Category Archives: Math

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.

Come on Down!

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Pigeons outperform humans at the Monty Hall Dilemma

Pigeons, on the other hand, rely on experience to work out probabilities. They have a go, and they choose the strategy that seems to be paying off best. They also seem immune to a quirk of ours called “probability matching”. If the odds of winning by switching are two in three, we’ll switch on two out of three occasions, even though that’s a worse strategy than always switching. This is, of course, exactly what the students in Hebranson and Schroder’s experiments did. The pigeons, on the other hand, always switched – no probability matching for them.

In short, pigeons succeed because they don’t over-think the problem. It’s telling that among humans, it’s the youngest students who do best at this puzzle. Eighth graders are actually more likely to work out the benefits of switching than older and supposedly wiser university students. Education, it seems, actually worsens our performance at the Monty Hall Dilemma.

Pigeons are also unwelcome at casinos, but this may not solely be due to their immunity to the gambler’s fallacy.

Where is the Table?

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Backreaction: Experiments with GPS

The biggest mystery in the universe is clearly the male brain. What happens if you leave my husband alone with a GPS receiver? He’ll spend several hours measuring the position of a table. For what I’m concerned the table is on the patio. Besides this, I’m every product developers nightmare since instead of reading manuals or tutorials I randomly click or push buttons till I’ve figured out what they’re good for. That’s a good procedure to find out every single way to crash the system, but usually not particularly efficient to actually use the device or software. Stefan instead goes and reads the manual!

GPS receivers are the ultimate guy toy, since it’s an electronic gadget which pretty much guarantees you’ll never have to stop to ask for directions.

Paging Professor Eppes

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Fighting crime with math: Model explains hot spots of illegal activity

Using a decade of data from the Los Angeles Police Department, UC Irvine criminologist George Tita and colleagues developed a mathematical model of how urban crime hot spots form and spread. It reveals two distinct types of areas that respond differently to suppression tactics.

Illegal activity follows a discernible pattern, Tita says: “Criminals forage for opportunities to commit crimes, much like bees search for pollen or butterflies for nectar. Foraging patterns are predictable, whether you study human or insect behavior.”

Take That, DuPont Circle

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Vortex Junction: The Next-Gen Roundabout

Roundabouts work great in low traffic volume areas because the number of vehicles in the intersection at one time is low. They eliminate traffic stops like signs or lights and allow traffic to move smoothly. When they’re installed in high traffic areas, roundabouts can become a nightmare. The trouble with roundabouts, especially big ones, is drivers are always jockeying for position along the outside lane since there are always vehicles entering into, in the intersection and attempting to exit along the outer diameter. This is a problem the Vortex Junction solves.

I don’t know if this is the answer, but it’s an interesting idea.

Traffic circles in and around DC, especially DuPont, should have been mentioned in Dante’s Inferno. High volume, poor signage, modifications that render them even more problematic (through lanes on the diameter and traffic lights) and inconsistent right-of-way protocols (some places people in the circle have the right-of-way, for others it’s those entering the circle. WTF?)

I avoid DuPont circle like it’s made of toxic broccoli.

One Ringy-Dingy, Two Ringy-Dingy

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Over at Cosmic Variance, JoAnne tells a story about dialing Pi on the phone:

Several years ago, before pi-day was famous, a student called the phone number associated with the digits in pi that appear after the decimal point, i.e., 1-415-926-5358. Apparently this is rather common now, and in fact, appears to be promoted as a mnemonic for the first 10 decimal places for those folks we need to have those numbers handy at all times. But this story happened in earlier times, back before the Bay Area split into several area codes. And, as the clever reader has already guessed, that student reached the SLAC main gate. How cool to phone pi and reach the main gate of a major national scientific research laboratory!

I remember the Cesium atomic clock frequency as a phone number: 919-263-1770. It should be a number in the Raleigh, NC region, but there is no listing for it. I’ve never actually called it.

No Confidence

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Odds Are, it’s Wrong

They seem to be looking specifically at medical (and related) research; I don’t know if there is a greater prevalence of an underlying problem — not publishing null results — in those fields as compared to elsewhere.

Over the years, hundreds of published papers have warned that science’s love affair with statistics has spawned countless illegitimate findings. In fact, if you believe what you read in the scientific literature, you shouldn’t believe what you read in the scientific literature.

“There is increasing concern,” declared epidemiologist John Ioannidis in a highly cited 2005 paper in PLoS Medicine, “that in modern research, false findings may be the majority or even the vast majority of published research claims.”

Lies, Damned Lies, and Forbes

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Cut Pay For Government Workers

I’m going to rail against this, but it’s only partly because I’m a Federal employee. It’s mostly because the authors are being deceitful.

If this were an airline or an automaker, the solution would be a no-brainer: It would be time for a big pay cut. If the company didn’t cut pay, or increased it, creditors and investors would question the seriousness of management.

The 2010 budget has a freeze of senior staff pay, and the 2011 budget that has been drafted proposes to extend
this pay freeze to all senior political appointees throughout the Federal Government and continue the policy of no bonuses for all political appointees. This is exactly the behavior that many taxpayers wanted, and often did not get, of high-level executive pay in the private sector in businesses that were being bailed out or supported by federal money.

But here’s the biggie:

[T]otal compensation per federal worker–cash earnings plus fringe benefits–now averages twice that of the private sector. So cutting cash earnings by 10% across the board seems not only reasonable, but justified.

The basic problem here is that this isn’t an apples-to-apples comparison — the spectrum of workers in the federal government is not even close to that of the private sector. Part of the reason for this is that there are many private-sector contractors that do work for the government, and a lot of these are low-paying, unskilled jobs, such as the janitorial staff. Many government jobs require a college degree, unlike a large number of private-sector jobs. I know that my local environment is not representative, but I’d be surprised if as many as 10% of the civilian government positions in the command don’t require a college degree, and perhaps a third of the staff have advanced degrees of some sort. This kind of comparison of averages of dissimilar distributions is at best incredibly misleading and at worst an out-and-out lie, like if you were comparing the compensation of the employees of a fast-food restaurant with the architectural and engineering firm on the next block, and concluding the A&E folks were overpaid.

What would be appropriate is a comparison of similar jobs within the government and private sector. Take me (please!) The median salary for a physicist working in industry was over $100k back in 2004 (couldn’t find anything newer), which was certainly more than I was making at the time, even with my locality pay for living in the DC area. I can think of many jobs where you would take a pay cut to work for the government — lawyers, I understand, can make a nice living in the private sector, much better than government lawyers or judges. And my Google-fu tells me that the article’s authors, Brian Wesbury and Robert Stein, both had stints in the federal government. They should have no trouble reporting how their private sector salary and compensation stacks up against what they received as federal employees, but that isn’t mentioned in the article.