Saturday, April 09, 2011

HIQ Smarty-pants

Robert W. Johnson has compiled a list of what he alleges to be the 18 smartest people in the world, together with their alleged IQs. Now it turns out that those on list are chess players (4), authors(3), politicians (2), actors (2), physicists(2), mathematicians(2), a business man, an engineer, and a precocious 12-year old. Terence Tao tops the list with a purportedly “verified” IQ of 230.

Tao is indeed one super smart guy, but is an IQ of 230 really credible? There are two usual definitions for IQ. One, relevant only for young children, is the ratio of so-called mental age to chronological age, as demonstrated on some test. (Full disclosure, your author was once credited with an IQ of 200 based on the fact that at his then chronological age of 40, he already had the mental performance of an average 80 year old). The second method computes IQ based on the statistics of performance on a test – and this is the only score considered appropriate for adults. This standard awards an IQ score of 100 for the mean score and 15 points for every standard deviation above the mean.

On this scoring system Tao’s 230 is 8.67 standard deviations (SD) above the norm, Chris Hirata’s 225 is 8.33 SD and Paul Allen’s 160 a more modest 4 SD. If we look a bit more closely at the normal distribution, we find that while about 16 % of people have an IQ above 115 (1 SD), and a bit more than 2% are at or above 130 (2 SD), only 3 out of 100,000 can match or exceed Paul Allen’s 160 (4 SD). Of course to accurately assess such a score, many more than 100,000 people would need to take the test.

The air gets really rarified when we go to 5.3 SD = IQ 180 (Bobby Fisher, James Woods, John H. Sununu). Statistically, only six people in 100 million do that well.

So what about Terry Tao? SD = 26/3 converts to about 2 people per quintillion (2 x 10^-18), which would make Terry (and Chris, at 4 x 10^-17) smarter than anybody who is ever likely to live.

So on statistical grounds alone, don’t trust any IQ over 150 (5 out of every 10,000).

And definitely don’t trust anybody who claims an IQ of 200 (Z = 20/3, 1.3 x 10^-11).