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.
Good points. But – I looked at Ethan’s analysis again, and it is not so bad. He did what I do quite often – throw together a simple analysis. He never really makes this analysis more than it is. I think his main point is that Usain was different than those before him.
The media, however, that is a different story. Yes, they blew this out of proportion. Here is an article that is about something popular and that has something they can latch onto. No surprise the media twisted it a little.
Agreed.
It’s fun to fit data to curves, but without an underlying model (which seems impossible in this case) it’s pretty absurd to draw conclusions from it.
Sheez, everybody knows Jamaicans have a higher concentration of Actinen A and that Jamaican yams give you the runs. Seriously, sprinting is about maximizing your turnover and maintaining it for as long as possible. Bolt has ridiculous turnover but others are faster. What makes him special is the fact that he decelerates slower than others, thanks to his greater stride length (he’s 6-5 and all legs) and all that 400 training. It won’t be too long before other athletes approach Bolt’s numbers. Little Tyson gay ran 9.68 last September.
Although Bolt’s 100m time is unusual, it is pretty usual, considering all events in track and field, to have an unusual time in there somewhere. Michael Johnson’s 19.32 200m, Paula Radcliffe’s 2:15 marathon, Beamon’s long jump mentioned in the article, Gebrselassie’s 12:44 5000, and probably plenty of other world records might have similar dips if plotted in the same way. We should look at all the events, then see if this one is truly unusual.