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2011 in numbers
00:28:12
A guide to interesting, informative or just plain idiosyncratic numbers of the year.
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- [00:00]
Tim Harford
You're listening to a More or Less podcast from the BBC. For more information about the program, please go to the website BBC.co.uk radio4 hello. And if you're listening to our Sunday repeat, Happy New Year. This is a special edition of More or Less and it'll serve as a guide to interesting, informative or just plain idiosyncratic. Numbers of the Year the credit crunch and the continuing financial crisis have made really big numbers a familiar part of our news bulletins and everyday language. Billions and trillions are tossed around as though they're just a step away from each other. But a couple of letters makes all the difference. After all, there are a thousand billions in each trillion and roll over trillions. There's a new kid on the block.
- [00:48]
Linda Yu
My number of the year is a quadrillion. That is a thousand trillion trillions or one followed by 15 zeros. Not a number that many of us would have had come across, especially in the context of the total amount of debt. Cuz that's when this number, which is rarely used, was first raised. It's a number mentioned just recently by a Japanese vice minister when he was talking about the level to which Japanese government debt could climb. He forecast that by March of next year, the total amount of government debt in Japan could exceed a quadrillion. Now let me make it clear, that is in Japanese yen. So in dollar terms it's about 13.8 trillion. And that number is astounding. And it is more than twice the size of the entire Japanese economy. But I suppose for me, we've now gotten to a place where the amount of public sector debt is being expressed in numbers that we would have never come across before is symptomatic of some of the ailments afflicting the world economy right now. Another couple of numbers which I think captures this very well, which is the median debt to GDP ratio of developed economies versus developing economies. If you take the G20, you break them up into developed economies and emerging economies, you'll see that this is the very first time, outside of world wars, in which the debt levels of the developed economies is higher than that of developing economies. For developed economies in the G20, it's 80% of GDP. That is twice as high as it is for emerging economies in the G20.
- [03:04]
Tim Harford
Linda Yu of Oxford University and Bloomberg Television and a quadrillion yen in debt, by the way, is 7,846,186 yen, or about £65,000 for every man, woman and child in Japan. Staying with money. Let's get something a bit closer to home from Moneybox reporter Ben Carter.
- [03:25]
Ben Carter
This number will have affected a lot of people this year. 137. That's the amount in pence it would have cost you to buy a litre of unleaded petrol on May 9, when petrol prices hit an all time high. But why was the price of petrol so high when the price of oil itself was 20% lower than its 2008 peak? In July 2008, the price of Brent crude oil hit a record $147 a barrel. In May of this year it was roughly $112. So people were justifiably asking why petrol prices were higher than they were in 2008 when unleaded petrol was £1.20 a litre. There are three reasons for this. Despite the government reducing the fuel duty by a penny in this year's budget, it's still nearly 8 pence more than it was in 2008. Currently, 57.85 pence of every litre sold is taken in duty. The second reason is an obvious one. VAT has gone up to 20%. Around 23 pence in every litre is taken in VAT, so the government's total share is roughly 65% of the price of each litre. The third reason is the exchange rate. Barrels of oil are priced in dollars, and in 2008 the pound was a lot stronger against the dollar than it is now. So at the peak $147 a barrel equated to around 74 pounds in May, and $112 barrel of oil, the price was around 70 pounds. To put things in context, if the exchange rate and tax had remained at 2008 levels, we'd only have been paying £1.11 as opposed to £1.37. However, if the price per barrel gets back to 2008 levels, then under the current taxation and exchange rate, we'd be paying over £1.50 per litre.
- [05:27]
Tim Harford
When Moneybox diva Paul Lewis heard we were speaking to his underling Ben Carter, naturally he was disappointed not to be taking part in the program himself, so how could we refuse? But when we asked Paul what his number would be, we were surprised that what he came up with was so diminutive.
- [05:44]
Paul Lewis
My number of 2011 is one. When it appeared for the first time on 10 November, it marked a significant moment in banking. Now, don't hiss. I know they are the villains in our year round financial pantomime. Do we trust them? I ask.
- [05:59]
Linda Yu
No.
- [06:00]
Paul Lewis
The audience ROARS back. But when the number one appeared Six weeks or so ago, it began to look as if the banks had stopped trusting each other to explain at any time the banks hold billions of pounds, ok, it's our money, but they hold it for us. And instead of just keeping it in a vault marked other people's money, they lend it out to each other as if it was their own. What they charge for borrowing our money is called BBA Libor, that's short for British Bankers Association London Interbank Offered Rate. And the three month Libor is what they charge for lending money to be paid back in three months time. Normally this Libor is within a gnat's whisker of the official bank rate, currently half of 1%. And it started 2011 at 0.75 and stayed pretty flat. But then in August it began to rise steadily and on the 10th of November it crossed one double the bank rate. And this week it it's around 1.07 and still rising. That rate is a measure of the risk that the money lent will not be paid back in three months time. And by rising more than a third in four months, it shows trust among banks is falling. And yes, the last time the banks stopped trusting each other was the crisis of 2008.
- [07:19]
Tim Harford
Paul Lewis. Next up is a statistical eminence, the national statistician, Jill Matheson.
- [07:26]
Jill Matheson
I think this has been a really important year for statistics. Throughout the year we've been documenting what's happening to the economy, so a huge amount of interest in that. Towards the end of the year there was particular interest in the labour market figures, with ONS reporting in December that unemployment had reached 2.64 million. That's the highest from 17 years. And I expect that interest in the labour market to continue into 2012. We also showed at the same time that the number of people working beyond the age of 65 had doubled in just 10 years to just short of 900,000 people today. And the continued ageing of the population was perhaps demonstrated by the 12 and a half thousand people who celebrated their 100th birthday during 2011. And we expect that number to rise to more than 100,000 over the next 25 years. So continuing aging of the population. But the personal highlight of the year for me was March 27th. That was census Day. Since then we've been busy processing the forms. Fantastic operation with over 25 million forms in a warehouse in Manchester being scanned in shifts on huge flatbed scanners and then captured and computerized and coded. And the processing will continue well into 2012. Huge operation that's gone brilliantly well so far.
- [09:17]
Tim Harford
Jill Matheson, the national statistician. And we interrupt this special Numbers of the Year edition of More or Less to bring you this message.
- [09:25]
David Spiegelhalter
Probability does not exist.
- [09:28]
Tim Harford
Probability does not exist. Professor David Spiegelhalter Winton professor for the Public Understanding of Risk at Cambridge University, tells us that probability does not exist. Is his whole academic discipline built on sand? Well, apparently the idea is isn't news to statisticians.
- [09:44]
David Spiegelhalter
Well, I was taught this 40 years ago by my tutor in Oxford who's translating a book by an Italian mathematician called Dave Finetti, who wrote this book called Theory of Probability. And the first line of the whole book says, probability does not exist. He puts it in the whole realm of fairies and witches. So this is a rather extreme point of view, but one I've held all my career. Let me do a little example. I've got a coin and I'm going to flip it. So what's your probability? This is going to come up heads.
- [10:11]
Tim Harford
Well, I think you're a fair person, so it's probably a real coin. So 50. 50. 50% chance it comes up heads.
- [10:18]
David Spiegelhalter
Okay, I flipped it, slap it on the back of my hand, I'm looking at the result. So, Tim, what's your probability that it's heads?
- [10:26]
Tim Harford
You're sitting in a studio in Cambridge, so I can't see the coin. You. You know, whether it's come up heads or not, it doesn't really feel right. But if I had to bet on it, I suppose that I would have to say it's 50.
- [10:41]
Mark Woolport
50.
- [10:42]
David Spiegelhalter
Yeah. Unless you can read my mind. But for me, it's 100%. It is, in fact, heads. The idea of that is supposed to show that in those contexts that probability does not depend on the coin itself. It depends on our relationship to the coin, what we know about it. And this holds in everyday life that our probabilities for events depend on what we know. They're constructed on the basis for our judgment and knowledge. And therefore it's quite reasonable that two can have two different probabilities for the same event. Now, it's very tempting to think that a coin has got some underlying propensity or true odds to come up one way or another. And some philosophers think that's what probability is. I'm not very keen on that at all. You know, it's a very abstract idea. How can you find these things? Well, you know, what really are they? And I don't see how it applies to situations where we use probability all the time, like my chance of having a heart attack or stroke in the next 10 years, which is about 12%. Or Arsenal winning their next match, or
- [11:39]
Tim Harford
a mortgage propensity of a mortgage payer to default on the mortgage. It's a very, very important probability. But do they have an underlying propensity to default?
- [11:49]
David Spiegelhalter
Well, you could invent one, but it really does seem a very metaphysical, abstract concept that doesn't seem much use at all. So this perspective that I hold and many other people hold just says that probabilities, we can use them, they obey the laws of probability theory, mathematical laws. However, the best way to think about them is as reasonable betting odds in the situation in which we find ourselves, that we construct on the basis of our knowledge and experience.
- [12:16]
Tim Harford
Do you think that this makes any practical difference to the way that we think about probability or act in the world?
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David Spiegelhalter
I think it's very important because it means that you don't start telling people this is your risk of something or this is your chance. It's not, it's what might be, you know, what, somebody might insure you or something like that. But when we, we fill up insurance forms, we just put in a certain amount of information and they work out what are possible odds of us having various events happen to us, but they're not our probabilities.
- [12:45]
Tim Harford
Professor David Spiegelhalter and after all that, here's David's number of the year.
- [12:51]
David Spiegelhalter
3200. These were the odds given by NASA of anyone being hit by the UARS satellite, which fell to Earth somewhere in September. They put out some lovely data. They said half a ton of space junk is going to come down. It's going to cover about 22 square meters. The biggest bit is going to be about 150 kilos. That's like a couple of washing machines or an adult gorilla. And it's going to hit the ground at 100 miles an hour. Now, where did they get that 3200 from? Oh, you can do some lovely sums. You know, the radius of the Earth, the distance to the center of the Earth is about 6,000 kilometers. You can do your GCSE maths and work out the surface area of the Earth. 4 PI r squared is about 500 million million square meters. Now, NASA obviously assumed that we each occupy about 1 square meter. Just think about that. It's our space. We can. It's not like squeezing into the more or less offices. We've got a bit of space there. So that means that you occupy 1,500 million millionth of the Earth's surface. Now, 22 of these square meters are going to get hit by the junk. So the chance of you being hit a particular person is 1 in 22 million million. But there are 7 billion people on the Earth, so the chance to hit somebody is 7 billion divided by 22 trillion. And that works out as 1 in 3200. So that's where they got their number from. I think that's really cool.
- [14:16]
Tim Harford
David Spiegelhalter, you're listening to More or Less, in association with the Open University. Hi, I'm Tim Harford and these are just some of the numbers of the year. The world population hit 7 billion this year, probably. And earlier this series, we tried to see if the world's population would still fit on the Isle of Wight. Sadly, we found the world has outgrown its island home. But our next number is an indication that the rate of growth may have slowed somewhat.
- [14:44]
George Monbiot
I'm George Monbiot, I'm a Guardian columnist, I'm a writer and a professional troublemaker. And my number of the year is 2.5. And that is now the average fertility of women on Earth. It has fallen from 6 just 60 years ago, from 6 to 2.5. And this is a fantastic triumph for women's empowerment. It means that women have much more choice over their reproduction than they had before. It's because they have access to family planning, which wasn't available for many people before then. And it means that they have economic opportunities other than just having children. So 2.5 is a number we should celebrate. It's getting pretty close to 2.1, which is the replacement rate for the population. And indeed later this century it could even dip below 2.1. So we could see a load on the environment being reduced as well.
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Tim Harford
George Monbiot, finding an appreciative audience there. Who's next?
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Mark Woolport
I'm Mark Woolport, I'm the director of the Wellcome Trust. And one of the major things that the Wellcome Trust funds is the Wellcome Trust Sanger Institute, which is where a third of the first human genome was sequenced. My number is £3,000. And that is what it costs today to sequence a human genome. Whereas the very first human genome, whose sequence was completed finally in 2003, cost £600 million. So there's been a 200,000 fold reduction in the cost of sequencing a human genome in about the last eight years. The other enormous changes are in the time it takes to sequence a genome. So that very first human, human genome took scientists from all over the world. About 10 years to sequence. One run of a machine that can sequence now five human genomes takes just two weeks. This extraordinary change means that we can now apply genome science to really understanding variation between each one of us in health and disease. We're beginning to see, for example, cancer genome sequence. So many mutations have been discovered which are the cause of human cancers, and for some of these, drugs are beginning to be developed. It's not only human sequences that we can analyze on a gigantic scale. We're now able to use genome sequences to identify organisms, to work out how they might cause disease, to identify their susceptibility and their resistance to different antibiotics. And importantly, we can study their transmission from one person to another, from one part of the world to another. Two examples of that are that with the flu pandemic last year, we were able to show that closing national borders would have had no effect at all, because from genome sequences of the flu virus, it was possible to show that it had entered the UK before the first clinical cases were identified. Sadly, it was also possible to show that the epidemic of cholera that affected Haiti after the earthquake was almost certainly brought in by some of the forces brought to help from South Asia.
- [18:12]
Tim Harford
Sir Mark Wolport, director of the Wellcome Trust. Our next number of the year comes from Tracy Brown from the pressure group Sense about science.
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Tracy Brown
On 11th March this year, the Tohoku earthquake caused a tsunami on Honshu in Japan, killing thousands of people. We were told at first that the estimate of the dead was a thousand, and rapidly rose to 5000, 7000, 8000, until we were looking at a figure of around 20,000 dead or missing. And yet another number dominated the discussions in those days following the tsunami. The Fukushima 50. 50 workers at the Fukushima plant trying to cool the reactors so that there wasn't the release of nuclear waste into the atmosphere and the surrounding area. And this was something that dominated. I read the Independent six pages of disaster, page after page after page where we lost sight completely of the 20,000 who were dead or missing and the hundreds of thousands who had been displaced from their homes. Why was it that the Fukushima 50 became the stuff of headlines, the stuff of the disaster? And yet the 20,000 became something that we couldn't really relate to. Was it because there was a search for heroes? I mean, there weren't actually 50 working in the plant. I think it might also be our fear of nuclear power that came to dominate our way of looking at what had happened on Honshu. As a result of that fear, Germany cancelled its nuclear program. And according to a London investment bank, that's going to lead to 300 million tonnes more of CO2 between now and 2020. Perhaps our fear of nuclear power was so strong that we forgot to look at the human cost that was actually unfolding right in front of our eyes. Another explanation is also that we just can't relate to numbers like 20,000. We're immune to them. Evolutionary psychologists say that it's because we have actually been programmed not to relate emotionally to numbers on that scale. And it is probably all of those things that came together in March 2011 to mean that our focus was on the Fukushima 50 and not on 20,000 debt.
- [20:43]
Tim Harford
The way the press reports events is at the centre of our next number from Owen Spotswood of the fact checking website. Full fact.
- [20:51]
George Monbiot
Full Fact's number of the year is £500 million. Or to be more precise, it's £500 million. So this is a figure we've seen prop up again and again in 2011. It's been used to describe everything from the amount that might be raised by the treasury through a boob tax on the cosmetic services industry, right through to the cost for last month's public sector strikes. It's one of those numbers that's popped up so often that we've had to kind of step back and ask, wow, isn't it really convenient that so many important debates can be framed with such a neat, headline friendly number? And of course, when you scratch the surface a little, it becomes apparent that it's a bit more complicated than that. To take last month's public sector strikes as an example, while all the papers and news channels reported the strike would cost a cool half a billion pounds, what the treasury had actually said was that they expected it to cost anything between 280 million and 500 million, depending upon a number of factors, such as the proportion of schools that closed and the total number of workers not at their desks. So while the lower estimates here, for example, that around two thirds of schools would be shut or partially closed, the upper estimate assumed a figure of 90%. Now, in the event, the Department for education announced that 62% of schools had shut their gates, while a further 12% were partially closed. So that's a grand total of 76%. This would suggest that in reality, the impact of the strikes was actually closer to the lower estimate of 280 million than the higher estimate of 500 million, although I suspect it will be the latter figure that will stick in people's memories.
- [22:28]
Matt Parker
My name is Matt Parker. I'm based in the maths department at Queen Mary University of London, and my favourite number from this year was 1.902-16058. It's a wonderful mathematical constant, but don't worry if you don't recognise it. In fact, this year in June, a lot of people saw this number and didn't recognise how amazing it is and its significance for prime numbers. Actually, 2011 has been a very good year for prime numbers. Not only is 2011 itself prime, it's also a sum of consecutive primes. If you add 11 consecutive primes starting at 157, you will get 2011. The only thing missing from 2011 as a great prime year was that it's not a twin prime that would absolutely make the year. The next twin prime year we get is 2027 and that is a twin prime, because just two years later in 2029, that's also a prime year. We know there are an infinite number of primes, we will always have prime years. But we don't know if there's an infinite number of twin primes. We do know they're more scarce than prime numbers. If you were to add all the prime numbers, it would tend off to infinity. In fact, if you add the inverse of all the prime numbers, so if you add a half plus a third plus a fifth, so on, that will also explode off to infinity. If you add together the inverses of just the twin primes, that converges to a value that will eventually equal 1.902-16058 and so on, which is why that's such a great mathematical constant. It's called Bruhn's constant. And it shows us, even if we don't know how many twin primes there are, we know that they're very rare compared to normal primes. Now, the people in June 2011 who saw this number were the guys running an auction for a suite of patents for which Google was bidding. And Google bid a Bruins constant of billions of dollars. For this auction, they bid 1,902,160,540, which confused everyone else in the auction until later on, Google also bid PI billion, at which point everyone realised what they were doing. I love those guys. And so that's why Bruun's constant was my number of the year.
- [24:48]
Tim Harford
Matt Parker and we've structured more or less like a newspaper this week by ending with some sport.
- [24:54]
Robert Mastro Domenico
Hi, my name's Robert Mastro Domenico, and I'm a sports statistician for Global sports statistics I'd like to talk about 2.9. This is the average number of goals reported for this season after 98 games on the BBC's Football Tactic blog under the article Is Premier League Defending getting worse? Now this is a really interesting article as at the time of writing we had a few shock results in the
- [25:22]
Jill Matheson
Premier League Arsenal's humiliating 82 defeat to Manchester United.
- [25:26]
George Monbiot
Wayne Rooneys City were 51 winners against
- [25:29]
Tim Harford
spurs at White Hart Lane. Twice they came from behind, but Arsenal rounded off a miserable week for Chelsea
- [25:33]
George Monbiot
with a final 53 victory at Stamford Bridge.
- [25:35]
Matt Parker
After thumping the champions 61 at Old Trafford, Sir Alex Ferguson promises there will
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Robert Mastro Domenico
be a big response now these are big games where we generally don't expect to see a lot of goals. Now this 2.97 goals per game is reported as the Highest value since 1967-68 season and this is compared to the average number of goals taken from the first hundred games of last season, which they give us 2.5. These numbers seem quite different and the article asks the question is Premier League defending getting worse? In the article, former Arsenal defender and BBC pundit Lee Dixon says he thinks it's more likely down to the Premier League attacking getting better combined with the defending getting worse. And he says that while teams have been more adventurous this season season defenders are being hindered by the growing rule changes which have given their own opponents an advantage. So 2.97 goals per game seem to support this view if taken at face value, as it appears much bigger than 2.59 goals per game. However, on more or less I know you don't take the numbers at face value. So delving deeper, the difference between 2.97 and 2.59 can be shown to not be stuck statistically significant. So given this result, I was interested in seeing how many goals would be needed to be scored over the period of 100 games to show a statistically significant difference when compared to what happened last season. My findings showed that you'd need to have around 3.1 goals per game to show a statistically significant difference between what we had seen last season. So is the Premier League attacking getting better and defending getting worse as Lee Dixon suggested? Well, the numbers don't really seem to support this. However, whilst statistically we're not seeing significantly more goals per game, we still have one of the best leagues in the world giving us one of the best seasons on record.
- [27:36]
Tim Harford
Robert Mastro Domenico with the last of our numbers of the year, we'll be back next week at our usual time. Until then, you can always surf on over to our website@BBC.co.uk more or less do please keep your questions and comments coming in via more or lessbc.co.uk. goodbye. More or Less was presented by me, Tim Harford of the Financial Times. The producer was Wesley Stevenson and the editor, Richard Varden. The program is made in association with the Open University. For more information and terms go to BBC.co.uk radio4.