# Eugine_Nier comments on A few questions on International Rationality - Less Wrong Discussion

15 30 April 2012 10:27PM

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Comment author: 01 May 2012 03:33:45AM 2 points [-]

Your argument was atheism is weakly correlated with vocab. Vocab is weakly correlated with intelligence. Therefore, atheism is weakly correlated with intelligence.

Comment author: 01 May 2012 03:41:44AM 4 points [-]

Ah, I see your point. However, a) vocab is highly correlated with intelligence, not weakly so, b) vocab is not just highly correlated with a single intelligence metric, but is correlated with such in a variety of different metrics of intelligence. While it is possible to construct variables such that A and B are correlated, with B and C correlated, and A and C anti-correlated, it is quite difficult to do so with a large set of distinct variables that all have such correlations with each other and have a single pair be anti-correlated, especially when one has the same set of correlations even when one controls for a variety of other variables. Moreover, as a probabilistic matter if one as three variables with two pairs correlated, it is much more likely that the remaining pair will be correlated than anti-correlated, assuming that variables don't have too pathological a distribution.

Comment author: 01 May 2012 06:23:51AM 5 points [-]

Moreover, as a probabilistic matter if one as three variables with two pairs correlated, it is much more likely that the remaining pair will be correlated than anti-correlated, assuming that variables don't have too pathological a distribution.

Where you you get that? The intended probability space isn't clear, but if I take three random directions in N-dimensional space for large N, I find that the chance of two pairs having an angle less than pi/2 and the third an angle greater than pi/2 is about 1.4 times the chance of all three being less than pi/2. The ratio rises to about 3 if I add the requirement that the corresponding correlations are in the range +/- 0.8 (the upper liit of correlations generally found in psychology).

Comment author: 01 May 2012 01:57:28PM *  1 point [-]

Hmm, that's a good point. I'm aware vaguely of theorems that say what I want but I don't have any references or descriptions off hand. It may just be that one is assuming somewhat low N, but that would be in this sort of context not helpful. I do seem to remember that some version of my statement is true if the variables match bell curves, but I'm not able at the moment to construct or find a precise statement. Consider the claim withdrawn until I've had more time to look into the matter.