually really does"},{"startTime":2095.421,"endTime":2096.764,"body":"hold water mathematically speaking."},{"startTime":2097.345,"endTime":2102.503,"body":"And it's because of all these ways that connections can happen, the power of all"},{"startTime":2102.503,"endTime":2107.661,"body":"these combinations allows these seeming coincidences to happen much more often than we might intuitively"},{"startTime":2107.661,"endTime":2108.005,"body":"think."},{"startTime":2108.955,"endTime":2109.245,"body":"Okay?"},{"startTime":2109.245,"endTime":2113.605,"body":"So I've spent half an hour saying it's not well coincidence."},{"startTime":2113.605,"endTime":2114.805,"body":"It's, you know, it's all coincidence."},{"startTime":2114.805,"endTime":2115.765,"body":"It's gonna happen anyway."},{"startTime":2116.385,"endTime":2120.823,"body":"Is am I ever going to say something's more than coincidence or am I just"},{"startTime":2120.823,"endTime":2125.261,"body":"gonna \u003claugh\u003e explain why we should expect these coincidence exciting as they are, but they"},{"startTime":2125.261,"endTime":2126.445,"body":"don't necessarily mean anything?"},{"startTime":2126.835,"endTime":2131.194,"body":"Well, sometimes things are more than coincidence and that's when we can start to think"},{"startTime":2131.194,"endTime":2131.485,"body":"scientifically."},{"startTime":2131.995,"endTime":2138.145,"body":"I'll give you just one example, very famous example from history, uh, John Snow, uh,"},{"startTime":2138.145,"endTime":2138.965,"body":"investigating cholera."},{"startTime":2139.825,"endTime":2144.422,"body":"And this is a little map, very famous map, which shows that there is a"},{"startTime":2144.422,"endTime":2149.019,"body":"cluster of cholera cases in a particular area near a street called Broad Street, not"},{"startTime":2149.019,"endTime":2150.245,"body":"too far from here."},{"startTime":2150.905,"endTime":2154.325,"body":"And so he notices this, maybe it's just a coincidence."},{"startTime":2154.325,"endTime":2157.685,"body":"Is it a coincidence he didn't think it was what could be causing it?"},{"startTime":2157.705,"endTime":2159.805,"body":"That's that's when we started to think scientifically."},{"startTime":2159.985,"endTime":2162.085,"body":"We say this is a strange pattern."},{"startTime":2162.615,"endTime":2164.045,"body":"Maybe it's more than coincidence."},{"startTime":2164.185,"endTime":2167.301,"body":"But then you have to think of or try and think of a reason why"},{"startTime":2167.301,"endTime":2167.925,"body":"this might happen."},{"startTime":2167.995,"endTime":2169.005,"body":"What is causing it."},{"startTime":2169.395,"endTime":2173.716,"body":"It's not just, oh, divine intervention has decided, you know, eventual God does not like"},{"startTime":2173.716,"endTime":2176.885,"body":"the inhabitants of no, there must be a reason for this."},{"startTime":2176.885,"endTime":2177.605,"body":"What's the reason?"},{"startTime":2178.385,"endTime":2182.645,"body":"And he, he realized, okay, there's there's a water pump just there on that street."},{"startTime":2183.545,"endTime":2188.095,"body":"And so then he has this theory that maybe cholera is waterborne and not airborne"},{"startTime":2188.095,"endTime":2189.005,"body":"as previously thought."},{"startTime":2189.305,"endTime":2194.273,"body":"So he's got now got hypothesis to explain this seeming coincidence, but it's not a"},{"startTime":2194.273,"endTime":2194.605,"body":"coincidence."},{"startTime":2195.195,"endTime":2196.925,"body":"Then you have to test your hypothesis."},{"startTime":2197.025,"endTime":2198.045,"body":"You can't just stop there."},{"startTime":2198.505,"endTime":2199.845,"body":"How do you test the hypothesis?"},{"startTime":2200.105,"endTime":2203.969,"body":"You remove the handle of the water pump, then no one can access that water"},{"startTime":2203.969,"endTime":2204.485,"body":"from that."},{"startTime":2204.485,"endTime":2205.605,"body":"Well, and guess what?"},{"startTime":2205.605,"endTime":2206.805,"body":"The cholera cases went away."},{"startTime":2207.195,"endTime":2207.925,"body":"Went right down."},{"startTime":2208.185,"endTime":2210.285,"body":"And so he's got, he's noticed something."},{"startTime":2210.585,"endTime":2211.885,"body":"He thinks it's not a coincidence."},{"startTime":2211.905,"endTime":2216.045,"body":"He forms a hypothesis, then he tests the hypothesis that's doing science."},{"startTime":2217.695,"endTime":2219.725,"body":"There are lots of people not doing science in the world."},{"startTime":2220.085,"endTime":2224.885,"body":"I have to tell you, um, right in astronomy for hundreds of years, of course"},{"startTime":2224.885,"endTime":2229.685,"body":"thousands of years astronomers have spotted patterns, the ways in which planetary bodies behave and"},{"startTime":2229.685,"endTime":2233.205,"body":"tried to understand and explain them formed hypotheses, tested the hypotheses."},{"startTime":2233.675,"endTime":2240.142,"body":"That is very different from saying, Hey, the moon exactly covers the sun during a"},{"startTime":2240.142,"endTime":2241.005,"body":"total eclipse."},{"startTime":2241.625,"endTime":2242.845,"body":"That's really spooky."},{"startTime":2243.185,"endTime":2247.065,"body":"And we know the moon is smaller than the sun, but the moon is 400"},{"startTime":2247.065,"endTime":2250.946,"body":"times smaller than the sun, but the sun is 400 times further away than the"},{"startTime":2250.946,"endTime":2251.205,"body":"moon."},{"startTime":2251.755,"endTime":2253.325,"body":"Whoa \u003claugh\u003e that."},{"startTime":2253.465,"endTime":2258.047,"body":"So that yes, it's a really cool thing, but without some sort of reason as"},{"startTime":2258.047,"endTime":2262.325,"body":"to why that might happen, why that would have to happen in some way."},{"startTime":2262.585,"endTime":2267.218,"body":"We are just saying it's a nice coincidence and there are very, very many astronomical"},{"startTime":2267.218,"endTime":2270.925,"body":"bodies and there are many measurements that we can take about them."},{"startTime":2271.625,"endTime":2275.59,"body":"And when you have lots of numbers and you can play with them and manipulate"},{"startTime":2275.59,"endTime":2279.556,"body":"them in various ways, it's quite easy to find things that appear to link to"},{"startTime":2279.556,"endTime":2280.085,"body":"each other."},{"startTime":2280.385,"endTime":2284.795,"body":"And so there's some of this I've, I've investigated, so you don't have to, but"},{"startTime":2284.795,"endTime":2289.205,"body":"there's online, there's a certain amount of stuff that isn't really very, uh, correct, \u003claugh\u003e."},{"startTime":2289.575,"endTime":2291.205,"body":"Sorry if I'm breaking this to you for the first time."},{"startTime":2291.485,"endTime":2293.565,"body":"I just wanna give you a couple of examples."},{"startTime":2294.305,"endTime":2298.91,"body":"And this is the kind of thing that can, can fool people into, into thinking"},{"startTime":2298.91,"endTime":2300.445,"body":"there's something deeper going on."},{"startTime":2300.465,"endTime":2303.085,"body":"But really it's just the fact that there are so many ways to combine numbers."},{"startTime":2303.145,"endTime":2309.559,"body":"So here is what's supposed to be an amazing sort of, you know, sacred mystical"},{"startTime":2309.559,"endTime":2312.125,"body":"alignment of something or other, right?"},{"startTime":2312.235,"endTime":2312.805,"body":"What do you do?"},{"startTime":2312.805,"endTime":2317.771,"body":"You take the length of the earth year in days, multiply by the length of"},{"startTime":2317.771,"endTime":2318.765,"body":"the lunar month."},{"startTime":2319.105,"endTime":2320.045,"body":"Why are we multiplying?"},{"startTime":2320.135,"endTime":2320.645,"body":"Don't know."},{"startTime":2320.875,"endTime":2326.921,"body":"Then you multiply by the golden ratio, the lovely phi, wonderful sort of mystical sacred"},{"startTime":2326.921,"endTime":2327.325,"body":"thing."},{"startTime":2327.745,"endTime":2328.405,"body":"Why are we doing that?"},{"startTime":2328.455,"endTime":2328.925,"body":"Don't know."},{"startTime":2328.995,"endTime":2331.885,"body":"Then you divide by pie, another lovely mathematical consonant."},{"startTime":2331.945,"endTime":2332.565,"body":"Why are we doing that?"},{"startTime":2332.775,"endTime":2333.285,"body":"Don't know."},{"startTime":2333.785,"endTime":2337.635,"body":"And the answer is that you get, it's not a whole number, but to the"},{"startTime":2337.635,"endTime":2338.405,"body":"nearest whole number."},{"startTime":2338.715,"endTime":2340.045,"body":"It's 5, 5, 5, 5."},{"startTime":2341.025,"endTime":2341.805,"body":"Are you impressed?"},{"startTime":2343.345,"endTime":2343.565,"body":"No."},{"startTime":2343.895,"endTime":2344.245,"body":"Weird."},{"startTime":2344.435,"endTime":2346.485,"body":"Okay, but no wait, I haven't got to the best bit."},{"startTime":2346.935,"endTime":2348.085,"body":"Let's bring a pyramid into this."},{"startTime":2348.165,"endTime":2350.645,"body":"'cause they always have to come in, right?"},{"startTime":2351.165,"endTime":2354.165,"body":"Pyramids, like here's a cross section, great pyramid of Giza."},{"startTime":2354.545,"endTime":2356.285,"body":"So it's got a triangular cross section there."},{"startTime":2356.455,"endTime":2358.445,"body":"We're not gonna take that triangle, that would be too easy."},{"startTime":2358.775,"endTime":2363.245,"body":"We're gonna take the equilateral triangle that just fits inside inscribe, an equilateral triangle."},{"startTime":2363.755,"endTime":2365.925,"body":"What is the side length of that equilateral triangle?"},{"startTime":2367.035,"endTime":2368.765,"body":"5 5, 5 0.5 feet."},{"startTime":2369.315,"endTime":2369.805,"body":"Amazing."},{"startTime":2369.945,"endTime":2375.005,"body":"So, and obviously you are stunned and amazed by this, uh, mystical phenomenon."},{"startTime":2375.255,"endTime":2379.639,"body":"There are some questions we might have about this, um, which we'll we might think"},{"startTime":2379.639,"endTime":2381.685,"body":"about if that isn't impressive enough yet."},{"startTime":2381.685,"endTime":2384.045,"body":"I'll just give you one more amazing thing, okay?"},{"startTime":2384.355,"endTime":2389.631,"body":"Draw a circle now inside the pyramid and the inscribed circle has the diameter just"},{"startTime":2389.631,"endTime":2392.445,"body":"the same as the length of the year."},{"startTime":2392.835,"endTime":2393.485,"body":"It's amazing."},{"startTime":2394.065,"endTime":2395.845,"body":"So there are some questions, it's questions."},{"startTime":2396.145,"endTime":2397.405,"body":"One most important question."},{"startTime":2397.665,"endTime":2398.885,"body":"Why are we measuring this in feet?"},{"startTime":2400.325,"endTime":2402.605,"body":"\u003claugh\u003e, ancient Egyptians did not use feet."},{"startTime":2402.945,"endTime":2404.325,"body":"Aliens probably do not use feet."},{"startTime":2404.515,"endTime":2408.485,"body":"Feet as the name suggests, uh, derived from the foot, which is a human thing."},{"startTime":2408.965,"endTime":2412.685,"body":"\u003claugh\u003e not used by the ancient Egyptians or probably aliens or anyone else."},{"startTime":2412.905,"endTime":2416.725,"body":"Um, so why, why are we suddenly deciding we're gonna measure things in feet?"},{"startTime":2417.305,"endTime":2420.721,"body":"Uh, if you want to draw a circle that represents the earth in some way,"},{"startTime":2420.721,"endTime":2424.137,"body":"why don't you make its diameter the damage of the earth and not some other"},{"startTime":2424.137,"endTime":2424.365,"body":"thing."},{"startTime":2424.785,"endTime":2429.45,"body":"And then that little asterisk, that fair to say, um, in fact the diameter isn't"},{"startTime":2429.45,"endTime":2431.005,"body":"that it's two feet more."},{"startTime":2431.585,"endTime":2436.206,"body":"Uh, but as the writer of the website I got this from says, um, that"},{"startTime":2436.206,"endTime":2440.828,"body":"probably represents the Earth's atmosphere, those extra two feet \u003claugh\u003e, it's fine, it's gonna be"},{"startTime":2440.828,"endTime":2441.445,"body":"fine \u003claugh\u003e."},{"startTime":2441.785,"endTime":2446.285,"body":"But of course then it immediately negates the spurious precision of these, you know, four"},{"startTime":2446.285,"endTime":2446.885,"body":"decimal places."},{"startTime":2446.985,"endTime":2450.678,"body":"But oh, but two feet plus or minus in either direction, you know, completely negates"},{"startTime":2450.678,"endTime":2450.925,"body":"this."},{"startTime":2450.945,"endTime":2452.245,"body":"So it's really easy."},{"startTime":2452.305,"endTime":2455.441,"body":"As I've said, there are a lots of numbers in the world, mathematician, telling you"},{"startTime":2455.441,"endTime":2458.577,"body":"there are lots of numbers and you can manipulate them in lots of different ways"},{"startTime":2458.577,"endTime":2459.205,"body":"and combine them."},{"startTime":2459.585,"endTime":2461.925,"body":"So really, of course you can make these things."},{"startTime":2462.305,"endTime":2467.93,"body":"And just to emphasize this, I want to present to you my very important findings"},{"startTime":2467.93,"endTime":2469.805,"body":"on the Mystic Gresham numbers."},{"startTime":2470.445,"endTime":2472.605,"body":"\u003claugh\u003e Thomas Gresham, founder of Gresham College."},{"startTime":2473.525,"endTime":2475.765,"body":"I think he may have been able to predict the future."},{"startTime":2475.865,"endTime":2477.965,"body":"So look at the right 1, 3, 5, 7, and nine."},{"startTime":2477.965,"endTime":2483.612,"body":"The important very important sacred odd numbers have lots of different meanings in different civilizations"},{"startTime":2483.612,"endTime":2484.365,"body":"and traditions."},{"startTime":2485.105,"endTime":2489.2,"body":"I'm gonna show you a triad of ways that these five numbers, uh, have, are"},{"startTime":2489.2,"endTime":2490.565,"body":"important to the Gresham legacy."},{"startTime":2491.325,"endTime":2492.325,"body":"I should put a bigger thing on this."},{"startTime":2492.395,"endTime":2493.405,"body":"This is all, all nonsense."},{"startTime":2493.425,"endTime":2496.765,"body":"I'm telling you right now, be aware of it all the way through, right?"},{"startTime":2496.905,"endTime":2500.205,"body":"So 1, 3, 5, 7, 9, the first three that we're gonna see, you can"},{"startTime":2500.205,"endTime":2500.645,"body":"already see."},{"startTime":2500.905,"endTime":2503.285,"body":"And there are three stars on the coat of arms there."},{"startTime":2503.865,"endTime":2505.565,"body":"So that leaves 1, 5, 7 and nine."},{"startTime":2507.025,"endTime":2509.365,"body":"Oh my goodness, that's the year that Thomas Gresham died."},{"startTime":2509.715,"endTime":2510.765,"body":"Amazing, right?"},{"startTime":2510.945,"endTime":2513.245,"body":"We want two more sets of 1, 3, 5, 7, 9."},{"startTime":2513.345,"endTime":2517.899,"body":"If you take that 1, 5, 7, 9, just flip the two numbers, the last"},{"startTime":2517.899,"endTime":2522.454,"body":"two numbers over 1, 5, 9, 7 50 97 the year Gresham college was found"},{"startTime":2522.454,"endTime":2523.365,"body":"it amazing, right?"},{"startTime":2523.745,"endTime":2526.409,"body":"If you take still the 1, 5, 7, 9, now flip the five and the"},{"startTime":2526.409,"endTime":2526.765,"body":"nine over."},{"startTime":2527.435,"endTime":2528.885,"body":"This is where it gets really spooky."},{"startTime":2528.945,"endTime":2529.445,"body":"Or you ready?"},{"startTime":2530.415,"endTime":2531.565,"body":"Let's see, I was born"},{"startTime":2532.165,"endTime":2537.165,"body":"\u003claugh\u003e,"},{"startTime":2534.765,"endTime":2536.925,"body":"I I'm your laughs are laughs of all I know."},{"startTime":2537.185,"endTime":2540.205,"body":"So, but hang on there, there, there's, I promised you three sets of these numbers."},{"startTime":2540.585,"endTime":2542.085,"body":"So where are the other two threes?"},{"startTime":2542.355,"endTime":2545.285,"body":"Well, I'm the 33rd Gresham press of geometry."},{"startTime":2545.865,"endTime":2548.365,"body":"So, okay, now you are impressed, right?"},{"startTime":2549.315,"endTime":2551.605,"body":"\u003claugh\u003e, so did Thomas Gresham."},{"startTime":2551.625,"endTime":2555.128,"body":"No, surely maybe this is an indication that he knew he had a plan that"},{"startTime":2555.128,"endTime":2558.632,"body":"was all accommodating in this lecture right now, which is happening on the fifth day"},{"speaker":"of the third month at 1","startTime":2558.632,"endTime":2562.136,"body":"00 PM And if you don't want me to speak"},{"speaker":"of the third month at 1","startTime":2562.136,"endTime":2564.005,"body":"for 79 minutes, we better leave it there."},{"speaker":"of the third month at 1","startTime":2564.305,"endTime":2568.833,"body":"But I wanna, I wanna, okay, this is all just to say, you know, some"},{"speaker":"of the third month at 1","startTime":2568.833,"endTime":2573.361,"body":"of the, this is clearly silly, but sometimes, you know, all of this stuff with"},{"speaker":"of the third month at 1","startTime":2573.361,"endTime":2577.889,"body":"the pyramids and, and the cosmic coincidences, you know, it's one can get drawn into"},{"speaker":"of the third month at 1","startTime":2577.889,"endTime":2582.417,"body":"these things, but you can really easily, I, you know, just in a few minutes"},{"speaker":"of the third month at 1","startTime":2582.417,"endTime":2586.946,"body":"you can really easily do something with numbers that on the surface looks sort of"},{"speaker":"of the third month at 1","startTime":2586.946,"endTime":2589.965,"body":"good, but it doesn't really hold water, doesn't make sense."},{"speaker":"of the third month at 1","startTime":2590.425,"endTime":2596.338,"body":"Um, and okay, finding all these things about the pyramids is silly but harmless unless,"},{"speaker":"of the third month at 1","startTime":2596.338,"endTime":2602.252,"body":"you know, we think of the effect on the blood pressure of real archeologists, but,"},{"speaker":"of the third month at 1","startTime":2602.252,"endTime":2608.165,"body":"but there are some coincidences or the misunderstanding of coincidence can have really serious real"},{"speaker":"of the third month at 1","startTime":2608.165,"endTime":2613.685,"body":"life implications and can change people's lives, um, and affect them very, very seriously."},{"speaker":"of the third month at 1","startTime":2613.985,"endTime":2620.102,"body":"And I wanna just talk for a few minutes more seriously about the use of"},{"speaker":"of the third month at 1","startTime":2620.102,"endTime":2623.365,"body":"statistics, probability, misunderstandings of coincidence in legal cases."},{"speaker":"of the third month at 1","startTime":2623.845,"endTime":2628.645,"body":"I wanna give you a general example first, uh, which is a prevalent thing and"},{"speaker":"of the third month at 1","startTime":2628.645,"endTime":2631.205,"body":"it's even got a nickname, the prosecutor's fallacy."},{"speaker":"of the third month at 1","startTime":2631.465,"endTime":2633.365,"body":"And this is, well, I'll give, just make up an example."},{"speaker":"of the third month at 1","startTime":2633.865,"endTime":2637.973,"body":"Um, let's say there's a crime committed and you get some sort of forensic evidence,"},{"speaker":"of the third month at 1","startTime":2637.973,"endTime":2642.082,"body":"some partial DNA or blood marker or something that you find at the scene of"},{"speaker":"of the third month at 1","startTime":2642.082,"endTime":2646.191,"body":"the crime, and you then run that through your database of known criminals and you"},{"speaker":"of the third month at 1","startTime":2646.191,"endTime":2649.205,"body":"find a match, you go, okay, well that's clearly the guy."},{"speaker":"of the third month at 1","startTime":2649.545,"endTime":2653.197,"body":"So there's, you know, court case and when it comes up and the prosecutor will"},{"speaker":"of the third month at 1","startTime":2653.197,"endTime":2656.85,"body":"say, well look, we found this match and they might even put some numbers, and"},{"speaker":"of the third month at 1","startTime":2656.85,"endTime":2659.285,"body":"we all know numbers to tell you lots of things."},{"speaker":"of the third month at 1","startTime":2659.475,"endTime":2664.485,"body":"They might say, only one in 10,000 people have that particular marker in their DNA."},{"speaker":"of the third month at 1","startTime":2664.825,"endTime":2668.756,"body":"So this guy, look at him looking shifty already, he must be him \u003claugh\u003e only"},{"speaker":"of the third month at 1","startTime":2668.756,"endTime":2669.805,"body":"one in 10,000 people."},{"speaker":"of the third month at 1","startTime":2669.805,"endTime":2670.645,"body":"What are the chances?"},{"speaker":"of the third month at 1","startTime":2671.065,"endTime":2675.283,"body":"Um, it must be this guy, but they are, that's the wrong number to think"},{"speaker":"of the third month at 1","startTime":2675.283,"endTime":2675.565,"body":"about."},{"speaker":"of the third month at 1","startTime":2676.955,"endTime":2682.153,"body":"What we really want to know is given that someone has that DNA marker, what"},{"speaker":"of the third month at 1","startTime":2682.153,"endTime":2685.965,"body":"is the chance then of them being guilty or, or innocent?"},{"speaker":"of the third month at 1","startTime":2686.945,"endTime":2691.126,"body":"So let's say it is one in 10,000 people in London, there are 9 million"},{"speaker":"of the third month at 1","startTime":2691.126,"endTime":2691.405,"body":"people."},{"speaker":"of the third month at 1","startTime":2691.865,"endTime":2696.758,"body":"So that means that in London we'd expect 900 people to have this particular DNA"},{"speaker":"of the third month at 1","startTime":2696.758,"endTime":2697.085,"body":"marker."},{"speaker":"of the third month at 1","startTime":2698.435,"endTime":2698.725,"body":"Okay?"},{"speaker":"of the third month at 1","startTime":2698.795,"endTime":2703.546,"body":"Well that means if we pick a random person from that population of 900 people"},{"speaker":"of the third month at 1","startTime":2703.546,"endTime":2708.297,"body":"that have this thing in the, in their DNA, then the chances that we want"},{"speaker":"of the third month at 1","startTime":2708.297,"endTime":2713.048,"body":"to know what are the chances that they're innocent given that they have that marker,"},{"speaker":"of the third month at 1","startTime":2713.048,"endTime":2713.365,"body":"right?"},{"speaker":"of the third month at 1","startTime":2713.365,"endTime":2714.845,"body":"That's, that's the question we want to know."},{"speaker":"of the third month at 1","startTime":2715.185,"endTime":2720.496,"body":"And of course, there's somebody in those 900 is guilty, um, but the other 899"},{"speaker":"of the third month at 1","startTime":2720.496,"endTime":2721.205,"body":"are innocent."},{"speaker":"of the third month at 1","startTime":2721.425,"endTime":2726.655,"body":"So if you pick a random person with that, with that particular DNA or blood"},{"speaker":"of the third month at 1","startTime":2726.655,"endTime":2729.445,"body":"marker, then there's a 99.9% chance they're innocent."},{"speaker":"of the third month at 1","startTime":2730.515,"endTime":2735.007,"body":"We'd have to have concrete evidence of another kind that the person, the suspect actually"},{"speaker":"of the third month at 1","startTime":2735.007,"endTime":2736.805,"body":"had been involved in some way."},{"speaker":"of the third month at 1","startTime":2736.805,"endTime":2740.43,"body":"There's some reason to think they might be involved in the crime before this, you"},{"speaker":"of the third month at 1","startTime":2740.43,"endTime":2742.605,"body":"know, before we can make any conclusion from that."},{"speaker":"of the third month at 1","startTime":2743.385,"endTime":2746.805,"body":"So high likelihood of them still being innocent, okay?"},{"speaker":"of the third month at 1","startTime":2746.825,"endTime":2750.49,"body":"I'm gonna give you a real example now, and this is just a shocking miscarriage"},{"speaker":"of the third month at 1","startTime":2750.49,"endTime":2752.445,"body":"of justice that happened a few years ago."},{"speaker":"of the third month at 1","startTime":2752.465,"endTime":2754.925,"body":"You might remember, uh, the case of Sally Clark."},{"speaker":"of the third month at 1","startTime":2755.025,"endTime":2758.645,"body":"So Sally Clark, um, it's really a terrible thing that happened."},{"speaker":"of the third month at 1","startTime":2758.645,"endTime":2763.125,"body":"So she had a baby and very unfortunately, um, the baby died suddenly."},{"speaker":"of the third month at 1","startTime":2763.425,"endTime":2767.085,"body":"So it's called sudden infant death syndrome or sometimes called caught death."},{"speaker":"of the third month at 1","startTime":2767.225,"endTime":2770.983,"body":"So the baby died, it was tragic, and then a couple years later she had"},{"speaker":"of the third month at 1","startTime":2770.983,"endTime":2771.485,"body":"another child."},{"speaker":"of the third month at 1","startTime":2772.305,"endTime":2776.976,"body":"And very sadly, that baby died as well suddenly, and people got suspicious and she"},{"speaker":"of the third month at 1","startTime":2776.976,"endTime":2778.845,"body":"was accused and tried for murder."},{"speaker":"of the third month at 1","startTime":2779.035,"endTime":2780.765,"body":"They said she must have smothered the babies."},{"speaker":"of the third month at 1","startTime":2781.075,"endTime":2782.485,"body":"This couldn't happen by chance."},{"speaker":"of the third month at 1","startTime":2783.385,"endTime":2789.441,"body":"And one of the key, uh, witnesses for the prosecution was a pediatrician called Roy"},{"speaker":"of the third month at 1","startTime":2789.441,"endTime":2789.845,"body":"Meadow."},{"speaker":"of the third month at 1","startTime":2790.625,"endTime":2794.446,"body":"And he said these three things in his testimony, he said, okay, the chance of"},{"speaker":"of the third month at 1","startTime":2794.446,"endTime":2796.485,"body":"a SID'S death in a family like that."},{"speaker":"of the third month at 1","startTime":2796.545,"endTime":2802.525,"body":"So affluent, everyone's healthy, nobody smokes, is about one in eight and a 5,000."},{"speaker":"of the third month at 1","startTime":2802.755,"endTime":2803.045,"body":"Okay?"},{"speaker":"of the third month at 1","startTime":2803.075,"endTime":2806.988,"body":"Then he said, that means the chance of two deaths happening of Sids in a"},{"speaker":"of the third month at 1","startTime":2806.988,"endTime":2810.902,"body":"family like that is one in eight and a half thousand squared, which is one"},{"speaker":"of the third month at 1","startTime":2810.902,"endTime":2811.685,"body":"in 73 million."},{"speaker":"of the third month at 1","startTime":2812.145,"endTime":2814.605,"body":"And that would only occur by chance once in a century."},{"speaker":"of the third month at 1","startTime":2815.825,"endTime":2817.245,"body":"So there's, there's a lot wrong with that."},{"speaker":"of the third month at 1","startTime":2817.335,"endTime":2821.328,"body":"There was a immediate outcry after this, perhaps not immediate, but there was an outcry"},{"speaker":"of the third month at 1","startTime":2821.328,"endTime":2823.725,"body":"and people, um, there was an appeal against this."},{"speaker":"of the third month at 1","startTime":2824.505,"endTime":2828.805,"body":"The biggest problem with with that is the middle statement, right?"},{"speaker":"of the third month at 1","startTime":2828.955,"endTime":2834.041,"body":"That the odds one in eight and a half thousand is probably about right, but"},{"speaker":"of the third month at 1","startTime":2834.041,"endTime":2839.128,"body":"he made the assumption that these things are independent of each other, and that unfortunately"},{"speaker":"of the third month at 1","startTime":2839.128,"endTime":2840.485,"body":"is not the case."},{"speaker":"of the third month at 1","startTime":2840.825,"endTime":2841.805,"body":"We don't quite know why."},{"speaker":"of the third month at 1","startTime":2842.265,"endTime":2846.495,"body":"But in a family where there has already been one Sid's death, actually it's about"},{"speaker":"of the third month at 1","startTime":2846.495,"endTime":2850.725,"body":"10 times more likely than for the general population that there will be a second."},{"speaker":"of the third month at 1","startTime":2851.015,"endTime":2854.683,"body":"There may be some genetic factor, we don't quite understand what it is, but the"},{"speaker":"of the third month at 1","startTime":2854.683,"endTime":2858.351,"body":"chances of raise, so actually it's not one in 73 million, it's more like one"},{"speaker":"of the third month at 1","startTime":2858.351,"endTime":2859.085,"body":"in 7 million."},{"speaker":"of the third month at 1","startTime":2859.545,"endTime":2862.005,"body":"Now you might say, okay, well that's still really unlikely."},{"speaker":"of the third month at 1","startTime":2862.265,"endTime":2867.615,"body":"So, you know, she probably did still do this, but again, we are not comparing"},{"speaker":"of the third month at 1","startTime":2867.615,"endTime":2868.685,"body":"the right things."},{"speaker":"of the third month at 1","startTime":2869.425,"endTime":2875.692,"body":"If you compare the probability of two SID'S deaths, um, one in 7 million with"},{"speaker":"of the third month at 1","startTime":2875.692,"endTime":2881.959,"body":"the probability of the babies not dying, then yes, but what we have to compare"},{"speaker":"of the third month at 1","startTime":2881.959,"endTime":2888.227,"body":"is the probability of two Sid's deaths with the probability that she murdered her babies,"},{"speaker":"of the third month at 1","startTime":2888.227,"endTime":2888.645,"body":"right?"},{"speaker":"of the third month at 1","startTime":2889.105,"endTime":2890.765,"body":"And that's much, much lower."},{"speaker":"of the third month at 1","startTime":2891.585,"endTime":2895.445,"body":"Um, so yeah, seconds is death 10 times as likely."},{"speaker":"of the third month at 1","startTime":2895.905,"endTime":2901.065,"body":"But, uh, if you look at the, and they did do this, if you look"},{"speaker":"of the third month at 1","startTime":2901.065,"endTime":2906.226,"body":"at the data for the probability of, um, two babies dying of suddenly infant death"},{"speaker":"of the third month at 1","startTime":2906.226,"endTime":2911.387,"body":"syndrome compared to the probability of two babies being murdered by their mother, of course"},{"speaker":"of the third month at 1","startTime":2911.387,"endTime":2916.548,"body":"the, well, I hope it's of course the Sid's deaths much more common than than"},{"speaker":"of the third month at 1","startTime":2916.548,"endTime":2919.645,"body":"than the other possibility about nine times more common."},{"speaker":"of the third month at 1","startTime":2920.305,"endTime":2925.049,"body":"And so these statistics sort of glibly used and, and got this woman convicted of"},{"speaker":"of the third month at 1","startTime":2925.049,"endTime":2928.845,"body":"murder to add to her other just awful ordeal that she'd experienced."},{"speaker":"of the third month at 1","startTime":2929.265,"endTime":2933.854,"body":"And this just shows, you know, we, it's so important for people to understand a"},{"speaker":"of the third month at 1","startTime":2933.854,"endTime":2938.444,"body":"bit about probability, a bit about statistics, a bit about when things are coincidences and"},{"speaker":"of the third month at 1","startTime":2938.444,"endTime":2943.033,"body":"how often coincidences can happen in order that we, you know, we can have a,"},{"speaker":"of the third month at 1","startTime":2943.033,"endTime":2947.623,"body":"a conversation, a kind of numerate conversation in these court cases and understand what the"},{"speaker":"of the third month at 1","startTime":2947.623,"endTime":2949.765,"body":"implications are and what's really going on."},{"speaker":"of the third month at 1","startTime":2950.745,"endTime":2951.685,"body":"So that was okay."},{"speaker":"of the third month at 1","startTime":2951.685,"endTime":2953.645,"body":"That was pretty somber for me, I thought."},{"speaker":"of the third month at 1","startTime":2953.865,"endTime":2956.648,"body":"Um, you know, it's important to say, but I would like to finish on a"},{"speaker":"of the third month at 1","startTime":2956.648,"endTime":2957.205,"body":"slightly lighter note."},{"speaker":"of the third month at 1","startTime":2957.685,"endTime":2961.885,"body":"Slightly lighter note to send you off into your days, um, um, you know, with"},{"speaker":"of the third month at 1","startTime":2961.885,"endTime":2964.685,"body":"something a bit more light on your, on your minds."},{"speaker":"of the third month at 1","startTime":2964.865,"endTime":2968.525,"body":"So let's think about an amazing coincidence that happened."},{"speaker":"of the third month at 1","startTime":2968.565,"endTime":2969.765,"body":"A very astonishing thing."},{"speaker":"of the third month at 1","startTime":2969.785,"endTime":2972.965,"body":"So a few years ago, and there was an episode of the BBC's program."},{"speaker":"of the third month at 1","startTime":2973.145,"endTime":2973.885,"body":"Who do you think he was?"},{"speaker":"of the third month at 1","startTime":2973.885,"endTime":2978.205,"body":"If you're not familiar with this, uh, it's a kind of family history program."},{"speaker":"of the third month at 1","startTime":2978.235,"endTime":2981.793,"body":"They get a celebrity and they look at their family history and they say, oh,"},{"speaker":"of the third month at 1","startTime":2981.793,"endTime":2985.352,"body":"you know, you've related to, oh look, 200 years ago, so and so was a"},{"speaker":"of the third month at 1","startTime":2985.352,"endTime":2987.725,"body":"scullery maid and someone else served on the whatever ship."},{"speaker":"of the third month at 1","startTime":2987.945,"endTime":2990.805,"body":"And they give them an interesting bit of information about their family history."},{"speaker":"of the third month at 1","startTime":2991.185,"endTime":2995.997,"body":"So in 2016, there was an episode with, uh, the actor Danny Dyer, and there"},{"speaker":"of the third month at 1","startTime":2995.997,"endTime":2999.205,"body":"was an amazing revelation they showed in this big scroll."},{"speaker":"of the third month at 1","startTime":2999.225,"endTime":3002.956,"body":"He can look at his look, go back so and so, so, so, and then"},{"speaker":"of the third month at 1","startTime":3002.956,"endTime":3003.205,"body":"royalty."},{"speaker":"of the third month at 1","startTime":3003.985,"endTime":3006.005,"body":"He was directly descended from royalty."},{"speaker":"of the third month at 1","startTime":3006.685,"endTime":3007.805,"body":"Remember, I think it was Edward iii."},{"speaker":"of the third month at 1","startTime":3007.805,"endTime":3010.125,"body":"And then if you go back, William the Conqueror, right?"},{"speaker":"of the third month at 1","startTime":3010.125,"endTime":3012.525,"body":"So Danny Dyer directly descended from William the Conqueror."},{"speaker":"of the third month at 1","startTime":3013.585,"endTime":3015.765,"body":"Wow, how exciting is that?"},{"speaker":"of the third month at 1","startTime":3016.165,"endTime":3019.031,"body":"I thought, well, what are the ch you know, maybe some of us might be"},{"speaker":"of the third month at 1","startTime":3019.031,"endTime":3019.605,"body":"related to royalty."},{"speaker":"of the third month at 1","startTime":3020.105,"endTime":3021.045,"body":"So let's think about this."},{"speaker":"of the third month at 1","startTime":3021.345,"endTime":3024.205,"body":"Our family tree, and we all know what a family tree looks like."},{"speaker":"of the third month at 1","startTime":3024.235,"endTime":3028.005,"body":"It's us, two parents, four grandparents, eight great grandparents."},{"speaker":"of the third month at 1","startTime":3028.445,"endTime":3030.882,"body":"I can't stretch any higher than that, but it doubles and doubles and doubles each"},{"speaker":"of the third month at 1","startTime":3030.882,"endTime":3031.045,"body":"time."},{"speaker":"of the third month at 1","startTime":3031.225,"endTime":3036.071,"body":"So if you go back 30 generations, about 900 years by that point, we've got"},{"speaker":"of the third month at 1","startTime":3036.071,"endTime":3040.918,"body":"in that family tree, we've got two to power, 30 empty boxes that we have"},{"speaker":"of the third month at 1","startTime":3040.918,"endTime":3041.565,"body":"to fill."},{"speaker":"of the third month at 1","startTime":3041.905,"endTime":3043.845,"body":"So how many names is that?"},{"speaker":"of the third month at 1","startTime":3044.595,"endTime":3046.085,"body":"Well, it's over a billion."},{"speaker":"of the third month at 1","startTime":3047.235,"endTime":3049.045,"body":"It's over a billion right now."},{"speaker":"of the third month at 1","startTime":3049.045,"endTime":3055.37,"body":"There's an immediate, practical issue there, and that is the population of the entire world"},{"speaker":"of the third month at 1","startTime":3055.37,"endTime":3059.165,"body":"in 1100 ad is only 320 million estimates say."},{"speaker":"of the third month at 1","startTime":3059.425,"endTime":3061.325,"body":"So how on earth can this be, right?"},{"speaker":"of the third month at 1","startTime":3061.635,"endTime":3065.409,"body":"Well, of course what has to happen is that the same people are gonna have"},{"speaker":"of the third month at 1","startTime":3065.409,"endTime":3067.925,"body":"to perform more than one role in the family tree."},{"speaker":"of the third month at 1","startTime":3067.925,"endTime":3072.661,"body":"So, you know, your great-great-great-great, great great aunt, might have been the same person as"},{"speaker":"of the third month at 1","startTime":3072.661,"endTime":3073.925,"body":"your great-Great-great-great great grandmother."},{"speaker":"of the third month at 1","startTime":3074.305,"endTime":3080.313,"body":"Um, and so if we go back far enough, this kind of nice bifurcating thing"},{"speaker":"of the third month at 1","startTime":3080.313,"endTime":3086.322,"body":"actually starts to become a clustered, interlinked tangle of multiple, uh, relationships and, and connections"},{"speaker":"of the third month at 1","startTime":3086.322,"endTime":3087.925,"body":"on your family tree."},{"speaker":"of the third month at 1","startTime":3088.305,"endTime":3090.165,"body":"And that's not just your family tree."},{"speaker":"of the third month at 1","startTime":3091.005,"endTime":3096.271,"body":"Actually everybody, if you go back, those 900 years has got those billion spaces in"},{"speaker":"of the third month at 1","startTime":3096.271,"endTime":3100.485,"body":"their family tree, which are gonna have multiple people in multiple places."},{"speaker":"of the third month at 1","startTime":3100.865,"endTime":3105.115,"body":"And the same 320 million people, or even fewer than that, if we look at"},{"speaker":"of the third month at 1","startTime":3105.115,"endTime":3109.365,"body":"European ancestry, uh, are gonna have to be on lots of, lots of family trees."},{"speaker":"of the third month at 1","startTime":3110.105,"endTime":3113.405,"body":"And the extent to which this is the case is really quite startling."},{"speaker":"of the third month at 1","startTime":3113.465,"endTime":3119.038,"body":"So a mathematician called Joseph Chang, um, wrote about this and he describes something called"},{"speaker":"of the third month at 1","startTime":3119.038,"endTime":3120.525,"body":"the identical ancestor point."},{"speaker":"of the third month at 1","startTime":3120.525,"endTime":3124.858,"body":"So in Europe, the identical ancestor point is between 800 and a thousand years ago,"},{"speaker":"of the third month at 1","startTime":3124.858,"endTime":3125.725,"body":"let's say 900."},{"speaker":"of the third month at 1","startTime":3125.945,"endTime":3127.445,"body":"That's about between those numbers."},{"speaker":"of the third month at 1","startTime":3127.905,"endTime":3128.845,"body":"So what is this point?"},{"speaker":"of the third month at 1","startTime":3129.275,"endTime":3135.593,"body":"Well, at that point, so you can show that about 20% of the people alive"},{"speaker":"of the third month at 1","startTime":3135.593,"endTime":3139.805,"body":"in Europe back then actually haven't got any living descendants."},{"speaker":"of the third month at 1","startTime":3140.105,"endTime":3143.725,"body":"Either they didn't have children or their children didn't, their family line died out."},{"speaker":"of the third month at 1","startTime":3144.185,"endTime":3148.325,"body":"But for the anyone in the remaining 80%, let's say William the conqueror, we know"},{"speaker":"of the third month at 1","startTime":3148.325,"endTime":3151.085,"body":"he's got at least one living descendant, Danny Dyer \u003claugh\u003e."},{"speaker":"of the third month at 1","startTime":3151.985,"endTime":3156.365,"body":"So he, he is one of the people who has at least one living descendant."},{"speaker":"of the third month at 1","startTime":3157.315,"endTime":3158.325,"body":"It's amazing, but true."},{"speaker":"of the third month at 1","startTime":3158.325,"endTime":3159.205,"body":"It's really counterintuitive."},{"speaker":"of the third month at 1","startTime":3159.745,"endTime":3164.989,"body":"But of those people alive back then, if they have any living descendant at all,"},{"speaker":"of the third month at 1","startTime":3164.989,"endTime":3169.885,"body":"then they are the direct descendant of everybody alive now with European ancestry, everybody."},{"speaker":"of the third month at 1","startTime":3170.625,"endTime":3176.205,"body":"So we are all descended from, from royalty, right?"},{"speaker":"of the third month at 1","startTime":3176.205,"endTime":3177.005,"body":"So we're all descended."},{"speaker":"of the third month at 1","startTime":3177.005,"endTime":3179.845,"body":"If we have European ancestry, we are all descended from William the Conqueror."},{"speaker":"of the third month at 1","startTime":3179.945,"endTime":3182.987,"body":"And actually you can take this worldwide, you have to go back a bit further"},{"speaker":"of the third month at 1","startTime":3182.987,"endTime":3184.205,"body":"to cover everyone in the world."},{"speaker":"of the third month at 1","startTime":3184.545,"endTime":3188.605,"body":"But the world identical ancestor point is about 3,600 years ago."},{"speaker":"of the third month at 1","startTime":3189.225,"endTime":3194.747,"body":"So anyone alive in, uh, 1600 BC who has any living descendants is the direct"},{"speaker":"of the third month at 1","startTime":3194.747,"endTime":3197.325,"body":"descendant of every single one of us."},{"speaker":"of the third month at 1","startTime":3197.825,"endTime":3199.005,"body":"And that's really amazing."},{"speaker":"of the third month at 1","startTime":3199.465,"endTime":3204.005,"body":"So on that happy note, your majesties, I shall finish for today."},{"speaker":"of the third month at 1","startTime":3204.005,"endTime":3204.405,"body":"Thank you."},{"speaker":"of the third month at 1","startTime":3209.385,"endTime":3213.426,"body":"The problem with the six degrees of freedom is simply that you don't know who"},{"speaker":"of the third month at 1","startTime":3213.426,"endTime":3213.965,"body":"to pick."},{"speaker":"of the third month at 1","startTime":3214.105,"endTime":3214.325,"body":"Yes."},{"speaker":"of the third month at 1","startTime":3214.665,"endTime":3220.285,"body":"If you want a connection with Richard Nixon, right, who would you pick?"},{"speaker":"of the third month at 1","startTime":3220.475,"endTime":3224.367,"body":"Well, you've got no idea, but you've probably only got two degrees of freedom away"},{"speaker":"of the third month at 1","startTime":3224.367,"endTime":3225.405,"body":"from Yeah, yeah, yeah."},{"speaker":"of the third month at 1","startTime":3225.405,"endTime":3231.005,"body":"Anyway, and, and so I wondered if you would talk about that aspect of statistics."},{"speaker":"of the third month at 1","startTime":3231.505,"endTime":3232.245,"body":"Yes, you are right."},{"speaker":"of the third month at 1","startTime":3232.635,"endTime":3234.885,"body":"It's knowing how to find these links."},{"speaker":"of the third month at 1","startTime":3234.885,"endTime":3237.885,"body":"And of course there are, there are now there are plenty of ways we can"},{"speaker":"of the third month at 1","startTime":3237.885,"endTime":3238.485,"body":"do this online."},{"speaker":"of the third month at 1","startTime":3238.565,"endTime":3242.187,"body":"I mean, there, you know, maps of the internet, and that's how the, you know,"},{"speaker":"of the third month at 1","startTime":3242.187,"endTime":3245.085,"body":"Google and other search engines work by knowing what the links are."},{"speaker":"of the third month at 1","startTime":3245.235,"endTime":3248.165,"body":"They've got, um, it's based entirely on, on graphs."},{"speaker":"of the third month at 1","startTime":3248.165,"endTime":3252.078,"body":"These networks, uh, the, the search engine will look through and look at what's linked"},{"speaker":"of the third month at 1","startTime":3252.078,"endTime":3254.165,"body":"to what, which pages are linked to others."},{"speaker":"of the third month at 1","startTime":3254.465,"endTime":3258.079,"body":"So if you have a big, you know, database, you can search these things and"},{"speaker":"of the third month at 1","startTime":3258.079,"endTime":3259.525,"body":"try and find these shortest parts."},{"speaker":"of the third month at 1","startTime":3259.525,"endTime":3263.567,"body":"Of course, we don't have that in front of us, but there was an experiment"},{"speaker":"of the third month at 1","startTime":3263.567,"endTime":3267.61,"body":"quite a while ago, this, you know, before the internet, but maybe in the sixties,"},{"speaker":"of the third month at 1","startTime":3267.61,"endTime":3270.845,"body":"there was an experiment where people were given a name of someone."},{"speaker":"of the third month at 1","startTime":3271.275,"endTime":3275.332,"body":"This is in America, they were given just someone's name, uh, and you know, so"},{"speaker":"of the third month at 1","startTime":3275.332,"endTime":3276.685,"body":"and so, South Carolina, whatever."},{"speaker":"of the third month at 1","startTime":3277.025,"endTime":3281.525,"body":"And they had to get to them by, send a letter to them by sending"},{"speaker":"of the third month at 1","startTime":3281.525,"endTime":3284.525,"body":"it to someone they knew who might know this person."},{"speaker":"of the third month at 1","startTime":3284.705,"endTime":3288.226,"body":"So kind of try to exploit who might be likely to be able to get"},{"speaker":"of the third month at 1","startTime":3288.226,"endTime":3289.165,"body":"this to this person."},{"speaker":"of the third month at 1","startTime":3289.325,"endTime":3289.805,"body":"I never know."},{"speaker":"of the third month at 1","startTime":3290.025,"endTime":3294.041,"body":"And they found that actually, and of course this is within imperfect information, you're just"},{"speaker":"of the third month at 1","startTime":3294.041,"endTime":3294.845,"body":"making educated guesses."},{"speaker":"of the third month at 1","startTime":3294.845,"endTime":3299.416,"body":"But they could do that usually within four steps because people were actively trying to"},{"speaker":"of the third month at 1","startTime":3299.416,"endTime":3301.245,"body":"think about how it might work."},{"speaker":"of the third month at 1","startTime":3301.305,"endTime":3304.779,"body":"So if we can try and engineer these things, as you say, and then we"},{"speaker":"of the third month at 1","startTime":3304.779,"endTime":3308.253,"body":"can improve our, our chances of being aware of the links, but the links are"},{"speaker":"of the third month at 1","startTime":3308.253,"endTime":3308.485,"body":"there,"},{"speaker":"of the third month at 1","startTime":3309.145,"endTime":3316.15,"body":"I'm fascinated by origins, uh, and proba probability in terms of science, uh, particle physics,"},{"speaker":"of the third month at 1","startTime":3316.15,"endTime":3317.085,"body":"et cetera."},{"speaker":"of the third month at 1","startTime":3317.085,"endTime":3317.405,"body":"Mm-Hmm."},{"speaker":"of the third month at 1","startTime":3317.445,"endTime":3322.149,"body":"\u003caffirmative\u003e, uh, the fact that the universe began and the fact that life began and"},{"speaker":"of the third month at 1","startTime":3322.149,"endTime":3325.285,"body":"it ha has happened is a probability of that one."},{"speaker":"of the third month at 1","startTime":3325.785,"endTime":3326.005,"body":"Mm."},{"speaker":"of the third month at 1","startTime":3327.485,"endTime":3327.965,"body":"\u003claugh\u003e."},{"speaker":"of the third month at 1","startTime":3328.525,"endTime":3329.045,"body":"I mean, yeah."},{"speaker":"of the third month at 1","startTime":3329.185,"endTime":3333.685,"body":"So, so this is, we could have talked a bit about the philanthropic principle, right?"},{"speaker":"of the third month at 1","startTime":3333.685,"endTime":3338.335,"body":"That says it's amazingly unlikely on the face of it that, you know, there's this"},{"speaker":"of the third month at 1","startTime":3338.335,"endTime":3342.985,"body":"planet that's just the right distance from a sun of just the right temperature that's"},{"speaker":"of the third month at 1","startTime":3342.985,"endTime":3344.845,"body":"not, you know, unstable or stable."},{"speaker":"of the third month at 1","startTime":3344.865,"endTime":3348.446,"body":"And then we've got the moon that helps us not to be hit by asteroids"},{"speaker":"of the third month at 1","startTime":3348.446,"endTime":3348.685,"body":"constantly."},{"speaker":"of the third month at 1","startTime":3348.685,"endTime":3352.405,"body":"And there are tides and there's water and the temperatures right in this goldilock zone."},{"speaker":"of the third month at 1","startTime":3353.225,"endTime":3355.485,"body":"So on the face of it, gosh, that's awfully unlikely."},{"speaker":"of the third month at 1","startTime":3355.585,"endTime":3360.197,"body":"But on the other hand, it had to have happened, as you say, probability one"},{"speaker":"of the third month at 1","startTime":3360.197,"endTime":3362.965,"body":"'cause we are there to ask the question, right?"},{"speaker":"of the third month at 1","startTime":3362.985,"endTime":3365.685,"body":"So it's kind of, given that it's happened, what's the probability that it's happened?"},{"speaker":"of the third month at 1","startTime":3365.865,"endTime":3366.765,"body":"One \u003claugh\u003e, you know?"},{"speaker":"of the third month at 1","startTime":3367.395,"endTime":3367.685,"body":"Yeah."},{"speaker":"of the third month at 1","startTime":3368.355,"endTime":3372.599,"body":"It's, you, you probably need to find Chris Linox next book, which is called The"},{"speaker":"of the third month at 1","startTime":3372.599,"endTime":3373.165,"body":"Accidental Universe."},{"speaker":"of the third month at 1","startTime":3373.165,"endTime":3373.605,"body":"Perfect."},{"speaker":"of the third month at 1","startTime":3373.845,"endTime":3374.365,"body":"\u003claugh\u003e, talking"},{"speaker":"of the third month at 1","startTime":3374.365,"endTime":3375.525,"body":"About exactly that point."},{"speaker":"of the third month at 1","startTime":3375.635,"endTime":3376.485,"body":"It's all planned."},{"speaker":"of the third month at 1","startTime":3377.045,"endTime":3382.045,"body":"\u003claugh\u003e."},{"speaker":"of the third month at 1","startTime":3377.835,"endTime":3378.685,"body":"Next question over here."},{"speaker":"of the third month at 1","startTime":3378.685,"endTime":3379.005,"body":"Thank"},{"speaker":"of the third month at 1","startTime":3379.005,"endTime":3379.085,"body":"You."},{"speaker":"of the third month at 1","startTime":3379.085,"endTime":3379.525,"body":"Um, hello."},{"speaker":"of the third month at 1","startTime":3379.545,"endTime":3383.601,"body":"So as a sort of random aside, I remember getting on a tube journey once"},{"speaker":"of the third month at 1","startTime":3383.601,"endTime":3385.765,"body":"and in three carriages, one after the other."},{"speaker":"of the third month at 1","startTime":3385.785,"endTime":3386.725,"body":"So one line after the other."},{"speaker":"of the third month at 1","startTime":3386.805,"endTime":3390.245,"body":"I, I knew someone on each carriage, which always struck me as it's quite improbable."},{"speaker":"of the third month at 1","startTime":3390.345,"endTime":3393.603,"body":"But I'd like to know, when you see a random statistic, something that seems absolutely"},{"speaker":"of the third month at 1","startTime":3393.603,"endTime":3396.645,"body":"extraordinary, what's the thought process to go through in a sort of lay sense?"},{"speaker":"of the third month at 1","startTime":3396.645,"endTime":3396.845,"body":"You know?"},{"speaker":"of the third month at 1","startTime":3396.885,"endTime":3398.965,"body":"'cause it seems there's like errors of assumption."},{"speaker":"of the third month at 1","startTime":3399.355,"endTime":3399.645,"body":"Yeah."},{"speaker":"of the third month at 1","startTime":3399.795,"endTime":3402.445,"body":"That is just the sense of the scale of something, you know."},{"speaker":"of the third month at 1","startTime":3402.445,"endTime":3405.005,"body":"So what actually do you think about when you see these things?"},{"speaker":"of the third month at 1","startTime":3405.505,"endTime":3409.355,"body":"So I might, I mean, the sort of general term might be what's the denominator"},{"speaker":"of the third month at 1","startTime":3409.355,"endTime":3410.125,"body":"of the \u003claugh\u003e?"},{"speaker":"of the third month at 1","startTime":3410.125,"endTime":3413.245,"body":"You know, so how many times have they of this test been done?"},{"speaker":"of the third month at 1","startTime":3413.465,"endTime":3417.835,"body":"So if you see an advertisement that says, you know, um, all these people tried"},{"speaker":"of the third month at 1","startTime":3417.835,"endTime":3422.205,"body":"this amazing beauty product and 18 out of 19 said it was great, but how"},{"speaker":"of the third month at 1","startTime":3422.205,"endTime":3426.285,"body":"many sets of 19 people have they asked \u003claugh\u003e in order to get that?"},{"speaker":"of the third month at 1","startTime":3426.305,"endTime":3431.605,"body":"So yeah, what's, what's the pool of, of possibility for this outcome to have happened?"},{"speaker":"of the third month at 1","startTime":3431.985,"endTime":3433.165,"body":"And that, that's part of it."},{"speaker":"of the third month at 1","startTime":3433.425,"endTime":3436.44,"body":"Um, and, and of course the more, the more trials you have, the more likely"},{"speaker":"of the third month at 1","startTime":3436.44,"endTime":3437.245,"body":"it is to occur."},{"speaker":"of the third month at 1","startTime":3438.155,"endTime":3443.405,"body":"Also, I think thinking about the, the near miss possibility."},{"speaker":"of the third month at 1","startTime":3443.545,"endTime":3447.349,"body":"So if are, if someone said, well, this is close enough, so that's another way"},{"speaker":"of the third month at 1","startTime":3447.349,"endTime":3449.125,"body":"to get things happen, much more likely."},{"speaker":"of the third month at 1","startTime":3449.225,"endTime":3453.483,"body":"So if you make some prediction and you were nearly right, \u003claugh\u003e, uh, I, I'm"},{"speaker":"of the third month at 1","startTime":3453.483,"endTime":3457.741,"body":"gonna try and predict a random number and I'm gonna say it's 54 and you"},{"speaker":"of the third month at 1","startTime":3457.741,"endTime":3459.445,"body":"know, oh, well it was 50."},{"speaker":"of the third month at 1","startTime":3459.635,"endTime":3463.165,"body":"Okay, well, near enough, then you massively increase your chance of getting it right."},{"speaker":"of the third month at 1","startTime":3463.225,"endTime":3466.405,"body":"So you, you can be interrogating the, the reported output."},{"speaker":"of the third month at 1","startTime":3467.065,"endTime":3470.805,"body":"You know, are they, how many trials were there before this successful one?"},{"speaker":"of the third month at 1","startTime":3471.025,"endTime":3474.325,"body":"Uh, how close is it to what you really were thinking of?"},{"speaker":"of the third month at 1","startTime":3474.335,"endTime":3477.205,"body":"Those are the, those are two really key things I think to remember."},{"speaker":"of the third month at 1","startTime":3477.585,"endTime":3481.795,"body":"Um, and just to be aware, you know, there's, with the more combinations you allow,"},{"speaker":"of the third month at 1","startTime":3481.795,"endTime":3486.005,"body":"the more likely, as we saw with my very exciting revelations about Thomas Quish \u003claugh\u003e"},{"speaker":"of the third month at 1","startTime":3486.905,"endTime":3487.325,"body":"Ladies."}]}