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bramflakes comments on Terminology Thread (or "name that pattern") - Less Wrong Discussion

8 Post author: sixes_and_sevens 03 July 2014 11:47AM

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Comment author: bramflakes 04 July 2014 09:47:39PM 10 points [-]

General case:

Small differences in the means of a normal distributions cause large differences at the tails.

Motivating example:

East Africans are slightly better at distance running than the rest of the world population, so if a randomly-picked Ethiopian and a randomly-picked someone-else compete in a marathon, the Ethiopian has a better chance of winning, but not by very much. But at the extreme right tail of the distribution (i.e. at Olympic-level running competitions), the top runners are almost all Ethiopians and Kenyans.

In my head I call it "threshold amplification" but I wonder if there's an official name for this.

Comment author: satt 02 August 2014 02:42:58PM *  2 points [-]

I've suspected for a long time that that was the insight Carl Sagan had while high and showering with his wife:

I can remember one occasion, taking a shower with my wife while high, in which I had an idea on the origins and invalidities of racism in terms of gaussian distribution curves. It was a point obvious in a way, but rarely talked about. I drew the curves in soap on the shower wall, and went to write the idea down. One idea led to another, and at the end of about an hour of extremely hard work I found I had written eleven short essays on a wide range of social, political, philosophical, and human biological topics. Because of problems of space, I can’t go into the details of these essays, but from all external signs, such as public reactions and expert commentary, they seem to contain valid insights.

(It is a little interesting, & amusing, to see someone inferring the "invalidit[y] of racism" from an observation more often used as a justification for racial hereditarian attitudes!)

Comment author: gwern 05 July 2014 01:21:35AM *  3 points [-]

I would love a name for this too since the observation is important for why 'small' differences in means for normally distributed populations can have large consequences, and this occurs in many contexts (not just IQ or athletics).

Also good would be a quick name for log-normal distribution-like phenomenon.

The normal distribution can be seen as the sum of lots of independent random variables; so for example, IQ is normally distributed because the genetics is a lot of small additive variables. The log-normal is when it's the multiple of lots of independent variables; so any process where each step is necessary, as has been proposed for scientific productivity in having multiple steps like ideas->research->publication.

The normal distribution has the unintuitive behavior that small changes in the mean or variance have large consequences out on the thin tails. But the log-normal distribution has the unintuitive behavior that small improvements in each of the independent variables will yield large changes in their product, and that the extreme datapoints will be far beyond the median or average datapoints. ('Compound interest' comes close but doesn't seem to catch it because it refers to increase over time.)

Comment author: VincentYu 07 July 2014 01:47:51AM 2 points [-]

IQ is normally distributed because the genetics is a lot of small additive variables.

IQ is normally distributed because the distribution of raw test scores is standardized to a normal distribution.

Comment author: gwern 07 July 2014 02:44:07AM 1 point [-]

And why was the normal distribution originally chosen? Most of intelligence seems explained by thousands of alleles with small additive effects - and such a binomial situation will quickly converge to a normal distribution.

Comment author: ThisSpaceAvailable 14 July 2014 11:33:40PM 1 point [-]

The phrase "additive effects" doesn't make sense except in reference to some metric. If your metric is IQ, then that's circular.

Comment author: gwern 14 July 2014 11:51:51PM 0 points [-]

If your metric is IQ, then that's circular.

No, it's not, because IQ is itself extracted from a wide variety of cognitive measures.

Comment author: ThisSpaceAvailable 16 July 2014 02:08:04AM -1 points [-]

You seem to be claiming that there are some unspecified underlying other metrics of which IQ is simply a linear combination. If so, then IQ is not the ultimate metric. Which doesn't contradict my claim (claiming that P is not true does not contradict the claim that P -> Q). It does raise the question of what those metrics are.

Comment author: gwern 16 July 2014 03:26:52PM *  0 points [-]

It does raise the question of what those metrics are.

To expand on what I just said: IQ is a factor extracted from a wide variety of cognitive measures, whose genetic component is largely explained by additive effects from a large number of alleles of small effect with important but relatively small nonlinear contributions. That is, intelligence is largely additive because additive models explain much of observed variance and things like the positive manifold of cognitive tests.

Please be more precise in your comments, or stop wasting my time due to your lack of reading comprehension and obtuseness like you did before in my Parable post.

Comment author: ThisSpaceAvailable 14 July 2014 11:34:19PM 0 points [-]

I think that "multiplicative" or "geometric" describes such phenomena.

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