Wednesday, March 02, 2005

Out on the tail

As the world's population gets larger, should we expect more Newtons, Mozarts and Tiger Woods or should we expect fewer? By this, I mean should the gap between the best in a field and the second best, be larger than the gap between the second best and the rest? If you presume that the aptitude level of people for some enterprise is normally distributed then the answer is no. The probability to be between n standard deviations and n+1 standard deviations above the mean decreases exponentially. As you go out onto the tail, the probability of someone being a standard deviation better than you is decreasing very quickly. Thus we should see a lot of people bunched near the top.

So why is it that we have Tiger Woods? Tiger is dominating golf like no one since perhaps Bobby Jones in the twenties and Ben Hogan in the early fifties. He was more dominant over a stretch of five years than Jack Nicklaus ever was although his dominance declined slightly last year. There are many more golfers now then there were fifty years ago so if anything we should see a much more competitive environment. Except for Woods and perhaps Vijay Singh, this is true as there is very little separating the rest. Dominance is not just limited to golf. Ten years ago we had Michael Jordan in basketball and Wayne Gretzky in hockey. Right now we have Barry Bonds in baseball and Lance Armstrong in cycling. These people are dominating or have dominated their sports as much or more than anyone else before.

Part of the reason is surely that a normal distribution is a bad approximation for the tail. Anyone in finance certainly knows this. The central limit theorem does not converge uniformly over the entire range, so even though the bulk is well described by a normal distribution, the tail can still experience low number statistics. Thus as the population increases, more of the tail gets sampled and that could actually increase the probability of rare events not decrease it as would be expected. So my prediction is that we will see more dominant athletes in the future.

Now what about physics and music? By this argument we should see more anomalies in these areas as well. However, it is not clear who is the Newton of our day. Ed Witten maybe? I think the reason is that there are fewer objective measures of mastery in these areas as compared to sports. A lot of what leads to great impact in physics is the choice of problem. In this case, there is a greater element of luck. One could be way out on the tail in terms of sheer brilliance (if that can even be measured) but not have a great impact if they worked in a dead end field. In this case, physics may suffer from low number statistics in the bulk and the tail so there will be no correlation of dominance with population size.

Music has a similar problem. Who in the 20th century compared to Mozart? Diatonic Western classical music reached its acme with Mahler. After that, composers either became atonal or "popular". The 20th century was the century of performers. Perhaps if Rubenstein, Heifetz, or Yo Yo Ma was born in the 18th century they would have been great composers. The playing field changed in the 20th century so the question of dominance became more difficult to answer. In 200 years, we may look back at the 20th century and consider a Jazz or Rock musician to be the Mozart of the day.

1 comment:

Anonymous said...

The Next Einstein? Applicants Welcome

He didn't look like much at first. He was too fat and his head was so big his mother feared it was misshapen or damaged. He didn't speak until he was well past 2, and even then with a strange echolalia that reinforced his parents' fears. He threw a small bowling ball at his little sister and chased his first violin teacher from the house by throwing a chair at her.

There was in short, no sign, other than the patience to build card houses 14 stories high, that little Albert Einstein would grow up to be "the new Copernicus," proclaiming a new theory of nature, in which matter and energy swapped faces, light beams bent, the stars danced and space and time were as flexible and elastic as bubblegum. No clue to suggest that he would help send humanity lurching down the road to the atomic age, with all its promise and dread, with the stroke of his pen on a letter to President Franklin D. Roosevelt in 1939, certainly no reason to suspect that his image would be on T- shirts, coffee mugs, posters and dolls.

Einstein's modest beginnings are a perennial source of comfort to parents who would like to hope, against the odds, that their little cutie can grow up to be a world beater. But they haunt people like me who hanker for a ringside seat for the Next Great Thing and wonder whether somewhere in the big haystack of the world there could be a new Einstein, biding his or her time running gels in a biology lab, writing video game software or wiring a giant detector in the bowels of a particle accelerator while putting the finishing touches on a revolution in our perception of reality.

"Einstein changed the way physicists thought about the universe in a way the public could appreciate," said Dr. Michael Turner, a cosmologist from the University of Chicago and the director of math and physical sciences at the National Science Foundation.

Could it happen again? "Who or where is the next Einstein?"

No question is more likely to infuriate or simply leave a scientist nonplussed. And nothing, of course, would be more distracting, daunting and ultimately demoralizing than for some young researcher to be tagged "the new Einstein," so don't expect to hear any names here.

"It's probably always a stupid question," said Dr. Lawrence Krauss, a cosmologist at Case Western Reserve University, who nevertheless said he had yet to read a profile of a young scientist that does not include, at some level, some comparison to Einstein.

Dr. Stephen Hawking, the British cosmologist and best-selling author, who is often so mentioned, has said that such comparisons have less to do with his own achievements than the media's need for heroes.

A Rare Confluence

To ask the question whether there can be a new Einstein is to ask, as well, about the role of the individual in modern science. Part of the confusion is a disconnect between what constitutes public and scientific fame.

Einstein's iconic status resulted from a unique concurrence of scientific genius, historical circumstance and personal charisma, historians and scientists say, that is unlikely to be duplicated.

Dr. David Gross, who shared the Nobel Prize for Physics last year, said, "Of course there is no next Einstein; one of the great things about meeting the best and the brightest in physics is the realization that each is different and special."

Physics, many scientists like Dr. Gross say, is simply too vast and sprawling for one person to dominate the way Einstein did a century ago. Technology is the unsung hero in scientific progress, they say, the computers and chips that have made it possible to absorb and count every photon from a distant quasar, or the miles of wire and tons of sensors wrapping the collision points of speed-of-light subatomic particles. A high-energy physics paper reporting the results from some accelerator experiment can have 500 authors.

"Einstein solved problems that people weren't even asking or appreciating were problems," said Dr. Edward Witten of the Institute for Advanced Study in Princeton, N.J., Einstein's stomping grounds for the last 32 years of his life. "It could be there are big questions nobody is asking, but there are so many more people in physics it's less likely big questions could go unasked."

But you never know.

"One thing about Einstein is he was a surprise," said Dr. Witten, chuckling.

"Who am I to say that somebody couldn't come along with a whole completely new way of thinking?"

In fact, physicists admit, waxing romantic in spite of themselves, science is full of vexing and fundamental questions, like the nature of the dark energy that is pushing the universe apart, or the meaning of string theory, the elegant but dense attempt to unify all the forces of nature by thinking of elementary particles as wiggling strings.

"We can frame an Einsteinian question. As you know, asking the question is the key," said Dr. Leon Lederman, a Nobelist and former director of the Fermi National Accelerator Laboratory. He likes to think, he added, that it will be solved by "a Brazilian kid in a dirt floor village."

Dr. Turner said he hoped and expected that there would continue to be Einsteins. One way to measure their impact, he suggested, was by how long it took society to digest their discoveries and move on.

By this metric, he said, Isaac Newton beats out Einstein as the greatest of all time (or at least since science was invented). Newton's world lasted more than 200 years before Einstein overthrew it.

"Einstein has lasted 100 years," he said. "The smart money says that something is going to happen; general relativity won't last another 200 years." ...