See also related posts.

There does not appear to be an ‘‘ability threshold’’ (i.e., a point at which, say, beyond an IQ of 115 or 120, more ability does not matter). Although other things like ambition and opportunity clearly matter, more ability is better. The data also suggest the importance of going beyond general ability level when characterizing exceptional phenotypes, because speciļ¬c abilities add nuance to predictions across different domains of talent development. Differential ability pattern, in this case verbal relative to mathematical ability and vice versa, are differentially related to accomplishments that draw on different intellectual strengths. Exceptional cognitive abilities do appear to be involved in creative expression, or ‘‘abstract noegenesis’’ (Spearman and Jones, 1950). That these abilities are readily detectable at age 12 is especially noteworthy.

This figure, describing the same study population, may also be of interest:

Earlier discussion:

Scores are normalized in units of SDs. The vertical axis is V, the horizontal axis is M, and the length of the arrow reflects spatial ability: pointing to the right means above the group average, to the left means below average; note the arrow for business majors should be twice as long as indicated but there was not enough space on the diagram. The spatial score is obviously correlated with the M score. Upper right = high V, high M (e.g., physical science) Upper left = high V, lower M (e.g., humanities, social science) Lower left = lower V, lower M (e.g., business, law) Lower right = lower V, high M (e.g., math, engineering, CS)

## 12 comments:

What's up with the plots in Figure 2? The usage of circles/ellipses implies that the two measures are statistically independent. I doubt this is the case if the data are SAT scores from gifted 13-year olds. It is far easier for 13-year olds to excel at the SAT math component, than at the verbal component (probably more so, because SAT-V is highly dependent on vocabulary, which continues to accumulate, whereas the SAT-M caps out at algebra, geometry, and simple probability/stats).

But social science, what do you expect? ;)

The highest group scored above the 1 in 10,000 level of what population? The SAT taking population (college bound 17 year olds) or the general 13 year old population? But on just one section of the SAT? Wouldn't it make more sense to look at their composite SAT score since it's more g loaded than either math or verbal.

Phenotypes are nice, but is there any evidence for an M-V-S trichotomy of "cognotypes" (e.g., brain regions, distinctive mental capacities) or even "metritypes" (e.g., robust and test-independent dimensions from PCA or factor analysis)? V and S are defensible, more so than "g", but what is the evidence for M as an intrinsic attribute rather than a stylized domain of competence such as SAT-M, math grades M, Putnam-M, PhD attainment M, and composites of such. Or a generalized ability to concentrate for long periods on certain types of details that are emotionally unappealing to most individuals, that appears as low "M" in the general population and high "M" in the subpopulation, due to the lifelong stylized M-competence detection systems known as School and the Economy.

I asked this under the preceding blog post, together with some comments on the state of PCA / factor analyses of IQ tests in the literature (as far as I have able to locate it), that you might find interesting if you have not seen them.

If anyone here believes in the M-V-S story as a currently known psychometric fact (not just a sociological metaphor or future research agenda) this would be a good time to cite specific literature.

Maybe I misunderstand, but that is what I construe Figure A is, quartile markings for composite scores.

I think of M as a combination of S + g + V. M is a good measure of overall intelligence. On the Most current edition of the WAIS, vocabulary is no longer the most g loaded subtest. Now the most g loaded 2 subtests measure M: figure weights and arithmetic. My math teacher used to say "if you are good at math, then that means you are good at logic"

If the axes are individually normalized, then the eccentricity of the ellipse is a measure of the statistical dependence of each axis on the other.

Is that so? You need some evidence that the non-g components of S and V contribute to M. I could imagine that non-g S contributes to M, but it is hard for me to envision that non-g V also contributes.

I was exceptional at math in elementary school because I excelled in abilities that I thought were non-g such as arithmetic and I have an excellent rote memory, but I thought my relative decline (in competition with people who had better work ethics or > 2.5 SD M) was due to the material becoming more abstract or perhaps spatially loaded. Now arithmetic is highly g-loaded? Perhaps for the general population since I look at my own ability to do mental math rather derisively since I thought it had little to do with actual intelligence.

Don't you ever talk your way through math problems? That's verbal reasoning. Also algebra is verbal while geometry is spatial.

That talking ability doesn't seem to invoke complex verbal reasoning tested on, let's say the GRE, nor does this talking ability seem independent of g.

I was actually better at geometry than algebra despite having relatively low S. I tend to make simple mistakes on algebra on fairly complex problems, but I can get the problem if I am allowed carefully review my work or do the problem twice while avoiding the error. I think algebra recruits working memory more than g.

Also HS geometry doesn't require much S; that's probably demanded in higher math.

The top 1 in 10,000 scored a > 700M or > 630 V on a pre-1995 SAT subtest when they were while they were 13.

There is the CHC theory. You can take what the SAT-M measure as a representation of Gq(quantitative reasoning) + Gf (important component if they test at young age, they claim that ) +Gc, SAT-V of GC+Gf+lots of Grw (reading/writing ability). Naturally, working memory and Processing Speed permeate all cognitive processes so also the SAT. http://alpha.fdu.edu/psychology/chc_theory.htm

I think "M" can be seen as a superset of fundamental cognitive processes related to numerosity plus "other stuff" that appeared as humans evolved. In Pinker's "How the Mind works" he mentions 3 abilities related: Probability, Arithmetic and logic. Maybe Arithmetic is the most pure measure of "M", it evolves directly from numerosity and relies very little on other modules. I'm not talking about rote mental calculation, that in fact is more a mechanical process based on good algorithms, good representation of information (can be visual or verbal, have seen both on mental calculators)plus working memory and speed of memory retrieval, but about a facility with fermi-like problems and intuition about numbers and number representatives.

Having high S without M makes a you a good architect not a geometer, the converse is not true with geometers but can be with other types of mathematicians like number theorist or logicians but probably is not because most measures of M, like everyone knows, are measuring also S so are not independent because of the way they are measuring it not because they aren't (maybe they are not who knows?)

It would be interesting to know test what kind of abilities are related to different types of math. You can't visualize all math and can't just symbolically manipulate your way through (can you?).

For example:

topology, geometry, M+S

algebra?, number theory, combinatorics pure M?

Logic, Category Theory, set theory V+M?

Other areas like analysis, probability, Mechanics have multiple perspectives so can use all types of abilities

What do you think?

Yes, I like this.

I don't think high school geometry requires much S.

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