Thomas, many of the differences between women and men are not ‘natural’, they are enforced in many ways. Walk into a Toys R Us store some day to get a feel for how solid is the wall between pink and blue.

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]]>Here’s something I remember reading somewhere (in John Allen Paulos’ book “Innumeracy”?) that may be of interest.

Consider two normal distributions with the same standard deviation, say sigma = 1, one with a mean of 0 and the other with a mean that is almost the same, say a mean of 0.1. If you DIVIDE the former by the latter, then you get (after simplifying some):

exp[ 0.005 – (x)(0.1) ].

For x = 0, 1, 2, 3 (i.e. for these numbers of standard deviations to the right of x = 0), the RATIOS wind up being approximately

1.005, 0.91, 0.82, 0.74.

Now if the normal distribution were a simple exponential (i.e. the exponent was linear in the independent variable), then these ratios would be constant, like you see in population growth or radioactive decay. However, the normal distribution is “super-exponential”, due to the fact that the exponent is quadratic in the independent variable, and thus the output RATIOS for constant input INCREMENTS are not constant.

This illustrates that if two populations with the same standard deviation have slightly different means, then the relative proportions of the two populations can vary a lot when you look several standard deviations away from their (nearly identical) means.

]]>Consider two normal distributions with the same standard deviation, say sigma = 1, one with a mean of 0 and the other with a mean this is almost the same, say a mean of 0.1. If you DIVIDE the former by the latter, then you get (after simplifying some):

exp[ 0.005 – (x)(0.1) ].

For x = 0, 1, 2, 3 (i.e. for these numbers of standard deviations to the right of x = 0), the RATIOS wind up being approximately

1.005, 0.91, 0.82, 0.74.

Now if the normal distribution were a simple exponential (i.e. the exponent was linear in the independent variable), then these ratios would be constant, like you see in population growth or radioactive decay. However, the normal distribution is “super-exponential”, due to the fact that the exponent is quadratic in the independent variable, and thus the output RATIOS for constant input INCREMENTS are not constant.

This illustrates that if two populations with the same standard deviation have slightly different means, then the relative proportions of the two populations can vary a lot when you look several standard deviations away from their (nearly identical) means.

]]>As in the article, let’s introduce 2 chemicals that act in a slightly different way than proposed by the author. Let’s say these two chemicals, we’ll call them

“X chromosomes” and “Y chromosomes”, act in a manner to induce the production of other secondary chemicals suggested by the author – the “X chromosomes” induce a chemical that makes one not want to make others feel too bad and the “Y chromosomes” the other one…..

I need not go further; the remainder is trivial. A chemical argument IS a genetic argument. Now if we were giving girls one set of shots at birth and boys another, that would be different. But we don’t.

The mathematical model of what the author presents is only slightly more interesting. The means of the each set might be equivalent, but the variation might be different. But that’s not really how we ought to be viewing this argument. There is a variable that should be considered: the probability of making a meaningful advance in a field of study, in this case mathematics. At a certain point and left of that point, the probability is 0. To the right of that point, the variable increases approaching 100% as the deviance from the mean approaches infinity. The resultant curves will look significantly different, most likely favoring the gender with the greater variability.

I suspect this is more what Summers and Tierney are looking at, not a bell curve of natural ability, but a secondary curve of ability to contribute, which is significantly different.

Having 3 daughters, I know these debates will eventually enter their consciousness. And maybe they won’t be making critical advances in a given field. But that’s no reason to expect any less of them than their best.

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