a.n.a.lYSIS.

When Professor Ian Guymer wants to ill.u.s.trate the complex fluid dynamical processes inherent to his research on pollution dispersal, he has a go-to PowerPoint image: Winnie-the-Pooh. "My work is about predicting the movement of water. Where does it go, what is its path, when will it arrive somewhere?" he says.

This makes his research crucial in understanding what to do when our rivers are contaminated with effluent-one kind of poo stick. It also makes it crucial (if, admittedly, a little less important) in understanding the intricacies of the other kind of pooh sticks-the game invented, or at least immortalized, by the residents of the Hundred Acre Wood.

Water engineers actually consider pooh sticks one of the more useful tools of their profession- although they generally don't use sticks. No, they prefer fruit. "Oranges are the best. They help show you the flow, and biodegrade so environmentalists don't get angry," says Professor Guymer. They are also almost neutrally buoyant, floating just below the surface. But oranges are not the only fruit for a fluid dynamicist seeking to trace a river's path. "Depending on where you are in the world, the fruit changes. If you are on a really nice a.s.signment, you use coconuts."What has a lifetime of seeking a.s.signments with coconuts taught Professor Guymer, who sits on Britain's Inst.i.tution of Civil Engineers' water panel? Well, first, go for the middle. "If we look at the simplest possible shape-a rectangular concrete channel-then water velocity varies just due to distance from the boundary." Because water experiences friction when it comes into contact with the edge, it is slower at the sides and the bottom. So, in this case, drop your stick as far from the edges- including supports on the bridge-as possible.

If all rivers were uniform rectangular channels, though, Dr. Guymer probably would not have a job.

In the real world they are often a lot more complex than that. "The basic problem with a natural river is that you've got spatially varying flow velocity," he says, not exactly echoing A. A. Milne. Most important, at least as far as the serious pooh sticks compet.i.tor is concerned, there are eddies generated by obstructions upstream that can cause circular flows. "If your stick gets trapped in that, it will eventually get out but it may have to do one or two rotations," he says.

His final piece of advice does not require the skills of a civil engineering PhD to formulate. "Just make sure it doesn't get stuck," he advises. Choose a small stick-the bigger it is, the more likely it is that it will hit an obstruction. Preferably, you should also select one without anything that can get caught on reeds or the bridge. Depending on where you are, you could even go for an orange instead.SLOT CAR RACINGWHAT'S IT ALL ABOUT?

A driving simulator for a generation without computers that largely persists in a generation with computers because it's their dads doing the buying.

HOW DO YOU PLAY?.

Re-create all the thrills and spills of the golden age of Formula One-the danger and the excitement, the technical wizardry and the split-second timing-by pressing and depressing a single plastic b.u.t.ton.

HOW DOES IT END?.

When your mother/wife insists she needs the dining room table back.

a.n.a.lYSIS.

Johnny Herbert is one of motor racing's great all-rounders. As a Formula One driver, he competed for eleven years for seven teams, was on the podium seven times, and won three races. Before that he won the Le Mans 24-hours, the Formula Ford Festival, and British Formula 3. And, before even that, he came third in the South of England Junior Scalextric (slot car racing) championships.

"I'm a slot car boy. I used to spend hours on it in my parents' loft," he says. Was this where his career really began? If so, what can the keen slot car aficionado learn from a keen Formula One racer? Well, he argues, at least some skills are transferable-if not the ones about continually getting little metal brushes aligned so they don't get caught on the chicane. "It is a bit different from proper racing," he says. "You only have a single trigger." Even the most ardent slot car fan would have to acknowledge that the absence of gears, braking, and, indeed, a steering wheel, are something of a limitation in a driving simulator. "But there are links. Smoothness really comes into play, and so does antic.i.p.ation. Be smooth on the trigger when you're going back on the throttle, but not when braking.

And keep watching: as you go into the corner, that is the time to reapply the trigger."

Just as in the real thing, he advises having practice laps. "When you know what the car is doing, that's when you will know if you have pressed slightly too much and got a slide. Learn lap by lap what the car is doing, so you can respond. Really it's just about antic.i.p.ation, then squeezing the trigger slowly at the right time."PAPER AIRPLANESWHAT'S IT ALL ABOUT?

Origami, for people with very little interest in swans.

HOW DO YOU PLAY?.

Ideally, solve the Laplace equation for noncompressible two-dimensional airflow over a semirigid wing. Then, adjusting your design accordingly, wait until the teacher's back is turned and throw. The first bit is optional.

HOW DOES IT END?.

With detention.

a.n.a.lYSIS.

John Collins's great insight came in an aircraft hangar, with a paper plane that refused to go straight. "The plane would go halfway down the hangar, then suddenly it would make a U-turn. I was kind of at a loss-it was just doing things a plane shouldn't do." Every time he threw it, the same thing happened-the beginnings of a great distance throw then, without warning, it boomeranged.

Luckily for him, in his attempt to break the world distance record for paper airplane throwing, this hangar contained people rather used to making planes do things they shouldn't do: it was the home of Scaled Composites, the US company that also makes suborbital s.p.a.ce planes.

"One of the guys who designs the ignition systems on their engines was watching us fly." He thought he knew what was happening. "There was an anomaly on the wing, and the air was. .h.i.tting it at different places depending on the speed." As the paper plane slowed, the airflow changed. Suddenly at this point a small difference in how John had folded the wing became significant.

This gave John an idea.

Paper planes had always been part of John's life. Over the years he has come to appreciate the deep insights they give into aeronautics, and has gone from being a boy who liked to throw them to being a man who organizes paper plane contests for children to get them into science. And also, admittedly, being a man who likes to throw them.

In his attempt at the distance record he quickly came to two conclusions. First, he realized he needed to abandon the cla.s.sic dart design. "We quickly maxed it out. I realized we could only get it so far-we had to switch to a glider wing." He needed something broader, with more lift. Second, he came to the sad realization that someone else would need to throw it-someone with a stronger arm.

"A good throwing technique is key." His first thrower "had big hands and kept crushing the planes."

His second one "had a snappy throw and cut the planes in half." The third one, Joe Ayoob, was just right.But he still had the problem that afflicts all attempts to throw a paper airplane as far as possible: the need to compromise between lift and speed. "When you are going fast, initially you want low drag," he says. This means having the plane angled so that the nose is parallel with its travel. "When it is going slowly, you want stability." This means having the nose pointing slightly up. That day in the aircraft hangar he realized that if he could just design a plane that changed how its wing is angled in the air depending on its speed, there would be no need for compromise at all.

He began folding anew, but this time with one small change to the "dihedral angle," the angle made where the left and right sides of the wing meet. "The shape of the wings was different. They have a flatter dihedral angle at the nose, and we cranked up the dihedral angle farther back toward the tail."

The result was a plane with low drag at high speeds and high stability at low speeds.

Six weeks later it flew 226 feet and won a place in Guinness World Records. It also ensured that paper plane design would never be the same again. You don't have to be a rocket scientist to design a good paper airplane, but knowing one certainly helps.

Full instructions for folding this record-breaking paper plane are in John Collins's book, The New World Champion Paper Airplane Book , published by Random House US, and there are video guides online for John Collins and the Suzanne paper airplane that will walk you through the process of folding it.

Until recently, every time a physics teacher was. .h.i.t by a paper dart when their back was turned, they should have considered it an affront. Not to their authority, but to their subject. Because for most of the time that people have been making paper airplanes, n.o.body has known how they fly.In school we are taught how planes work. It begins with the airfoil-the curved cross-section of a wing. In the simplest understanding, this shape, longer on the top than the bottom, forces air to go faster along the upper edge, creating a pressure differential that generates lift. More complicated explanations might take in vortices, or the cutter condition, or Bernoulli's theorem.

But it begins with the airfoil.

The problem with this is, paper airplanes don't have airfoils. Their wings are completely flat- their pa.s.sage across a cla.s.sroom a minor aerodynamic miracle. Curvature can have no role in how they generate lift. So what does? It turns out it all comes from the angle of the wing relative to the airflow.

"Until the 1950s we didn't really know how they flew," says Steve McParlin. Steve is a fellow of Britain's Royal Aeronautical Society, and now teaches aerodynamics. The bulk of his career, or at least the uncla.s.sified version, was spent working on combat aircraft and supersonic wings.

It is in that work, on the fluid dynamics of wings designed to pa.s.s the speed of sound-whether on their way to intercept Soviets or not-that we find an unlikely congruence with paper airplanes. Both of them have to have flat wings: supersonic planes because it minimizes drag, and paper airplanes because, well, they're made out of paper.

Now we do know how they fly, and it has very little to do with airfoils. All of the lift is generated by the angle of the wing relative to the airflow. This has some unusual and less- predictable consequences.

When the air hits it at an angle, there is higher pressure on the lower half of the wing than the upper, generating a lift force. While that is an explanation for lift that almost anyone can understand, unfortunately it explains only a very small part of it. The rest comes from what happens when the air buffeting the wing goes round its edges.

"In the a.n.a.lytical solution, what happens is you get an infinite velocity as it goes round the corner," says Steve. This is another way of saying all his equations go wrong at the edges. "In real life," he adds comfortingly, "we don't have infinite velocities." Instead, above the wing the airflow curls up into a vortex.In conventional aerodynamics, that is the last thing you want. "V ortex flow was always considered a source of drag. It's only when the wing is very slender that vortex flow starts to form a coherent structure, instead of something that is horribly messy." And when they do form a coherent structure, they also generate lift, sucking the wing from above.CHECKERSWHAT'S IT ALL ABOUT?

"Everybody plays draughts,"* said Frank Dunne, an early twentieth-century writer on the game, "but comparatively few are draughts players." Unlike chess, you can be taught the rules in a few minutes, but the problem with this rapid learning curve is that it leads beginners to mistakenly believe they are not, to paraphrase Dunne, playing like an idiot.

HOW DO YOU PLAY?.

Set up your twelve white and twelve black pieces on the black squares, with two rows free in the middle. Move a selected piece one square diagonally forward per move, or remove an opponent's piece by jumping over it when adjacent, and if the next square is free to land on. If it is possible to take a piece, you have to. When you get a piece to the other side, it can move diagonally backward, too. See? Told you the rules were simple.

HOW DOES IT END?.

Always with a ma.s.sacre. Chess might allow for the relatively civilized option of regime change- remove the king and it's all over-but checkers draws from a take-no-prisoners, Mongol hordes approach to war. The loser is the one who is completely destroyed.

a.n.a.lYSIS.

The first thing that happened, after Jonathan Schaeffer completed the program he had been working on for almost twenty years, was that the hate mail began. "They said I was going to destroy the game, to ruin it-that no one was going to play." The world's checkers players were furious: Professor Schaeffer had created a computer opponent that could never lose.

Schaeffer is, by his own admission, a bad checkers player. Luckily, though, he is an excellent computer scientist. Starting in 1989, he began working on a program that could "solve" checkers- playing the optimal strategy whatever move its opponent made. It was a daunting task.

"There are 500 billion billion positions. Five hundred billion billion is not something people really understand. So I use an a.n.a.logy. Imagine you drain the Pacific Ocean. Imagine then I give you a teaspoon. What you are going to do is fill the teaspoon with water, dump it into the Pacific Ocean, and repeat. It takes 500 billion billion spoonfuls to fill. This is a game that is almost a billion times more complex than Connect 4."It is, however, a billion billion billion times less complex than chess, a game so complex that even our estimates of its complexity involve guesswork. Unlike chess, checkers seemed to be just-just- within the powers of humans to perfect. "There was a human player, Marion Tinsley, who was world champion," says Professor Schaeffer. "He was idolized. Between 1950 and 1990 he only lost three games. He was as close to perfection as you could imagine a human being. But," he adds, "he wasn't quite perfect. He would make a mistake. It may have been only once every ten to fifteen years, but he would make a mistake."

For many of the checkers players who angrily contacted Professor Schaeffer, they did so out of a sense that his program somehow besmirched the memory of Tinsley. Professor Schaeffer thinks this is silly. "I'm a compet.i.tive chess player. I know many players out there are better than me, but I still go and play because I want to get better. The fact that there is a computer player out there who happens to be much much better than me is irrelevant."

Gradually, though, the checkers community has grown used to the idea of there being an omniscient player-after all, for them Tinsley was practically indistinguishable from perfection anyway. Many have even found a use for the program itself: most notably in solving the "100-Year Problem."

"There was a position published in a magazine in the year 1800," says Schaeffer. "It was white to play, and the question was-is it a win or a draw? A few issues later somebody wrote an article saying it was a win, along with a.n.a.lysis. A couple of years later someone else wrote another article arguing it was a draw." The back-and-forth continued throughout the nineteenth century, until by 1900 the debate had at last ended. "Everyone agreed it was white to play and win."

In 1997, when the program was not even complete, a Grandmaster, Don Lafferty, sent Schaeffer the problem as a nice test of his program. He took less than a second to provide the answer. "It was a draw. Don said, 'How can that be?' I showed him the a.n.a.lysis and he said, 'Oh my G.o.d, it's so obvious.' It turned out all the previous human a.n.a.lysis from the third move on had been wrong."

These days, the 100-Year Problem is called the 197-Year Problem.*Draughts-or drafts-is another name for checkers.APPLE BOBBINGWHAT'S IT ALL ABOUT?

The least efficient method ever devised for getting one of your five-a-day.

HOW DO YOU PLAY?.

Momentarily abandon your dignity, and your knowledge of germ theory, to rummage like a pig in a bucket that has already had several other mouths rummaging in it, hopefully only a small proportion of which had norovirus.

HOW DOES IT END?.

With a very cold head, especially if you are playing it at the traditional time of Halloween.

a.n.a.lYSIS.

Ashrita Furman is currently working on the world skipping record, in the mile category. If he gets it, he will be the holder of "Let me see"-he thinks-"it's over two hundred" records. One of those is the record for the most number of records. Ashrita, in short, has broken a lot of records.

So it takes him some time to remember quite what tactics he employed for one of those two hundred-the most apples bobbed in a minute (he got thirty-four, in 2010).

"The point is training your jaws," he says after a while. "You have to go really wide, chomp down on that apple, and latch." He typically takes at least a month to train for a record and, for apple bobbing-which he enjoys so much he has broken his own previous record-he recommends choosing a summer month. "That's when it's actually enjoyable to duck your head in a bucket of cold water," he says. If you are spending four weeks, working full-time, putting your head in a bucket, such considerations matter.

Under the rules set down by Guinness World Records, he could choose his own apples. If you are able to, he strongly recommends this. "Experiment with the apple. I found harder apples are better- otherwise they disintegrate in the mouth and you come out with just chunks." Equally, though, "If they are too hard you can't get your teeth into them." Granny Smiths are about right; Golden Delicious may be at the soft end.

All of which may well be true. But was it a useful application of his time to reach these insights?

"Apple bobbing is silly, I admit, but it requires a lot of focus-you are working at top speed to latch on and get the apple out of the tub. It's a concentration exercise. As soon as you get one, you pull your head out and fling it, and focus on the next apple. I like the challenge of it: it is very simple, justapples and water and you. It's a fun, childlike activity, one of those things like hopping in a sack or running with an egg and spoon you do at a birthday party or fair."

On that note, what about egg and spoon racing or sack racing? Does he also hold records in those?

He thinks for a bit. He did, but apparently a lot of serious runners got into egg and spoon racing, and he lost many of his t.i.tles. "I think I still have one for fastest hundred meters with it in your mouth."

And sack racing? "Yes-I have the record for hopping in a sack fastest over a mile. I did that in Mongolia, racing against a yak. The yak wasn't in a sack." Of course not. That would be absurd.SIX DEGREES OF KEVIN BACONWHAT'S IT ALL ABOUT?.

We live in an interconnected world, and Kevin Bacon is the glue. Can you link Bacon to any other actor in the world, just by using films they worked on together?

HOW DO YOU PLAY?.

Did you know that Kevin Bacon plays Taxi Racer, the character who beats Steve Martin to a taxi in the 1987 film Planes, Trains and Automobiles? Did you know that the year before that, Steve Martin was the s.a.d.i.s.tic dentist in Little Shop of Horrors? Even if you did, you probably wouldn't have noticed Network Exec #1. Which is a shame, because the actor in this seminal role was Robert Arden, who, thirty years before, had been a bellboy (his career sort of plateaued early) in A King in New York, a film chiefly noted for being Charlie Chaplin's last acting credit. And, suddenly, you have connected Bacon to Chaplin.

HOW DOES IT END?.

Normally with someone trying to connect Bacon to Hitler, or to bin Laden. Which, with the help of Leni Riefenstahl and her doc.u.mentary filmmaker successors, is actually surprisingly easy to do.

a.n.a.lYSIS.

Gerard Depardieu is crucial. As is Cary Grant. The key to Six Degrees of Kevin Bacon, says Patrick Reynolds, a computer scientist, is to find "anchor points"-actors who connect between people whose careers don't otherwise overlap. "The hard ones are trying to reach an actor in the 1920s, or in a country where Kevin Bacon never worked," he says.

"John Wayne and Cary Grant get you to early twentieth-century American film." Others, such as Gerard Depardieu, straddle geographic rather than temporal divides. He has a "Bacon number" of 2, meaning that he worked with someone who worked with Kevin Bacon. "In two hops you can be in France." If you have the sort of friends who like northern European films, another good name to know is Stellen Skarsgrd. The Swedish actor, who appeared in Good Will Hunting, also has a Bacon number of 2-and takes you deep into the bleak realms of Scandinavian cinema. If you really must go there.For Indian movies, Amitabh Bachchan (The Great Gatsby and, er, Kabhi Khushi Kabhie Gham ) performs a similar role.

Patrick is not actually, he confesses, much of a movie buff. "It's a really hard game. It's a way for people to show off just how much knowledge they have of films." He doesn't have much knowledge of films. His particular talent in this regard is computer science-he runs The Oracle of Bacon, a website that will find the connections, if they exist, between Bacon and any other actor. They almost always do exist.

"Right now the furthest is ten hops. Most people are three hops, but most people you've heard of are two." If, tomorrow, you appeared in a sofa ad then, provided you were alongside someone with a slightly better career than you-who was a jeering peasant, say, in Robin Hood: Prince of Thieves- you will probably find you had a Bacon number of 3. Frankly, says Patrick, "even if the advert has a voice-over and he has done other voice-over work, you will likely have a Bacon number of four."

The unnerving conclusion is, much like with rats in New York City, none of us is ever more than a few steps from Kevin Bacon.

Paul Erdos is, in many ways, similar to Kevin Bacon. Both took a lot of drugs in the seventies, both have a prolific back catalog, both worked with some of the finest names in the industry, and both have a parlor game, with the same rules, named after them.

The difference is that while Six Degrees of Kevin Bacon generally involves connecting, say, Stan Laurel with Bacon via the knowledge of an obscure seventies film about a bank heist gone wrong, Six Degrees of Paul Erdos involves connecting Einstein to Erdos via the knowledge of an obscure branch of topology.

Paul Erdos was one of the hardest-working mathematicians in history, with his name on 1,500 papers. Traveling the world from job to job, he would turn up at a colleague's door, take some amphetamines, and work with him or her until they had coauth.o.r.ed a paper, then move on. He was to all intents and purposes a mathematical hobo, but he got away with it because he was brilliant-the arrival of Erdos was a benediction rather than an annoyance, even if he did end up sleeping on your sofa.

Today mathematicians talk about their "Erdos number." An Erdos number of 1 means you auth.o.r.ed a paper with him; 2 means you auth.o.r.ed a paper with someone who auth.o.r.ed a paper with him, and so on. But while a low Erdos number is something to be prized, there is another number even more boastworthy: the Erdos-Bacon number, the sum of both numbers.Some surprising names have very low Erdos-Bacon numbers. Natalie Portman's is 7: she has a Bacon number of 2, but also an Erdos number of 5, having collaborated on an academic paper when at Harvard. Stephen Hawking's is 7, after an appearance on Star Trek. But the lowest is probably MIT math professor Daniel Kleitman, who coauth.o.r.ed a paper with Erdos then found himself hired as an adviser and extra on Good Will Hunting, in which Matt Damon played a mathematical prodigy. His number is 3.

In the world of Erdos-Bacon numbers, films about mathematicians generally change everything.

It has taken time but, over the years, Kevin Bacon has come to an accommodation with his eponymous game. When he first learned of it, in the 1990s, "I was horrified," he admitted, speaking at a film festival in 2014. "I started to kind of hear about it in strange ways. People would come up to me and touch me and say, 'I'm one degree!' I didn't really know what was going on. . . .??

I thought it was a giant joke at my expense."

Of course, he was sort of correct. The charm of the game is that Bacon has been in a vast number of films but, because he is rarely top billing, knowing which ones requires a certain level of geekery. "I don't think it's a great testament to my ability," he said.

Two decades after it began, the game is still going strong-and Bacon has accepted it is not going to be a pa.s.sing fad. So, instead, he has embraced it. His charitable foundation is called Six Degrees, in its honor. He also admits he finds the Oracle of Bacon website surprisingly useful.

"Whether it's my age or my misspent youth, sometimes I forget whether I've worked with somebody or not," he said. "I'll look at the call sheet, check the name, and then I'll check their Bacon number. That way I can go on the set and say, 'Good to see you,' or 'Good to see you again.'?"COIN TOSSINGWHAT'S IT ALL ABOUT?

The arrival of coinage with the Ancient Greeks not only supplanted the barter system, it also made decision making in 50:50 situations considerably more efficient. After all, have you ever tried tossing a pig?

HOW DO YOU PLAY?.

Seriously? Oh, all right then. Find a quarter, choose heads or tails (heads is George Washington's head, tails is George Washington's . . .?er . . .?arms, actually), throw it in the air, and see which side ends up facing up.

HOW DOES IT END?.

With a greater understanding of the vicissitudes of fate. Or, at least, with a greater understanding of who has to bat/break/kick off first.

a.n.a.lYSIS.

The first thing you need to know, to understand what is almost certainly Matthew Clark's most- cited research paper, is that he is an ear surgeon, and ear surgeons don't much like nose surgeons.