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CarlShulman comments on Information theory and FOOM - Less Wrong
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This may be covered by the following assumption about 'spurts', but this doesn't seem to work for me.
If intelligence really could jump like that, shouldn't we expect to see that in humans already? For example, shouldn't we expect to see small mutations or genes with outsized effects on intelligence? Instead, we see that even a highly inbred population with many dozens of nasty genetic problems like the Ashkenazi only get 10 or 20 IQ points*, and we see a long-term stagnation in cranial capacity, and genetic surveys seem to (as far as I've heard) turn up hundreds or thousands of genetic variations weakly linked to small IQ increases. (I cover some related points in my article on evolution & drugs.) All of this makes intelligence look like it has a logarithmic relationship with diminishing returns.
* My understanding is that on a hypothetical 'absolute' scale of intelligence, as you get smarter, each IQ point corresponds to less and less 'actual' intelligence, due to the bell curve/relative ranking that IQ is - it's an ordinal scale, not a cardinal scale.
In what sense? As you go to higher IQs each additional IQ point means a greater (multiplicative) difference in the rarity of individuals with that frequency. Studies like those of Benbow and Terman show sizable continuing practical impact of increasing IQ on earnings, patents, tenured academic positions, etc.
ETA: Thanks for the clarification.
Because of the construction of the tests. As you go to higher points, each point represents fewer and fewer correctly answered questions. Matrix IQ tests can be mechanically generated by combining simple rules, and they show the same bell curve norms despite what look only like linear increases in number of rules or complexity.
And the Benbow and Terman studies and others do show practical impact, but they don't show a linear impact where each IQ point is as valuable as the previous, and they certainly do not show an increasing marginal returns where the next IQ point gives greater benefits than before!
Do you mean "at higher IQ values each additional point corresponds to less and less additional (expected) intelligence" or "at higher IQ values each additional point corresponds to less and less total intelligence"?
I mean the former - diminishing returns in measured intelligence (IQ) versus actual intelligence.
(I definitely am not saying that IQ points are uncorrelated with actual intelligence at some point, or inversely correlated!)
I didn't thus misinterpret: my prior on the latter meaning is low.
(I corrected my comment before you replied, sorry for acting confused.)