Thanks for the feedback, exactly the kind of thing I was hoping to get from posting here.
I have thought about a multiplicative model for intelligence, but wouldn’t the fact we see pretty-close-to-Gaussian results on intelligence tests tend to disconfirm it? Any residual non-Gaussianity seems like it can be explained by population stratification, etc, rather than a fundamentally non-Gaussian underlying structure. Also, like you say the polygenic evidence also seems to point to a linear additive model being essentially correct.
No, because intelligence test publishers deliberately re-express raw results so their curves have mean = 100 and SD = 15, a convention going back to Wechsler’s “deviation-IQ” idea.
I don’t think so, IQ is famously defined to be normally distributed, right?—but we’re not interested in convention. I was wondering if there’s there some Platonic way in which cognitive ability is naturally distributed between different humans? For example, height is mostly normally distributed, and human lifespan is Gompertz-distributed; it’s not very useful to talk about log-height or log-lifespan.
I’m open to the claim that there is no such natural scale for intelligence, or that at least the scale for intelligence is at least similarly natural in some linear and log-scale.
We could go with e.g. RE-bench and see what the distribution over tasks there is for humans...? Or literal program induction? Or ARC-AGI 1⁄2 and check how the natural distribution for 50% chance of solving a task is.
As for the additive structure of the genetics, my hunch is that it could be the log-transform of some underlying lognormal trait, but I don’t know enough about quantitative genetics to identify a flaw in that thinking if it exists.
Thanks for the feedback, exactly the kind of thing I was hoping to get from posting here.
I have thought about a multiplicative model for intelligence, but wouldn’t the fact we see pretty-close-to-Gaussian results on intelligence tests tend to disconfirm it? Any residual non-Gaussianity seems like it can be explained by population stratification, etc, rather than a fundamentally non-Gaussian underlying structure. Also, like you say the polygenic evidence also seems to point to a linear additive model being essentially correct.
No, because intelligence test publishers deliberately re-express raw results so their curves have mean = 100 and SD = 15, a convention going back to Wechsler’s “deviation-IQ” idea.
I don’t think so, IQ is famously defined to be normally distributed, right?—but we’re not interested in convention. I was wondering if there’s there some Platonic way in which cognitive ability is naturally distributed between different humans? For example, height is mostly normally distributed, and human lifespan is Gompertz-distributed; it’s not very useful to talk about log-height or log-lifespan.
I’m open to the claim that there is no such natural scale for intelligence, or that at least the scale for intelligence is at least similarly natural in some linear and log-scale.
We could go with e.g. RE-bench and see what the distribution over tasks there is for humans...? Or literal program induction? Or ARC-AGI 1⁄2 and check how the natural distribution for 50% chance of solving a task is.
As for the additive structure of the genetics, my hunch is that it could be the log-transform of some underlying lognormal trait, but I don’t know enough about quantitative genetics to identify a flaw in that thinking if it exists.