My heroic run of one hundred ninety-two FreeCell wins has been followed by a series of very short spurts. At one perilous moment, I even flirted with equaling my record for successive losses, which is two. My first, quite natural reaction, was that the computer program was punishing me for my hubris by selecting particularly difficult puzzles for me to struggle with, but then I bethought myself, as you might expect of Stephen Jay Gould.
Gould, for those of you who do not know, was the paleontologist and evolutionary biologist who died, very much too early, thirteen years ago at the age of sixty. Gould was one of three famous biologists who worked for years at Harvard -- Richard Lewontin and E. O. Wilson being the other two. Lewontin is one year older than my sister, Barbara, and graduated from Forest Hills High School the year before she did. They were graduate students together [with Wilson] in the Harvard Biology Department.
Gould is known in the profession for the revision of evolutionary theory called "punctuated equilibrium," but he became famous as a regular contributor of charming, fascinating essays in Science magazine. Several collections of those essays sit on my shelves, and were a source of enormous pleasure as well as fascinating information.
Generally speaking, I was an enthusiastic fan, but on one crucial matter, closely related to my experiences with FreeCell, I concluded that Gould had gone astray. In this post, I shall explain. [I was convinced that I had already written a post about this matter, but a search of my blog for Gould's name produced only one post, about a different matter.]
We are all familiar, I trust, with the notion advanced both by sports greats and by sports fans alike that athletes on occasion "get hot" or are "in the zone." When this happens to a Michael Jordan or a LeBron James, it is said, they "can't miss the basket." Batters in baseball are said to "get hot" and "go on streaks" when they see the ball more clearly and get "seeing eye singles" between the shortstop and the second baseman.
Appealing to some elementary but surprising facts about statistics, Gould argued that this was all hooey. A little mathematics, he pointed out, will tell us that four-hit games or triple doubles are more likely than one might expect from 320 hitters or basketball superstars. If you have a 320 batting average, then it will indeed happen rather often that you go four for four, just as a fair coin tossed repeatedly will come up heads five times in a row a good deal more often than one might imagine. Indeed, Gould said [he was, regrettably, a Yankee fan -- a deep character flaw, but even our heroes have clay feet], the one really statistically implausible record in all of baseball was Joe DiMaggio's never-equaled fifty -six game hitting streak.
I believe Gould to have been fundamentally wrong, for reasons I shall now explain. I never met Gould, alas, though I saw him speak once late in his life, but I was standing at the very back of a packed auditorium and there was no chance for me to ask a question. This post is meant to honor his memory, not to detract in any way from his legacy.
The central flaw in Gould's argument is the mistaken comparison between being a 300 hitter and picking marbles out of a mixed bag of red and black marbles three tenths of which are red. Gould is quite right that if you pick marbles from a bag [and then return them, shaking the bag before the next pull], you will get runs of more than or fewer than three in ten rather more often than you might expect [unless you knew some elementary statistics.] But being a 300 hitter is not at all like being a bag of marbles three tenths of which are red. The marbles, we may suppose, have no say in whether they get selected. Unlike M&Ms in TV commercials, they do not jostle for attention and crawl to the top of the heap in the bag to improve their chances of getting out of the bag.
But matters are rather more complicated with baseball players. A scout sent out to round up prospects will report back to the General Manager that he has located, in a small town high school, a natural who is a "guaranteed 300 hitter." The coach is no doubt focusing on the young man's observable athletic ability, his keen eyesight, his upper body strength, his ability to "hit a curve." And these, let us grant, are indeed roughly akin to a marble simply being red rather than black. But the scout's description of the prospect as a "300 hitter" is an educated guess as to how the young man will perform once he is wearing the team uniform.
Some baseball players ease up late in a game, when their team is way ahead and another hit will make no difference to the outcome. Others will bear down as the pitcher goes through his windup, no matter what the score, where the team is in the standings, or how he feels that day. There are players who have the ability to concentrate their faculties and focus their minds, by acts of will, when they choose to do so. They do not simply swing at the ball and wait to see what batting average their natural talent produces.
My favorite example is a perhaps apocryphal story about the legendary Ty Cobb, who was such a mean son of a bitch that even the dead players in Field of Dreams declined to invite him to Kevin Costner's Iowan farmland ball field. The story goes that Cobb was invited to play in an Old Timer's Game. When he stepped to the plate to bat, he turned solicitously to the catcher and said, "You might want to step back a pace. I haven't swung a bat in a while and I don't want to risk hitting you." The catcher obliged, and Cobb laid down a perfect bunt, beating the catcher's delayed throw to first base.
Actual players talk about getting hot and being in the zone. I think Gould was just plain wrong to dismiss such talk, mistakenly construing their batting or scoring averages as facts about them, like being red marbles, rather than as summations of the intersection of their native abilities and their potentially variable effort.
All of which leads me to conclude that I am not a Ty Cobb. When I have ripped off 192 wins, I relax, I get impatient, I figure a loss does not matter, and so I am prone to short streaks.
It is important to acknowledge your limitations.
But about punctuated equilibrium, I am quite prepared to accept Gould's word.