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Showing posts with label trick. Show all posts
Showing posts with label trick. Show all posts

Wednesday 7 October 2015

Why life is just one big confidence trick

Matthew Stadlen in The Telegraph


It was supposed to be an event targeted at young people and I’m not that young any more; it was meant to be a campaign designed to build confidence and I don’t see myself as the timid type; and anyway, I was there to interview World and Olympic Champion Jessica Ennis-Hill, not for an education in self-help. Yet I left Sky Studios the other day profoundly influenced by a single sentence.

Find something you love and then stick to it.

These words emerged from the mouth of Melvyn Bragg, the enduring broadcaster who has reached the very top of his profession. They amounted to Lord Bragg’s recipe for confidence. He was speaking on a panel put together by Sky Academy, a bursary scheme that supports emerging talent in the worlds of sport and the arts. His advice immediately lodged somewhere deep inside me, partly perhaps because Bragg is a luminary in my own field, partly perhaps because I’ve enjoyed meeting and interviewing him in the past. Its real impact, though, stems from its essential truth. If you love something, you’re more likely to be confident at it and therefore to succeed.

Despite my self-assurance, bred in me by my privileged schooling, my parents and a childhood environment in which I was surrounded by successful role-models, I do sometimes doubt my career trajectory. The life of the self-employed can provoke uncomfortable journeys into dark corners of the mind where confidence seems a distant relative. But Bragg reminded me that I do love what I do and that there is a very strong argument for sticking at it. There are echoes of a line from Paulo Coelho’s The Alchemist in Bragg’s philosophy: “Remember that wherever your heart is, there you will find your treasure.”

Of course, Bragg’s winning cocktail must include a decent dose of natural ability if it’s to translate into success. Simply loving something isn’t enough, you have to have some talent or aptitude too. It's a maxim that England’s rugby players must now know only too well. They no doubt love what they do (much of the time) and they are talented; but not talented enough, it turns out.

There were plenty of confident noises emanating from in and around the England camp last week ahead of the do-or-die match against Australia. Ben Morgan, one of the 18-stone forwards, threatened to expose the Wallabies’ infamous insecurities in the scrum; Danny Cipriani, the talented back excluded from England’s tournament squad, claimed that not a single Australian would get into the England team. In the event, England crashed out of their own World Cup, the English pack was humiliated in retreat and it was hard to see how more than one or two Englishmen would make it into the Australian team.

Stuart Lancaster's England appeared to suffer a crisis of confidence during their World Cup games Photo: REUTERS

So much for English confidence. But then again, maybe they were faking it. I was in the stands to watch their disintegration, part physical, part mental, in the final excruciating minutes against Wales the week before. Could every England player really have been that sure of themselves after such a bruising defeat, facing an Australian team fresh from winning the southern hemisphere’s coveted Rugby Championship? Perhaps. Or maybe self-doubt had crept in but they decided to subscribe to the Davina McCall blueprint for confidence.

The former Big Brother host, was, together with Ennis-Hill, Mumsnet founder Justine Roberts and YouTube personality Alfie Deyes, on the same panel as Bragg. McCall is not an obvious candidate for self-doubt, but speaking with impressive candidness, she talked about her own teenage issues with a chronic lack of confidence. Her remedy was to act as if she really were confident. Fake it, she advised. If you’re not confident, teach yourself to project confidence instead and eventually you might end up believing it.


Fake it to make it: Davina McCall admits to suffering from low confidence as a teenager Photo: Andrew Crowley

Mahatma Gandhi seemed to be saying something similar when he reflected, “Man often becomes what he believes himself to be. If I keep on saying to myself that I cannot do a certain thing, it is possible that I may end by really becoming incapable of doing it. On the contrary, if I have the belief that I can do it, I shall surely acquire the capacity to do it even if I may not have it at the beginning.”

Roger Uttley, a former England rugby coach, offered advice to the incumbent, Stuart Lancaster, via an interview with The Telegraph between the Wales and Australia games. “You have got to get over things quickly,” he said. “Stuart has to look the part in terms of his body language. It is tough to do that but important. Players feed off it.” Lancaster did put on a brave face, but he had already admitted to being “absolutely devastated” following the loss to Wales. Hardly the sort of message to be sending down from on high. The scoreline worsened against Australia and this time Lancaster was “absolutely gutted.”

Just how critical confidence is in sport had already been spelt out in an ITV interview given by Warren Gatland ahead of his side’s thrilling victory over the English. England have more money, more fans, more players – yet still Wales won. “When are you at your best?” Gatland was asked. “When I'm under a bit of pressure. It's always been my biggest challenge often with the Welsh players to keep building on that confidence and that self-belief that they are good enough to compete with the best teams in the world and they're good enough to go out there and win.”

Gatland was then asked what was the one quality he had as a player that has never left him. “Self-belief,” came the reply. Together with greater skill and fitness, what Wales demonstrated in those final frantic minutes was a core belief that they could still win a game that seemed lost at half-time. The players aped the confidence of their coach.


In the eye of the storm: Wales coach Warren Gatland Photo: AFP

During the recent Ashes summer, Sky Sports ran a series of programmes profiling some of cricket’s greatest stars of the past. Listening to Glenn McGrath speak about his record-breaking career, it was immediately obvious how pivotal self-belief was to his success. Just like the Welsh rugby team, confidence was welded onto ability, in his case onto his metronomic accuracy with the ball.

“The biggest battle I ever had when I was bowling out in the middle was with myself,’ he said. “And if I won that battle the rest was pretty easy. It's about having a bit of mongrel in you. You've got to be aggressive.” His two main strengths, he said, were that accuracy and a little bit of bounce. Then he added: “And just self-belief.” Interviewed for the same profile, McGrath’s former new ball partner, Jason Gillespie, reflected: “I don't think anyone came close to believing in their own ability as much as Glenn McGrath.”

Confidence is essential in politics too. It’s something that David Cameron projects so effectively that it is rarely, if ever, questioned in profiles of the Prime Minister. Despite his pledge to end “Punch and Judy politics" when he became leader, he has often been forthright and confrontational at the despatch box and exudes an air of watertight self-confidence that borders on a sense of entitlement. To what extent this is contrived, we don’t know, but much of it may have its roots in an elite public school education at Eton.

Wherever Cameron’s confidence comes from, it now stands in stark contrast to the hesitancy of Jeremy Corbyn. Maybe the Labour leader’s indecisiveness in interviews can be spun as the supreme confidence of a man with a mandate from his party’s grass roots not to play by the long established rules of Westminster politics. Up goes the cry: 'It’s the new politics!' But, if he continues to dither, he will continue to be cast by others as un-Prime Ministerial and as an uncertain figurehead.

Margaret Thatcher came across as even more self-assured than Cameron (and she was a state-educated grocer’s daughter). No one could claim that confidence is a male preserve. But it is, perhaps, worth asking whether gender sometimes plays a role. If you haven’t heard of impostor syndrome, it’s a phenomenon thought to be particularly prevalent among high-achieving women. It is, essentially, a conviction that success, however merited, is actually undeserved.

There is also that feeling of guilt so common, we’re told, among new mothers. In my interview with Ennis-Hill, she explained how anxious she’d been ahead of this summer’s World Championships in Beijing. When training wasn’t going so well, she imagined how she’d feel if she didn’t perform as she hoped. “I would have been away from my son for two weeks and I would have been absolutely devastated because I would be so mad with myself for being away. As a mum as well you feel guilty about everything, so it’s definitely the hardest thing I’ve ever, ever done,” she told me. How many men would have questioned themselves in this way?

Ennis-Hill spoke openly about one of the more challenging consequences of childbirth. “Your confidence does [take a] knock,” she said. “I was thinking, 'Oh gosh, I’ve got to train now as well and fit all this in. You’re up through the night and that has an impact on how you feel about everything and whether you can do it, and your self-belief. Everything’s a million times worse when you’re tired.” In a changing world, men also travel emotional postnatal journeys and undoubtedly suffer from sleep deprivation too. But they certainly aren’t forced to battle through changes to body shape.

And then there’s the question of why there are so many more prominent male comedians. Earlier this year, I asked Jason Manford for his explanation in an interview for the Radio Times. “Audiences on a Friday, Saturday night are a bit rowdy and I always think stand-up is a bit like flirting,” he said. “So when a bloke comes out and he does his thing, he’s making people laugh, this is what you do when you’re flirting one on one.

“So it’s harder for females sometimes to come on and be on the forefront because that’s not what we’re used to in our societal rules. It’s a bloke who’s on the forefront and generally the woman’s passive. For a female to be aggressive is not what we’re used to. So I think female comics generally have to work harder because of an audience’s preconceptions.”

Handling rejection, Manford believed, is another factor. “Blokes are more used to rejection. Generally it’s a bloke who asks a girl out. I’m stereotyping but that’s what we do. And I’ve noticed it on the circuit. A girl will come off stage, she’s had a bad gig, and she’ll go, ‘I must have said something wrong.’

“A guy will come offstage and he’ll go, ‘Maybe the sound was off’ or, ‘It was definitely the audience’. He’ll find an external reason for his failure."

Whether or not there’s something in Manford’s analysis, we still live in a society where – last time I checked anyway – the onus is more frequently on the man to chat up a woman. That involves confidence. Peacocking isn’t a ritual confined to the animal kingdom.

There’s no doubt that confidence is an attractive quality in both men and women. It can transform appearances and draw in admirers who would otherwise walk on by. It can also be, as we’ve seen, a pivotal ingredient in successful careers. But overconfidence not only becomes unappealing, it can mutate into arrogance, pride and, ultimately, a fall.

The ancient Greeks knew about nemesis following hubris thousands of years ago and I’ve always thought Piers Morgan’s Twitter profile is brilliantly clever. He is one of the most confident men on social media, but he’s carved an indemnity clause into his online presence with a simple, biographical bon mot: “One day you’re the cock of the walk, the next a feather duster.”

Monday 11 May 2015

Natural leaders are made in retrospect

Ed Smith in Cricinfo

There is no template for the perfect captain. Some of the game's greatest were not identified as such straightaway


It took five years of not winning and patience before success came for Mike Brearley (centre) and Middlesex in 1976 © Getty Images



So England finished a tour of the West Indies with some widespread areas of consensus. The results were disappointing, the immediate future is dodgy, opportunities were missed and the captain - according to many of the loudest voices - is not a natural leader.

The tour, of course, happened in 2008-09. England lost 1-0. But Andrew Strauss, after that tricky start, became one of the most successful England captains of modern times. Now England are turning to Strauss again, this time as director of cricket, because his leadership credentials are, of course, axiomatic. How quickly people forget views they once vehemently held. Memory is not quite the same thing as intelligence, or even judgement, but it is a good first step on the road towards greater scepticism.

The problem with analysing leadership, especially captaincy, is that people forget how rare it is for successful leaders to stand out as "natural leaders" from the very beginning of their tenure. In fact, the idea of "natural" leadership is usually a retrospective trick - or narrative fallacy - used to make sense of events that, at the time, felt far more contingent and unpredictable.

The most iconic example of great captaincy is also the most misused: Mike Brearley. Perception: Brearley could wander into any team, move gully a bit deeper, and, hey presto, you win by an innings. Reality: by the time Brearley did his Ashes conjuring trick in 1981, he had indeed established a reputation for tactical and managerial brilliance. Crucially, however, that reputation was hard-earned over many years at the coalface. Even more pertinently, Brearley's captaincy could easily have been cut short before anyone noticed how good he was.

Brearley took over as captain of Middlesex in 1971. The seasons of 1971, 1972, 1973, 1974 and 1975 slipped by without Middlesex winning the championship. Brearley has privately told me that in those early seasons he often found the job very difficult. Did he have enough support? Results improved, but not always evenly. In that six-year period, Brearley's gift for patience was tested. So was the constancy of Middlesex. As I write this, only one of the 18 captains of England's first-class counties has been leader for six uninterrupted seasons. Clearly there aren't dozens of Brearleys out there, if only clubs would persevere with them. But if Middlesex had been less patient - or, put differently, less anxious to jump at the first convenience - then England could have been deprived of a superb leader.

Which leads to the second problem with analysing captains. Pundits tend to have a fairly fixed idea of what a natural leader looks like, and then judge the incumbent against their own personal template.

To the alpha-male mindset, the captain should be the leader of the pack, the macho hero. To the Machiavellian world view, a captain should be streetwise and opportunistic. To the progressive, leadership relies on novelty and innovation. To the nostalgic, quite the reverse - the answers always reside in the past. To the laissez-faire, he must be relaxed. To the hard man, a captain must rule with fear.

All valid, none essential. There is no one such thing as the ultimate template for a good captain. All good leaders are different. Indeed, a preparedness to be different - rather than copying someone else - is perhaps the only prerequisite for being any good.

In terms of value added, few managers can match Billy Beane of the Oakland Athletics baseball team. His decisions and the wins that followed have earned Oakland hundreds of millions of dollars (as this article on FiveThirtyEight demonstrates). Despite an emotional temperament, Beane has tried to remove the cult of personality from his decision-making. This is leadership by methodology - thinking, or more accurately calculating, your way to victory.

At the other end of the spectrum stands Sir Alex Ferguson. Anyone who has read Ferguson's autobiography knows that the idea of "copying" Ferguson is inconceivable. His management was founded on the controlling and coercive nature of his personality. Some players seethe with violence. Very occasionally, that survives the transition into management. No leader achieves greatness by punching people. Some, however, clearly benefit from the impression that it would be a grave error for anyone to entirely rule out the possibility of the direct approach. Ferguson ran a pub before becoming a manager. "Sometimes I would come home with a split head or black eye. That was pub life. When fights broke out, it was necessary to jump in to restore order."

Now imagine hearing Pep Guardiola, Roberto Martinez or Arsene Wenger saying that. Inconceivable. Yet all are fine managers.



Despite England's poor finish in the West Indies, there has been no outward sign that Alastair Cook is wilting © Getty Images


Which leads us back to Alastair Cook. It is clear that Cook does not fit some preconceptions of cricketing leadership. He is not restless and ingenious, as Michael Vaughan was. He does not cast a magnetic and charismatic presence over the whole arena, as MS Dhoni does. And yet there have been fine captains who possessed neither of those assets.

Last week, after discussing captaincy in the commentary box, the brilliant statistician Andrew Samson passed me two pieces of paper about the records of two captains, each after 31 Tests in charge. The first read:

Runs: 2478
Average: 45.88
Hundreds: 8
Wins: 13
Losses: 9
Draws: 9

The second read:

Runs: 2792
Average: 60.69
Hundreds: 10
Wins: 6
Losses: 9
Draws: 15
Tied: 1

The first is Cook, the second Allan Border, the man who turned around Australian cricket in the 1980s. (Although, of course, the nature of the opposition should always be taken into account with comparative stats.)

Border had also faced criticism about his manner and tactics. But eventually his resilience and run-scoring provided such an inspiring example that his team fell in step
. The two men, so different on the surface - Border was known as Captain Grumpy, where Cook is courteous and self-deprecating - share an epic capacity for endurance. Border outlasted many bowling attacks and, eventually, his critics.

The case against Cook tends to rest on the conviction that he is about to crack, that he can't take much more. This theory is conveniently self-perpetuating because it encourages his detractors to press on with their endeavours. They look eagerly for signs that the strain is becoming too great. This type of thinking contributed to his sacking as ODI captain ridiculously close to the World Cup.

Yet in the West Indies - a patchy tour for England with some poor selection errors - there was no outward sign at all that Cook was wilting. Quite the reverse. His hundred in the third Test was almost faultless.

Many bowling attacks have pinned their hopes on Cook cracking, only to find the wait inconveniently lengthy. I wonder if the detractors of Cook's captaincy will experience a similar story.

Wednesday 4 December 2013

'Do you love your country?' is a trick question

Alan Rusbridger was asked by the home affairs select commitee if he loved his country, but national pride is a slippery concept
The Union Jack
'Nationalism depends on a kind of exceptionalism.' Photograph: Murad Sezer/Reuters
Do you love your country? When Keith Vaz, the MP who chairs the home affairs committee put the question to the Guardian's editor-in-chief, Alan Rusbridger, midway through yesterday's evidence session on the NSA leaks, it was, almost certainly, meant helpfully. It was that lawyerly thing of getting out into the open the answer to the opposition's charge (the rather hefty one of treason) before the opposition had a chance to put it themselves. Cue unqualified affirmation!
But do you love your country? Well do you? Quite right, it's a trick question. The answer's not what you say, or even the way that you say it. The answer is in the pause between the end of the question and the start of the answer. If you need to stop and think about it, then you might just as well say no. You almost certainly don't love your country in the way that the person who asked the question meant.
All the same, it's a question that needs answering. Because the more nebulous the idea of country becomes – the more multi-layered national identity and the less certain national boundaries – the more important it is to understand how you identify yourself, if only to see off the people who want the answer to be an unqualified yes, delivered with all the plausibility of a besotted suitor. Just see the Mail's attack on Ed Miliband's father to see how potent it can be. The question can't be avoided, so it has to be reframed.
People have been making communities probably at least since they discovered two people could hunt down a bison better than one. That's what got us where we are. But all sorts of things happen once you begin creating communities. For a start, it has some implication of exclusion. Probably early hunting tribes weren't all that kind to people who were a bit rubbish with a bow and arrow. Recognising people we think are like us is not just about self-definition, it's about self-protection.
In time, an evolutionary convenience developed, the way these things do, into a handy way of keeping people in line. That's why Samuel Johnson declared patriotism the last refuge of the scoundrel (leaving Boswell to explain that he meant the kind of patriotism that was really a mask for self-interest). But Johnson had already spotted its capacity to be a lethal political idea. Sure enough it became the deadly force that moulded 19th and 20th-century Europe into warring factions, the glue to empire and a straitjacket for the social order. Feel free to add in your own particular grudge. Patriotism has a long history as the weapon of the establishment against the challenger.
But it has also, from time to time, been a way of defending what matters against an establishment with other ideas. When John of Gaunt first defined England as a sceptred isle, he was despairing of Richard II who was going to leave it "bound in with shame". Alex Salmond is running the referendum campaign on similar lines. He's framing it in the context of how the union is stopping Scotland being the country that destiny intended. He's suggesting it's impossible to be truly Scottish if you also think of yourself as British.
For nationalism depends on a kind of exceptionalism. National pride means imagining that your country has something unique and irreplaceable about it. It becomes all too easily an intolerant concept. I love my country, in so far as I love inanimate objects at all. But I love my country, and quite likely it's different from yours.

-------

Patriotism is not the same as spineless adoration of the Establishment


Owen Jones in The Independent

I would want to honour courageous, often faceless Brits who stood up to power



“Do you love your country?” The smirking phantom of the pinko-hunting Senator Joe McCarthy hovered over Labour’s Keith Vaz as he uttered those words. Who knows if they were intended to menace or support the Guardian editor Alan Rusbridger, who was being interrogated by the home affairs committee over the Edward Snowden leaks. But the phrase is creepy nonetheless, not least in the febrile atmosphere over the National Security Agency revelations. Newspapers that have wailed over Leveson as a mortal threat to press freedom have indulged Government threats over the leaks. There is talk of journalists being locked away: and indeed, if the state begins prosecuting those who hold power to account, Britons interested in protecting our freedoms must surely take to the streets.
But patriotism is often subverted and manipulated by those with wealth and power. Loving your country means being subservient to the Establishment, or so goes their logic. Make the ruling class and the country interchangeable concepts, then those challenging the powerful can simply be swept aside as near-treasonous fifth columnists. To engage in a debate with those who question the ruling elite means legitimising their criticisms, treating them as reasonable criticisms, however wrong they may be. Far easier to discredit them instead, as those who despise the nation and whose motives are to do it harm.
The “Do you love your country” card is probably most notoriously used at times of war. It is patriotic to send young men and women to foreign countries to be slaughtered and maimed, but it is unpatriotic to bring them home to safety. It is used to strip civil liberties away, too, in the name of national security. Stripping away freedoms that our ancestors fought for becomes patriotic; defending our hard-won liberties becomes unpatriotic. It is used to oppress minorities. The rights of gay Britons becomes an insult to British “family values”. Immigrants may have helped build this country, but they are posed as a threat to national identity.
Questioning patriotism is a long-standing technique to crush dissent, not least from the left. Margaret Thatcher smeared the miners and their allies as “the enemy within” who, she claimed, were more of a threat than “the enemy without”. The Daily Mail recently, and infamously, smeared the socialist Ralph Miliband as “the man who hated Britain”. The absurdity of a newspaper that backed Hitler’s genocidal regime smearing a Jewish immigrant who fought the Nazis has been widely ridiculed. But actually the entire episode underlined how the very concept of patriotism is like a Rorschach inkblot test, where we all look at “the nation” and see what we want to see: we love aspects, and dislike, or even loathe, other features of it.
When defending the Mail’s smear that Miliband despised his country, the paper’s deputy editor reeled off a list of “great British institutions” that the left-wing academic had criticised: the likes of the Royal Family, the Church, the military and “our great newspapers” (don’t all choke at once). But of course, it is possible to reel off “great British institutions” that those on the right froth about: like the NHS (once described by the Tory Nigel Lawson as “the closest the English have to a religion”), the BBC, the public sector, and trade unions (once championed by Winston Churchill as “pillars of our British Society”).
Our history inspires pride and regret in different people, too. Some might champion monarchs and governments of centuries gone by, where I would want to honour courageous, often faceless Brits who stood up to power and injustice: like the Chartists, the suffragettes or anti-racist activists who were ridiculed, attacked and persecuted in their time. Some may relish the traditions of Empire, out of jingoism or ignorance or a combination of both, while I would regard it as a shameful and murderous stain on our nation’s past.
I love living in London partly because of its diversity, a feature of modern British life that others despise. Some prefer the tranquility of the open English countryside; others find it dull and claustrophobic, opting for the chaotic excitement of urban life instead. There are those of us who spend Sundays in Church, while others regard all incarnations of religion as a toxic blight on humanity. Some, like myself, hold that free-market capitalism is the engine of a profoundly unjust distribution of wealth and power; others devoutly believe that it is the catalyst for growth, prosperity and progress.
Not a single living Brit can honestly claim to love everything about something as complex and contradictory as Britain. But whatever Britain is, it certainly is not synonymous with those who rule it. And those who attempt to hold power to account as somehow un-British need to be faced down. We owe it our British ancestors who, in the teeth of opposition of other privileged and often tyrannical Brits, built this democracy, at such cost and with such sacrifice.

Sunday 11 December 2011

Pick a Card, Any Card

The standard way to mix a deck of playing cards—the one used everywhere from casinos to rec rooms—is what is known as a riffle (or "dovetail") shuffle. You begin by splitting the deck into two roughly equal stacks. Then you flick the cards with your thumbs off the bottoms of the piles in alternating fashion, interleaving the two stacks.

For games like blackjack or poker to be truly fair, the order of the cards must be completely random when the game begins. Otherwise a skilled cheat can exploit the lack of randomness to gain an advantage over other players.

How many riffle shuffles does it take to adequately mix a deck of 52 playing cards?
MAGIC7
Francesco Abrignani/Alamy
As it turns out, you have to shuffle seven times before a deck becomes truly scrambled. Not only that, the cards become mixed in a highly unusual way: The amount of randomness in the deck does not increase smoothly. The first few shuffles do little to disturb the original order, and even after six shuffles, you can still pick out distinctly non-random patches.

But right around the seventh shuffle something remarkable happens. Shuffling hits its tipping point, and the cards rapidly decay into chaos.

Magical Mathematics

By Persi Diaconis and Ron Graham
Princeton, 244 pages, $29.95

The seven-shuffles finding applies to messy, imperfect riffle shuffles. The deck might not be divided exactly in half, for instance, or the cards might be riffled together in a haphazard way. Far from undesirable, a little sloppiness is actually the key to a random shuffle.

A perfect (or "faro") shuffle, meanwhile, wherein the deck is split precisely in half and the two halves are zippered together in perfect alternation, isn't random at all. In fact, it's completely predictable. Eight perfect shuffles will return a 52-card deck to its original order, with every card cycling back to its starting position.
And this doesn't just work for 52 cards. A deck of any size will eventually return to its starting order after a finite sequence of faro shuffles, although the number of faros required isn't always eight—and doesn't increase linearly. If you have 104 cards, for instance, it takes 51 faros to restore the deck. For a thousand cards, it takes 36.

These findings are among the many fascinating results explored in "Magical Mathematics," a dazzling tour of math-based magic tricks. The authors, Persi Diaconis and Ron Graham, are distinguished mathematicians with high-powered academic pedigrees. Both are also accomplished magicians who have taught courses on mathematical magic at Harvard and Stanford.

Mr. Diaconis has an especially unusual résumé for a mathematician. In 1959, at age 14, he ran away from home to study with the great 20th-century sleight-of-hand master Dai Vernon—a man who once fooled Harry Houdini with a card trick. After spending 10 years under Vernon's tutelage, Mr. Diaconis returned home to New York and enrolled in night school, eventually earning a full ride to a Ph.D. program in mathematics at Harvard.

The book's title may strike some people as odd in its pairing of magic and math, but the two subjects share a common lineage that goes back centuries. In fact, some of the earliest recorded magic tricks were based in math. Fibonacci's 1202 manuscript "Liber Abaci," the foundation of modern arithmetic, contains a number of magic tricks, including several versions of the famous three-object divination, wherein a spectator mentally selects one of three objects and the magician correctly identifies the spectator's choice.

The earliest recorded card tricks, meanwhile, appear in a math text written around 1500 by a Tuscan friar who was close friends with Leonardo da Vinci. And one of the first magic manuals was compiled in the 17th century by Claude Gaspard Bachet de Méziriac, an early number theorist.
MAGIC8
Player/Alamy

But mathematical magic truly came of age in the 20th century, with the growth of magic as a mainstream hobby. "In the past hundred years, a revolution has taken place," the authors write, citing the thousands of math-based magic tricks now in circulation.

In their breezy yet authoritative book, Messrs. Diaconis and Graham showcase some of the genre's best creations as well as many new ones of their own devising. Included are tricks with coins and cards (the reader will want to have a deck handy), a divination routine that employs the I Ching—the 5,000-year-old Chinese fortune-telling book—and, my personal favorite, a gambling demonstration in which the spectator shuffles a deck of cards but somehow still manages to deal himself a royal flush in spades.

This last effect exploits something known as the Gilbreath Principle, a beautiful property discovered in the 1950s by a mathematician who worked for many years at the Rand Corp. Take a deck of cards and arrange it in alternating red-black order. Now deal half of the deck facedown into a pile—thus reversing its order—and riffle shuffle the two piles together. Finally, deal the cards face up in pairs.

Each pair will contain one red and one black card (though not necessarily in alternating order). This is the Gilbreath Principle. This same idea applies to any repeating pattern of cards. If, for instance, the deck is arranged so that the cards cycle through the four suits—clubs, hearts, spades, diamonds, clubs, hearts, spades, diamonds, and so on throughout the deck—and the same procedure is executed, then every four cards dealt off the top will contain a complete set of suits. This result, combined with a few clever subtleties, is the basis of the royal-flush effect.

All the tricks in "Magical Mathematics" are of the "self-working" variety—meaning they require little or no physical skill—and while a grasp of the underlying mathematics is helpful, it is by no means a necessity. Even math-phobes will be able to astound audiences by simply following the directions and consulting the many full-color illustrations provided throughout the text.

The mixing of magic and math is more than just a means to new tricks. It has also spawned a host of major mathematical breakthroughs. "Some magic tricks use 'real mathematics' and lead to questions beyond the limits of modern mathematics," the authors write. "Sometimes, we have been able to solve the math problems."

The seven-shuffles result is one such solution. Mr. Diaconis became interested in the math of shuffling after he encountered a card trick published in the early part of the 20th century by Charles Jordan, a chicken farmer and champion puzzle solver who invented several groundbreaking card tricks. In this particular effect—called "Long Distance Mind Reading," because it could be performed through the mail—the spectator shuffles before and after picking a card, but the magician still finds his selection.

Mr. Diaconis realized that for the trick to work shuffling had to be less effective than people generally assumed. While at Harvard, he teamed up with a mathematician named David Bayer and the two undertook a theoretical analysis, building on work done at Bell Labs in the 1950s. Their landmark 1992 paper—"Trailing the Dovetail Shuffle to its Lair"—rigorously proved that anything less than seven shuffles is inadequate. Not only that, their results had implications for a wide class of "mixing" phenomena—from stirring cake batter to compounding chemicals.

Similarly, the remarkable "looping" property of perfect shuffles is a facet of group theory—a branch of abstract mathematics that deals with, among other things, symmetric structures. Group theory has applications to chemistry, biology and, most notably, physics, where it provides the mathematical framework for the Standard Model—the overarching theory of subatomic particles and forces.

There's also a deep link between the perfect shuffle and the binary number system—the universal language of modern computing. To appreciate the connection, you first have to understand that there are two ways to do a faro. You can either weave the cards together so that the top and bottom cards stay in place—this is called an "out-faro"—or you can do what is known as an in-faro, in which the top and bottom cards each move inward by one card.

Now let's say that the ace of spades is on top, and you want to move 25 cards above it, so that the ace will be 26th from the top. The sequence of faros required to bring about this arrangement can be found by writing the number 25 in binary notation, like this: 11001. For each 1, you do an in-faro, and for each 0 you perform an out-faro. In this case, you would do two in-faros (11), followed by two outs (00) and, lastly, one more in (1).

Shuffling is one example of something seemingly ordinary that subtends an elegant mathematical structure. Juggling is another. "Mathematics is often described as the science of patterns," Messrs. Diaconis and Graham (a former president of the International Jugglers' Association) write. "Juggling can be thought of as the art of controlling patterns in time and space. Both activities offer unbounded challenges."

The central challenge in the mathematical study of juggling is to figure out which sequences of throws are possible and to categorize them according to the number of balls they require and their length—or period. Toward that end, mathematicians have developed a notation, called "siteswap," that uniquely describes all possible throwing sequences.

A siteswap pattern consists of a string of numbers, each of which specifies how much time one ball—or club, or chainsaw, or banana—spends in the air. The classic three-ball cascade, for instance, is denoted 333, because each ball is aloft for the same amount of time (three beats), and the sequence repeats after every third throw.

The remarkable thing about siteswap is that it allows jugglers to devise new patterns on paper and determine whether they're juggleable with a few simple calculations, all without tossing a single ball. What's more, the average of the digits in a pattern tells you the number of objects needed to juggle it—3 in the case of 441, for example, since the average of 4, 4 and 1 is 3.

Siteswap has led to the discovery of hundreds of unknown throwing sequences, many with just three or four balls. "Once the connection has been made between juggling (sequences) and mathematics, all kinds of doors, both mathematical as well as juggling, are thrown wide open," the authors note. "Many jugglers have been working hard to master the almost unlimited number of new patterns suggested by siteswaps."

Throughout the book, Messrs. Diaconis and Graham shuttle back and forth between magic and math, probing each trick for hidden mathematical insights and developing new magic based on what they find. In the process, they encounter a number of unsolved problems, some of which have prize money attached to them. It's a fun ride, even if you don't follow the nuances of every theorem and proof, and a refreshing change from the bombastic sort of magic one typically encounters on television.

Lovers of recreational mathematics, and especially fans of the late Martin Gardner, who contributed the foreword, will find many pleasures in "Magical Mathematics." And while exposing magic secrets in a book intended for the general public may raise hackles among some old-guard magicians, exploring the math behind these tricks will, in truth, only deepen the mystery. For, as the authors remind us, sometimes the methods are as magical as the tricks themselves.
 
—Mr. Stone is the author of the forthcoming "Fooling Houdini: Magicians, Mentalists, Math Geeks, and the Hidden Powers of the Mind."