Monthly Archives: April 2010

Old-School Experiment with Light

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Uncertain Principles: Measuring the Angular Momentum of Light

Being a formal and mathematical book, it pretty much leaves the subject there, but my immediate reaction is to look for an experiment that proves the angular momentum is real. So I did a little Googling, and turned up a paper from 1936(!) that does just that. And I talked about it in class, because I think experiments are way cool, and like to bring them in whenever possible. Having looked this up and read it carefully, I figure I might as well write it up for ResearchBlogging while I’m at it.

Call Sign: Melanogaster

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Fruit Fly Aerial Maneuver Explained

To study insect maneuvers, Jane Wang and Itai Cohen of Cornell University and their colleagues put several flies in a chamber that was illuminated from three perpendicular directions by bright projectors. When a fly passed through a pair of crossed laser beams, three high-resolution cameras were triggered to film at 8000 frames per second. Each camera recorded the fly’s shadow from one of the projectors. A new computer algorithm developed by the group automatically combined the two-dimensional silhouettes into a three-dimensional reconstruction of the fly.

They're Usually More Interested in Knots

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Mathematics Reveal Universal Properties Of Old Rope

Despite rope’s obvious geometric properties, the art of rope making has been strangely neglected by mathematicians over the centuries. Today, Jakob Bohr and Kasper Olsen at the Technical University of Denmark put that right by proving the remarkable property that ropes cannot have more than a certain number of turns per unit length, a number which depends on the diameter of the component strands.

And that’s just the start. They go on to show that a rope with a smaller number turns than this maximum will always twist in one direction or another under tension.

Nutty Bolt Analysis is Screwed Up

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I see that the The Math of the Fastest Human Alive has been zombified, as it has been reprinted in a few places, most recently being Esquire magazine and on ESPN. The article bothered me when it first came out and it bothers me still.

Ethan plotted the world record times for the 100 meters and fit them to an exponential

Okay, first off, mathematically, it looks like the theoretical limit of how fast humans can run the 100 meter dash is somewhere around 9.2 seconds, but it looks like we won’t get there for hundreds of years.

Yes — mathematically. From the standpoint of an ad hoc fit to an exponential, it’s OK as far as it goes. It’s not a particularly great fit, but the problem is that there’s no justification for the fit — no mechanism. It’s meaningless, and furthermore, it’s wrong. Because it should really predict in both directions, and it doesn’t. The fit shows that after you remove the 9.2 sec offset, it should take about 70 years to cut the time in half. i.e. ~10.4 sec in 1920 is 1.2 seconds above the baseline. So one should get to 0.6 sec above the baseline — 9.8 sec — in about 1990, and to 9.5 sec in 2060. Pretty close for eyeballing it.

So now let’s go in the other direction. In 1850, the time should be 2.4 seconds above the baseline, or 11.6 seconds. 1780 would be 14 seconds flat, and 1710 the fastest human alive ran the 100-meter dash in 28.4 seconds. Go back to around 1500 and it’s a full minute, which is walking speed for today’s humans. You’ll excuse me if I don’t believe that I can walk as fast as the fastest human could sprint 500 years in the past. The curve-fitting is meaningless without the next step of coming up with a mechanism, on which you could base a model. There clearly are limitations on how fast a human could run, but any resemblance of the physical prediction to the number from this analysis would be accidental. Whether it will take hundreds of years to get there is a specious claim.

But second off, you can also see that Usain Bolt is running much faster than humans ought to be running right now.

This is also crap. The numbers from the graph don’t give you an “ought to be” value. If it did, then those record holders from 1975 through Bolt’s recent exploits “ought to” have run faster than they did. Go tell Carl Lewis he was an underachiever. In reality, one would expect there to be noise in the numbers. One could measure this and see if Bolt is better than the prediction in a statistically significant way (I’m guessing yes). This would still be ad-hoc, but it would be a little more complete.

There are reasons one might expect some kind of statistical spread to the numbers; if sprinting ability has some random spread, you would expect the competitors to be the population many standard deviations out on the fastest end. The drop in world-record times is going to be a combination of improvements in health and training methods, along with sampling a larger fraction of the population due to both raw number increases and cultural and economic factors — sports is a leisure-time pursuit, and if your economic situation doesn’t allow it, you aren’t going to compete in track and field. We’re doing more sampling of the fastest times, and the number will get smaller as a result. The notion that

A runner capable of beating Bolt, he says, “hasn’t been born yet.”

may be true, but isn’t supported by this graph. It’s also possible that the runner has been born (and died), but he was born into poverty and/or war, or died over a hundred years ago and never got a chance to run track, or any other number of possible scenarios. We don’t sample all of the population. Maybe Bolt is really near the physical limit, and it’s just a statistical fluke that he’s running track here and now. We don’t really know. Sadly, though, the media has latched onto this analysis, and people might think it means something.