Tails You Win: The Science of Chance

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0:00:02 > 0:00:05All our lives, we are pulled about and pushed around

0:00:05 > 0:00:07by the mysterious workings of chance.

0:00:08 > 0:00:10When chance seems cruel,

0:00:10 > 0:00:11some call it Fate.

0:00:13 > 0:00:15And when chance is kind,

0:00:15 > 0:00:17we might call it Luck.

0:00:17 > 0:00:18Scoring a big win...

0:00:18 > 0:00:22..being saved from disaster...

0:00:22 > 0:00:25..or meeting that special someone.

0:00:25 > 0:00:28But what actually is chance?

0:00:28 > 0:00:32Is it something fundamental in the fabric of the universe?

0:00:32 > 0:00:34Does chance have rules?

0:00:34 > 0:00:36And does it really exist at all?

0:00:37 > 0:00:38And if it does,

0:00:38 > 0:00:41could we one day even overcome it?

0:00:41 > 0:00:46This is the story of how we discovered how chance works...

0:00:46 > 0:00:48..learnt to tame it...

0:00:48 > 0:00:52..and even to work out the odds for the future.

0:00:53 > 0:00:56How we tried, but so often failed,

0:00:56 > 0:00:57to conquer it...

0:00:57 > 0:01:00and may finally be learning to love it.

0:01:21 > 0:01:24Chance plays its part in all our lives,

0:01:24 > 0:01:28though mine perhaps more than most.

0:01:28 > 0:01:30I'm a mathematician at Cambridge University

0:01:30 > 0:01:33and trying to make sense of chance is my job.

0:01:34 > 0:01:37I study how we can use the mathematics of chance

0:01:37 > 0:01:39to calculate probabilities,

0:01:39 > 0:01:43numbers that can give us a handle on what might happen in the future.

0:01:51 > 0:01:54SPLASHING SOUND EFFECT

0:01:58 > 0:02:01APPLAUSE SOUND EFFECT

0:02:05 > 0:02:07GASPING SOUND EFFECT

0:02:07 > 0:02:09Did you know that, on average,

0:02:09 > 0:02:13each person in Britain has a one-in-a-million daily chance

0:02:13 > 0:02:15of some kind of violent or accidental death?

0:02:17 > 0:02:19To put it in perspective, 1 in a million

0:02:19 > 0:02:23is roughly the chance of flipping heads 20 times.

0:02:23 > 0:02:25Imagine it like this.

0:02:25 > 0:02:26Flip a coin,

0:02:26 > 0:02:2820 heads, you're dead.

0:02:28 > 0:02:30Heads...

0:02:30 > 0:02:34Heads. Oh, dear!

0:02:34 > 0:02:36Heads...

0:02:36 > 0:02:38Tails! Oh, phew!

0:02:40 > 0:02:44It's easy to say that it's 50/50 for a coin to come up heads,

0:02:44 > 0:02:47but we can even put a probability on things

0:02:47 > 0:02:50that seem utterly chaotic and unpredictable.

0:02:52 > 0:02:55San Francisco.

0:02:55 > 0:02:56In October 1989,

0:02:56 > 0:03:01a huge, magnitude 7 earthquake struck totally without warning.

0:03:01 > 0:03:02Many people died.

0:03:11 > 0:03:15Today, San Francisco is its usual laid-back and beautiful self.

0:03:17 > 0:03:21But the people here know another disaster could hit at any moment.

0:03:23 > 0:03:25I know that my family members,

0:03:25 > 0:03:28we all have the earthquake kits and we try to have things ready,

0:03:28 > 0:03:31but, other than that, we're not very fazed by it, I don't think.

0:03:31 > 0:03:32Not until the big one comes.

0:03:32 > 0:03:36I believe in being prepared but I also believe that it is fate.

0:03:36 > 0:03:38I've been here for over 20 years

0:03:38 > 0:03:40and...it kind of puts you in a place

0:03:40 > 0:03:43where you live a bit more in the moment,

0:03:43 > 0:03:45where you know as much as you prepare,

0:03:45 > 0:03:47something could hit at any time.

0:03:48 > 0:03:51For millennia, we've met the uncertainties of life

0:03:51 > 0:03:54with just a fateful shrug of the shoulders.

0:03:54 > 0:03:57But mathematics can help us quantify fate,

0:03:57 > 0:03:59even if we can't banish it.

0:04:13 > 0:04:15What we now know from our studies is that

0:04:15 > 0:04:20the likelihood of a major earthquake hitting the Bay area

0:04:20 > 0:04:24is something like 63% over the next 30 years.

0:04:24 > 0:04:27But, associated with this 63% number,

0:04:27 > 0:04:29which sounds very precise,

0:04:29 > 0:04:32there's actually a huge range of uncertainty.

0:04:32 > 0:04:35It could be mid-40%

0:04:35 > 0:04:37or it could be 80%.

0:04:38 > 0:04:43Probabilities are often as much a matter of judgement as arithmetic.

0:04:43 > 0:04:47But they can still really help people decide what to do.

0:04:48 > 0:04:51After the 1989 earthquake,

0:04:51 > 0:04:52there were a lot of aftershocks

0:04:52 > 0:04:57and a woman called me and she said, "I'm so nervous to be here."

0:04:57 > 0:05:00"I think I want to drive to Los Angeles to visit my daughter."

0:05:00 > 0:05:05And I said, "I don't think that's a good idea," and she said, "Why?"

0:05:05 > 0:05:08I said, "Well, the likelihood that you'll be injured

0:05:08 > 0:05:11"in an automobile accident is much higher

0:05:11 > 0:05:14"than the likelihood that an aftershock will harm you."

0:05:17 > 0:05:19There's no escaping chance.

0:05:19 > 0:05:22But if we can understand how it works,

0:05:22 > 0:05:25then perhaps we can even turn it to our advantage.

0:05:25 > 0:05:28This was what the first mathematicians to investigate it

0:05:28 > 0:05:30hoped to do.

0:05:30 > 0:05:32To, as it were, tame chance.

0:05:33 > 0:05:35The scholars of the ancient world,

0:05:35 > 0:05:38the Egyptians, Babylonians, Greeks and others,

0:05:38 > 0:05:42laid down the foundations for geometry, algebra, number theory,

0:05:42 > 0:05:43and so much more.

0:05:44 > 0:05:46But extraordinarily,

0:05:46 > 0:05:49they never even got started on the maths of chance.

0:05:49 > 0:05:54It wasn't until the Renaissance that a few pioneering thinkers

0:05:54 > 0:05:56first got to grips with probability.

0:05:56 > 0:05:59But unlike the ancients,

0:05:59 > 0:06:02they weren't loftily pursuing knowledge for its own sake.

0:06:03 > 0:06:07They were trying to crack the secrets of gambling.

0:06:08 > 0:06:10The first was Gerolamo Cardano,

0:06:10 > 0:06:13from the Italian city of Milan.

0:06:13 > 0:06:15Cardano was a doctor.

0:06:15 > 0:06:19But he was also an obsessive life-long gambler.

0:06:19 > 0:06:22This was written in the 1570s,

0:06:22 > 0:06:24the earliest known work on probability.

0:06:24 > 0:06:28In it, Cardano set out a seasoned gambler's tips and insights,

0:06:28 > 0:06:30including how to cheat,

0:06:30 > 0:06:31and in one chapter,

0:06:31 > 0:06:36laid out the most fundamental principle of probability.

0:06:38 > 0:06:42Cardano realised a probability was also a fraction.

0:06:42 > 0:06:44So with the roll of a dice,

0:06:44 > 0:06:48the probability for each side coming up was one sixth.

0:06:50 > 0:06:52And it gets more interesting with two dice.

0:06:54 > 0:06:58With two dice, and 36 possible combinations,

0:06:58 > 0:07:00there's only one way to throw a 2.

0:07:02 > 0:07:04But you're much more likely to get a 7.

0:07:06 > 0:07:10Cardano's insight works with games like dice

0:07:10 > 0:07:14because we can assume that each of the faces is equally likely.

0:07:14 > 0:07:17Provided, as Cardano puts it in his book,

0:07:17 > 0:07:19"the dice are honest."

0:07:19 > 0:07:21This may seem simple to us now

0:07:21 > 0:07:24but it was the very first step in working out how to tame chance.

0:07:37 > 0:07:39Las Vegas.

0:07:39 > 0:07:42A place Cardano would have surely loved.

0:07:44 > 0:07:47The people who run this city have the measure of chance so well,

0:07:47 > 0:07:50they've built an entire glittering industry out of it.

0:07:52 > 0:07:55It's vital, even so, that anyone here CAN get lucky.

0:07:56 > 0:07:59You could even bet one dollar and win a million.

0:08:02 > 0:08:05Mike Shackleford is a professional gambler.

0:08:05 > 0:08:09His living depends on his command of casino maths.

0:08:23 > 0:08:26I analyse every casino game out there

0:08:26 > 0:08:29and my goal is to find out the probability

0:08:29 > 0:08:32of every possible event in every game.

0:08:34 > 0:08:37Almost always, the odds are going to be in the casino's favour.

0:08:37 > 0:08:38For example,

0:08:38 > 0:08:44in roulette, the house advantage is 5.26% under American rules.

0:08:44 > 0:08:47That means that for every dollar the player bets,

0:08:47 > 0:08:51on average he can expect to lose 5.26 cents.

0:08:53 > 0:08:56Not only do the casinos understand the probabilities perfectly,

0:08:56 > 0:08:59they also know that most of the punters don't.

0:09:01 > 0:09:04And these games can really mess with our minds.

0:09:18 > 0:09:21You'll see a series of outcomes from a slot machine

0:09:21 > 0:09:24and believe that there's a pattern to what you've just seen

0:09:24 > 0:09:28but that's really just the human brain playing a trick on you

0:09:28 > 0:09:32because what's happened in the past has no predictive value

0:09:32 > 0:09:34for what is going to happen next.

0:09:34 > 0:09:37Yes, the machine may have had this series of payouts in the past.

0:09:37 > 0:09:39It may have been hot or cold.

0:09:39 > 0:09:41But that has no bearing or no influence

0:09:41 > 0:09:44on what is going to happen on that next game.

0:09:44 > 0:09:47So you could hit the jackpot symbol

0:09:47 > 0:09:48two games in a row.

0:09:51 > 0:09:54We just hit the biggest jackpot we've ever hit here.

0:09:54 > 0:09:568,600 dollars!

0:09:56 > 0:09:59We just went to this machine about half an hour ago,

0:09:59 > 0:10:01so...we got lucky!

0:10:03 > 0:10:06Jackpots don't worry the casinos.

0:10:06 > 0:10:09They know the slots are programmed

0:10:09 > 0:10:11to deliver high house edges in the long run.

0:10:13 > 0:10:16Smart players, like Mike, rarely touch them.

0:10:18 > 0:10:23A professional gambler plays games where the odds are in their favour.

0:10:23 > 0:10:26Probably the most well known is card-counting in Blackjack.

0:10:29 > 0:10:31In Blackjack, every time a card is dealt,

0:10:31 > 0:10:34the odds change for all the cards that are left.

0:10:36 > 0:10:38Mike tracks the cards that are dealt,

0:10:38 > 0:10:40to work out how those odds are changing.

0:10:41 > 0:10:45So, if the player notices that in the first 25% of the shoe

0:10:45 > 0:10:49a lot of small cards came out, more than expected,

0:10:49 > 0:10:53he knows that the remaining cards are going to have a surplus of big cards.

0:10:53 > 0:10:55So he will adjust his bet size

0:10:55 > 0:10:57and he will change how he plays

0:10:57 > 0:11:01and by doing that, he can get the odds in his favour.

0:11:01 > 0:11:05On a good day, Mike can get a 1% advantage over the house.

0:11:05 > 0:11:07It doesn't sound much

0:11:07 > 0:11:09but it could mean a lot of money.

0:11:09 > 0:11:12The casinos, of course,

0:11:12 > 0:11:14don't like card counters

0:11:14 > 0:11:16and Mike's been banned from almost every joint in town.

0:11:20 > 0:11:22In the world of games,

0:11:22 > 0:11:25if you know the rules, you can figure out the probabilities.

0:11:27 > 0:11:30But what about the chances of life and death itself?

0:11:30 > 0:11:32EVIL LAUGHTER

0:11:32 > 0:11:35BELL TOLLS, SPOOKY MUSIC

0:11:38 > 0:11:42To be able to put probabilities on our own lives

0:11:42 > 0:11:46needed another great mathematical leap.

0:11:46 > 0:11:48And this time, the rewards would be even bigger.

0:11:52 > 0:11:55For most of history, it was almost a given

0:11:55 > 0:11:58that we had not the slightest inkling

0:11:58 > 0:12:00of when our time on earth was up.

0:12:00 > 0:12:02Death visited when he wanted

0:12:02 > 0:12:04and the results were never pretty.

0:12:08 > 0:12:12Thank goodness for the consolation of eternal life in the hereafter!

0:12:14 > 0:12:17The sculptors who carved this terrifying monument

0:12:17 > 0:12:20were capturing the brutal truth of our mortality

0:12:20 > 0:12:23as a warning to everyone here, quaking in the pews.

0:12:23 > 0:12:26But around the time this was carved, about 300 years ago,

0:12:26 > 0:12:29scientists began trying to work out

0:12:29 > 0:12:33the mathematical chances, for each individual,

0:12:33 > 0:12:35that Death would soon be paying them a call.

0:12:37 > 0:12:42The revelation was that you could study one group of people,

0:12:42 > 0:12:44the residents of this parish, for instance,

0:12:44 > 0:12:46and see how old they were when they died.

0:12:46 > 0:12:49From this, you could estimate the chances of death

0:12:49 > 0:12:51at each age for everybody else too.

0:12:52 > 0:12:54This was a radical idea.

0:12:54 > 0:12:55Count the dead

0:12:55 > 0:12:58and Death would become less of a divine punishment

0:12:58 > 0:13:01and more of a predictable force of nature.

0:13:03 > 0:13:05The man who really cracked

0:13:05 > 0:13:08how to apply the maths of chance to human lives

0:13:08 > 0:13:12was Edmund Halley, the famous astronomer.

0:13:15 > 0:13:18Edmund Halley had no interest in what went on in there.

0:13:18 > 0:13:21What fascinated him was what had happened out here.

0:13:21 > 0:13:24Most people now remember him for his famous comet,

0:13:24 > 0:13:27but I salute him as one of history's greatest nerds!

0:13:27 > 0:13:29Halley realised that he could calculate

0:13:29 > 0:13:32the probabilities of life and death.

0:13:32 > 0:13:34All he needed was some good data.

0:13:37 > 0:13:3983...

0:13:41 > 0:13:4352...

0:13:43 > 0:13:4527...

0:13:46 > 0:13:49In faraway Breslau, now a city in Poland,

0:13:49 > 0:13:52locals were spooked by an ancient superstition

0:13:52 > 0:13:55that being aged 49 or 63

0:13:55 > 0:13:58was particularly risky.

0:13:59 > 0:14:01To prove the superstition wrong,

0:14:01 > 0:14:05a Breslau clergyman collected details of all the town's deaths

0:14:05 > 0:14:09and circulated these to the leading scientists of the day.

0:14:11 > 0:14:13Halley got hold of the data

0:14:13 > 0:14:17and realised the results would have an impact far beyond Breslau.

0:14:28 > 0:14:30Halley constructed a table

0:14:30 > 0:14:33that was made up of, essentially, two columns.

0:14:33 > 0:14:36The first column was age

0:14:36 > 0:14:40and the second column was how many people were alive at that age.

0:14:40 > 0:14:43The first column started at birth with 1,000 people,

0:14:43 > 0:14:45and as the ages increased,

0:14:45 > 0:14:49what we saw is that the number of people alive decreased

0:14:49 > 0:14:50and this wasn't uniformly.

0:14:52 > 0:14:57Halley found nothing special about 49 or 63.

0:14:57 > 0:15:00But his data showed that the older you got,

0:15:00 > 0:15:03the greater the chance of you dying.

0:15:05 > 0:15:07It seems obvious to us now.

0:15:07 > 0:15:08But before Halley,

0:15:08 > 0:15:11people thought the chances much the same for everyone,

0:15:11 > 0:15:12young and old alike.

0:15:14 > 0:15:18And Halley's table had an immediate practical benefit.

0:15:18 > 0:15:21Halley's tables were also ground-breaking

0:15:21 > 0:15:22because not only did he publish

0:15:22 > 0:15:25the probability of death at a certain age,

0:15:25 > 0:15:26he took that one step further

0:15:26 > 0:15:29and applied that to the price of a pension

0:15:29 > 0:15:31or the price of life assurance.

0:15:31 > 0:15:35He included formulae as to how you could actually come up

0:15:35 > 0:15:36with a price for a pension.

0:15:39 > 0:15:41People in the 17th century wanted to buy pensions

0:15:41 > 0:15:44and life insurance, just like they do today.

0:15:46 > 0:15:48But before Halley, anybody who provided them

0:15:48 > 0:15:50was in danger of going bankrupt.

0:15:51 > 0:15:54So Halley's breakthrough would form the foundation

0:15:54 > 0:15:57for the entire pensions and life insurance industry.

0:15:57 > 0:16:01And death would never seem as capricious and mysterious again.

0:16:04 > 0:16:06And what of Edmund Halley?

0:16:07 > 0:16:10He lived all the way to 86,

0:16:10 > 0:16:12off his own table!

0:16:12 > 0:16:14Costly if you were his pension provider!

0:16:20 > 0:16:24Today, the insurance and pensions industry is huge,

0:16:24 > 0:16:26and has collected so much data

0:16:26 > 0:16:28they can correlate your life and death chances

0:16:28 > 0:16:31to your gender, your address,

0:16:31 > 0:16:33your job and your lifestyle.

0:16:33 > 0:16:36And knowledge of the odds could help us all.

0:16:40 > 0:16:43So what do we know about what affects our chances,

0:16:43 > 0:16:45for better or for worse?

0:16:45 > 0:16:49Imagine this 100 metres is 100 years of possible life.

0:16:49 > 0:16:53How many of those years are we actually going to see?

0:16:53 > 0:16:56How far along this track are we going to get?

0:16:59 > 0:17:02When I was born, the average British male

0:17:02 > 0:17:06expected a much shorter life than if born today.

0:17:06 > 0:17:09I was born in the 1950s and back then,

0:17:09 > 0:17:13my expected lifespan was just 67 years.

0:17:13 > 0:17:15But thanks to medical advances

0:17:15 > 0:17:18and changes to the way we live and work,

0:17:18 > 0:17:21our chances are continually getting better.

0:17:21 > 0:17:25The average lifespan is actually rising by three months a year.

0:17:25 > 0:17:29If I were born today, I could expect to live to 78.

0:17:31 > 0:17:33Even better, the longer you live,

0:17:33 > 0:17:35the longer you can expect to live,

0:17:35 > 0:17:38because you've been lucky enough not to die young.

0:17:38 > 0:17:39So at my age now,

0:17:39 > 0:17:43I can expect to live not to 67...

0:17:43 > 0:17:45..or 78...

0:17:45 > 0:17:48..but...

0:17:48 > 0:17:50..82.

0:17:51 > 0:17:53But what's not so cheerful

0:17:53 > 0:17:56is the effect of all those things I might do throughout my life

0:17:56 > 0:17:59that could stop me getting this far, or even further.

0:18:01 > 0:18:03Research tells us that

0:18:03 > 0:18:06for every day you're five kilos overweight, like I am,

0:18:06 > 0:18:09you can expect to lose half an hour off your life.

0:18:13 > 0:18:14Aah!

0:18:14 > 0:18:16Sad to say,

0:18:16 > 0:18:19if you're a man sinking three pints a day

0:18:19 > 0:18:22then that's also half an hour.

0:18:22 > 0:18:25But what about exercise? Won't that make things better?

0:18:25 > 0:18:28Yes, it will. But there's a catch.

0:18:28 > 0:18:30A regular run of half an hour

0:18:30 > 0:18:32and you can expect to live longer.

0:18:32 > 0:18:34Half an hour longer.

0:18:34 > 0:18:37So I hope you actually like running.

0:18:37 > 0:18:40Cos that's how you just spent your extra half hour.

0:18:41 > 0:18:45Surprise, surprise, the worst news is for all you smokers.

0:18:45 > 0:18:48Two cigarettes costs half an hour.

0:18:48 > 0:18:51But the average smoker's on nearly 20 a day.

0:18:51 > 0:18:53And it all adds up.

0:18:56 > 0:19:01Doing something that costs half an hour a day...

0:19:01 > 0:19:03Well, that's more than a week off each year

0:19:03 > 0:19:07and, in the long run, that's a whole year off your life.

0:19:07 > 0:19:11For that 20-a-day smoker,

0:19:11 > 0:19:14that's a staggering 10 years you should expect to lose.

0:19:17 > 0:19:18All these figures tell us a lot.

0:19:18 > 0:19:20But as for chance itself,

0:19:20 > 0:19:22that's certainly not disappeared.

0:19:24 > 0:19:26When I say I can expect to live to 82,

0:19:26 > 0:19:28I'm not actually making a prediction.

0:19:28 > 0:19:32It may be shorter or, with luck, it may be longer.

0:19:32 > 0:19:3382 is the average.

0:19:33 > 0:19:38Imagine 100 possible future me's, each equally likely.

0:19:41 > 0:19:44I'm 58 now and as the years roll by,

0:19:44 > 0:19:48in more and more of these possible futures, I die,

0:19:48 > 0:19:51until by the age of 82

0:19:51 > 0:19:54about half of my future selves will be dead

0:19:54 > 0:19:56and about half still alive.

0:19:57 > 0:20:00Which is going to be me? That's just chance.

0:20:01 > 0:20:05Beyond 82, more and more drop dead.

0:20:05 > 0:20:10And there's a very small chance I could live to be very old indeed.

0:20:12 > 0:20:16If I were a smoker, it's just possible I'd beat the odds.

0:20:19 > 0:20:22But overall, my chances wouldn't look nearly so good.

0:20:25 > 0:20:29Of course, many people would say going on about risks

0:20:29 > 0:20:31is being a big killjoy.

0:20:32 > 0:20:35The writer Kingsley Amis famously said,

0:20:35 > 0:20:37"No pleasure is worth giving up

0:20:37 > 0:20:39"for the sake of two more years

0:20:39 > 0:20:42"in a geriatric home at Weston-super-Mare."

0:20:43 > 0:20:45But I believe understanding the risks

0:20:45 > 0:20:50might actually help us to have more fun, not less.

0:20:50 > 0:20:52OK. Just put one arm through there for me...

0:20:52 > 0:20:56the other through there and turn around. Thank you.

0:20:56 > 0:20:58What we'll do is we'll start strapping you in.

0:20:59 > 0:21:02Many of my favourite experiences would be impossible

0:21:02 > 0:21:04without taking some risk,

0:21:04 > 0:21:06but I'm about to do something I've never done before

0:21:06 > 0:21:08which really does involve risk.

0:21:12 > 0:21:15The best way to compare risky activities

0:21:15 > 0:21:18is to use the micromort,

0:21:18 > 0:21:20a cheery little unit which represents

0:21:20 > 0:21:22a one-in-a-million chance of death.

0:21:34 > 0:21:36Skydiving is actually safer than you might think.

0:21:36 > 0:21:39There's only about a seven-in-a-million chance of dying.

0:21:39 > 0:21:41That's seven micromorts.

0:21:41 > 0:21:44That's about the same risk as 40 miles on a motorbike.

0:21:44 > 0:21:46But there's still a risk.

0:21:46 > 0:21:48And you may think I should be old enough to know better.

0:21:48 > 0:21:52But I think it could be rational to take more risks when you get older.

0:21:55 > 0:21:59An average 18-year-old has a chance of dying in the next 12 months

0:21:59 > 0:22:01of about 500 micromorts.

0:22:03 > 0:22:07But at my age, the equivalent is 7,000 micromorts.

0:22:11 > 0:22:137,000 micromorts doesn't sound great, does it?

0:22:13 > 0:22:17But my extra risk of skydiving is only seven micromorts more.

0:22:17 > 0:22:18That's not much difference.

0:22:21 > 0:22:23So the risk is actually pretty low.

0:22:25 > 0:22:26But the funny thing is,

0:22:26 > 0:22:29now I'm actually in the plane and there's no backing out,

0:22:29 > 0:22:31it suddenly seems a lot worse.

0:22:33 > 0:22:37Will my parachute fail? I don't know.

0:22:37 > 0:22:40Will we be blown into a tree? I don't know.

0:22:42 > 0:22:45Will I be sick with fright over my jumpsuit?

0:22:45 > 0:22:48The probability of that is getting close to 100%!

0:22:53 > 0:22:55It's the moment of truth.

0:22:58 > 0:22:59Here we go!

0:23:04 > 0:23:06Yes, I'm a Professor of Risk

0:23:06 > 0:23:10and I've made a sound decision rooted in the numbers,

0:23:10 > 0:23:12but as I fall, I can't help thinking

0:23:12 > 0:23:14there's a chance I'll die very soon indeed.

0:23:19 > 0:23:22I could buy myself a pair of silver hairbrushes.

0:23:22 > 0:23:24Oh, hello!

0:23:24 > 0:23:25I'm having a go at these premium bonds.

0:23:25 > 0:23:28They're wonderful things - you can't lose.

0:23:28 > 0:23:31Look, there are staggering prizes each month,

0:23:31 > 0:23:33you can get your money back any time you like,

0:23:33 > 0:23:36and, what's more, all your tickets go back into each draw

0:23:36 > 0:23:38whether you've been lucky before or not!

0:23:38 > 0:23:40I might win a thousand quid!

0:23:40 > 0:23:42I love a bit of a flutter.

0:23:42 > 0:23:43Not a word to Bessie about that!

0:23:45 > 0:23:46In 1956,

0:23:46 > 0:23:49Britain introduced a brand new kind of savings scheme,

0:23:49 > 0:23:51Premium Bonds,

0:23:51 > 0:23:54that instead of paying you interest

0:23:54 > 0:23:57gave you the chance to win big prizes.

0:23:57 > 0:24:00At its heart was something created by mathematicians,

0:24:00 > 0:24:04a world of pure chance, randomness.

0:24:06 > 0:24:08This is a world where every element

0:24:08 > 0:24:10is disconnected from every other,

0:24:10 > 0:24:13that operates beyond our influence or control.

0:24:14 > 0:24:17The Premium Bonds monthly prize draw

0:24:17 > 0:24:20needed complete randomness

0:24:20 > 0:24:22to make sure it was scrupulously fair.

0:24:38 > 0:24:40There was quite a lot of human interest in randomness

0:24:40 > 0:24:42for the first time,

0:24:42 > 0:24:44where people began to think about,

0:24:44 > 0:24:46"what are the chances of my winning?"

0:24:46 > 0:24:49But what it required was

0:24:49 > 0:24:52a source of random numbers

0:24:52 > 0:24:55and a special purpose computer was built for this

0:24:55 > 0:24:58and it was one of the very first special purpose computers.

0:24:58 > 0:25:01We're going to an electronic machine, if you understand what that is,

0:25:01 > 0:25:05but thank goodness its complicated name is ERNIE for short.

0:25:05 > 0:25:11ERNIE stood for Electronic Random Number Indicating Equipment.

0:25:11 > 0:25:13Truly random numbers are hard to produce,

0:25:13 > 0:25:16and ERNIE got them by sampling the electrical noise

0:25:16 > 0:25:18from a series of vacuum tubes.

0:25:18 > 0:25:20It was state-of-the-art engineering.

0:25:22 > 0:25:26Randomness really, in a certain extent, means unpredictable,

0:25:26 > 0:25:28but also, for the purposes of ERNIE,

0:25:28 > 0:25:31it needed to be unpredictable and unbiased

0:25:31 > 0:25:34and my job as a young mathematician

0:25:34 > 0:25:36was to show that it really was unbiased

0:25:36 > 0:25:39to any particular Premium Bond number.

0:25:39 > 0:25:42This was quite a skilled and lengthy task

0:25:42 > 0:25:45to say those weasel words that mathematicians use,

0:25:45 > 0:25:50"We have no reason to suppose that ERNIE is not random."

0:25:58 > 0:26:02For me, as a mathematician, complete randomness is fascinating.

0:26:02 > 0:26:05It's full of curiosities.

0:26:05 > 0:26:08And unexpectedly, it turns out to have its own rules,

0:26:08 > 0:26:10patterns and structure.

0:26:13 > 0:26:19This is officially the most boring book in the world. Ever.

0:26:19 > 0:26:22It's called One Million Random Digits

0:26:22 > 0:26:24and that's literally what it is.

0:26:24 > 0:26:27Page after page of random numbers.

0:26:29 > 0:26:32Say what you like about this book, though,

0:26:32 > 0:26:34at least the plot is unpredictable.

0:26:36 > 0:26:37Printed in 1955,

0:26:37 > 0:26:43these numbers were produced by an early computer rather like ERNIE.

0:26:43 > 0:26:45And people have used them since

0:26:45 > 0:26:48for everything from randomised clinical trials

0:26:48 > 0:26:50to encrypting communications.

0:26:51 > 0:26:54I might not read this book cover to cover,

0:26:54 > 0:26:57but I promise you there are some really interesting parts.

0:26:57 > 0:27:01I mean, look at this. 00000.

0:27:01 > 0:27:03And here's another great bit.

0:27:06 > 0:27:0812345.

0:27:08 > 0:27:11It seems really strange to see these.

0:27:11 > 0:27:12I mean, how can these be random?

0:27:12 > 0:27:16But, of course, they're as random as the numbers next to them.

0:27:16 > 0:27:20Not only can you expect to find patterns like these,

0:27:20 > 0:27:23you can even calculate how often you expect to find them.

0:27:23 > 0:27:25A perfect sequence of five numbers.

0:27:25 > 0:27:28There should be 50 of these in the book.

0:27:28 > 0:27:31And the same number five times in a row,

0:27:31 > 0:27:33there should be about 100 of these.

0:27:33 > 0:27:34You can even expect,

0:27:34 > 0:27:37somewhere in these one million random numbers,

0:27:37 > 0:27:40the same number to occur seven times in a row.

0:27:40 > 0:27:42And I've found it.

0:27:43 > 0:27:476666666.

0:27:53 > 0:27:55What makes randomness so useful

0:27:55 > 0:27:58is that it is completely unpredictable...

0:27:58 > 0:27:59but in a predictable way.

0:28:02 > 0:28:04So predictable that it has its own shape.

0:28:07 > 0:28:09A lottery is a great example.

0:28:11 > 0:28:13Each National Lottery draw is...

0:28:13 > 0:28:15well, random.

0:28:15 > 0:28:18There seems no pattern at all.

0:28:18 > 0:28:21But there are also seemingly strange results.

0:28:22 > 0:28:27Today, after something approaching 2,000 National Lottery draws

0:28:27 > 0:28:30over 20 years, there are huge differences

0:28:30 > 0:28:32in how often different numbers have come up.

0:28:33 > 0:28:37Number 38 has been picked 241 times...

0:28:37 > 0:28:41..while number 20 has come up just 171.

0:28:43 > 0:28:45It might look like something's wrong,

0:28:45 > 0:28:47but taking all the results together,

0:28:47 > 0:28:51the totals match the shape of randomness remarkably well.

0:28:53 > 0:28:55And even the outlying results

0:28:55 > 0:28:58are just where the shape shows they should be.

0:29:04 > 0:29:06Here we go. Let's pick some numbers.

0:29:08 > 0:29:11It's not a great bet, I admit.

0:29:11 > 0:29:15There's only a 1-in-14-million chance of me winning the jackpot.

0:29:15 > 0:29:17In fact, I'm very unlikely to win anything at all.

0:29:17 > 0:29:19There's only a 1-in-56 chance

0:29:19 > 0:29:23of me getting the smallest prize of £10.

0:29:23 > 0:29:25Overall, the lottery only pays back

0:29:25 > 0:29:2745% of the money it takes in.

0:29:27 > 0:29:30Far, far worse than any casino game.

0:29:30 > 0:29:33If you must play,

0:29:33 > 0:29:35though you can't change your chances of winning,

0:29:35 > 0:29:39you can improve your chances of not sharing the jackpot.

0:29:39 > 0:29:42Many people pick birthdays or other significant dates,

0:29:42 > 0:29:44so avoid the numbers up to 31.

0:29:44 > 0:29:46You may even want to steer clear

0:29:46 > 0:29:48of that supposedly lucky number, 38.

0:29:50 > 0:29:53In the end, it doesn't matter what numbers you choose,

0:29:53 > 0:29:56every combination, say 1, 2, 3, 4, 5, 6,

0:29:56 > 0:29:58is as likely as any other.

0:29:58 > 0:30:01That's because it's completely random.

0:30:06 > 0:30:10But randomness can confuse us.

0:30:10 > 0:30:14For example, use the shuffle feature on the original iPod

0:30:14 > 0:30:17to play its tracks in random order and before too long

0:30:17 > 0:30:20you're very likely to land on the same album again.

0:30:22 > 0:30:24People found it so off-putting

0:30:24 > 0:30:27that the shuffle on later-generation iPods was supposedly tweaked.

0:30:30 > 0:30:31Apple famously explained,

0:30:31 > 0:30:35"We're making it less random so it feels more random."

0:30:42 > 0:30:47Patterns and connections like this are what we call coincidences.

0:30:47 > 0:30:49And no matter how much we should expect them,

0:30:49 > 0:30:51they nonetheless still make our heads spin.

0:30:53 > 0:30:57I love coincidences so much

0:30:57 > 0:30:59I decided to try to collect them.

0:30:59 > 0:31:02Luckily, it's an interest the nation shares.

0:31:02 > 0:31:06Let's talk about coincidences now, at 7:24, why do they happen?

0:31:06 > 0:31:08- Professor David Spiegelhalter, good morning.- Good morning.

0:31:08 > 0:31:11You are an expert in risk and chance, is what I'm reading,

0:31:11 > 0:31:13at Cambridge University,

0:31:13 > 0:31:15but why are you interested in chance and coincidence?

0:31:15 > 0:31:16Well, it's part of my job.

0:31:16 > 0:31:19I'm Professor of the Public Understanding of Risk,

0:31:19 > 0:31:22so everything to do with chance, uncertainty and coincidences

0:31:22 > 0:31:23is what I'm interested in.

0:31:23 > 0:31:27And we've set up this website where we're collecting coincidence stories

0:31:27 > 0:31:29which people are sending in,

0:31:29 > 0:31:32and the sort of things where people, when they happen to them, say,

0:31:32 > 0:31:34"Ooh, what are the chances of that?"

0:31:34 > 0:31:37And we're trying to work out what the chances of that really are.

0:31:37 > 0:31:41It's like a family having three children all with the same birthday,

0:31:41 > 0:31:44born in different years, but all three children being born

0:31:44 > 0:31:47on the same birthday. You'd think, "Wow, what are the chances of that?"

0:31:47 > 0:31:49Well, we can work those out.

0:31:49 > 0:31:52Since there's a million families in this country with three children,

0:31:52 > 0:31:54we'd expect there's about 8 families like that.

0:31:54 > 0:31:56Now, we've found three of them.

0:31:56 > 0:31:59People read great significance into these things, though.

0:31:59 > 0:32:01Are they misguided in doing that?

0:32:01 > 0:32:04Well, it's Friday 13th, exactly the day that shows people do believe

0:32:04 > 0:32:06in luck and fortune and things like that...

0:32:06 > 0:32:08But I suppose I'm being a bit scientific about them,

0:32:08 > 0:32:11so some of them we try to take apart and do the maths,

0:32:11 > 0:32:13but other ones are just amazing.

0:32:13 > 0:32:16There's a lovely example last year where a French family,

0:32:16 > 0:32:17their house was hit by a meteorite.

0:32:17 > 0:32:20Well, that's pretty surprising itself,

0:32:20 > 0:32:23but their name was Comette. Isn't that just beautiful?

0:32:23 > 0:32:25"What are the chances of never experiencing a coincidence?"

0:32:25 > 0:32:26says Steve in Cheshire.

0:32:26 > 0:32:30Oh, very low indeed. That would be really, really bizarre.

0:32:30 > 0:32:32Good one, Steve.

0:32:32 > 0:32:357:29. What are the chances of any decent weather over the weekend?

0:32:35 > 0:32:37'Pretty good, actually, Rachel.

0:32:37 > 0:32:40'We've got some clear skies out there at the moment,

0:32:40 > 0:32:42'but because of those clear skies

0:32:42 > 0:32:45'temperatures are hovering at or just below freezing...'

0:32:45 > 0:32:48The radio show was a huge success.

0:32:48 > 0:32:51The stories flooded in. Over 3,000 of them.

0:32:51 > 0:32:57We got lots of coincidences with numbers, names and words.

0:32:57 > 0:32:59And loads of calendar ones,

0:32:59 > 0:33:03including one more of those rare triple birthdays.

0:33:03 > 0:33:06Some of these stories are really amazing.

0:33:06 > 0:33:09Lots of them are about running into friends and acquaintances

0:33:09 > 0:33:12in the most unlikely places. And I love this one.

0:33:13 > 0:33:16Mick Preston was on a cycling holiday in the Pyrenees

0:33:16 > 0:33:19and during one stop-over, he wrote his friend, Alan, a postcard.

0:33:19 > 0:33:23But, incredibly, on the way to post it, he bumped into Alan,

0:33:23 > 0:33:26who just by chance was on holiday in the same place,

0:33:26 > 0:33:29so Mick gave him the postcard in person.

0:33:29 > 0:33:31As Mick himself said,

0:33:31 > 0:33:33that was a waste of a good stamp!

0:33:38 > 0:33:42What's striking is that although these and other coincidences

0:33:42 > 0:33:46happened a long time ago, people were so jolted by them

0:33:46 > 0:33:48they still remember them years later.

0:33:49 > 0:33:53I think our brains are hard-wired to look for cause and effect,

0:33:53 > 0:33:57to try to come up with reasons why things happen.

0:33:57 > 0:34:00So when things happen for no apparent reason at all,

0:34:00 > 0:34:02we find it really spooky.

0:34:02 > 0:34:05We just don't seem to easily accept

0:34:05 > 0:34:08that we might not be able to understand or control

0:34:08 > 0:34:09what happens in our lives.

0:34:14 > 0:34:18Random events that have no explanation beyond chance

0:34:18 > 0:34:20saturate our lives...

0:34:22 > 0:34:24..but some people think they can eliminate the random -

0:34:24 > 0:34:29control everything - and that chance has nothing to do with them at all.

0:34:30 > 0:34:35Ed Smith was once said to be the golden boy of English cricket.

0:34:35 > 0:34:37For years he held an idea about chance -

0:34:37 > 0:34:39or, as he called it, "luck" -

0:34:39 > 0:34:43that he shared with many of his fellow sporting professionals.

0:34:55 > 0:34:58When I turned full-time professional in 1999,

0:34:58 > 0:34:59we had all these meetings

0:34:59 > 0:35:02about how we were going to approach the season

0:35:02 > 0:35:04and someone put his hand up and said,

0:35:04 > 0:35:06"I don't think we should say, 'bad luck,' to each other.

0:35:06 > 0:35:08"That's an excuse. It's not bad luck.

0:35:08 > 0:35:10"If someone gets out, it's their fault."

0:35:10 > 0:35:13I think as sportsmen we're conditioned to think that,

0:35:13 > 0:35:16that you are in total control.

0:35:16 > 0:35:18I mean, if you, if you walk out to bat in professional cricket

0:35:18 > 0:35:21and you say, "Well, maybe I'll be lucky and maybe I won't,

0:35:21 > 0:35:24"and maybe someone will bowl a good ball I'll be out, and I can't do anything about it,"

0:35:24 > 0:35:27then you're stacking the deck against yourself before you even begin.

0:35:30 > 0:35:34Ed played for England and became captain of Middlesex.

0:35:35 > 0:35:37Everything went well for him,

0:35:37 > 0:35:43until one day during a county cricket match at Lord's.

0:35:43 > 0:35:45So, we're in the middle of this match, it's going well,

0:35:45 > 0:35:47we're pretty much cantering to victory.

0:35:47 > 0:35:50We're on a bit of a streak of five, six wins in a row, everything's going well

0:35:50 > 0:35:54and I'm doing the most routine thing in cricket, I'm running a two.

0:35:54 > 0:35:56It happens all the time, you know...

0:35:56 > 0:35:58it's not particularly demanding, athletically,

0:35:58 > 0:36:00to run 20 yards and then come back again.

0:36:00 > 0:36:04And I ran the first one and then you just rub the bat in,

0:36:04 > 0:36:06and I just, sort of, collapsed.

0:36:06 > 0:36:09And I'm lying in this, and have this shooting pain in my ankle,

0:36:09 > 0:36:14and it was only quite a few weeks later that there was an X-ray,

0:36:14 > 0:36:17and it turned out that I'd broken my ankle,

0:36:17 > 0:36:20and I wasn't going to play any time soon!

0:36:20 > 0:36:23I missed the rest of that season and then I retired, effectively,

0:36:23 > 0:36:27at the end of that season and didn't play professional cricket again.

0:36:27 > 0:36:31In a single moment, Ed's entire career vanished.

0:36:31 > 0:36:34He had been touched by chance.

0:36:34 > 0:36:37No-one and nothing was to blame.

0:36:37 > 0:36:41I think I found it hard to accept. You know, my own willpower,

0:36:41 > 0:36:46my determination to control, to shape my own life, was so great

0:36:46 > 0:36:49but the reality is that I wasn't in control.

0:36:49 > 0:36:52The fact that I had a broken ankle was just a fact.

0:36:52 > 0:36:55It was a circumstance that had happened to me.

0:36:55 > 0:36:59So, it was like a clash between, er, my own desire to control everything

0:36:59 > 0:37:03and the fact of luck, and, you know, luck won.

0:37:05 > 0:37:07The moral of Ed's story is clear -

0:37:07 > 0:37:10don't beat yourself up about every failure.

0:37:10 > 0:37:12But the opposite is also true -

0:37:12 > 0:37:16don't be too chuffed with yourself about every success.

0:37:19 > 0:37:21Remember this?

0:37:21 > 0:37:25I know you can't get rid of luck, but right now I wish you could!

0:37:28 > 0:37:31The parachute hasn't failed at least!

0:37:33 > 0:37:36I don't seem to be being blown into a forest!

0:37:36 > 0:37:38And I haven't even been sick!

0:37:41 > 0:37:44That was so cool! Can we do it again?

0:37:47 > 0:37:51You know, the really interesting thing is that whilst I was confident

0:37:51 > 0:37:56I would land safely, I couldn't be absolutely certain.

0:37:56 > 0:38:00The question is, "Why not? Why does chance exist?"

0:38:10 > 0:38:14The story of science, for centuries, has been a triumph -

0:38:14 > 0:38:18unlocking the mathematical laws behind everything,

0:38:18 > 0:38:20from the atom to the universe.

0:38:24 > 0:38:30So why is there still room for the random? For unpredictability?

0:38:30 > 0:38:33Why, instead, can't everything in nature be determined?

0:38:34 > 0:38:38In which case, we could get rid of chance altogether

0:38:38 > 0:38:41and I would be out of a job.

0:38:46 > 0:38:51In the 1680s Isaac Newton revolutionised science

0:38:51 > 0:38:54with a set of universal laws.

0:38:54 > 0:38:57He calculated the orbits of moons and planets...

0:38:57 > 0:39:01even predicted the timings of eclipses

0:39:01 > 0:39:05and, of course, explained the fall of an earthbound apple.

0:39:05 > 0:39:06Oh!

0:39:08 > 0:39:12Newton's friend, Edmund Halley, predicted the returns of comets...

0:39:15 > 0:39:19..and other scientists eagerly worked to discover new laws

0:39:19 > 0:39:21and make more predictions.

0:39:21 > 0:39:24"The Enlightenment", it came to be called.

0:39:27 > 0:39:31In 1779, the French scientist Pierre-Simon Laplace

0:39:31 > 0:39:32had a bold vision.

0:39:33 > 0:39:36If some vast intellect

0:39:36 > 0:39:38could not only comprehend all the laws of nature,

0:39:38 > 0:39:42but could also measure everything, even down to the tiniest atom,

0:39:42 > 0:39:45then he might predict the future precisely.

0:39:45 > 0:39:48And uncertainty would simply disappear.

0:39:50 > 0:39:51Hmm.

0:39:52 > 0:39:55In theory, with the right mathematics,

0:39:55 > 0:39:58everything in the physical universe could be measured and predicted,

0:39:58 > 0:40:01just like the movement of the stars and the planets.

0:40:01 > 0:40:04So, for example, if I threw a dice

0:40:04 > 0:40:07I could predict exactly how it would land.

0:40:10 > 0:40:14This theory is what we call "scientific determinism".

0:40:14 > 0:40:18In theory, if we gather the data and do the calculations,

0:40:18 > 0:40:21we should be able to get rid of chance altogether,

0:40:21 > 0:40:25but, in practice, prediction has proved frustratingly hard.

0:40:25 > 0:40:28It's as if there is something about our physical world

0:40:28 > 0:40:31that makes prediction all but impossible.

0:40:33 > 0:40:35Despite the promise of the laws of Newton

0:40:35 > 0:40:39and all the scientists who followed him, we remain in the dark.

0:40:39 > 0:40:40But why?

0:40:41 > 0:40:46In the 20th century, scientists - like meteorologist Ed Lorenz -

0:40:46 > 0:40:49discovered that even tiny influences could have immense

0:40:49 > 0:40:51and unpredictable consequences.

0:40:54 > 0:40:58As Lorenz put it, "The flap of a butterfly's wings in Brazil

0:40:58 > 0:41:00"could cause a tornado in Texas."

0:41:02 > 0:41:07The theory of determinism had to acknowledge complexity and chaos.

0:41:07 > 0:41:09The laws of physics weren't wrong,

0:41:09 > 0:41:12but the real world was just too complicated

0:41:12 > 0:41:14to ever fully comprehend.

0:41:15 > 0:41:20Also in the 20th century, physicists, like Werner Heisenberg,

0:41:20 > 0:41:22delving ever deeper into the nature of matter,

0:41:22 > 0:41:27realised there was an absolute limit to what they could ever know.

0:41:27 > 0:41:30In his work on quantum mechanics,

0:41:30 > 0:41:33Heisenberg set out the uncertainty principle -

0:41:33 > 0:41:36essential parts of the subatomic world

0:41:36 > 0:41:40could at best only ever be described as a probability.

0:41:43 > 0:41:47The dreams scientists once had of conquering chance

0:41:47 > 0:41:48have been shattered.

0:41:48 > 0:41:51Quantum mechanics has shown us a subatomic world

0:41:51 > 0:41:53that is fundamentally uncertain.

0:41:53 > 0:41:57Beyond the subatomic, we are still governed by mechanical

0:41:57 > 0:41:59and therefore deterministic laws,

0:41:59 > 0:42:03but, paradoxically, the mathematics of chaos and complexity

0:42:03 > 0:42:06means that things are still ultimately unpredictable.

0:42:07 > 0:42:09So what is chance?

0:42:09 > 0:42:13Is it real? Is it something out there in the fabric of the universe?

0:42:13 > 0:42:17Or is chance in here? Just an excuse?

0:42:17 > 0:42:21What Laplace called, "Merely the measure of our ignorance?"

0:42:21 > 0:42:22Or is it a bit of both?

0:42:22 > 0:42:24After centuries of discovery,

0:42:24 > 0:42:28we are still not much closer to knowing what chance really is.

0:42:31 > 0:42:35One thing is certain - chance is here to stay.

0:42:35 > 0:42:39What's more, it has actually been put to work.

0:42:39 > 0:42:42Faced with complex and unpredictable problems,

0:42:42 > 0:42:45scientists have found ways to use chance itself

0:42:45 > 0:42:49to convert blind uncertainty into computable probability.

0:42:52 > 0:42:54In the early years of the Cold War,

0:42:54 > 0:42:57nuclear physicists at Los Alamos

0:42:57 > 0:43:00were working to design a new atomic bomb.

0:43:00 > 0:43:03They wanted to predict when an atomic chain reaction

0:43:03 > 0:43:05might go critical,

0:43:05 > 0:43:09but the physics was so complex that at each step in the chain

0:43:09 > 0:43:12they were uncertain about what would happen next.

0:43:12 > 0:43:15So they turned to the mathematics of chance.

0:43:17 > 0:43:20For each step, they chose an outcome at random

0:43:20 > 0:43:25and then calculated what the resulting chain reaction would do.

0:43:25 > 0:43:28Then they randomly chose a new set of outcomes

0:43:28 > 0:43:30and calculated a new result.

0:43:32 > 0:43:35They did this repeatedly until they had hundreds of different,

0:43:35 > 0:43:39but equally likely, possible results.

0:43:39 > 0:43:42And combining them all gave the Los Alamos scientists

0:43:42 > 0:43:44an extremely accurate probability

0:43:44 > 0:43:46for what the chain reaction would do for real.

0:43:48 > 0:43:51They called it the Monte Carlo method,

0:43:51 > 0:43:55like rolling a dice over and over again.

0:43:57 > 0:43:59And the bomb worked.

0:44:09 > 0:44:12Today, that very same Monte Carlo method,

0:44:12 > 0:44:16creating arrays of possible futures to compute probabilities,

0:44:16 > 0:44:20is being used to try to solve problems in many different fields.

0:44:20 > 0:44:23And what's most exciting for me and my fellow Brits

0:44:23 > 0:44:25is that this might help to answer

0:44:25 > 0:44:30that all-important question: When I go out, do I take an umbrella?

0:44:38 > 0:44:43In the 1920s, the economist John Maynard Keynes

0:44:43 > 0:44:46wrote a famous book about chance.

0:44:46 > 0:44:50And for the ultimate metaphor of impenetrable uncertainty

0:44:50 > 0:44:52he chose the British weather.

0:44:56 > 0:45:01He wrote, "Is our expectation of rain, when we start out for a walk,

0:45:01 > 0:45:03"always MORE likely than not,

0:45:03 > 0:45:06"or LESS likely than not, or AS likely as not?

0:45:06 > 0:45:12"I am prepared to argue that on some occasions none of these alternatives hold,

0:45:12 > 0:45:15"and that it will be an arbitrary matter

0:45:15 > 0:45:17"to decide for or against the umbrella."

0:45:20 > 0:45:22But we want certainty.

0:45:22 > 0:45:26And so we demand it from our weather forecasters.

0:45:26 > 0:45:29And then after wet weekends and washed-out holidays

0:45:29 > 0:45:33we blame the poor old forecasters for getting it wrong.

0:45:33 > 0:45:37Hello, it was a disappointing day in many places

0:45:37 > 0:45:41and I'm optimistic it's going to be a better day for most of us tomorrow.

0:45:41 > 0:45:45Britain's most famously wrong weather forecast

0:45:45 > 0:45:47was on 15th October, 1987.

0:45:47 > 0:45:49Good afternoon. Earlier on today,

0:45:49 > 0:45:53a woman rang the BBC and said she heard a hurricane was on the way.

0:45:53 > 0:45:55Well, don't worry, there isn't.

0:45:55 > 0:45:57But there was!

0:45:57 > 0:46:01That night England was lashed by the strongest winds

0:46:01 > 0:46:03for almost 300 years.

0:46:03 > 0:46:07NEWS: Southern England suffered the full fury of the freak hurricane force winds,

0:46:07 > 0:46:09in their wake, a trail of devastation,

0:46:09 > 0:46:12the worst damage to property since the Second World War.

0:46:12 > 0:46:14Nowhere escaped unscathed.

0:46:18 > 0:46:22Today the most advanced meteorologists don't try making predictions

0:46:22 > 0:46:24like Michael Fish did.

0:46:24 > 0:46:28In Reading at the European Centre for Medium-Range Weather Forecasts,

0:46:28 > 0:46:32they use a form of Monte Carlo method

0:46:32 > 0:46:36to make forecasts using probabilities instead.

0:46:36 > 0:46:38To show why they do this,

0:46:38 > 0:46:43they've revisited the same weather data Michael Fish had in 1987.

0:46:54 > 0:46:58What this shows us is that October '87 was an exceptionally

0:46:58 > 0:47:03unpredictable and exceptionally chaotic situation

0:47:03 > 0:47:08and so it was always going to be impossible to make a precise, deterministic forecast.

0:47:09 > 0:47:14Weather forecasts go wrong because even small errors

0:47:14 > 0:47:18at the beginning can grow into huge differences after just a few days.

0:47:18 > 0:47:22And that's as true for everyday weather as it is for hurricanes.

0:47:25 > 0:47:28To tackle the problem, Tim Palmer and his colleagues

0:47:28 > 0:47:30routinely compute 50 different forecasts,

0:47:30 > 0:47:35each with slightly varying starting points to reflect the uncertainty.

0:47:35 > 0:47:40Before returning to the hurricane, Tim shows us an everyday example.

0:47:40 > 0:47:44So we're looking at today's weather forecast

0:47:44 > 0:47:47right at the beginning of the forecast period.

0:47:47 > 0:47:50These are all basically giving the same type of weather.

0:47:50 > 0:47:53A weather forecaster would look at these pressure maps and say,

0:47:53 > 0:47:57"There's a northwesterly airstream coming down over the UK,

0:47:57 > 0:48:00it's giving us slightly cool temperatures,

0:48:00 > 0:48:05but fundamentally it's exactly the same no matter which of these 50 forecasts you're looking at.

0:48:05 > 0:48:09Taking the same set of forecasts to three days in the future,

0:48:09 > 0:48:12it's a different story.

0:48:12 > 0:48:14Now there are discernible differences.

0:48:14 > 0:48:18For example, member 14 has a stronger wind, there are tighter gradients

0:48:18 > 0:48:22in the pressure than member 15 and that's telling us that

0:48:22 > 0:48:27although we can be certain of the general direction of the wind, it's coming from the northwest,

0:48:27 > 0:48:30the strength of the wind we cannot be so certain about.

0:48:30 > 0:48:33So we have to make a prediction in probabilistic terms.

0:48:33 > 0:48:37To work out the probabilities, Tim counts how many

0:48:37 > 0:48:40of the three-day forecasts show a particular kind of weather.

0:48:42 > 0:48:45It turns out that in about 30% of the forecasts

0:48:45 > 0:48:48there are gale force winds over much of England.

0:48:48 > 0:48:52Similarly rainfall, we find across much of England about 30%.

0:48:52 > 0:48:57What this DOESN'T mean is that it's raining for 30% of the day.

0:48:57 > 0:49:01What it means is that over the 50 possible futures,

0:49:01 > 0:49:04in 30% of them it is raining.

0:49:04 > 0:49:10So what can Tim see using the new method with the 1987 hurricane data?

0:49:10 > 0:49:13There's around a 20 to 30% probability

0:49:13 > 0:49:17over parts of southern England of hurricane force winds.

0:49:17 > 0:49:20Now, the probability normally of hurricane force winds

0:49:20 > 0:49:23in southern England is negligibly small,

0:49:23 > 0:49:28so even though there's a divergence of solutions, there's real information here.

0:49:28 > 0:49:32Adapting the Monte Carlo method and embracing chance

0:49:32 > 0:49:34gives much better results.

0:49:34 > 0:49:37But in Britain the forecasts most of us see don't give us

0:49:37 > 0:49:39this kind of information yet.

0:49:40 > 0:49:45We should now be trying to get this type of information out on the daily weather forecast.

0:49:45 > 0:49:47And indeed I think it will enhance

0:49:47 > 0:49:51the credibility of meteorologists themselves to be able to say

0:49:51 > 0:49:56not only is weather forecasting an uncertain science,

0:49:56 > 0:50:00but we can actually quantify the uncertainty in a very precise way.

0:50:11 > 0:50:15If you were a cynic, you might think that weather forecasters

0:50:15 > 0:50:19who give you probabilities and not predictions are just

0:50:19 > 0:50:23hedging their bets, ducking out of doing the one thing they're supposed to

0:50:23 > 0:50:27so they can never be accused of being wrong again.

0:50:27 > 0:50:28But I don't agree.

0:50:28 > 0:50:32Better a reliable probability than a wrong prediction.

0:50:32 > 0:50:36And knowing the probabilities we can all make our own decisions.

0:50:36 > 0:50:38THUNDER CLAPS

0:50:40 > 0:50:42Like to bring that umbrella.

0:50:53 > 0:50:56Remember that San Francisco probability?

0:50:56 > 0:51:00A 40 to 80% chance of an earthquake?

0:51:00 > 0:51:03In 1906, the city's worst-ever earthquake

0:51:03 > 0:51:06killed 3,000 people

0:51:06 > 0:51:09and destroyed almost 30,000 buildings.

0:51:12 > 0:51:16Even if a similar catastrophe in the future can't be predicted,

0:51:16 > 0:51:18it certainly can't be ignored.

0:51:19 > 0:51:24So today scientists are applying new mathematical methods to the problem.

0:51:25 > 0:51:29They're computing probabilities literally building by building,

0:51:29 > 0:51:32so bold decisions can be taken about what to do.

0:51:39 > 0:51:42In Berkeley, across the bay from San Francisco,

0:51:42 > 0:51:46one major fault runs right across the pitch

0:51:46 > 0:51:49of the California Memorial Stadium,

0:51:49 > 0:51:52home of the Golden Bears Football Team.

0:51:52 > 0:51:57They're rebuilding the stadium at a cost of over 200 million dollars.

0:51:57 > 0:51:58The fault starts

0:51:58 > 0:52:01just to the west of the south scoreboard,

0:52:01 > 0:52:04and you can see in the bowl

0:52:04 > 0:52:08there are those double stair-step curves at two points,

0:52:08 > 0:52:12- that's where our joints are for that piece of the stadium.- Right.

0:52:12 > 0:52:16It allows this part of the building to move independently

0:52:16 > 0:52:20in an earthquake from the two sides of the stadium on either side of it.

0:52:20 > 0:52:25- Right.- The base of the entire part of that building is on layers of sand

0:52:25 > 0:52:28- and high density polyethylene plastic.- That's amazing.

0:52:28 > 0:52:33It allows that part of the building to move a little easier than it would otherwise,

0:52:33 > 0:52:37so when the ground moves six feet horizontal and two feet vertical,

0:52:37 > 0:52:41it can just go along for the ride and the rest of the stadium is protected.

0:52:42 > 0:52:46The stadium is just one part of a massive building

0:52:46 > 0:52:49and strengthening programme all round San Francisco Bay.

0:52:50 > 0:52:54A colossal 30 billion has been committed in total.

0:52:54 > 0:52:57Will it be enough? They can only hope so.

0:53:00 > 0:53:03Even if we knew exactly what earthquake is going to occur,

0:53:03 > 0:53:06we may not know exactly how strong the shaking will be

0:53:06 > 0:53:10and how it will vary across the city because of different soil types.

0:53:10 > 0:53:15So you set a standard, you agree the buildings will be built to that

0:53:15 > 0:53:17and then you hope that that's good enough.

0:53:17 > 0:53:21You can't actually engineer chance out of the system altogether.

0:53:24 > 0:53:29At least in San Francisco they've a good idea of what to expect,

0:53:29 > 0:53:31even if they can't know exactly.

0:53:31 > 0:53:33But there's one last sting in the tail.

0:53:33 > 0:53:38Chance can sometimes come up with something you never even thought of.

0:53:39 > 0:53:42As we know, there are known knowns,

0:53:42 > 0:53:44there are things we know we know.

0:53:44 > 0:53:47We also know there are known unknowns.

0:53:47 > 0:53:50That is to say we know there are some things we do not know.

0:53:50 > 0:53:53But there are also unknown unknowns,

0:53:53 > 0:53:55the ones we don't know we don't know.

0:53:55 > 0:53:59And if one looks throughout the history of our country and other free countries,

0:53:59 > 0:54:03it is the latter category that tend to be the difficult ones.

0:54:03 > 0:54:09Donald Rumsfeld may have just been trying to excuse an unfolding disaster in Iraq.

0:54:09 > 0:54:13But "unknown unknowns" are a real and profound challenge for us all.

0:54:14 > 0:54:16And don't we just know it.

0:54:21 > 0:54:26The Bank of England is the rock-solid institution

0:54:26 > 0:54:29to which we all turn in these turbulent times.

0:54:30 > 0:54:33Surely I can find some certainty here?

0:54:37 > 0:54:40I'm meeting Spencer Dale.

0:54:51 > 0:54:55The Bank of England is the main financial institution in the country.

0:54:55 > 0:55:00People want it to tell them what's going on in the economy, but can you predict what's going to happen?

0:55:00 > 0:55:04Unfortunately not. Forecasting the economy is very difficult to do,

0:55:04 > 0:55:08in part because the economy is very large and complex

0:55:08 > 0:55:13and it's made even more difficult because it depends on people

0:55:13 > 0:55:17and their decisions and that makes trying to model behaviour

0:55:17 > 0:55:21and how the economy is going to change over time even more difficult.

0:55:23 > 0:55:26Every quarter, the Bank makes a forecast for the nation

0:55:26 > 0:55:29in the form of what it calls a "fan chart".

0:55:29 > 0:55:31And it deliberately builds in uncertainty.

0:55:33 > 0:55:36The chart shows that Britain's future economic growth

0:55:36 > 0:55:41might have a 5% chance of lying in each one of the shaded bands.

0:55:42 > 0:55:46This was the Bank's chart from 2007,

0:55:46 > 0:55:48just before the big crash.

0:55:48 > 0:55:50At the time we made this forecast,

0:55:50 > 0:55:52we thought in three years' time

0:55:52 > 0:55:55the annual growth of the economy may be anywhere

0:55:55 > 0:55:58between 5% or close to zero.

0:55:58 > 0:56:02But the Bank is even less certain than that.

0:56:02 > 0:56:05It also leaves room for the unknown unknowns.

0:56:05 > 0:56:08This only shows 90% of probability.

0:56:08 > 0:56:13So it's shows you 90 times out of 100 we think the economy will go somewhere in this range.

0:56:13 > 0:56:16So there's a one-in-ten chance it could just do anything?

0:56:16 > 0:56:20There's a one-in-ten chance it will fall outside of this fan chart.

0:56:20 > 0:56:25We don't try and put precise probabilities on those very extreme outcomes.

0:56:27 > 0:56:31With these charts, the Bank is making one thing clear -

0:56:31 > 0:56:33we must expect the unexpected.

0:56:34 > 0:56:38And soon after the Bank made this chart, chance struck.

0:56:40 > 0:56:43It was a genuinely surprising event, the economy to behave in a way

0:56:43 > 0:56:47which we hadn't seen for almost an entire generation.

0:56:47 > 0:56:50The environment which we operate in is inherently uncertain,

0:56:50 > 0:56:53the future is uncertain

0:56:53 > 0:56:56and the impact of our decisions are often very uncertain.

0:56:58 > 0:57:02Some people might want to hammer the Bank of England

0:57:02 > 0:57:04for not knowing what's around the corner.

0:57:04 > 0:57:07But you can't blame them for the nature of chance.

0:57:07 > 0:57:11And though the Bank can't give us the information we want,

0:57:11 > 0:57:14I think they show the way to the wisdom we need.

0:57:20 > 0:57:24There's just no use in looking for absolute certainty.

0:57:24 > 0:57:27We can never rely on predictions.

0:57:29 > 0:57:33We can tame chance, but only up to a point.

0:57:34 > 0:57:37Putting numbers on chance is a powerful way

0:57:37 > 0:57:40to get a handle on the future.

0:57:40 > 0:57:43But these numbers can only ever be as good

0:57:43 > 0:57:46as the information we have to hand.

0:57:46 > 0:57:49Though we try to measure reality with precision,

0:57:49 > 0:57:52sometimes they're little more than guesses.

0:57:52 > 0:57:55What all this means is that uncertainty

0:57:55 > 0:57:58is an essential part of being alive.

0:57:58 > 0:58:00And whether our uncertainty

0:58:00 > 0:58:03ultimately comes from out there or in here

0:58:03 > 0:58:05won't, in the end, matter,

0:58:05 > 0:58:10because either way surprises will most certainly happen.

0:58:10 > 0:58:12For instance, in this year of the Diamond Jubilee,

0:58:12 > 0:58:17I found a chicken nugget in the shape of Her Majesty the Queen!

0:58:17 > 0:58:19What's the chances of that?

0:58:53 > 0:58:56Subtitles by Red Bee Media Ltd