IQ and real world success

from a letter to me by Grady Towers dated March 12, 1999
Used with permission from the author

Have you never wondered why the world is not ruled by those with two hundred plus IQs? If IQs were of such overwhelming importance, the world should be, shouldn't it?

Well, there's a mathematical explanation why it isn't. The following Gedankenexperiment will show you that reason.

Imagine that you have a highly reliable IQ test that is normally distributed and correlates positively with some real world criterion that is also normally distributed. If you plot all the data pairs from these measurements, you should obtain a scatter diagram that looks like this ellipse.

One can deduce three things from this diagram:

1. The very highest level of real world accomplishment is not made by those with the very highest level IQs.

2. Those with the very highest level IQs tend to have real world achievements just below the very highest levels.

3. Of those in the IQ range most conducive to real world achievement, most do not achieve at the highest level, or even reach that of the very highest IQs. IQ scores tell you what league you're playing in, not how well you can bat.

This is an idealization, of course. It departs from reality in two ways. In the first place, the correlation between IQ scores and most criteria, as used in this illustration, is not as high as that shown. In reality, the ellipse would be much fatter and the disparity between test and accomplishment would be correspondingly more. And in the second place, real world accomplishments are almost always positively skewed, so that a two horned ellipse would be a better representation -- what I personally call a planarian scatter diagram, for obvious reasons.

The real question, naturally, is what are the boundaries for real world success? It turns out that there are actually two: one for practical real world achievements, and a second for theoretical accomplishments. The first consists in an IQ span of about 30 points between 120 IQ and 150 IQ (see Hollingworth). The second is also comprised of a 30 point span from about 150 IQ to 180 (see Roe). IQ scores measure the ability to carry out symbolic thinking. Those in the practical range use symbolic systems to solve problems; those in the theoretical range invent and modify the symbolic systems themselves. The business of the mathematician is to prove theorems, not solve problems. Much the same could be said of the scientist, poet or philosopher.

There are exceptions to this rule, to be sure: Bobby Fischer has an IQ over 180, and Truman Capote had one over two hundred. But in the main, this generalization is a good one.

There's one last corollary to the foregoing. It's a well known fact that the standard deviation for IQ is somewhat greater among men than among women. This suggests that proportionally more women should fall into the practical range than they do into the theoretical one. Could this be why most mathematicians are men, and so many stockholders are women?

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