Higgs boson statistics

Summary

More or Less: Higgs Boson Statistics (December 16, 2011)

Host: Tim Harford (BBC Radio 4)

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Episode Overview

This episode of "More or Less" dives into how statistics—particularly the concepts of statistical significance and sigma levels—are used (and often misunderstood) in the context of scientific discoveries, with a specific focus on the reported evidence for the Higgs boson at CERN. In addition, the episode touches on statistical oddities with double yolked eggs, the history and practical impact of Fibonacci's arithmetic in medieval Europe, and the folly and economic theory behind attempts to “corner the market” in commodities—from gold to plastic toys.

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Main Theme: Sigma Levels and the Higgs Boson

Understanding "Sigma" in Science ([01:06] – [07:10])

• Listener Question: Robert Matthew, a physicist, asks for an explanation of "two, three, and five sigma evidence" as used in media reports about the Higgs boson discovery, noting frequent misuse and misunderstanding of these statistics.
• What is Sigma?:
  • Sigma levels indicate how far a result deviates from expectation under the assumption that there is no real effect (i.e., the result is a “fluke”).
  • The media and even some physicists incorrectly present a "two sigma" finding as “there’s only a 5% chance it was a fluke” or "five sigma" as "one in a million chance" of a fluke. This is misleading.

Key Explanation ([01:34] – [04:06])

“What it actually means... it’s the probability of getting at least as impressive evidence as you actually got on the assumption that fluke was the true explanation. Now, instantly you can see that there’s probably an issue with simply flipping that figure around and saying... it’s also the probability that fluke really is the explanation for the results...”
— Robert Matthew ([01:34])

• Core Misconception: Probability of X given Y (e.g., spots given measles) is not the probability of Y given X (measles given spots)—a confusion rampant in reporting statistical significance.
• Physicists vs. Other Scientists:
  • Physicists aim for five sigma before claiming a discovery, but interpret significance incorrectly. Many other scientists consider two sigma adequate for publication, leading to unreliable findings.
  • In medicine, for example, the failure rate of studies is much higher than the “5% fluke” statistic would suggest, exposing flaws in the standard interpretation.

“If the bar was set an awful lot higher, a lot of science, medical science, it would never see the light of day because of its failure to reach the real level of evidence that’s actually required.”
— Robert Matthew ([04:24])

Why Not a "Photo" of the Higgs? ([05:56] – [06:48])

• Nature of the Higgs boson: It cannot be directly detected. Its existence is inferred statistically from rare side effects among trillions of events in the Large Hadron Collider.

“Sifting out that very weak signal from all that noise is the devil’s own job, and it’s very impressive that they can do it at all.”
— Robert Matthew ([06:14])

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Double Yolkers and Probability Clustering ([07:21] – [11:16])

Listener Responses and Egg-Statistics

• Background: Follow-up from last week’s investigation into the odds of finding multiple double yolked eggs in one box.
• Main Finding: Odds are not as astronomically small as pure chance suggests because double yolk eggs cluster when eggs are collected from young hens who are more likely to produce them and are sorted by size.

“If you don’t realize that such clustering is occurring, your maths will be wrong. Potentially by a factor of trillions or more. Exactly. This kind of error underpins the early phases of the credit crunch...”
— Tim Harford ([11:23])

Independent Verification

• Charlotte McDonald investigates: Multiple English producers and packers confirm that double yolked eggs are commonly packed together when sourced from young flocks.
• Rarity and Labeling: If double yolkers are detected systematically, boxes will be clearly labeled.

Clustering Analogy

• Bigger Picture: Failing to account for clustering is a statistical pitfall, analogous to errors in financial risk assessment (as during the credit crunch).

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The Fibonacci Revolution: How Arithmetic Changed Business ([12:35] – [17:10])

Interview with Keith Devlin, Author of The Man of Numbers

• Fibonacci's Real Contribution:
  • Published Liber Abaci, introducing Hindu-Arabic numerals and practical arithmetic to Europe.
  • Roman numerals were impractical for commerce, as sophisticated calculations left no record (audit trail), and only experts could compute.

“Roman numerals are fine for adding and subtracting, but that’s not very useful when you’re working out volumes of things that you want to buy. And so you need multiplication and division, and Roman numerals are hopeless for that.”
— Keith Devlin ([14:00])

• Impact:
  • Enabled businesspeople to do their own calculations and keep records, facilitating the rise of commerce and capitalism.
  • Liber Abaci included real-world examples—division of profits, pricing, basics for running a company.

The (Misplaced) Fame of the Fibonacci Sequence

• Interesting Fact: The famous Fibonacci sequence is only an aside in Liber Abaci. Its naming happened centuries later.

“The one person who wouldn’t be surprised would have been Leonardo himself, because he really had nothing to do with the damn thing.”
— Keith Devlin ([16:20])

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Cornering Markets: RAM Man and Real Commodities ([17:19] – [26:58])

From Gold to Plastic: The RAM Man Project ([17:19] – [24:33])

• Jamie Moks tries to corner the market in Ram Man (a Masters of the Universe toy) to make it “the new gold,” basing this on the social construction of value.
• Economic Lessons:
  • Professor Eric Smith (University of Essex) explains that manipulating prices by hoarding works only if demand and secrecy hold—a scenario rare in reality.

“The aim is to get sufficient control of a good... and then get a hold of enough of it to manipulate the price. And of course, once the price gets high and you can manipulate the price, you can sell high.”
— Prof. Eric Smith ([19:33])

Practical Barriers

• Moks’ public campaign undermines his chances—everyone knows he’s the buyer, so he can’t buy cheap.
• The global supply is much larger than his hoard.
• Economic theory (Coase conjecture) predicts that speculative hoarding often fails as others wait for the price to drop.

“Isn’t the problem that ultimately the only person you’re affecting is yourself because you’re the only person who’s interested in buying them?”
— Wesley Stevenson ([23:26])

Real-World Attempts: Copper Market Corner ([24:41] – [26:58])

• Yasuo Hamanaka (Sumitomo, 1990s): Attempted to corner the world copper market, at one point controlling 5% globally.
• Outcome:
  • Initially successful (price manipulation and profits), but failed due to increased supply from China.
  • When the market detected weakness, the attempt collapsed, prices fell, and he was removed from his job.

“As more and more copper came onto the market, he found it harder and harder to control the market. And in the end, prices fell against him.”
— John Gapper ([26:36])

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Cake Ratios: The Mathematics of Pound Cake ([27:56] – [29:10])

• Listener Segment: Mary Ellen Foley discusses the simple mathematical beauty of the pound cake—a 1:1:1:1 ratio of flour, butter, sugar, and eggs.
• The large size is less important than the proportionality, making the recipe easy to scale, paralleling simple arithmetic principles highlighted earlier in the episode.

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Notable Quotes & Moments

• On Sigma Significance: "Probability that a patient has got spots, given they've got measles, is about 100%. But ... the probability that someone has got measles, given they’ve got spots, is a completely different question..." — Robert Matthew ([01:53])
• On Risk Clustering: “This kind of error underpins the early phases of the credit crunch, where subprime mortgages were packed together in financial cartons..." — Tim Harford ([11:23])
• On Historical Impact: “It’s impossible for us to realize the beginning of the 13th century. Nobody in Europe had ever seen that kind of thing before.” — Keith Devlin ([14:54])
• On Market Cornering: “Virtually always never go right. And a lot has to do with information in the market. Who knows what you’re doing... You need a lot of money.” — Prof. Eric Smith ([20:53])
• On Recipe Ratios: “As long as the weights are the same... it’s the ratio that’s important.” — Mary Ellen Foley ([28:57])

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Useful Timestamps

• 01:06 Sigma significance and its misinterpretation
• 06:14 Why the Higgs cannot be "photographed"
• 07:21 Double yolked eggs: listener responses and statistical clustering
• 12:35 Keith Devlin on Fibonacci and the revolution in arithmetic
• 16:20 The origins (and myth) of the Fibonacci sequence
• 17:19 The economics of commodities: RAM man toy hoarding
• 24:41 Real-life attempts to corner markets: the copper example
• 27:56 The mathematical beauty of the pound cake ratio

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Summary

This episode expertly deconstructs widespread statistical misconceptions, particularly the meaning of “sigma levels,” using timely news about the Higgs boson. By paralleling statistical pitfalls in science with similar errors in everyday contexts (like egg packaging and risk management), it offers a practical guide to understanding numbers. Historical insight into Fibonacci’s role in democratizing arithmetic and contemporary case studies in economic manipulation (both comic and real) round out a rich, accessible exploration of how mathematical thinking—and misthinking—shape our world.

Transcript

[A]

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 welcome to More or Less, your weekly guide to the numbers in the news and in life. This week, there'll be wonderment. In medieval Italy, it's impossible for us

[B]

to realise the beginning of the 13th century. Nobody in Europe had ever seen that kind of thing before.

[A]

And we'll respond to your frenzied commentary on the matter. Mathematics of double yolked eggs. Do keep those emails coming in To More or lessbc.co.uk, whether you love what we're doing, hate it or just want to ask a question. One loyal listener, Robert Matthew, has done just that.

[C]

It would be good to hear a more or less analysis of the meaning of two, three and five sigma evidence that's being routinely abused, not only by the media reporting the Higgs boson supposed discovery, but also by some physicists themselves.

[A]

It turns out that Mr. Matthew is a trained physicist and a visiting reader at Aston University. I called him to chat this one through.

[C]

When the result was announced at CERN on Tuesday, there was talk about two experiments there finding what they described as two sigma evidence for the existence of the Higgs. And this was often explained in terms of it representing just 5% chance that the result was just a fluke.

[A]

Now, this is what, more or less listeners might be familiar with the idea of statistical significance, because you're getting at the same concept, right?

[C]

Yes, that's right. And it's often banded around as being a measure of the probability that your result is just a fluke. Now, unfortunately, it doesn't mean that. What it actually means, and here the definition is something that you need to slightly concentrate for. It's the probability of getting at least as impressive evidence as you actually got on the assumption that fluke was the true explanation. Now, instantly you can see that there's probably an issue with simply flipping that figure around and saying, oh, so it's also the probability that fluke really is the explanation for the results, because you can't simultaneously assume something and then use exactly the same result to claim it as evidence for what you're looking for. Sort of an everyday analogy of the problem here of doing that flipping around is a doctor has a patient come into the surgery and the patient's covered with spots. Now, everyone knows that the probability that a patient has got spots, given they've got measles, is about 100%. But clearly the probability that someone has got measles, given they've got spots, is a completely different question, and could be a completely different probability. And that's the core of this misconception about these sigma levels. When the scientists say they've got a two sigma level of evidence, they say it means there's a 5% chance their result is a fluke. It actually doesn't mean that. And this is why the physicists have reached for a much higher level of significance called a five sigma, which again, they're erroneous, often explaining as a one in a million chance that their result is a fluke. Now, it turns out that the definition of sigma is such that as more and more evidence comes in, the exact interpretation of it becomes less and less important. After a while, the data sort of dominates the interpretation. But for these low levels of evidence, like two sigma, which the physicists have turned their back on, in this particular case, it does make a difference. And the scary thing is that although the physicists routinely sort of turn their back on mere 2sigma level of evidence, most scientists regard a 2sigma level of evidence as representing a really good strength of evidence that they really are onto something. And that is a publishable result. And that is basically a very worrying phenomenon that's very widespread throughout science.

[A]

And it seems also that the physicists at cern, rather than correcting the statistics, they're just saying, well, we're just going to aim for more. We're going to use the same misconception and we're going to talk about the odds in the same mistaken way, but we'll just put the bar higher in some vague way and then we'll be right.

[C]

Yes, that's right. And it's definitely the case that five sigma level of evidence is more impressive than just two sigma. But it's far from clear to me that they're doing it for the right reasons. I think too many physicists and scientists in general are laboring under the misconception that when they've got a two sigma level of evidence, they've got a sort of 95% confidence that the result they've got isn't a fluke. It doesn't mean that. And in fact, in some areas of science, they're beginning to discover this. Like in clinical science, in medicine, you would expect if there's a 5% chance that result is a fluke, that about 1 in 20 of medical studies just fall by the wayside when people try to replicate them, but the actual failure rate is alarmingly higher than that in some cases, it's over 80%, 80% failure rate. So that should have been warning people that there's something wrong with the standard interpretation of these sigma levels. But unfortunately, this issue keeps being swept under the carpet. Nobody seems to want to address it. And I can't help feeling one of the reasons for that is that most scientists don't have access to something like the Large Hadron Collider, where they can just spend a few more years gathering colossal amounts of data and analyzing it. Most clinical data is based on, you know, 100 or a few hundred patients, and they're really stuck with it. And if the bar was set an awful lot higher, a lot of science, medical science, it would never see the light of day because of its failure to reach the real level of evidence that's actually required.

[A]

One of the things that's been puzzling me about this whole Higgs boson business, I assumed they were going to basically show us a photo and they will find it, put it in a box, and, you know, there it is, we found it. And I didn't really expect that they would start coming out with all of this. 2 sig, 3 sigma, 5 sigma. That's a bit of a puzzle.

[C]

Yes. The reason for that lies in the nature of the Higgs boson, for a start, no one will ever see can't be directly detected in a particle accelerator. Its existence has to be inferred by its side effects, which is what they're actually looking for. And these side effects occur pretty rarely, even in the trillions and trillions of events that they are creating inside the Large Hadron Collider. And sifting out that very weak signal from all that noise is the devil's own job, and it's very impressive that they can do it at all.

[A]

I'm very glad we've answered your question.

[C]

You're welcome anytime.

[A]

Loyal listener, Robert Matthew. Thank you. You're listening to More or Less with me, Tim Harford. Our email [e-mail] was full to bursting this week. I'm sure you can guess why. Was it our analysis of the supermarket price war? Was it the way we filleted the statistics on childhood literacy? Or perhaps our insightful reporting into the efficiency of public spending in Italy? No, it was this experiment.

[D]

This is quite tense.

[A]

It's a double yolk. There you go. The amazing beauty of statistics. That was us last week investigating the probability of getting a carton full of double yolk eggs. In theory, the odds against this are astronomical. One in a quintillion reflecting the fact that each consecutive double yolked egg is a one in a thousand event. But we said we don't think that's how the statistics work, because double yolked eggs are like buses. They all come along at once. And we also thought we did a pretty good job of working out exactly why they cluster. After speaking to a veritable expert who works for a company providing supermarkets with eggs, he told us that young hens are likely to produce double yolk eggs. He also told us that young hens usually produce small eggs, but the double yolkers are large. So a box of large eggs from a young flock may well contain several double yolkers. 223 of you, which is almost a quintillion in more or less mailbag terms, took the trouble to email us. Some of the emails were even supportive. In the early months of my pregnancy

[D]

18 years ago, I cracked six successive

[A]

double yolkers into a some friends and I had in a cafe in the Yorkshire Dales last year. Between us, we had a dozen double yolked eggs. Recently, we had a double yolk experience when all 30 eggs in one tray were double Y.

[D]

Double yolkers are sorted out with a bright light scanner and put to one side to be sold as double yolks. Double yolkers. You can buy a box of double yolker eggs. Do you not think that your profiterole

[C]

cook has bought one?

[A]

As you may have gathered, many people were dissatisfied offering various alternative explanations for how so many double yolked eggs got into one box. We asked Charlotte MacDonald, who was not involved with our original broadcast, to carry out a thorough, independent investigation. What have you found, Charlotte?

[D]

Well, I wanted to get the story from the farm gate itself, so I called a Yorkshire farmer whose young flock recently produced a lot of double yolk eggs. He told me that these young chickens produce small eggs normally, but when they lay a large one, you can be pretty sure it's a double yolker. So he then sends them to the packing company. All the large ones will be packed into trays or boxes and they're likely to be double yolkers.

[A]

Ok, that tallies exactly with what we reported last week. But it's just one farmer. Who else did you call?

[D]

The company that check, stamp and pack his eggs.

[A]

What do they say?

[D]

That you get all double yolkers in a box when they process the eggs of a young flock that has just started to lay.

[A]

Ok, but that's just in Yorkshire.

[D]

Yes. So I spoke to an egg packing company in Lincolnshire.

[A]

What do they say?

[D]

They told me the same thing.

[A]

Anyone else?

[D]

I spoke to one in Cheshire.

[A]

They told you the same thing?

[D]

Yes.

[A]

Not good enough. Charlotte, the very loyalty of our listeners is in question here.

[D]

Well, Tim, I also spoke to someone in Norfolk who is both a farmer and boxes his eggs and he told me the same thing.

[A]

Is that supposed to impress us?

[D]

Well, his story was independently verified by two further farmers.

[A]

Ok, ok, we believe you, you've checked it. But I'm curious. Some of our listeners suggest that employees at egg packing plants fish out double yolk eggs for themselves, and if they fish out too many, they put them back in the box at the end of the day. Hence boxes of double yolk eggs.

[D]

Well, I was told that might happen at a smaller company and indeed we've had an email from a listener to say he personally has done that, but this doesn't seem to be the main story. For one thing, it's time consuming to check for double yolked eggs, and so this wouldn't be something you'd do as a matter of routine unless you were already in the double yolked eggs business. These double yolk eggs are actually in short supply. If you have a process for detecting double yolk eggs, you'd make sure the resulting cartons were clearly marked as exactly that.

[A]

Ok, Charlotte, by the way, did you do anything else this week, apart from research eggs?

[D]

Well, a few items for later in the series. Tim and I also baked a cake which was, I have to admit, incredibly simple. The ingredient proportions are all equal. They have a neat ratio of 1:1:1:1:1: A binary cake.

[A]

I love it.

[D]

Yeah, exactly. And one listener, Mary Ellen Foley, has suggested a recipe with this ratio and we'll pop it into our podcast.

[A]

Thank you, Charlotte. And by the way, there were a few people who wondered why anyone cares. Good question. As we've seen, when unlikely events cluster together, you will tend to see apparently inconceivable occurrences showing up far more often than you might expect. If you don't realize that such clustering is occurring, your maths will be wrong. Potentially by a factor of trillions or more. Exactly. This kind of error underpins the early phases of the credit crunch, where subprime mortgages were packed together in financial cartons on the assumption that it was just impossible that many mortgages would fall into default at the same time. Unfortunately, mortgage defaults are rather like double yolked eggs, only less tasty. And now to the business innovations of the past, and in particular, to a book of simple medieval arithmetic for businessmen More than eight centuries old. Its author was Leonardo of Pisa, better known as Fibonacci. I spoke to Keith Devlin from Stanford University in California. He's better known to many in the United States as National Public Radio's math Guy. And he's author of a new book, the man of Numbers, which tells the tale of Leonardo of Pisa and his book Liba Abaci.

[B]

It really was the first comprehensive, actually the first coverage at all of modern, what we now call Hindu Arabic arithmetic, the kind of arithmetic that we all learn when we're in the elementary school.

[A]

Was Leonardo a popularizer of things that had been done outside Europe then?

[B]

Oh, yeah, yeah. In fact, the modern arithmetic, including counting with the 10 digits from 0 through 9, all the algorithms, all of the methods we learn at school that had been invented by Indian mathematicians in about the first six or seven centuries of the current era. Then the, the Arabic speaking traders in the Muslim world who were trading between North Africa and Europe and the Orient, they discovered these methods and they started using them in their trade. And then some of their scholars started developing them. And one of the offshoots was what we now call algebra. And so for several hundred years, it was those traders that were sort of develop it and using it. And it was in North Africa when Leonardo, who was a teenager, who'd gone over to join his father, who was a customs official in Buja in North Africa, Leonardo sees these traders in the coffee shops using this incredible method. And he recognizes at once this can change the world. If I can package this and make it accessible to ordinary people, then anyone can do their own arithmetic and suddenly anyone can set up in business.

[A]

And the key thing here is, I mean, it's not to modernize. It's not anything very remarkable. It's not as it's not a sort of a particular trick. It's just leaving Roman numerals behind.

[B]

Roman numerals are fine for adding and subtracting, but that's not very useful when you're working out volumes of things that you want to buy. And so you need multiplication and division, and Roman numerals are hopeless for that. So when people did calculations, they did one of two things. Either they counted on their fingers. They had actually had a very sophisticated finger system. The other way they used to calculate was with a board on which lines were ruled, on which you move pebbles around, then you record the answers in Roman numerals. So first of all, that meant you had an expert to do it for. You couldn't do your own calculations. You had to have someone who'd spent many years becoming efficient at using one of these two physical calculating methods. Another drawback was there's no audit trail. If you carry out a long calculation and then one of the two parties disputes the answer, you can't just go back over the working like we would today. The workings disappeared. You have to carry out the whole calculation again. So it's ineffective.

[A]

You've done it on your fingers. You've done it.

[B]

It's on your fingers. Yeah. It's okay for two people trading goods that are on the backs of camels, that's fine. But if you're talking about building a commercial empire, which is what the business people in Pisa were trying to do in the early 13th century, you need an efficient way of doing arithmetic. That leaves a record. It's impossible for us to realize the beginning of the 13th century. Nobody in Europe had ever seen that kind of thing before. The measure of the size of the revolution that followed Leonardo's publication of Liber abaci is precisely that what had once been impossible became completely taken for granted and regarded as just, well, duh, of course we can do arithmetic. That's a big revolution. The genius of Leonardo was he knew that in order to sell this method to the business people, he had to present it in their language in a way that made it transparently obvious to them that this was useful to them. It is full of hundreds and hundreds of hundreds of extremely practical problems. There's a whole chapter, chapter 10 of Liber Bacchi is called on companies and their members. That's about all the arithmetic you need to know in order to set up and run a company. How to divide up the profits, how to charge for your goods, and so forth. And it was incredibly practical.

[A]

Now, you said Leonardo of Pisa is more commonly known as Fibonacci. I think people will be surprised you haven't mentioned the Fibonacci sequence.

[E]

Yeah.

[B]

The one person who wouldn't be surprised would have been Leonardo himself, because he really had nothing to do with the damn thing. As well as doing all these practical problems, every now and then, he would throw in a whimsical problem just to sort of lighten the load. And one of the whimsical problems was a problem about a fictitious rabbit population. And you have to figure out how many rabbits there are in this population after they've been breeding for a year. That problem wasn't orig original to him. It's just a little throwaway example to give a bit of light relief. Then, in the 19th century, a French mathematician who's looking through Leonardo's work, sees this sequence in Liber Verbacci, knows that this sequence has interesting properties to do with the way flowers and plants grow and that kind of thing, and he gives it a name. So in the 19th century, it becomes known as the Fibonacci Sequence. That's the only connection between Leonardo and the Fibonacci Sequence, I'm afraid.

[A]

Keith Devlin, author of the man of Numbers. Hmm. Wesley Stevenson's here. What's that you've got there?

[F]

This, Tim. This is the latest new commodity which is set to take on gold, copper and cocoa.

[A]

Are you sure? Because it looks awfully like an unloved

[F]

plastic toy, but this has a very special quality.

[C]

By the power of Greyskull,

[G]

I have a problem.

[A]

I can't believe you found an excuse to play that. And it's not even a He man figure. And I'm not sure how it makes it a commodity.

[F]

Well, no, it's not he man himself, but it is about to become incredibly valuable.

[H]

So Ram man is from the 80s cartoon He man and the Masters of the Universe. I've actually just picked up one that will pop rather pathetically, I can tell straight away. So he's got a little trigger on the back. He rams. It was the 80s, it was kind of literal show.

[F]

So this is Jamie Moks. He's a performance artist and a man who's trying to buy up as many Ram man figures as possible to make them rare. It's a project he started because he couldn't work out why we were putting so much value in one commodity, gold.

[H]

Basically, I believe there is no reason for gold to be worth money. Really. Like, everyone was like, stop investing in a home and invest in gold. And then I was like, that's the only reason that is, is because everyone agrees gold is worth money. So if I could sort of buy enough and take enough, I could affect the price and try and create a new commodity.

[I]

Yeah. Actually, he's hit on a very interesting economic truth.

[A]

Who's this guy?

[F]

Professor Eric Smith, he's head of economics at the University of Essex, whom Jamie took to the pub to learn about how the economy works.

[I]

Jamie's initial idea about the fact that gold had more value than its pure utilitarian or material usages was actually quite a good insight on his part. We use it in a variety of production processes, jewelry and so on. There's an appeal there. But the actual price of gold reflects liquidity or money or a monetary component.

[A]

This idea of cornering the market's Interesting. I mean, Jamie clearly couldn't do this in gold because he couldn't afford it.

[F]

Yes. And one of the reasons that he chose Ram man above the main characters in the cartoon, he man, is that they're actually cheap and available. And as Professor Eric Smith says, this makes them ideal.

[I]

The aim is to get sufficient control of a good a commodity, some asset, something that's durable, and then get a hold of enough of it to manipulate the price. And of course, once the price gets high and you can manipulate the price, you can sell high.

[A]

Given that most people don't even remember Ram man and the figure itself is, well, it's pretty rubbish. Whereas there must be a plentiful supply that's going cheap.

[F]

It would seem like Jamie has overcome one hurdle in his plan for Ram man domination. But it was when I asked him how much he was paying for them. This is when I became a bit concerned that he doesn't quite get it.

[H]

There is no consistency at all. So I have bought one for 20p upwards to the most expensive Ram Man I've ever bought is £192.50. That was mint. Ram man in box. And, yeah, I no longer have him. We sold him at the end of Edinburgh Fringe Festival for a profit. No,

[F]

here I should explain that Jamie isn't just buying Ram man. He also has a show which is a bit like a sales pitch about wise collecting and to convince people that Ram man is really the new gold.

[A]

Because to raise the price, there needs to be a demand.

[F]

Yes, and this is his attempt to create some demand beyond the normal collectors and fanatics.

[A]

So is it possible?

[F]

Well, I'll let Professor Eric Smith answer that.

[I]

In principle, it is possible, but it depends upon a lot of things just going right and they virtually always never go right. And a lot has to do with information in the market. Who knows what you're doing and what you're trying to do. You need a lot of money.

[A]

Okay, so let's run through the problems here. So he's not helping himself. He's planning to push the price up in order to sell them at a profit, but he needs to buy them cheaply. And he's got a problem because he's broadcasting the whole scheme to everybody, which means people won't want to sell to him or won't want to sell to him cheaply. And then if he does succeed in getting a huge stash of Ramon figures, then when he tries to sell them at a high price, that will make the price fall. And in any case, people will Be waiting for the price to fall. By the way, economics nerds, this is called the Coase conjecture, after the Nobel laureate Ronald Coase. And it's going to be all too easy for people to wait for the price to fall because let's face it, the world is not desperate for a steady supply of RAM man figures.

[F]

Yeah, it's. It's not looking good, is it?

[A]

You know, Wes, more unscrupulous people could really take advantage of Jamie.

[F]

Here, let me just reach in here. I want to know how much you're going to give me for this RAM man.

[H]

Alright. The important things when pricing up a RAM man is whether he has an axe, whether he has mangles or he's quite pretty. Does he park?

[F]

But what do you think that RAM man is worth?

[H]

Around £6.99. £8, something like that. I'd be happy to pay.

[F]

You think eight pounds?

[B]

Yeah.

[F]

Should we shake on that?

[H]

Yeah, I'd be happy to pay.

[G]

There we are.

[F]

Eight pounds. That's a good deal done.

[A]

I think that's a very good deal done. Wes, how much did you pay for it?

[F]

Oh, it was quite expensive, Wes. Well, okay, it was £4.99, but I had to pay the postage as well.

[A]

Wes, you made a profit, okay, that's going to Children in Need. And I suppose you have at least added to his collection. But to corner the market in RAM man figures, he's going to need quite a few of them. Do you know what proportion of the world's supply of RAM man figures he has?

[F]

Yeah, he's got 151 so far and he spent over £1,500. But I think he's a little off target.

[H]

Quite a lot, possibly around 2 million.

[A]

And you have 151.

[H]

Yeah, I have noticed the price going up very slow. But RAM man sort of didn't sell and no one considered him to be worth that much money. And slowly me buying them looks like they're going or selling more.

[F]

Isn't the problem that ultimately the only person you're affecting is yourself because you're the only person who's interested in buying them?

[B]

No.

[I]

Yes.

[H]

No.

[C]

Yes.

[H]

That is ultimately a problem. But the more and more people are convinced, if I convince enough people to believe and want to show that we matter in the economy, then ultimately I do affect the economy.

[A]

I suppose it's not certain that Jamie's plan's doomed. I mean, just because it's a rubbish plastic toy that nobody wants doesn't mean it might suddenly not become big.

[I]

These RAM Men can become valuable as part of an art or cultural phenomenon. So there is this thing in cultural economics where value is determined by some sort of symbolic content rather than physical characteristics, rather than just the utilitarian material usages. Then it can actually become quite profitable for him to have these RAM men. And I think Jamie is trying to embed this symbolic content into the RAM men just as well as he kind of observed that there's almost a symbolic content or a belief about the value of gold that becomes self sustaining.

[A]

I think Jamie has a long way to go.

[F]

Yeah, I think it's probably unlikely that anyone's going to be investing in RAM man anytime soon.

[A]

Yeah, but Jamie isn't the first person to try to corner a market. And I spoke to John Gapper of the Financial Times. John has a new electronic book, how to Be a Rogue Trader. And he told me about another famous example.

[E]

Yes, it's actually been tried repeatedly by different individuals in different markets, particularly with physical products and commodities. There's one notable case in the 1990s of a copper trader called Yasuo Hamanaka, who worked for Sumitomo, a big Japanese trading company. And he systematically tried to corner the world market in copper by buying up not only futures, copper futures, but also the physical substance itself.

[A]

So futures are promises to deliver copper later, is that right?

[E]

That's correct. They're a form of derivative and they're basically a contract that says, I will deliver a certain amount of copper on a future date. Normally you don't actually have to deliver it, but you settle the contract financially. But Hamanaka actually also bought an enormous amount of copper. At one point, he controlled 5% of the world copper market and it was sitting in warehouses around the world.

[A]

Okay, so it was a hugely ambitious attempt. Presumably 5% of the world copper market's a lot of copper. I mean, how did it work out for Hamanaka?

[E]

Well, for a long time it actually worked out pretty well for him. Even though other traders on the London Metal Exchange knew what he was doing or sensed what he was doing, nobody was quite sure how much he owned. And every time people tried to trade against him, he just bought more and more and squeezed them out and actually made consistently a lot of profits. Sumitomo was very proud of him. They put him in their annual report as being a great example of a successful trader. But then the whole thing collapsed in 1995.

[A]

And why did it collapse?

[E]

Well, one reason was that China started producing more copper.

[A]

And so a natural response to high prices, I suppose.

[E]

Exactly. So what he effectively did was he forced, he drove up the price, made it more economical to mine the stuff, and then, of course, China started doing it. And as more and more copper came onto the market, he found it harder and harder to control the market. And in the end, prices fell against him. Sumitomo removed him from his job and then everybody realized there was an enormous weakness.

[A]

And they piled in John Gapper of the Financial Times, and before him, Ram man enthusiast Jamie Moks, economist Eric Smith, and our very own Wesley Stevenson. Thank you, Wesley. And that's all we have time for this week. We'll try to rustle up something vaguely festive for you next week. Perhaps a good mathematical card trick or some such. And if your yuletide revels will drag you away from the radio, our Sunday evening repeat will be on Christmas Day. After all, then why not subscribe to our podcast via BBC.co.uk more or less and never miss another mathematical recipe. I mean, never miss another program. Our email address is more or lessbc.co.uk. do keep the ideas and comments coming. We look forward to hearing from you. Goodbye. That was a More or Less podcast from the BBC, presented by me, Tim Harford of the Financial Times. The producer was Ruth Alexander and the programme was edited by Richard Varden. And now here's Charlotte MacDonald.

[D]

Yes, I'm not particularly talented in the kitchen, but even I can manage cakes with just four ingredients of equal proportions. We were contacted by Mary Ellen Foley, who suggested such a recipe. Here she is.

[G]

I'm a loyal listener of More or less, so I heard them ask for recipes that had some mathematical interest, and I immediately thought of pound cake, which everybody in America knows about. It's something like a Madeira cake, very, very common. But probably most people haven't thought about how it got the name. Traditionally, it was made with one pound each of flour, butter, sugar and eggs. So you get this beautiful ratio of one to one to one to one. And if you really use a pound of flour and a pound of sugar and so on, then you would get an enormous cake or several small cakes. So really, people don't make it with the full pound, but it's the ratio that's important. So half a pound to a half a pound, et cetera, as long as the weights are the same. And then you add, depending upon what kind of recipe you've been handed down from your grandmother, any salt or baking powder or vanilla or whatever your family uses.

[D]

And then you mix all these ingredients into a bowl, pour the mixture into a cake tin and pop it into the oven to get your beautiful one to one to one to one cake. Thank you, Mary.