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Numbers of the year
00:28:05
A guide to 2013 in numbers - the most informative, interesting and idiosyncratic of by...
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- [00:00]
A
Thank you for downloading More or Less from the BBC. This is the version of the programme first broadcast on BBC Radio 4. Here's Tim Harford.
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B
Hello and welcome to More or Less. It's become a seasonal tradition of ours to take a look back at the most intriguing, striking or just plain delightful numbers of the year. And since we've not heard from Knotty Ash yet, what better way to start than to listen to a bit of Ken Dodd. Oh, and a bit of David Spiegelhalter.
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C
Happiness, happiness, the greatest gift that I possess.
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D
My number of the year is 7.3. This is the average response given by about 165,000 people when the Office for National Statistics asked them on a scale from 0 to 10, how happy were you yesterday? It's about the same as last year. About 15% were completely manic and said 10. 1% were really miserable and said 0, but only 10% said 4 or less. The question are you satisfied with your life? Got an average of 7.5. Higher if people were married, lower if they're unemployed, slightly higher for females, the most miserable age is 45 to 54. I remember it very well. And the highest is 65 to 79. I can't wait. Those smug Danes, when they were asked how happy they were yesterday, said 8.4, even in spite of the gloomy crime dramas they watch, While Bulgarians said 5.5 were the worst in Europe. That means, though, that if the happiest Bulgarians come to the uk, the average happiness in both countries will go down. Now, this is a curious effect known as the Will Rogers phenomenon. He was an American humorist who said that when he was talking about the Oklahoma migrants going to California before the Second World War, he. He said when the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states. What Will Rogers was getting at that if the dimmest Okies left Oklahoma and moved to California, where they were brighter than the brightest Californians, then the average intelligence level in both states would go up.
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B
David Spiegelhalter, professor of the Public Understanding of Risk at Cambridge University, he was on Start the Week in May. You know, now he's on more or less. Perhaps the average intelligence of both programme's guests has fallen as a result. I don't know why the smartest, most sparkling contributors flock to the more or less party. It seems so unfair. But then life isn't fair. As Linda Yu explains, my number of
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E
the year is 95 because it's the eye catching figure of the economic Recovery. Five years on from the worst crash in a century, income inequality has risen sharply during the recovery. In the US the top 1% of income earners have captured 95% of the incomes gained since 2009. A study at the University of California at Berkeley found that the richest 1% saw their incomes rise by 31.4%, while the bottom 99%, so the rest of us saw their incomes go up by only 0.4%. Because so few people have seen their incomes rise, it's really hard to see how the recovery could be broad based. This was the gist of the disagreement between two Nobel Prize winning economists, Paul Krugman and Joseph Stiglitz. Stiglitz sees this inequality as a main cause of why the recovery is so slow, while Krugman thinks that is too simple an explanation. I think if you look at how this recovery has been done, in other words, supported by lots of easy money instead of, say more government spending. And that easy money has fed into stock markets around the world hitting record highs. If that's the main source of growth, as in stock prices going up, then maybe it's not too surprising that the richest, who own more stocks than the poor, see their incomes go up, in which case they would see more of the gains. But that's not enough to support the rest of the economy. And that's one of the reasons why we still don't have economies recovered, for instance, in Britain at two pre crisis levels. But of course, as with all these economic disagreements, I suspect this one is going to run and run.
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B
Linda Yu, the BBC's chief business correspondent, all this economic talk is all very well, but not terribly delicious. Simon Singh has that covered. He's been thinking about that most Christmassy of foods, the pancake.
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F
My number of the year is 22. It relates to a problem called pancake sorting. And pancake sorting is about imagining you have a stack of pancakes and they're of different sizes and they're in the wrong order and you want to get them into the right order by using a spatula. You put your spatula in somewhere in the stack and you flip over some pancakes. So let's imagine we only have one pancake that's bound to come in the right order. So the pancake number for one pancake is zero. Don't need any flips. If you have two pancakes and they're in the wrong order, then the pancake number is one, because you only need one flip to flip them both over. So the pancake number for two pancakes is one pancake number for three pancakes. Turns out if it comes in the worst possible order, you need three flips to do that. And you can work out the pancake number for various numbers of pancakes. And the pancake number for 19 is 22. Now, that's my number of the year and it's my number of the year because nobody knows the pancake number for 20 pancakes. And this problem was invented by a chap called Jacob Goodman, and this year was his 80th birthday. He invented the problem about 30, 35 years ago and this was his 80th birthday this year. So I gave him a ring just to wish him happy birthday. And it was lovely just to chat about him and this problem that's been around for decades.
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B
Now, I'm going to ask the typical Philistines question, which is, is there a practical application of this kind of maths? But there may be one that we haven't discovered yet. But do we know of any yet?
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Yeah, very, very much so, because what you're looking at is you're reordering data in a way. You can look at it from a computer scientist point of view. They would want to know, look, we've got a pile of data, it's in the wrong order, how quickly can we reorder it? So computer scientists are interested and biologists are interested because you can get sequences of genes. I think it's something like that. The cabbage and the turnip have very similar genes, but in a different order.
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B
They've been pancake flipped.
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They've been pancake flipped. So the speed at which that can happen from an evolutionary point of view depends on the number of flips required to reorder them. So evolutionary biologists are interested too.
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B
And Simon, why did you get interested in pancakes in the first place?
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F
So I got interested because apart from
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that, they're completely delicious.
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F
Yes, absolutely. Absolutely. Well, it wasn't Shrove Tuesday. I wasn't kind of looking through my pancake puzzle folder. Two people, two famous people who've tried to tackle this problem. One of them is Bill Gates. The only research paper that Bill Gates has ever written was on the subject of pancake numbers. And the other person that's published on this area is a chap called David X Cohen, and he's taken a slightly different version of that problem, which is not the simple pancake problem, but the burnt pancake problem. In that scenario, you don't just want the pancakes in the right order, you want them in the right orientation with the burnt side down. So it's an even trickier. Version of the same problem. And David X. Cohen is partly famous for looking at the burnt pancake problem, but he's even more famous because he's a writer of the Simpsons and co creator of Futurama. And he's one of these sneaky mathematical comedy writers who's been putting mathematics into those two TV shows, the Simpsons and Futurama.
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B
What sort of maths gets smuggled in Homer Simpson's mouth or whoever's mouth?
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Oh, gosh, some of it's really obscure. Well, maybe not so obscure to the listeners of your show, because I know they're very, very clued up on these things. But things like Fermat's Last Theorem, the P versus NP problem. This is an unsolved problem in mathematics. It's worth a million dollars if you can solve it. And it crops up in an episode called TreeHouse of Horror 6. Euler's identity, arguably the most beautiful equation in all of mathematics, crops up in an episode called Money. Bart, in Futurama, we have Klein bottles, we have Murbius strips, we have the Aleph null cinema. Aleph null is a scale of infinity, which suggests there are even bigger scales of infinity. So all of this stuff is kind of just smuggled into the background of these two shows.
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B
So do you think that other cartoon shows should be using more maths? Or maybe math shows such as More or Less should be, you know, being funnier,
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F
I find more or less hysterical. You often make me titter as I listen to you. But there is an animated Show, I think, SpongeBob SquarePants. Does SpongeBob live live in a pineapple at the bottom of the sea?
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Something like that?
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I think so. And pineapples have Fibonacci numbers embedded in their pattern. They have eight spirals going in one direction and 13 spirals going the other direction. Eight and 13 are Fibonacci numbers, but SpongeBob's pineapple does not have eight and 13, so it doesn't obey that mathematical principle.
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It's just an enumerate cartoon. Impossible. Pineapple?
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Yeah, we shouldn't expect all cartoons to have difficult maths embedded in them, but they should at least get the natural mathematics correct within them.
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Simon Singh, whose latest book is the Simpsons and Their Mathematical Secrets. I'll be enjoying a spot of cold turkey pancakes in due course, I'm sure, but I feel guilty for having accused spongebob of participating in an enumerate show without giving him a right of reply. Anything to say for yourself, SpongeBob?
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No, not that.
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Anything but that.
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Thought. Not let's hope for more insight from Dr. Pippa Malmgren, founder of Principalis Asset Management and former financial market adviser to George W. Bush.
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For me, the most interesting number this year is the number 73. It's the periodic table number for an element nobody's ever heard of called tantalum. Yet we're incredibly dependent on this rare earth metal. It's essential for all telecommunications, defense equipment. Your mobile phone won't work without it. And I think it's interesting because it serves as a reminder that in the world economy lots of the most important things that we need are actually very limited in the supply. And there are lots of things that in the world economy that we need to think about, the limits on the supply. And I don't mean this as like a tree hugging green person. It's not an environmental issue. I mean, we assume that there's always enough finance to pull something like tantalum out of the ground, when in fact we continue to have a problem with banks lending because they're so inhibited by their own debt problem. Food is another issue. We sort of assume that somehow, yes, with technology we'll be able to feed the world. We forget that phosphates are essential to the production of food. And like tantalum, it's a rare thing. It's hard to make. And to build a factory today that can make phosphates, you won't get any return on your capital for 15 years. Right now, nobody's prepared to fund that. So this is another example of things like mined assets. We just take for granted that you pull stuff out of the ground when you need it. What's the shortage of talent today to dig the stuff out of the ground? For the last 25 years, if you had any math skills, you went into finance because that paid the most. And I think this year is really interesting because it's the first year that the graduates of the Colorado School of Mines, which is America's best engineering school, will be paid more than Harvard Business School graduates, thus enticing young people with math skills to actually go back into the real economy, which is a great thing. But it means we've also got a global shortage of engineers right now. So again, you assume if you need something like tantalum, you just get it. Yeah, well, guess what? We don't have enough engineers and we probably won't for some years to come until we fix and redress this imbalance. So tantalum, we really literally wouldn't have the global economy we have today without it.
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Pippa Malmgren you may know that football's transfer window opens at the moment 2014 begins. BBC radio doesn't respect such niceties. We've already poached a legendary veteran to rival the evergreen Ryan Giggs. Paul Lewis of Moneybox.
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My number of the 33.86. Now that's the number of petaflops achieved in 2013 by the new holder of the title World's fastest computer. Now, PETA is a million billion. That's 10 to the power 15. A flop is one floating point operation per second. Think multiplying two really long numbers together in a second. That's a flop. So a petaflop computer can do a million billion long multiplications every second and get them right. When the list of fastest computers was published in June, China's new Tianhe 2 computer went straight in at number one. It achieved 33.8 seconds, six petaflops, nearly twice as fast as the runner up. That was a computer called Titan in the US Department of Energy. Now, no one knows quite what the National University of Defense Training will use Tianhe 2 for, but it doesn't matter. It's really fast. And it was still the fastest in the latest list published in November with its record 33.86 petaflops. Now that's 33,860 million billion billion sums every second Computing record seldom last long. Two months before China's Great Leap Forward, the first one petaflop machine, which was king in 2008, was decommissioned. It was too slow. When the next list comes out, Tianhe 2 may beat itself. Its theoretical top speed is more than 50 petaflops. But even that record may soon go. The geeks are betting on a one exaflop machine. That's a billion sums every billionth of a second by 2017.
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Paul Lewis. To put Paul's number in a historical context, the cost for a set of hardware that would theoretically operate at a modest 1 billion floating point operations per second is just 16 cents these days. But it would have cost $82 in 2003, $15 million in 1984, and a mind boggling $1.1 trillion back in 1961, when Moneybox was just a twinkle in Vincent Duggleby's eye, and of course, in 1961, $1.1 trillion was a lot of money, just over $8 trillion in today's terms, and in fact, not far off the size of of the entire global economy of the day. My next guest has picked a much smaller yet equally fascinating number. It's Dr. Hannah Fry from the Centre of Advanced Spatial Analysis at University College London.
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My number of the year is the number four, and I've chosen this in honour of American mathematician Kenneth Apple, who died earlier on this year at the age of 80. So Apple is best known for solving the famous four color problem. And this problem says that if you take any map, so imagine a map of the world, you'll only ever four colours to fill it in in a way that no two neighboring countries or regions are sharing the same colour. So this problem had been unsolved for over a century and in hundred years or so, when the problem stood, the mathematicians had failed to find any map, either real or imaginary, which needed any more than four colours. But unfortunately, to prove conclusively that a map needing five colours couldn't exist, you'd have to check an infinite number of maps. But Kenneth Apple and his colleague Wolfganhakken made a big breakthrough, reducing the infinite number of possible maps down to just 1,476 much simpler maps which contain the characteristics of every possible configuration. And then they used a computer to find a four colour solution for every one of those maps, in turn proving that four colors was enough to fill in any conceivable two dimensional map, so that no two neighbouring regions have to share a color.
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Now, is this regarded as acceptable mathematicians? It seems a bit. It's sort of cheating, isn't it, to get a computer to do your coloring in for you? Shouldn't you be doing your coloring in all by yourself? I mean, it doesn't seem to have the standards of purity and elegance that we expect in a mathematical proof.
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No, that's definitely true. So at the time, mathematicians thought that the use of computers was really ugly and brutish and they likened this proof that the two people came up with as trying to proofread a phone book. But actually this proof did do a lot to change the attitudes of mathematicians towards computers, because they really managed to demonstrate how powerful they could be.
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Is it now completely standard then to use computers to provide mathematical proofs? And what sort of fields of maths would that be would be useful in?
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It happens a lot more. So you can use a computer to almost piece together proofs without overseeing it at all, without really needing a mathematician at all. So taking a series of logical steps and bashing them together until you end up with a result that you weren't necessarily expecting. So some mathematicians are looking at pushing that frontier, but it also does things like checking for prime numbers, for example. So Actually, earlier on this year, the MERS N prime, a new MERS N prime was, was discovered, and that was discovered using a computer. And it is happening more and more in pure mathematics that people are using computers to check tedious calculations that you otherwise wouldn't be able to do by hand.
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Are we also generating new ideas for proofs then? Are we sort of taking jigsaw puzzles? Well, that's a mathematically true set of equations. And then there's another true statement and another true statement. And let's just randomly put them together and see whether any of them prove anything interesting.
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Yeah, exactly. That happens. Yeah.
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So mathematicians are being put out of a job, computers randomly crunching equations.
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Yeah. I mean, you still need a mathematician to check whether what they come up with is, you know, even useful or valuable. But that does happen. A lot of mathematicians really dislike that, though. I mean, so a lot of pure mathematicians are only really interested in the idiosyncratic beauty of the subject and the essence elegance of the proofs that come out. And these type of computer generated proofs are not considered in that realm.
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They might just happen to be useful. Who cares about that?
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Exactly, exactly.
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To stay on the subject of maps, Antarctica is at the bottom of the globe. You noticed a strange fact about Antarctica this year.
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H
I did, yeah. So the 2011 census, a lot of the data that came from that had been prepared and was released over the course of this year. And one particular statistic really caught my attention, which is that, astonishingly, 51 people in the UK were apparently born in Antarctica, despite there Only ever being 11 people born in Antarctica.
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I'm impressed that anybody was ever born in Antarctica.
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H
But there are 11, apparently. There are actually 11. But I think this probably suggests slightly more that there are 51 people in the UK with a very particular sense of humour when it comes to filling in the census form.
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This is your religion is Jedi Knight phenomenon.
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Yeah.
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So actually with that one and the last census in 2001, so there was 390,000 people, 390,127 people, in fact, who said that they were Jedi Knights on the form. But this time around that, that joke's got a bit old now, unfortunately. I think it was just that the
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Star wars films came out and they were terrible. No one wanted to claim to be a Jedi.
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H
So Jedi Knights have now been overtaken by Judaism and Buddhism in the number of answers. But a new couple of jokes have started creeping in. So there's the free thinkers, of which there are 513 responses. And the realists the first one of
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them was a free thinker. I'm not sure about the other 512. No. Should we worry about this? Does this put the census into disrepute?
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H
No, I don't think so. I mean, these are very, very small numbers of answers. I mean, they're sort of amusing outliers, effectively. And I don't think it takes away from the fact that the census still provides us with just the most comprehensive overview of the social makeup of Britain as it stands.
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B
Hannah Fry, if you were actually born in Antarctica, write in and tell us about it. Or for that matter, write in and tell us about it. If you're actually a Jedi knight. But we'll be asking for proof, I can assure you. My next guest is Merryn Somerset Webb, the editor in chief of Money Week. It's not easy to say Merrin SOMERSET Webb. But then it's not easy to say quantitative easing. Merrin and I are both going to try, though.
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A
My number of the year this year is $142 million. That's the price that a set of three studies by Francis Bacon sold for at auction at the begin November. That is the highest price ever for a piece of artwork at auction in nominal terms. And to me, this shows us the way that quantitative easing across the world has leached into real asset prices. We knew it would happen. It was forecast by the central banks. But I think it's happened to a slightly more extreme level than any of us really expected.
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B
So quantitative easing, is this printing money, to put it crudely, or central banks creating money. Why would that drive up the price of Francis Bacon paintings?
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A
Well, there's an awful lot of arguments about how quantitative easing money gets into the asset markets. But the best way to look at it, I think, is as though it's a hot potato, you know, so the central bank buys an asset from somebody, buys a bond of some kind, whatever, hands the money to the guy who had the bond. The guy who had the bond now has the money. What's he going to do with the money? He's going to buy something else. So maybe he goes and he buys an equity. The guy who had the equity now has the money. He goes and buys something else. You've injected money into the economy and people are shifting it from person to person to person to person, buying new assets, and eventually it ends up all over the place. So you can look at the price of prime housing across the world. You can look at the price of classic cars. Another thing that's going completely berserk and you can look at art prices and then of course you can look at stock markets again, all going completely berserk for no obvious fundamental reason.
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And should we look at this as a successful stimulation of the global economy, which of course is what it was designed to do, or should we look at it as something that's simply making the rich people who already owned portraits by Francis Bacon and so on, making the rich richer while nobody else benefits? Or is it doing a bit of both?
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It's doing a bit of both, but more of the helping the rich. I think at this point you have to remember that without QE we probably would have had very severe deflation in the end. And I think at this point you'd be hard pushed to find anyone who would say that the first little bit of QE wasn't a good idea, it prevented a deflationary collapse. But I think at this point almost everybody would say that QE is effectively now a fiscal policy in that it's a redistribution policy. It's shifting money from the not so well off to the well off, and therefore it's no longer a policy the central banks should be following.
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B
And when do you think central banks are going to stop?
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I don't think they're ever going to stop, really. I think once you've let a genie like this out of the bottle, how do you stop? How do you stop when you stop? You have to accept that markets around the world will fall and you have to be ready for that. It's a really tough thing for a central banker to do. I mean, of course it will happen one day, but I think the tightening of monetary policy will probably take quite a lot longer than any of us expect. When it comes, it'll come fast, but I think it'll be a way off. You've got to be a very, very brave central banker to be the one who stands up and says, I don't care if the stock market crashes.
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B
Mark Carney, the new governor of the bank of England, he seemed to be quite courageous in his recent confrontation with MPs in late November in Is he going to be the person to pull the plug?
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A
He may be, I mean, you know, impossible to tell. This is a matter of moral character, I think, in many ways. And he's given us incredibly fuzzy guidance about when he might or might not raise interest rates. And of course we're taking a break from qe, but we still have these super, super low interest rates at 300 year lows. When does that change? We know when it does. Change. It brings pain for the people who are living on very, very low interest rates. And he tells us that he will start thinking about it when unemployment hits around 7%. But, but he's not telling us that he will do anything at 7%, just that he'll start thinking about it. Now I'm thinking about an awful lot of things that I might do at some point in the future. And we all know that most of them I'm never going to do.
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B
And let's be clear what we think of as an end to qe. I mean, is this an end to the process of creating new money? Is this destroying the new money that was previously created, hoovering it back out of the economy? Or is it something else? Is it raising interest rates? Rates and not affecting the money supply at all?
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A
Well, obviously they're very different. QE and raising interest rates. When I talk about the end of qe, I'm talking about the end of printing more. I find it almost impossible to imagine the process of pulling all the money out of the economy. That seems very unlikely.
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B
Merrin, Somerset Webb. The actual winning bid for Francis Bacon's Three Studies of Lucian Freud was a mere $127 million. But the buyer needed to look down the back of the sofa for the $15.4 million commission. That took the total cost to 142. Now that's a big number, but we know a bigger one. And it's a prime number. A very special kind of prime number. It's a Mersenne prime. Mersenne primes are named after a 17th century French monk. And as of last year, only 47 had been found. Geeky songstress Helen Arnie takes up the story.
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In January, Professor Curtis Cooper found a number. Not an ordinary number, but a number that's humongous. So I don't want your mold pies and you can keep your minced wine. Cause all I want for Christmas is the world's biggest prime. It's two to the power of 578-851-61 minus 1 Mersenne 48 the perfect gift gift for everyone. So give me, I'll give me this Christmas time a 17 million digit Christmas prime. It's rarer than a cracker joke that actually makes you laugh. As useless as a pair of roller skates for a giraffe. If I had one I could do whatever I like with it. Well, anything I want apart from dividing it except by itself and 1 it's 2 to the power of 578-851-6 1 minus 1 if I tried to sing it in ours I'd need 1181 so give me a, give me this Christmas time a 17 million digit Christmas rhyme so type it and text it or write it and post it Bake it in bread and then slice it out if you can't calculate it and send it in time I'll accept 16 million decimal places of pie so give me, I'll give me this Christmas time a 17 million digit Christmas prime one more recursion give me, oh, give me this Christmas time a 17 million digit Christmas prime.
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Helen arnie pining after Mersenne 48 and sadly, that's all we have time for today and for 2013. If you've spotted any statistical sins, please email more or lessbc.co.uk and if you want to know more about the program, please go to BBC.co.uk more or less from me and all of the More or Less team A Very Happy New
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Year More or Less was presented by Tim Harford, the Financial Times' undercover economist, and made in association with the Open University. You can Download many more Radio 4 programs for free. Find these at BBC CO UK Radio 4.