Stretching that Hit

Winning the World Series with math

To figure out just how critical the turns are, Carozza did a calculation comparing the straight-line path with a circle around the bases. A path that follows a circle turned out to be a whopping 25 percent faster.

When Carozza presented his calculation at a colloquium talk in the math department at Williams College, Stewart Johnson, one of the professors in the audience, got intrigued. The circular path is so long that it can hardly be the fastest, he figured. So what path is the fastest?

Johnson ran a simulation on his computer, tweaking the circular path in tiny ways to make it shorter and faster, until no more tweaks could improve it. The result was surprisingly close to a circle, both in its shape and its speed: It swung nearly as wide and was only 6 percent faster than Carozza’s circle.

“This cries out for an empirical test,” Winston says. “It would be easy to do. If it holds up, God, that goes in the New York Times sports section.”

Magnus-ificient

Carlos ’97 free kick no fluke, say French physicists

While their research quickly confirmed the long-known Magnus effect, which gives a spinning ball a curved trajectory, their research revealed fresh insight for spinning balls that are shot over a distance equivalent to Roberto Carlos’ free kick.

The friction exerted on a ball by its surrounding atmosphere slows it down enough for the spin to take on a greater role in directing the ball’s trajectory, thereby allowing the last moment change in direction, which in the case of Carlos’ kick left Barthez defenceless.
The researchers refer to their discovery as the ‘spinning ball spiral,’ comparing the spiralling effects of Roberto Carlos’s kick with the shorter-distance (20-25 m) ‘circular’ free kicks shot by the likes of Beckham and Platini.

‘People often noticed that Carlos’ free kick had been shot from a remarkably long distance; we show in our paper that this is not a coincidence, but a necessary condition for generating a spiral trajectory.’

Here’s the kick in question:

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More Sports and Science

The sports reported as science bit has made its way around, and I while I was thinking of things to perhaps improve the analogies, it occurred to me that the whole part about “people don’t understand that jargon, can you dumb it down?” can be recast as “science is like a sport you’ve never seen before.”

If you’ve never seen a particular activity, and your only option was to watch (i.e. there’s nobody to explain it to you), how would you figure out the rules? You’d observe and look for patterns. You’d take note of repeated actions to see that they are consistent: player uses foot or head to hit the ball. You also may notice that some things don’t happen: hand touching the ball stops play. But then there are exceptions: doesn’t apply to the guy with the big gloves. He seems to be the only one who can handle the ball, and he wears a different colored jersey . Or, with baseball: if the ball touches the ground, the players seem to react differently than when it is hit in the air.

With repeated observation, you can guess at some of the rules. You can build a model and start to predict what would happen under certain conditions to see if your guess at the rules is correct. If it doesn’t, you have to know if there was something different about the circumstances to know if this is an exception or you were just plain wrong. Some of the more obscure rules take a lot of watching to uncover, and will look like anomalies at first. How many baseball games would you have to watch to see the infield fly rule invoked, and how many time would you have to see it before you could figure out the specific conditions under which it applies?

Observational science is just like this. At least part of astronomy, geology and paleontology, and perhaps others, rely solely on the ability to make repeated observations and figure out laws from the patterns of what does and doesn’t happen.

At the next level, you can also infer behavior that is due to strategy, which is based on the rules but not strictly part of it. There’s no rule in baseball that says the first baseman must hold a runner on, but the ability to take a lead and steal a base dictates this action. Much like the elliptical orbits plants being a derived behavior, based on the more fundamental rule of gravity being an inverse-square law. The orbits were noticed first, though, and the underlying rule was deduced later.