At the 1968 Olympics in Mexico City, a man called Bob Beamon made one giant leap, both for him and mankind. He loped down the long jump runway and took off. When he landed in the sand a second later, he had jumped further than any man ever had, further than any man ever would for another 23 years, further than any other man ever would for another 21 years and counting.
Usain Bolt (centre). Photo Reuters
People have analyzed that phenomenon in swimming, but leave that be. There are explanations for Beamon’s leap, but leave that be, too. Consider instead the progression of records in just two athletic disciplines. That puts in perspective the occasional supernova performances like Beamon’s.
Start with the 100 metres (m): at the Olympics, always the flagship race, the glamour event whose winners are hailed as the fastest man and woman on earth. Marginally faster, that is, than me.
The first time a men’s 100m record was recognized by the International Association of Athletics Federations was when Donald Lippincott ran it in 10.6 seconds in 1912. But just to make comparisons easier, take the record that existed in 1928: Charlie Paddock’s 10.4 seconds. Forty years later, Beamon’s Olympics was the first one in which the 100m winner ran it in less than 10 seconds. That winner was Jim Hines, who finished in 9.95 seconds.
In 40 years, the record had dropped by 0.45 seconds (10.4 to 9.95). Over the next 40 years, such stars as Carl Lewis, Maurice Greene and finally Asafa Powell lowered the mark all the way to 9.74 seconds. That’s 0.21 seconds better than Hines, but that’s less than half the 0.45 second decline the previous 40 years had seen.
Mathematicians know trends like this that taper off. If improvements get smaller and smaller, their eyes light up: “Ah,” they’ll say sagely, “there’s a limit here somewhere!” It’s a mathematical idea that such trends suggest a limit to how fast a man can run 100m, and that athletes are getting ever closer to it.
To understand this, ask yourself if a man will ever run the 100m in, let’s say, one second. Difficult to even imagine, unless we evolve into superhumans with jets in our behinds. Yes, one second is an impossibly quick limit. But is there a more realistic limit runners are approaching but may also never reach?
Well, that’s just the story the 80-year progression of the 100m record tells. Maybe, the story goes, that limit is 9.7 seconds.
Was.
Along came Usain Bolt. The Jamaican thoroughbred smashed the world record in May 2008, then again at the Beijing Olympics, and yet again a year later. In 15 months, he lowered the mark to 9.58 seconds: 0.16 seconds faster than Asafa Powell, not much less than the improvement the previous 40 years had seen. A remarkable feat. Out on this limb, I say it won’t be broken soon.
Take the long jump, now, and ask: is there a limit to how far a man can jump? Just as I cannot imagine a man running 100m in one second, I cannot imagine a man leaping, say, 100m. So certainly that’s a limit for the long jump. But is there a more realistic limit?
Well, that’s the story the progression of the men’s long jump record tells. In 1928, it was 7.90m. In 1935, Jesse Owens jumped a then-outstanding 8.13m. That wasn’t bettered till 1960, when Ralph Boston first jumped further than Owens had. Through the 1960s, in increments that grew generally smaller—ah, there’s a limit here somewhere!—Boston stretched the record. In 1968, his 8.35m effort was the world record: 45cm better than in 1928. Maybe the long jump limit is 8.40m.
Was.
Along came Bob Beamon. In Mexico, his 8.90m leap obliterated Boston’s mark by an incredible 55cm, plenty better than the improvement the previous 40 years had seen. And then it took 23 years for someone to beat Beamon: Mike Powell managed 8.95m in 1991, which remains the world record today.
The big story? Athletic performances naturally approach limits. That much is clear if you look at how records progress. The limit, seen in exactly this way, is a familiar and useful mathematical concept that underlies, for example, the science of calculus.
But since these are humans and not mathematical concepts, every now and then we get phenomena—Owens, Beamon, Bolt—who redefine limits. One giant leap at a time. Or for Bolt, burning up that 100m track, several dozen churning strides at a time.
Might make even mathematicians wonder, are there limits at all?
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences. Comments are welcome at dilip@livemint.com
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