Functional Genomics, Nanopore Sequencing, and Mathematicians
First, a quick aside on Razib's post below:
"! The differences between the languages are deeper than this, but you can read the book to find out how-it makes me wonder a bit whether Asians really do have greater mathematical abilities than Europeans (I don't know whether the names for numbers are very long in African languages of course, and Dehaene would never touch such a subject)."
Bah, this is PC nonsense. American born Asians who speak English do just as well at math. Dehaene is obviously quite PC (as Razib noted) and is simply searching for an excuse to "explain away" Asian ability.
As for the "ceiling effect" in math - I'm not sure whether it is a function of visualization ability alone or other components as well (e.g. generalized processing ability). Certainly visualization is a contributing factor, but I think that the reason visualization is usually reported is that it's the most PC way of saying "IQ".
I think that as we identify the genetic roots of high IQ, we'll find factors that control the math ceiling. We can go from there to functional genomics and figure out what they do. [Gratuitous aside: People like Murtaugh/Orwin
et al. who doubt that this is possible (without any real supporting arguments, mind you) can watch from the sidelines while we deal with the "impossible" question of genetic influences on intelligence - racking up Science/Nature papers and making money hand over fist while changing the world... muhuhuhahaha!]
One thing I would find quite interesting is an analysis of the genomes of mathematicians. Once we get "instant genome sequencing" methods like
nanopore sequencing to work, we can get a tremendous amount of information on the genetics of subpopulations. Such fine sampling is probably not justifiable till the price per genome point hits the $10^3-10^4 range, but we'll get there soon enough.
Perhaps the best population to analyze with such methods would be mathematicians, as mathematical ability is the single most relevant factor to our success as a technological society. An additional point of methodological importance is that there is a clear division between the three major classes of mathematicians that hints at genetic roots more directly than in other fields. That is, a mathematician's choice of subfield (analysis/algebra/geometry = logic/formalism/visualization) is more likely to have genetic roots than (say) an engineer's choice between electrical engineering and chemical engineering. I would be very interested to see genetic differences between analysts, algebraists, and geometers. Personally, I've always been far better at visualization (geometry) and formalism (algebra) than I have been at logic (analysis), though these are relative things, of course. Finding the genetic roots of such differences and mapping them to thei relevant protein products and brain structures would be fascinating...and have direct applications in human engineering.