Coincidences

So, in one of those weird life coincidences, I was catching up on my Science reading at Starbucks this morning, and came across this review by Stephan Mertens of the book Guesstimation. The review (and the book) is about how physicist Enrico Fermi cultivated the skill of back of the envelope calculations--being able to roughly approximate results from limited data and general knowledge. For instance, the number of cells in a human being is deducible from an estimation of the smallest object the eye can see, the power of early very poor microscopes, the density of water, the mass of the average human, and the fact that we float. Interestingly, the result of this calculation is exactly the number you always see bandied about--100 trillion. They picked a pretty good example!

Other suggested problems in estimation are: How long a hot dog can be made from a typical cow? How many people are airborne over the US at any given moment? What is the photon flux at the eye from a faint visible star? How many piano tuners are there in Chicago?

One of the suggested rules of thumb when making wild approximations is to use the geometric mean rather than arithmetic mean. The geometric mean is the square root of the product of the bounds of the estimate, where the regular mean is the sum of the bounds divided by two. Thus, if your best estimate of the number of people who could fit in a VW bug was that it is more than one and less than 100 (a pretty poor estimate), the average is 50, but the geometric mean is 10, which is a pretty good guess. The geometric mean keeps the large value from dominating the result.

Anyway, I realized that geometric mean is precisely what I was using in the denominator of the CCV metric I've been speculating about. I should have realized that earlier, but I wasn't paying attention. A friend had suggested that a problem with using the CCV might be that it would be biased towards larger values, but I think that this means that that wouldn't be the case. Curiouser and curiouser...