Why can we assume that all the little things affect intelligence independently? Are synergies obviously rare, and how rare do they have to be for the central limit theorem to apply? In the simplest alternative model I can think of, incremental advances could be multiplicative instead of additive, which gives a log-normal distribution instead of a bell curve. This case is uninteresting because you could just say you’re measuring e^intelligence instead of intelligence, but I can imagine more complicated cases.
Side note: I think it is not well known that for the quintessential normally distributed random variable, human height, the lognormal distribution is in fact an equally good fit. And on the other end of the variance spectrum: I became biased toward the lognormal distribution when I observed that it is a much better fit for social network degree distributions than the much-discussed power-law. It is a very versatile thing.
Why can we assume that all the little things affect intelligence independently? Are synergies obviously rare, and how rare do they have to be for the central limit theorem to apply? In the simplest alternative model I can think of, incremental advances could be multiplicative instead of additive, which gives a log-normal distribution instead of a bell curve. This case is uninteresting because you could just say you’re measuring e^intelligence instead of intelligence, but I can imagine more complicated cases.
Side note: I think it is not well known that for the quintessential normally distributed random variable, human height, the lognormal distribution is in fact an equally good fit. And on the other end of the variance spectrum: I became biased toward the lognormal distribution when I observed that it is a much better fit for social network degree distributions than the much-discussed power-law. It is a very versatile thing.
Good point.