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Everyone can be a world champion at SOMETHING

Posted in Physics, tagged , , , , , on August 18, 2014| 9 Comments »

Magnus Carlsen is the current world chess champion. He’s the best in the world at something. Not that many people can make that claim, can they?

Magnus Carlsen at FIDE World Chess Championship

Then again, there are lots of things in the world that you could be best at. Whistling, lemur training, lemon-pie-making, juggling, lying, rock climbing, sleepwalking. Somewhere in the world, there is “the best in the world” at each of these pursuits. Maybe my chances of being best at something are not so bad, after all? Maybe I just have to find the right thing…

Consider the modern pentathlon. In this sport, athletes compete in five events—fencing, shooting, swimming, running, and horse jumping—to achieve the overall best combined score. The winner need not be the best at any one specific event, but must have proficiency in all five.

Let’s say I am in the 99th percentile in all five events: very good, but not world class. [Here I am assuming that I’m in the 99th percentile of all humans, not just people who fence.] Taken individually, I wouldn’t have a prayer of making the Olympics. For example, the 99th percentile in épée fencing would still mean that there are

(0.01)^1 * 7,000,000,000 = 70,000,000

people with a similar proficiency around the world. Doesn’t seem that impressive, does yet? But I’m in the 99th percentile in all five events, right? So in reality there are only

(0.01)^5 * 7,000,000,000 = 0.7

people like me. That is, there’s just me. I’m probably the best at this combination of events. I should medal in the modern pentathlon.

And this brings me to my broader point. If you can think of five events in which you are in the 99th percentile individually, then in all likelihood you would be world champion if these events were combined into a single composite event. For those scoring at home, here’s where the number five comes from:

(0.01)^N * 7,000,000,000 = 1 (a single champion)

N ln (0.01) = ln [1/(7 x 10^9)]

N = [–ln (7 x 10^9)] / [ln (0.01)] = 4.9 ≈ 5

Let’s take my own skill set and see how I would do. I am certainly in the 99th percentile when it comes to physics. (Remember, I am comparing myself to the general population, not just physicists. I would never claim to be in the 99th percentile of people with physics PhD’s.) I am probably in the 99th percentile when it comes to chess (considering that I am in the 85th percentile for tournament players based on an 1800 rating). But am I good, really good, at anything else?

I will claim without proof that I am also in the 99th percentile (among the general population) in the following additional skills:

  • Knowledge of classical music
  • Playing the recorder
  • Geometry

Remember, I am not claiming any particularly high proficiency in any of these things. I just claim a 99th percentile rank in the general population. And individually, any one of these skills would only put me in the company of some 70 million others.

But now: make a hybrid event, where competitors have to take a battery of tests on physics, geometry, and classical music, then perform on the recorder, and then play chess… I believe I may do well in such an event. I might even be world champion.

Of course, nothing is that simple. I have ignored the fact that some of these skills may be correlated. Anyone who can play the recorder will probably also know about classical music. And many physicists will also be good at geometry. This means that my competition will be stiffer than I suppose, since if the events aren’t mutually exclusive then I’ve calculated the probabilities incorrectly. But I can improve my chances by making the five events as disparate as possible. I might change “Geometry” to “Movie Trivia”, for example.  My chances of becoming world champion would thereby be increased.

If you think that “99th percentile” is too high a bar, we could lower it to 90th percentile. Most people are in the top 10% at several things. Redoing our calculation, we get N = 9.8 in this case. So if you can find ten things you’re fairly good at and combine them, you too can be a world champion.

Of course, you also have to convince the Olympic governing body that that particular concatenation of events is worthy of a medal. But hey, that’s your problem.

I have some geometry to do.

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Chess is a horrible metaphor

Posted in Uncategorized, tagged , , , , , , , on December 11, 2012| 4 Comments »

War is nothing like chess.

War is nothing like chess.

I am a big chess fan.

I can name every chess world champion since Morphy; I could probably name around 17 of the world’s current top 20; I can checkmate a lone king with two bishops and a king; I have a good working knowledge of just about every opening there is.

(And by working knowledge, I don’t just mean I’ve “heard” of the Sicilian defense.  I don’t just mean that I know that 1. e4 c5 2. Nf3 Nc6 3. d4 cxd 4. Nxd4 Nf6 5. Nc3 e5 is the Sveshnikov.  I mean that I am fully aware of the differences between the 9. Nd5 and 9. Bxf6 Sveshnikov, and prefer the former.)

The problem is, I’m just not that good.

Oh, I can beat most casual players…the ones that begin a game by moving a rook pawn (to a4, say) and then move their rooks out vertically (to a3, say).  In USCF rating terms, my rating is around 1800, which (to my own surprise) is about the 85th percentile for tournament players.  So objectively, I am not bad at all.  But I am good enough to be aware of just how much better other players are.  I have a friend Shawn who is a master (here he is drawing a grandmaster).  I am in awe of his tactical strength, and his fine sense of dynamics.  I have beaten him dozens of times in speed chess, but for every game I win, he wins 10.

It has taken me a while to get to the point of this blog post, which is this: I like chess because of its icy logic and its mathematical purity.  For this reason, chess is a horrible metaphor for war, or for life.

Chess is used in books and movies for two basic purposes.  The first is to establish the intelligence of a character.  For example, Lisbeth Salander (in The Girl with the Dragon Tattoo) is an expert at chess.  This was a bad choice on the author’s part: Lisbeth is also an expert hacker and financial genius, has an eidetic memory, and is an incredible detective—why stretch credulity even further?  A lot of great chess players are certainly smart, but the correlation doesn’t go the other way: many smart people are terrible at chess.  Einstein was probably weaker than me.  Oppenheimer was even worse.  Comedian Howard Stern, a player of about my strength, would crush either one.

The other use for chess in books and movies is as metaphor.  In The Seventh Seal, Antonius Block plays a game of chess against Death.  In Harry Potter and the Philosopher’s Stone (the original title; not the dumbed-down American version) someone plays chess with someone else (like I remember?)  In both cases the chess itself is ludicrous.  For example, at one point Death captures Block’s queen; Block says that he “didn’t see that”.  (Really?  Did Block just learn the rules the day before?)  But I don’t want to evaluate the chess in such works per se; rather, I want to see how well chess works as a metaphor.

First, chess as war.  I can’t think of any examples off the top of my head, but there seems to be an assumption that skill at chess somehow equates to skill at war.  But this is ludicrous: in chess, every move is transparent; you can always see what your opponent is doing, and everyone starts on a level playing field.  In terms of game theory, chess is a perfect information game.  I’m no Colonel Dax, but I don’t think war works that way.  There is always a fog of war, and an element of chance, so war is about contingencies, and adaptability, and bluff, and extrapolation.

Second, chess as life.  I have to admit, I don’t really get this metaphor at all.  Is life therefore a game?  A perfect information game?  If chess represents life, does that mean that I struggle throughout my life against an opponent (Satan?  Howard Stern?) who is trying to thwart me at every turn?  And if I play well, but my opponent does too, then am I destined for a draw?  What is a draw, in life?  Is it retiring at 65 to play shuffleboard in Orlando?

As much as I like chess, I think backgammon is a much better metaphor for war or for life.  In backgammon, there is an element of chance, and so the “the best laid schemes o’ mice an’ men” will often go awry.  That is why a good backgammon player will weigh contingencies.  What move leaves me in the best position, based on what dice rolls are possible, and what might happen?  In backgammon, you’re not just playing against an opponent, you’re playing against the fates themselves (in the form of the dice) and this makes the game feel more “real” to me.

People who don’t play backgammon often think that luck is a major part of the game.  This is true, on the level of a single game, but backgammon is played in matches of multiple games, and luck is much less important at that level.  This is because of the doubling cube.  With the doubling cube, a master will almost always defeat a weaker player, in the same way that a Napoleon will almost always win a war against a General Mack, even if an individual battle is lost here or there.

And so, life.  The dice aren’t always going to go your way.  You should plan with that in mind.  Look at your current position, figure out the possible contingencies—the possible ways God might play dice with your universe—and set up your pieces accordingly.  Even if you get gammoned, tomorrow’s another day.

[Note: I subconsciously chose an inept Austrian general to be the foil against Napoleon’s military genius.  But I want to be balanced in my portrayal of Austrians.  So I will remind everyone that Lise Meitner was Austrian, and she was a super-smart physicist.  And strangely, her father was Philipp Meitner, a chess master and part of the immortal draw.]

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