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PhilGoetz comments on Defecting by Accident - A Flaw Common to Analytical People - Less Wrong
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There are no causality arrows in my reasoning.
Perhaps you think that by "fitness" I meant evolutionary fitness, and that both beauty and intelligence cause fitness. But by "fitness" I meant health. Sorry, poor choice of words.
Fitness meaning health. That works. But I think that your model does involve causality - from health to both beauty and intelligence. And, of course then beauty and intelligence will be correlated. I apologize for not anticipating that possible meaning. Since you post about evolutionary theory so often, that denotation of "fitness" never entered my mind.
Say X and Y are two independent random variables. X is correlated to X+Y is correlated to Y, but X and Y are (by hypothesis!) not correlated.