Who are the 1% and the 99%?

Summary

More or Less (BBC Radio 4)

Episode: Who are the 1% and the 99%?
Date: December 23, 2011
Host: Tim Harford

Overview

This episode of "More or Less" explores the increasingly prominent notion of "the 1%" versus "the 99%" — a central slogan of global Occupy protests — and investigates, with statistical rigor and clear-eyed curiosity, just who these groups are, how their fortunes have changed over time, and what economic and statistical realities underlie the rhetoric. Alongside this main question, the episode features discussions with leading economists and statisticians, and culminates with a conversation on the mathematical principles behind card tricks with the legendary mathematician-magician, Professor Persi Diaconis.

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Key Discussion Points and Insights

1. Defining the 1% and the 99% ([01:01]–[03:20])

• What do people mean by "the 1%"?
  Tim Harford introduces the phrase’s protest origins and turns to Professor Sir Tony Atkinson for clarity.

• Income thresholds for the 1%:

  • UK: About £120,000 annual income to join the top 1%. ([01:47])
  • US: Around $340,000 (£220,000), though US figures refer to “tax units” (could be couples or individuals). ([03:20])
  • Quote — Prof Atkinson:
    “The first thing we know about the 1% is that they’re quite well off, roughly…to be in the top 1% of income in this country, you have to have an income every year of about 120,000.” ([01:47])

• Growth of income share:

  • In the UK, the share of income for the top 1% doubled from just under 7% (1980) to about 15–16% pre-financial crisis. ([01:47])
  • In the US, from about 8% (“beginning of the Reagan era”) to 18% by 2008. ([02:30])

• Pattern observed globally:
  Similar increases in top income shares are occurring in China, India, and elsewhere. ([02:42])

• Within-group inequality:

  • The top 0.1% (UK): Income threshold is around £500,000 per year.
  • In the UK, the 0.1% have “60 times” their proportionate share versus 15 times for the 1%. ([03:20])
  • Quote — Atkinson:
    “It’s a bit like a Russian doll, as it were…inside [the 1%] there’s yet more inequality.” ([02:42])

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2. The Changing Composition of the 1% ([04:10]–[05:23])

• Is the 1% a fixed group?
  Professor Donald Boudreaux (George Mason University) describes findings that “the 1%” isn't a static elite — only 44% of the US 1% in 2001 were still in that percentile in 2007.
  • Quote — Boudreaux:
    “It casts suspicion on the claim that the 1% are this unchanging plutocracy who somehow have control over society…” ([04:10])
• Mobility explained:
  People move in and out of the 1%—from students to analysts, or high earners becoming retirees.

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3. The 99%: Wage Growth and Inequality ([05:23]–[06:10])

• Stagnation of wage growth:
  • Stuart Lansley (“The Cost of Inequality”) notes that since the 1970s, UK wages have grown more slowly than the rest of the economy.
  • Since 2000, wages rose at half the rate of economic growth; real wages have even fallen recently, due to inflation.
  • The wage share of economic output has dropped from about 60% (1980) to 53% (now).
  • Quote — Lansley:
    “So 7% of the output of the economy has been transferred out of the pockets of wage earners as a group upwards…” ([06:10])

4. Taxation and the Rich ([06:10]–[08:18])

• Income taxes: Who pays what?
  • Top 10% of UK income taxpayers:
    • Earn 35% of total income, pay 56% of income tax.
    • Pay almost 2.5 times as much income tax (proportionally) as the lowest 90%
  • Top 1%:
    • Earn nearly 12.5% of income, pay nearly 27% of income tax—over three times as much, relative to income.
• Host’s caveat: These stats are before tax, reflect only declared income, and most government revenue is not from income tax alone.
• Quote — Harford:
  “Choosing the right statistics…you can give a very different impression of what’s going on.” ([07:45])

5. The Statistics You Choose ([08:18]–[09:46])

• Choosing your story:

  • Quote — Atkinson:
    “There is a school of thought…that says, well, it’s poverty we should really be concerned with, and that what happens at the top is simply irrelevant.” ([08:18])
  • If you want to show inequality at its worst, compare CEO vs. average worker pay; Atkinson notes that’s the data where “the most dramatic change has happened.” ([08:58])

• Median FTSE 100 CEO pay:

  • Increased from 47 times median UK earnings in 2000, to 88 times as recently as the data used.
    Note: CEO pay stats include share options, worker pay typically does not.

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6. Unanswered Questions: Inequality and Opportunity ([09:46]–[10:22])

• Quote — Atkinson:
  “One of the most important things we don’t know is some of the links between inequality and other things we’re very concerned about, for example, inequality of opportunity…” ([09:46])
• The episode notes our knowledge of exactly how top incomes affect opportunities for others is still lacking.

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7. The Playful Side: Communicating Risk and Magic ([10:22]–[27:08])

David Spiegelhalter’s Wipeout ([10:22]–[13:40])

• Regular More or Less guest and risk statistics expert David Spiegelhalter appears on BBC’s Winter Wipeout. He shares thoughts on humor, embarrassment, and taking risks, both academic and physical.
• Quote — Spiegelhalter:
  “It seemed a good idea at the time… I plugged the fact that I thought this embodied a really positive side of risk taking.” ([12:11])
• “When you get there and there’s an ambulance and divers… you’re not sure whether to be reassured or anxious because of it.” ([12:45])

The Mathematics of Magic: Persi Diaconis ([14:40]–[27:08])

• Card trick demonstration:
  • BBC editor/magician Hugh Levinson performs a mathematically-based card trick that inexplicably produces a royal flush from random shuffles.
  • “There was no sleight of hand…the key…is that bit with the pairs of cards where they go face up and face down. Now, I have read about this. I still don’t understand it.” – Levinson ([17:41])
• Enter Prof Persi Diaconis, magician and mathematician:
  • Explains foundational mathematical ideas that drive such tricks—namely, invariants and permutations.
  • Quote — Diaconis:
    “There’s an invariant that stays put.” ([19:44])
• Magic inspiring mathematics:
  • Diaconis ran away from home at 14 to travel with a legendary card magician, became fascinated with probability and combinatorics via magic, and eventually became a Stanford professor.
  • Quote — “I learned that…if you repeat [a perfect shuffle] eight times with a 52 card deck, the cards come back to order.” ([25:54])
• Deep questions in mathematics:
  • Some questions about shuffling decks remain unsolved in modern mathematics and are reminiscent of problems underlying codebreaking and algorithm design.

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8. Memorable Quotes (with Timestamps)

• On the changing 1%:
  “It casts suspicion on the claim that the 1% are this unchanging plutocracy…” — Prof. Donald Boudreaux ([04:10])
• On economic shifts:
  “7% of the output of the economy has been transferred out of the pockets of wage earners as a group upwards to a mix of sort of business and the richest members of society.” — Stuart Lansley ([06:10])
• On CEO pay growth:
  “Median pay of FTSE 100 chief executives has risen to 88 times UK median earnings, up from 47 times as recently as the year 2000.” — Tim Harford ([09:05])
• On mathematical magic:
  “There’s an invariant that stays put.” — Prof. Persi Diaconis ([19:44])

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9. Fun Extras ([27:57]–[30:02])

• Magician’s meatloaf recipe from "Super Subtle Card Miracles," read by Hugh Levinson. Host’s quip:
  “I have a feeling that 1% of our listeners are in ecstasy and the other 99%, including me, have no idea what you’re talking about.” ([30:02])

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Notable Moments & Segment Timestamps

• [01:01] — Listener asks: Who are the 1% and the 99%?
• [01:47] — Prof. Tony Atkinson defines income thresholds and discusses trends.
• [03:20] — UK/US comparisons; focus on top 0.1%.
• [04:10] — Prof. Boudreaux on the volatility of the 1%.
• [05:23] — Stuart Lansley on wage stagnation for the 99%.
• [06:10] — Tax contributions by income groups.
• [08:18] — Atkinson on different ways to present income inequality.
• [09:05] — CEO pay ratios highlight dramatic inequality growth.
• [10:22] — Unknown links between income and opportunity.
• [10:46] — Prof David Spiegelhalter on communicating risk.
• [12:38] — Spiegelhalter on risk and Winter Wipeout.
• [14:40] — Paul Daniels introduces Persi Diaconis.
• [15:11] — Magician's card trick demonstration.
• [18:26] — Diaconis explains the mathematics of the trick.
• [21:01] — Diaconis recounts running away to become a magician.
• [25:54] — Mathematical surprises in shuffling cards.
• [27:57] — Magician’s meatloaf recipe for a quirky ending.

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Tone and Language

• The episode combines Tim Harford's analytical curiosity, light wit, and respect for data with the colorful personalities of his guests.
• Insightful, sometimes playful, and always focused on clarity rather than bombast.

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Summary

For listeners and readers alike, this episode delivers on its promise to clarify, complicate, and sometimes debunk the statistics and stories underpinning the “1% vs 99%” debate. It traverses rigorous economic and statistical data, highlights both the uncertainty and the drama in the numbers, and segues into the surprising overlap between deep mathematics and the art of magic. Engaging experts, memorable stories, and sharp statistical analysis mark “Who are the 1% and the 99%?” as a classic More or Less episode.

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. We're about 50% festive this week as we interview a professor of the statistics of risk about what could be his riskiest venture to date, an outing on prime time television.

[B]

Yes, yes.

[A]

Uh oh. We'll present a special guest appearance from a gifted mathematician, not a household name, but one hugely admired by famous magicians such as this one.

[C]

He's a secret legend. Every profession has them.

[A]

Paul Daniels, who apparently is a loyal, more or less listener. We'll also be dealing with the serious economic and statistical issues of the day.

[D]

My name is Paul Carroll and I have a question.

[E]

We are 99%.

[D]

Would you please explain as precisely as you can, who are the 1% and who are the other 99%?

[A]

From the camp outside St. Paul's Cathedral in London to Zuccotti park in Manhattan and many other spots around the world, Protestors are calling ATT to what they see as the exploitation of the 99% by the 1%. This is presumably something to do with money. And so the first person we called for advice is one of the world's great experts on the subject of measuring income inequality. The economist Professor Sir Tony Atkinson of Nuffield College and the Martin School, both part of Oxford University.

[B]

The first thing we know about the 1% is that they're quite well off, roughly, to be in the top 1% of income in this country, you have to have an income every year of about 120 and thousand. In round terms we've seen in Britain in the last, I suppose, 15, 20 years, a definite improvement in terms of people living at the bottom of the distribution, trying to meet the poverty targets, particularly the child poverty target that the previous government set. But at the same time, we've seen the share of income going to the top 1%. That share has more or less doubled in about 30 years. Their share went from just under 7% in 1980 to around about 15, 16% just before the financial crisis.

[F]

Do you have figures for the United States?

[B]

Yes, the United States went from about 8%, a bit higher than us, but not a lot at the beginning of the sort of Reagan era, to round about 18% in 2008.

[F]

So they too have more than doubled.

[B]

Exactly, yes. It's also doubled, I should say, as far as we know, for example, in China, it's worth Noticing that there and India and other countries were also seeing this rise in top income shares. Of course, when we talk about the top 1% within that group, there's very big differences too. It's a bit like a Russian doll, as it were. If you one of these dolls, you open it up and you discover inside it there's yet more inequality.

[A]

The top 0.1%.

[B]

Indeed, if you get to them, or the top point, not 1%, BNC 0.1%, you have to have a half a million or so rather than 120,000. So I think that as soon as you begin to probe it, you discover inequality is rather deeply ingrained in the relationships between different people's economic positions.

[A]

In the UK, Professor Atkinson says that while the top 1% have 15 times, their proportionate share of the top 0.1% have 60 times. But should we care what the 1% are doing in America, the argument about income inequality is particularly heated. There you have to have $340,000 or 220,000 pounds to get into the top 1%, although that figure is higher in part because it refers to tax units, which may be individuals but can also include couples. Professor Donald Boudreau, an economist at George Mason University in Virginia, takes part in this war of statistics. He says it's wrong to assume that it's the 1% versus the rest. A recent American study shows that the composition of the 1% is always changing.

[D]

Of all the people who are in the top 1% in the U.S. income earning wise in the year 2001, only 44% of those people were still in the top 1% in 2007. That's not a terribly long time, but it does give some at least it's one snapshot picture. It casts suspicion on the claim that the 1% are this unchanging plutocracy who somehow have control over society and can get and keep all the wealth that they want at the expense of the rest of us.

[A]

The claim here is that today's impoverished students of statistical physics are tomorrow's overpaid financial analysts. Today's well paid managers and civil servants are tomorrow's pensioners and living comfortably but modestly. Undoubtedly true. Although whether it changes how we feel about inequality is another question. As a matter of simple arithmetic, most people spend most of their time as part of the 99%. So what's happening there? Stuart Lansley, the author of the Cost of Inequality, tells us that there was a time when economic growth automatically raised most people's living standards. Not anymore.

[G]

Average wages in the UK rose more or less in line with output since the late 1970s, wages have been falling behind. So since the millennium, for example, wages have been rising at roughly half the rate of increase in the size of the economy. And as we know, over the last few years, real wages have actually been falling partly because of the takeoff of inflation. So basically what's been happening is the share of output going to wage earners as a group has been falling. I mean, it stood at around 60% in 1980 and now it stands at more like 53%. So 7% of the output of the economy has been transferred out of the pockets of wage earners as a group upwards to a mix of sort of business and the richest members of society.

[A]

According to the annual survey of Hours and Earnings, the median wage, that's the wage earned by someone right in the middle. The median wage of full time workers is £26,200. Now, one of our listeners, Dave in Colchester, wrote to us via more or lessbc.co.uk to ask if the rich are creating more wealth, as Don Boudreau might put it, or filling their pockets with the output of wage earners as a whole, as Stuart Lansley might put it. In short, if the rich have more money, what sort of tax are they paying? All the figures we've given so far have been before tax. It's not easy to say how much VAT or council tax is paid by different income groups. Nor is it easy to know what to do about people who are rich but don't declare much income because they pay tax in Monaco, for example, or report everything as capital gains. But it's very easy to answer a narrower question, which is how much income tax is paid by people who declare high incomes to HM Revenue and Customs. And here's the the top 10% of UK income taxpayers, not the same as the top 10% of the population. The top 10% of income taxpayers earn 35% of total income and they pay 56% of total income tax. That means that proportionate to their income, the richest 10% are paying almost 2.5 times as much income tax as the poorest 90%. As for the top 1% of income taxpayers, they earn nearly 12.5% of income and pay nearly 27% of income tax. That's over three times as much income tax relative to income as the poorest 90%. Remember though, only about a third of HMRC's revenue comes from income tax. National Insurance, VAT, corporation tax and fuel duty all raise substantial sums. It Must be clear by now that by choosing the right statistics and calculating them in the right way, you can give a very different impression of what's going on. So if you want to present income inequality in a reassuring light, which measure would you use? Professor Sir Tony Atkinson.

[B]

In the United Kingdom, of course, the fact that the government has improved the distribution at the bottom means that if you do focus on, for example, what's happened to the people living below the poverty line, for example, as used by the European Union, then that probably gives a better picture of things have improved somewhat in the United Kingdom in the last 10 or so years. And I think also there is a school of thought which says that in economics at least, that says, well, it's poverty we should really be concerned with, and that what happens at the top is simply irrelevant.

[F]

And if I wanted to make things look as bad as they could, I suppose the wage of the chief executive versus the wage of the worker at the bottom, that's a measure we often get heard that makes things look pretty nasty.

[B]

Yes, and that's where the most dramatic change has happened in the last couple of decades. So if you want to see action, that's the place to look.

[A]

And if you're wondering what the top bosses earn, the Hutton Review of Fair Pay worked out that the median pay of FTSE 100 chief executives has risen to 88 times UK median earnings, up from 47 times as recently as the year 2000. But here's an example of how tricky the statistics are in this area. The calculation of CEO pay takes into account benefits and share options. The median pay for the UK workforce doesn't. So while there are plenty of statistics around, there is a fair amount of information missing. And while the arguments carry on, Professor Atkinson says there are still some fundamental questions to which we don't know the answer.

[B]

One of the most important things we don't know is some of the links between inequality and other things we're very concerned about, for example, inequality of opportunity and how far the kind of differences in incomes which we do observe and we now measure much better than we used to in times in the past, we know much more about that. But what that means in terms, for example, of people's life chances, how much these increased incomes at the top affect the educational possibilities, for example, or the career possibilities of young people. I think that's the kind of thing where we seriously need much more empirical investigation.

[A]

Professor Sir Tony Atkinson, you're listening to More or Less with me, Tim Harford. Our web address is BBC.co.uk more or less. And from one eminent professor to another, David Spiegelhalter, the Winton professor of the Public Understanding of Risk at Cambridge University, has been on the program many times before. Here's a quick recap of some of his brainiest observations.

[H]

If you're going to give people health advice, it would seem to me that you really have to balance the entire consequences of their change of behaviour in terms of all the possible outcomes that might happen. If that number could be just explainable by random variation, then it doesn't suggest anything's wrong at all. If it's a bit larger than that, then obviously it deserves further investigation. The procedure was 99.99% accurate. Well, you know, that means 1 in 10,000 errors this week, David, we like

[A]

to think maybe with a little help from this humble radio program, has managed to make the leap to prime time television. Having conquered the intellectual world, he set himself a new challenge to conquer the the athletic world. Decathlon marathon. No. BBC one's Winter Wipeout. And finally, it's Professor David Spiegelhalter, obe.

[F]

What am I doing here?

[H]

I don't stand a chance.

[B]

Yes, yes.

[D]

Uh.

[E]

Oh,

[F]

all right, Professor Spiegelhoff.

[A]

That was David Spiegelhalter on Winter Wipeout this week. I hadn't previously seen the show myself, but I now realize it's a bit like it's a knockout, but without the high philosophical concepts. After watching it, I had one question for David.

[D]

Why

[H]

it seemed a good idea at the time. It was my daughter's idea that we should both try to get on it. And I've always loved the program. I like slapstick. I've got a rather childish sense of humor and. But also, when I went along for the audition, I really plugged the fact that I thought this embodied a really positive side of risk taking. You know, it's taking a chance. It's going for something full belt with a real possibility of failure and humiliation, but also the possibility you may surprise yourself and everybody else.

[F]

I know everything's padded, but actually there's a quite big fall.

[A]

Was it risky?

[F]

Genuinely risky?

[H]

Yeah, yeah, I think it was. I mean, when you get there and there's an ambulance and divers and things like that, you not sure whether to be reassured, anxious because of it. People do get hurt and people break things. Every series a few people break things.

[F]

Well, certainly caused some entertainment. Did you feel, in retrospect, it served a vital role in the communication of scientific and probabilistic ideas?

[H]

Well, I don't really care. I had a great time. I thought it was a wonderful experience, but people seem to have, you know. Well, the people who talk to me don't seem to have thought too badly about it.

[F]

Well, no, we all respected you for it. And we'll start a petition to get Richard Dawkins to do it next year. Thank you very much, David.

[H]

I think Patrick Moore.

[F]

Patrick Moore, yes. Marcus De Sotoy, Stephen Hawking, Brian Cox, all the greats.

[H]

Brian Cox would have to win.

[F]

Really? Brian Cox be no good at all.

[A]

David Spiegelhalter, a professor able to laugh in the face of risk as well as communicate its finer academic points. The episode of Winter Wipeout is on iplayer until Saturday evening. If you're listening to the Sunday repeat, I'm so sorry you missed it, but David may well be relieved. As a special Christmas treat, we're honored to have a guest appearance from a top professor of maths and statistics.

[F]

If that sounds more like a sack

[A]

of coal than a Christmas gift, don't just take it from me, but from this loyal listener.

[C]

Hello, I'm Paul Daniels and I'm introducing you now to a gentleman you've probably never heard of. But amongst magicians who deeply in the know, Percy Diaconis is one of the legends of magic. He appeared on the scene out of nowhere as a very young man and baffled us all. And he was baffling us all using mathematical principles applied to card magic, entertainment. The guy is a genius. Hope you enjoy what he says.

[A]

Percy Diaconis is by all accounts a brilliant mathematician and a brilliant magician. Before we speak to the great man himself, he's locked in his ivory tower. In Stanford University in California, I've booked another special treat. Someone who can demonstrate one of Percy's tricks right in front of my eyes. BBC editors these days always have several strings to their bow. The editor of More Or Less is also the editor of Moneybox, while the editor of Crossing Continents, Hugh Levinson, doubles as the BBC's in house magician.

[E]

Now, you've seen these cards. They're completely normal cards. And I promise that what I'm going to do doesn't involve sleight of hand. You'll watch everything. I'd like you to take off. I'd know about a third of the deck, something like that.

[F]

Okay, so I've got 20 or so cards in my hand.

[E]

Now what we're going to do is we're going to mix them in six different ways, okay? And what I'd like to do is do what we normally do, which is

[F]

a shuffle overhand so just the regular shuffle, incredibly competent. Okay.

[E]

So any normal card player would do. That's our first type of person.

[F]

Okay.

[G]

Right.

[F]

So I've done that.

[C]

Right.

[E]

Okay. The second kind of person is a magician, in this case, a card magician. And what I'm doing is I'm going through the cards and some of them I'm turning face down, and some of them I'm.

[A]

You're looking at.

[E]

And we need an even number of cards. I'm just going to add another one on there. Okay. So that's how a magician might do something face up and face down. The third group of people are mathematicians, and mathematicians love binary. So we're going to work with pairs of cards. Now, here's a pair of cards. You could have them this way up or the other way up. I'm going to put them on the table the way they are or the other way up. It's up to you, Tim.

[F]

Okay, So I can see an 8 of spades face up, and there's another card face down. Flip them the other way around.

[E]

You did what you like. Now, the fourth type of person is a croupier in a casino, and that's going to be you.

[F]

Right?

[E]

And I'd like you to deal the cards into two piles alternately.

[F]

So just left, right, left, right, left, right, left, right, left, right, left. So we're giving these cards a very thorough shuffle. Some of them are face up, some of them are face down. Okay, now two piles in front of us. Right.

[E]

Fifth type of person. Fortune teller. Fortune telling is all about choice. I want you to choose either pile. Whichever pile you choose, I want you to pick up, turn over and put on the other pile, your choice.

[F]

Okay? So I'm going to pick up the left hand pile, turn it over and place it on top of the right hand pile.

[E]

Okay? That's the five types of people. The sixth type is you.

[F]

Right?

[E]

And I can see by the way you've handled these cards that actually you're a card cheat, a poker player, I'd say, because when we spread the cards out, some are face up, some are face down, as you'd expect with this kind of trick. But if we look at the five cards that are face up, those five cards after all this shuffling, are the

[F]

Jack, Queen, Ace, 10 and King of spades. So all the royal spades, and that's

[E]

the royal flushing spades, the highest possible hand in poker.

[F]

That is completely extraordinary. That's amazing. Are you gonna tell me how you did that?

[E]

What I can tell you is there was no Sleight of hand. And the key bit, the really interesting bit, is that bit with the pairs of cards where they go face up and face down. Now, I have read about this. I still don't understand it. It baffles me that it works, but somehow it works. And that's the honest truth.

[F]

What we really need is somebody who is both a professional mathematician and a professional magician. And by the magic of radio, we have such a person, Professor Percy Diaconis, who joins us from Stanford University. Professor Diaconis, my magician friends tell me you're something of a legend in magic.

[E]

And should I just say, we are not worthy?

[A]

Okay, we are not worthy.

[F]

And also a Stanford professor, which, of course, impresses nerds like me. Percy, do you know how this trick works?

[I]

Well, yes, I do. It's a trick that I've studied and developed. In fact, hidden behind it is some rather elegant mathematics. It's not so hard, and I'd like to have a go at trying to explain at least the least little bit, one of the mathematical thoughts that drives it. If you have four cards there, or if people who are listening at home can find four playing cards.

[F]

I have four playing cards now.

[I]

Okay. I'd like you to turn them in the following way. They should all be face down.

[F]

Yep.

[I]

And now if you can, turn over every other card. So the top cards face up.

[F]

Yep.

[I]

The second card, face down.

[F]

Yep.

[I]

Third card, face up. Fourth card, face down.

[F]

Okay.

[I]

And now hold them in your hand as if you were gonna deal or something like that.

[F]

Yep.

[I]

If you cut one card from top to bottom.

[F]

Yep.

[I]

How are they?

[F]

Okay, they're face down. Face up, face down, face up.

[I]

Right. And you could keep doing that. That is, you could cut any number of cards from top to bottom. Two or three. One. And they would be alternating. They would either be down, up, down, up, or up, down, up, down. So you could cut them as many times as you want, and that invariant would stay put.

[F]

Yes.

[I]

Yeah. Okay. That's. That's our first idea, that there's an invariant that stays put.

[F]

When I think back to what Hugh did to me, I sort of recognize, as you explain it like that. I'm thinking, well, he did, at one stage, just go through the deck, looking at the deck, and he flipped some cards over. So presumably at that point, he was able to set up his royal flush in a way that was not at all transparent to me, and then give me multiple opportunities to do what appeared to be a full shuffle, but, in fact, wasn't really making any difference to the fact that Hugh had put this royal flush in there. Have I got it?

[I]

If you were being graded on that answer, you'd get an A.

[A]

In my class, listening to you talk

[F]

about your interest in magic and your interest in mathematics, I think listeners who don't know your story will be imagining this nerdy kid, probably very good at maths at school, maybe a little sideline in card tricks, and then goes on to university and college and then eventually becomes a maths professor and does maths tricks on the side. But actually your road to becoming a mathematics professor and becoming a professional magician was a little bit more chaotic than that.

[I]

That's certainly true. I grew up in New York City and the kids, kids in New York City used to congregate at a local magic shop on Saturday afternoons. And I met the greatest exponent of purest sleight of hand of the 20th century, Dave Vernon, his name is. And one day he called me up and said, you know, I'm going to Delaware tomorrow, do you want to come? Going to a magic convention. And I didn't think twice. I packed a bag and how old were you? Went off. 14.

[F]

You ran away from home with a card shark?

[I]

Ran away from home and, and never went back. That is, we began traveling about and it was a wonderful, very supportive, protective world of inner circle magic. And Vernon was a legend and we would go from city to city and wealthy amateurs would put us up and he would have me demonstrate things and teach me tricks. And I literally never went back. I saw my parents about 17 years later and 17 years after that, so that was unusual. And now I, of course have kids of my own. If one of them disappeared, you know, I would go crazy. But somehow the police had other things to do than search for 14 year old runaway magicians. And I was left alone to traipse about and got interested in mathematics through magic in the following way. I heard a lot of talk about probability and got very interested and seemed to have a little bit of a gift for thinking about, oh, you know, suppose you roll a pair of dice, is it more likely that you get two sevens or a six or an eight? Asked a friend, is there someplace to read about this? And he pointed me to a book by William Feller, An Introduction to Probability and its Applications. And I bought a copy when I was 16 and I couldn't read it because I didn't know calculus, but I could turn the pages and I could see it was just fascinating.

[F]

You ended up at Stanford University as a professor. So presumably at some stage you took a class.

[I]

It's true. When I was 24, I enrolled at Knight in City College in New York's big free school. And I got fascinated by mathematics and the City College math department. My teachers refused to write letters to Harvard because they said, nobody from City College has ever gotten into the Harvard math department. So I applied to the statistics department instead. I didn't actually know what statistics was about. And I got Martin Gardner, who was a magic friend, to write a letter. And he wrote a letter saying, of the 10 best card tricks invented in the last 10 years, this kid invented two of them. Maybe you should give him a chance. And so they let me in, and I liked it, and they liked me.

[F]

I hate to bring it down to such a pragmatic level, but are there practical applications outside magical effects of the sorts of mathematics that you work on?

[I]

The mathematics behind card tricks is a part of mathematics called combinatorics. And it's an absolute mainstay of the way the computer works. People who design algorithms, who try to break codes, turn over those ideas and try to exploit them. The fact that the card trick we did for you, you saw, you heard, has an invariant in it, shows that not all permutations can occur. Well, those kinds of flaws are what helped Alan Turing crack the German Enigma code during the Second World War. The fact that the gadgets that were being used to randomize weren't doing an effective job allowed people to search and crack codes. And having a mind and experience that allows you to think about mixing processes as mathematics, but also translate them into the language of cards is crucial in that way.

[A]

I'm intrigued.

[F]

In your work, do you find the magical effects inspiring serious mathematical research, or is it the serious mathematical research that is inspiring the magical effects, or both?

[I]

It does go back and forth. I began as a magician and my introduction to any mathematical ideas when I was a kid, 12, 13, 14, we're through magic tricks. For example. One of the things I learned as a youth is that you can cut a deck of cards in half perfectly and shuffle them, dropping them 1, 1, 1, 1, 1,. So that every other card drops. And it's what would be called a perfect shuffle. And as kids are wont to do, if you practice enough, you can actually learn to do it. Then you can ask, well, what happens since it's perfect, there's no randomness to it at all. One of the things you find is that if you repeat that eight times with a 52 card deck, the cards come back to order.

[F]

He was just trying to demonstrate this. As you describe it you do eight perfect shuffles and you're back where you started.

[I]

It's right and it's quite astounding. And now if you try to think, well, suppose instead of shuffling a 52 card deck, I shuffle a 54 card deck. How many shuffles does it take to recycle? The answer changes a lot. It takes 52 shuffles to recycle a 54 card deck. And I'm afraid I learned that the long way by actually sitting there and doing it until they came back. Well, if you ask, suppose I had a deck of general size 2 end cards. How many times do you have to shuffle it to have it recycle? That question is beyond current mathematical understanding. That is we don't know. There's no formula, there's no simple rule for predicting how many times do you have to shuffle a deck until it comes back for general decks on the deepest mathematical assumptions, the Generalized Riemann hypothesis, we can say some things, but they're beyond proof. And I find it wonderful that there are things that a 13 year old kid could think about that touch mathematics in a very deep way and are beyond modern mathematics to understand.

[A]

Professor Percy Diaconis, among other things, the author of Magical the Mathematical Ideas that Animate Great Magic Tricks. And if you need a break from the turkey and mince pies this Christmas, you can see a stylish video of Hugh Levinson demonstrating that magical trick on the more or less BBC.co.uk more or less. And that's all we have time for this week. Please keep your emails coming in. Next week is the More or Less Year in Numbers. Until then, goodbye. More or Less was presented by me, Tim Harford of the Financial Times. The producer was Ruth Alexander, 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.

[E]

Tim, can I just add one thing because I know you've been having these recipes at the end of your podcasts and I've got a magician's recipe which I can give you.

[F]

All right. I can't resist it. Come on then.

[E]

Okay. This is from Frank Garcia's Super Subtle Card Miracles, which is the follow up to Million Dollar Card Secrets.

[F]

This is a ring bound. This looks like it's had a lot of love over the years.

[E]

Published in 1973. Okay. And what he says about the recipe and Million Dollar Card Secrets, that somebody refused to buy it because he didn't like chicken. But anyway, this recipe is for Super Meatloaf to serve four and it's got lots of jokes from magicians in but so I'll give it to you loaf 1 pound ground beef 2 eggs, beaten 2 tablespoons soy sauce 1 small bunch of scallions, trimmed and kitchen sliced 2 ounce jar of sliced pimientos 1 cup bread crumbs filling 4 thin slices boiled ham Half a cup minced Munster cheese, very American half a cup minced scallions one large onion, sliced thin Half a cup of water Ketchup Parsley flakes Combine the first six ingredients and mix thoroughly. Place the mixture on wax paper and flatten to form a large rectangle approximately 3/4 of an inch thick. Place overlapping slices of ham on meat. Do not riffle. Shuffle. Sprinkle minced cheese and minced scallions on the ham. Fold ham slices over the filling. Using the wax paper as a guide. Fold meat over the filling. Make sure that the ends and seams are sealed. Line a 7 times 12 times 2 inch baking dish with thinly sliced onion. Try not to make the dish too ornate or you'll arouse suspicion of misdirection. Pour 1/2 cup of water over the onion. Place the meat on this layer. Ice the top and the sides of the loaf with ketchup as you would a cake. Sprinkle with parsley flakes and bake at 325Fahrenheit for 1 hour and 15 minutes. Remove from the oven and let the loaf rest for five minutes before slicing. And it says at the end, Sal Fucci likes it served with spaghetti and butter sauce. Eddie Tullock doesn't care how it's made, since it's the end product that really counts. And George Schindler said, who's the editor of the book, I'd rather eat it than rewrite it.

[F]

I have a feeling that 1% of our listeners are in ecstasy and the other 99%, including me, have no idea what you're talking about. Thank you very much, Hugh.