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Numbers of the Year 2014.
00:27:41
Tim Harford and guests look back at some of the weird and wonderful numbers of 2014.
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A
Thank you for downloading the More Or Less podcast from the BBC, statistically proven to be the very best numbers program around. This is the extended edition of the programme, first broadcast on BBC Radio 4. Hello, and welcome to a brand new series of more or less your weekly guides to the numbers in the news and in life. With every last number of 2014 safely totted up and the unfilled database of 2015 stretching out ahead of us, it's time to find our bearings by asking our favourite people to tell us their favorite numbers of the year just past or occasionally the year to come. Where better to start than with David Spiegelhalter, a man who received a knighthood last year for his services to this program. I'm sorry, his services to statistics.
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B
My number is £5.7 billion. This was the amount that the Office of National Statistics estimated that prostitution contributed to the economy in 2012. And the the reason they had to do this is the EU has now regulated that both prostitution and illegal drugs should be part of national accounts and contribute to gdp. Now, you know, where did they get this figure from? And it's quite difficult to judge. Is that big, is that small? It's a big number. But the ONS nicely gave us a simple spreadsheet and say roughly where they got it from. They estimated this around 61,000 people working in prostitution in the UK. Average cost per visit about £67 and that each was seeing about 25 clients a week and working 52 weeks a year. Multiply those, those up and you get £5.7 billion. Now, this figure has been questioned by people close to the profession as being far too high. And I actually agree with them. If we go through those components, the 61,000 probably isn't too bad. There's lots of. It's very difficult to estimate and the trade is changing so rapidly in that the number of independents now with the Internet has grown enormously. You can go onto one website and see 30,000 people operating independently. But they also had some take your
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A
word for that on that day.
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B
Yeah, exactly. I don't necessarily recommend it, doing this research.
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A
The numbers are there.
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B
The numbers are there and there you also get services and costs and the average cost of 67 pounds probably isn't too bad. It might be a bit low, but again, as a profession it's a huge variability between street walking to high class escorts. Probably those numbers aren't too bad. The crucial thing is this assumption that each person working is seeing 1200 clients a year. And this seems very high indeed. And we can do a few little reality checks on this. It would mean, for example, that everybody working in prostitution was actually turning over £100,000 a year. And this doesn't seem plausible from people who know about these things. We can also say that the ONS assumptions mean that there's 75 million visits to prostitutes every year in this country. That's one and a half million a week. Now, from an alternative source, the latest NATSAL survey on sexual behavior estimate that, you know, around about 4% of men between 18 and 65 report paying for sex in the last five years. And over the last year probably figures about half a million. And that may be an underestimate, but probably not too bad. Half a million men paying for sex every year in this country, and you may think that sounds quite a lot, but in order to get to one and a half million visits per week each would have to be buying sex three times a week. And that does not reflect, as far as one can see, behavior. So I guess my feeling is that this figure is too high. I know, Ernest, are looking into it again. It'll require, you know, I think really quite a subtle approach in order to get a more realistic figure, and I predict it's going to come down substantially.
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A
You do slightly feel for the Office for National Statistics because unlike you, David, they're not experts in the sex trade. It's quite difficult to find out all of these things. But I suppose what you're saying is that the back of the envelope should have been enough to call into question this headline.
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B
Exactly. It's one of those things where actually a real back of the envelope calculation can be enormously advantageous. Ons have been using some of these sites. They, for example, to get their prices used one of the review sites that exists for reviewing prostitution, much in the same way as TripAdvisor does for hotels.
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A
Sir David Spiegelhalter, professor of the Public Understanding of Risk at Cambridge University. Now, this estimate of the size of the sex industry isn't some arcane statistical issue. It matters because it boosted the estimate of Britain's gross national income, and that in turn boosted the size of the bill that the European Union sent us. You may have seen headlines mentioning 1.7 billion pounds. That's quite a big number. Now, most of that number isn't down to the new estimates of the size of the sex industry, but perhaps £100 million is due to the Office for National Statistics trying to count the value of the sex and the drugs traded in the British economy The summer of 2014 saw the biggest show on earth, the World cup in Brazil. Germany defeated Argentina by a single goal in the final, but the tournament will be remembered for the manner of Germany's victory in the semi final, leaving the host nation in tears.
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C
That's a lovely little reverse ball, Sherlock.
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D
Andre Schuerle it's seven.
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E
I'm Helen Joyce, the international editor of the Economist, and my number of the year, it's actually a ratio, it's seven to one. It means two things to me as a former Brazil correspondent for the Economist, and both of them sad. One of them is the score that Germany got against Brazil in July in the semifinal of the World Cup. Germany got seven. Brazil went out on a humiliating one. It's also just as sadly about the ratio at the moment of inflation in Brazil to growth. You may remember that Brazil was one of the BRIC economies, the large emerging markets that were growing fast and that were going to transform the world's economy. That was a few years ago. Now we have a country that's perilously close to stagflation. It's got 7% approximately of its inflation and it's growing at even less than 1%. For me, this ratio sums up two ways in which Brazil has disappointed in the last few years since its arrival on the world stage. And I hope that this country that I still believe has huge, huge potential and for which I'm rooting, can turn this around and make it one to seven in the future.
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A
Helen Joyce of the Economist. Next up on our list of numbers of the year is the BBC's political editor, Nick Robinson. One of the battlegrounds in this year's general election will be the National Health Service. And as with most political battlegrounds, the statistical artillery will be involved.
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D
My number is £8 billion. That's the amount we were told had to be spent extra on the NHS by the chief Executive of the health service. That was the target for the end of the next Parliament. In other words, in five years time.
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A
So £8 billion, and that would be £8 billion a year over five years. £8 billion divided up over the five years. We'll get to 8 billion by the end of the five years.
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D
That's the one. We'll get to 8 billion by the end of the five years. In other words, at the end of the next Parliament, by the time there's another general election coming, not the one we're about to have, that the NHS would be spending each and every year £8 billion more than it currently is.
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A
And that number doesn't mean Much in isolation. So is that doubling the NHS budget? Is it increasing it by half a percent? What's the size of the budget to start with?
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D
Well, it's the curiosity of numbers in politics, isn't it, that people love billions because it sounds like an awful lot of money and they hate percentages, partly because people struggle with percentages and partly because it makes it sound like a lot less. Actually, it's a piffling sum. £8 billion.
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C
Even more piffling.
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A
Eight billion. Excellent.
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D
It is nothing at all. It is a fiver on the floor as far as the budget of the NHS is concerned. The NHS budget in England, and it's done separately in England, is well over 100 billion pounds. So 8 billion by that time involves a real terms increase of one and a half percent each year for five years. And you may say, well, in these austere times, one and a half percent in real terms, my goodness, that is luxury. But the figure that I like to compare it with always is Margaret Thatcher's cuts. And the word cuts is very firmly in inverted commas, because I'm always being told that Margaret Thatcher cut the nhs. In fact, she and her government are, on average, over the period, increased health spending by 3% in real terms, year on year on year. So this ambitious new target that all of them are struggling on, all the political parties to say that they will deliver, the new Chief Executive says is crucial, is half the rate of increase that Margaret Thatcher's government produced.
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A
So we have this target of 8 billion over the life of the next Parliament. Not as much money as it might seem. Where does George Osborne's recent announcement of an extra £2 billion fit into this?
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D
Well, he was trying to show that he was making a down payment on this, but gave the impression to people, I think, that given he was spending 2 billion next year extra, he'd just keep adding 2 billion. And that would add up to your rate. Not a bit of it. When you looked at it, 2 billion in the baseline of the NHS spending is just 2 billion. It doesn't become 8 magically, unless you add in real terms, another 2 billion, and then on top of that, another 2 and another 2 to reach your 8. But it gave the impression, didn't it, that. Well, not to you, of course, Tim, because you know about numbers. But it gave the impression to a lot of people that he'd magically found this 2 billion quid and that sort of solved the problem. Well, it really doesn't. And indeed, when you looked a bit closer at the 2 billion it wasn't quite what it seemed. So a headline largely in London based papers, about 2 billion turns out to be quite a lot of that money's going to Northern Ireland, Wales and Scotland. So for the English NHS, it's 1.7 billion. When you looked again, you discovered that just a bit under half of that £750 million was coming from within the existing budget for the Department of Health switched, yes, to the nhs away from back office, but nevertheless from the budget we would think of as going to Health. So the actual amount of new money wasn't that much at all.
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A
Nick Robinson, the BBC's political editor, as Nick mentioned, the NHS budget as a whole is more than 100 billion pounds. UK government debt is more than a trillion pounds. These are big numbers, really big numbers, but maybe we need bigger ones. Here's Dr. Pippa Malmgren, former economic adviser to President George W. Bush.
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F
My number is a quadrillion.
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A
That's a big number. A quadrillion is, if I remember, a thousand times a trillion. So why should we be talking about quadrillions?
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F
Well, I think this number is going to come up a lot more often. It's come up in the last year because the Japanese debt now exceeds one quadrillion. So in economics we have a practical example of this matter in the financial markets. You know, we talk about regulating the financial markets and you ask, well, how big are they? And the estimate now is that derivative transactions come to more than one quadrillion.
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A
Pippa Malmgren, her new book is called Signals. The next person to give us his number of the year is Carlos Villalta. He's a visiting fellow at the center for U.S. mexican Studies at the University of California in San Diego.
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G
And his number, 39,222. This is the number that we got from our new and actually the first time that we conduct a census on education, on elementary education in Mexico at the beginning of this 2014. And this represents the number of teachers when the census was being conducted. And the interviewers were asking the general directors, other teachers and the students who these persons were. They were actually not known in these schools.
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A
Hang on, There are nearly 40,000 people receiving teacher salaries while nobody in the schools they allegedly work at has ever heard of them. How on earth was this discovered?
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G
Very simple. At the beginning of the census, when they were planning on how to conduct the census, the National Institute of Statistics obviously contacted the Ministry of Education. And among the things that the National Institute of Statistics got from the Ministry of Education was the payroll. Basically the list of Teachers that receive a salary or a monthly paycheck in each of the schools, at the school level, the surveyors or the interviewers of the the National Institute of Statistics, they went through the list systematically and they were asking the people in the schools if they knew these individuals. And nobody, absolutely nobody, knew who these
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A
persons are.39,222 is a big number, but how big?
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H
How big?
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For example, compared to the number of teachers who work in Mexico's elementary school
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G
system, you would say, well, 39,222 is a lot of people. It is, but as a proportion it's not that big, is just 1.5%.
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A
Surely all of these phantom teachers have had their pay stopped immediately, haven't they?
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G
Theoretically, of course, in a rational world, the Ministry of Education would have to adjust this payroll, but we don't know if that happened.
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A
Professor Carlos Velalta with one of those scarcely believable numbers that's nonetheless true. Next up is Simon Singh, journalist and author of the book the Simpsons and Their Mathematical Secrets. Simon's number helps pay homage to a man who was very fond of mathematical games.
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C
My number is 100 because 2014 marked the centenary of the birth of Martin Gardner. There may be people scratching their heads and thinking, well, who's Martin Gardner and what's the big deal?
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Loyal, more or less listeners, they know who Martin Gardner, everybody else from Radio 4.
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C
He's a hero to so many people. He was one of the top hundred magicians of the 20th century. He's a hero amongst rationalists and amongst mathematicians. Percy Diaconis, who's a great statistician, once said of Martin Gardner.
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A
And also a great magician.
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C
And also a great magician as well. Absolutely. Yes, he said that Martin Gardner turned thousands of children into mathematicians, but he also turned thousands of mathematicians back into children because he wrote these wonderful columns and came up with these wonderful puzzles that inspired people to become mathematicians. But they were so playful that if you're a mathematician, it just made you smile like a 10 year old. So he's my hero. And this hundredth year has been an opportunity to remind people who don't know about Martin Gardner what a great and wonderful guy he was.
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A
And there are so many interesting mathematical curiosities and deep mathematical ideas that Martin made famous. I think everything from the Flexagons to the John Con Ways Game of Life, one of the early agent based simulations,
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C
fractals, all these great ideas that we talk about in kind of popular maths, were first broken in his column, which he ran for 25 years. In scientific American.
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A
So do you have a particular favorite?
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C
I wrote a book about codes and code breaking and the most important cryptographic breakthrough of the millennium. The story was broken in Martin Gardner's column. And it's this idea of public key cryptography. So if I want to send you a secret message, I have to scramble it up according to some recipe, and if you're going to unscramble it, you need to know that recipe. And that just seems annoying because I've got to get that recipe to you secretly. And if I could get the recipe to you secretly, then why don't I just use that route to send the message? So this idea of exchanging the key, exchanging the recipe, held back encryption for centuries, for millennia. But public key cryptography says that you can exchange a message with somebody you've never, ever met before without giving them any secret, and they will be able to decode that message. And Martin Gardner explained all of this and explained the mathematics. But maybe we'll avoid the mathematics and maybe use an analogy. We could talk about. I've got a precious object instead of a secret message. I put the precious object in a box, and I lock it with a padlock, and I send it to you. Now, you can't open it because I've got the key, and that's our key distribution problem. That's our recipe distribution problem. But what you do is you put your own padlock on the box and send it all the way back to me. So I've now got a box with two padlocks, my padlock and your padlock. I can undo my padlock because I've got the key. I've had that all along. I send the box back to you. There's only one padlock left. That's your padlock. You can undo that padlock, you can open the box and get the precious object, and at no time has the box been insecure. At no time have I had to give you a key, and you were able to open the box at the end of the day.
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A
So that's the analogy. Can you give us a hint about the mathematics involved?
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C
Yeah. So let's take that analogy and just put a twist on it. So this time, imagine I've got a million padlocks, okay? And what I do is I send padlocks around the world. So every post office has got one of my padlocks, and the padlocks are open. So now let's imagine you want to send me a precious object. What you do is you go to your local post office you say, can I have one of Simon's padlocks? You put the object in a box, you close the lid, you can lock the padlock. Because the incredible thing about padlocks, maybe it's not that incredible, but the beautiful thing about padlocks is that anybody can snap them shut, but you need the key to open them. So you can snap your padlock shut, you can send the box to me, and of course I can open it, because I've had the key all along. So it's no longer a key distribution problem, it's a padlock distribution problem. And I don't care who's got the padlock, because the padlock only locks up the messages. It doesn't help you unlock it. And so that's one step closer to what Martin Garden was talking about. It's one step closer to public key cryptography. And then if you want to go all the way, what you're looking for is a mathematical equation or a mathematical function that operates like a padlock so
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A
that you can snap it shut, but you can't open it unless you have the key.
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C
Yeah, exactly. In fact, why don't we just go the whole hog? One step closer still is multiplication. Anybody can multiply two numbers. If I say to you, what's nine times 11?
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You say it's 99.
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C
99, exactly. So multiplying we can all do very easily. But factoring, going backwards, undoing the padlock,
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say, right, you've got 99. Now, what numbers go in? You multiply together to make 99. And actually for 99, it's probably not so.
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H
Yeah.
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C
But if I think of two numbers and I can multiply them fairly quickly in my head, 323. Now, what two numbers do you multiply to get 323. Now, not one times 323 and not something with a fraction in it. That's kind of a really hard question. What two numbers do you multiply to get 323? Now, there are lots and lots of listeners, and one or two of them might have figured it out by now, but most people will be scratching their heads. And the answer is it's 19 times 17. Now, I can do that really easy. 19 times 17. Well, 20 times 17 is 340. Take away 17 is 323. The multiplication is trivial, the factoring, especially for a computer and especially for small numbers. Yeah. And so when I take big numbers, computers can still do it very, very quickly. But even computers cannot factor. That's why, if you look at your Calculator, you've got a nice big multiplication sign, but you don't have any factoring button because computers and calculators cannot factor.
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A
Or they can, but it just takes them a long time.
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C
That's right.
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And if you have a big enough number, even multiplying two big numbers together, no problem. But taking a very big number and then factoring it takes years, possibly even
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C
centuries, millennia, till the universe goes stone cold. Ultimately. So our entire global security, whether it's in terms of personal communications, diplomatic communications, financial transactions, medical records, all of these to a very, very large extent, these security issues rely on factoring being a fundamentally hard thing to do. And if a mathematician wakes up tomorrow and figures out how to factor quickly, there's kind of a moral dilemma there. Do you tell the world and disrupt this stable situation or do you keep it quiet? I'm not sure what I would do. This story was broken to the world by the great works of Martin Gardner, Simon Singh.
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A
My next guest is the presenter of moneybox, Paul Lewis. And somewhat out of character. Paul has a number from the world of personal finance.
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H
25 billion. And that's pounds.
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A
25 billion pounds. Sounds like a big number. What is it?
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H
It sounds a big number, doesn't it? This is now the total redress, paid for mis selling, payment protection insurance, PPI. 25 billion. The major credit providers, banks and a few credit card companies.
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A
So that is, I think, about 500 pounds per person in the UK, nearly, or quite a lot of money. Remind us what PPI is.
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H
Payment Protection Insurance was supposed to protect you if you couldn't repay a loan. So you take out a loan, they would sell you, sometimes automatically adding on Payment Protection insurance. And it could actually be more than the interest on the loan. It was so expensive. The problem was they didn't make it clear when you couldn't claim it if you were unemployed, or perhaps if you had a partner who was in work, or perhaps you were too old to claim it, or perhaps you lost your job for your own fault, all of those could invalidate the claim. And so it was widely Ms. Sold. The conditions weren't explained and it was extremely expensive and, of course, extremely profitable.
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A
So it was such a terrible product then that the regulator stepped in and said, you have to compensate your customers. And really, at that point we started getting spammed by all kinds of people offering to sort out our PPI claims.
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H
Yes, I mean, really, you can do it yourself if you've got a bit of paperwork or you even remember when the loan was taken out. Who it was with. You can write to the bank or the credit card company and they've all got procedures in place, in fact, warehouses full of thousands of people whose job it is to make sure the claims go through. And about 70% of them are generally accepted by the banks. When they're not, you can go to the financial ombudsman and get money from them. But if you want to pay somebody else A third, maybe 40% of your compensation, there are plenty of people ringing us up to offer to do that.
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A
And so this total is £25 billion. Do we know how much a typical claim is? We're talking about a lot of money here.
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H
It's in the low thousands. It's sort of £2,000 ish, from what I can see. They have different ways of working it out, but it's round about £2,000 for each successful claim, maybe a bit more with some of the banks. So it is a lot of money. And, you know, over the last few years, since 2011, when the banks started paying out, they've been paying out around £400 million every month. So it's like a kind of retail quantitative easing of money being pumped into the economy. And you do hear of people buying a new car, paying off debt. People do all sorts of things with it, put it into savings, spend it, help. Maybe they help their children with a deposit on a house.
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A
So it is quite an extraordinary episode. Is it over?
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H
No, no, not at all. Because the interesting thing is it's still going up and that's why we've just reached 25 billion. And every year, when the banks produce their annual reports, they say, well, we see this tailing off now and then every next year, they say, it didn't tail off as we expected. We've had to put more money into it. So it's still going on. And I think it will go on. It's not quite as big as it was. It sort of peaked around 500 million a month. In September, for example, it was 354 million pounds given out. So it's declining a bit, but it's not tailing off.
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A
Now, I don't want to play tiny, tiny violins for the banks because I think to some extent they're clearly getting what they deserve. And it must be hard to make a profit if you're a bank and you're having to pay out hundreds of millions of pounds a month.
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H
Well, you'd think so, wouldn't you? But the extraordinary thing is that every bank just about has made a profit from retail banking in just about every quarter through the financial crisis of 2008 and beyond. So although it's dented profits, it hasn't stopped them making profits. And as you say, this is a just redress. And looking at the estimates from HSBC and Barclays, they reckon they've now compensated about 4 out of 10 of their customers. So there are still 6 out of 10 who could well have been miss, sold a product, sold a very expensive product, who haven't yet got anything back and probably never will. So they're still keeping a lot of the profits they made on these products.
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A
Paul Lewis talking PPI compensation, which really is the gift that keeps on giving. Now, that's just about all we've got time for in our look back at some of the numbers of 2014. But there is just enough time to give you a song. Or more precisely, here's geeky songstress Helen Arnie with an ode to the Rosetta spacecraft's voyager to a certain hard to pronounce comet.
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I
Sleep well, little philae. You fulfilled your destiny. Four billion miles on the clock to do a science on a rock. Your jump down from Rosetta was so good, you jumped again and again. Whee. Low gravity. But when you came to land, it wasn't quite what EESA planned. Then you employed the best technology from 2004. That didn't stop you getting all the data you came for. Then the newsrooms of the BBC resounded with the echo of presenters rolling round the words. Chiri Umof, Jira, Tiri Tiramu, Chiri, Chirimoo, Chirimoomin, Chiri, Jira, Gary, Jerry, Jerry, Garry, Gary Lineker. Chiri Umoff. Gerisimianko. Nailed it. We watched with rising horror as your batteries ran cold. It turns out solar panels don't work so well down a hole. The only true space cowboys are Jamiro. Quiet. And you. And maybe Bruce Willis too. I hope you'll wake up one day when the sun comes into view. So sleep well, my little philae. You fulfilled your destiny. You rocked that rock. And that's how you roll on Comet 60.
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A
This is the extended edition of More Or Less, first broadcast on BBC Radio 4 and produced in association with the Open University.