Keeping in mind that the map is not the territory, here is my proposal for estimating associative horizon.
I currently believe that it is caused by an over-reliance on a short-circuited cognitive style that I call “observation and induction”, which I may eventually describe (but is, frankly, exactly what it sounds like). The personality trait corresponds to an eccentricity in both ability and achievement, and perchance an independence of mind. The independence of mind seems to be the easiest to pick out at a glance, but the most difficult to test. Eccentricity of achievement and ability are already available to us.
Initially, I’d thought it might be as easy as comparing verbal and quantitative ability (and so on, as necessary), and calling AH the disproportion between the modes of ability. Although a useful correlate, I think this would be a misleading metric because AH seems to be primarily a cognitive style or preference (similar to MBTI personality traits) rather than an ability per se.
Therefore, I (tentatively) propose that associative horizon may be measured as the disproportion in achievement, and possibly by disproportion in achievement within a subject vs. natural skill for the subject. In the latter case, a high AH personality with high quantitative intelligence may score well in one math class and poorly in another, and a high AH personality with high verbal intelligence may read four books per week but have no taste for poetry.
To make the full picture a bit clearer, I recently proposed that conscientiousness may be estimated by the discrepancy between grades and intelligence: a studious person may score well despite low intelligence, and a lazy person may score poorly despite high intelligence. Once the g-loadings of the classes are accounted for, I am saying now that a person with high AH is more likely to have grades all over the place.
(I added the part about g-loadings to account for high-intelligence folks who happen to score highly in g-loaded subjects because these require comparatively less work. Given two assignments requiring comparable work ethic for an ordinary student, one a ten-page research paper and the other a five-problem worksheet of high difficulty, an extremely intelligent person would prefer to complete the latter because to him it is merely a matter of writing down the answers.)
This discrepancy would probably exist at the lower levels as well. For example, my Calc 3 experience was extremely erratic. It took me a long time to learn and understand how to do multiple integrals and the chain rule for derivatives in multiple variables (for that matter, I’ve never managed to grok the chain rule for one variable). On the other hand, I was extraordinarily gifted in calculating divergence and curl (able to perform these in my head in five seconds or less), and the proofs for Green’s and Stokes’ theorems seemed so obvious that I was able to “see” the whole business before the professor was halfway finished explaining them, and I’d never been much good with proofs. Hell, I’m still not.
I attribute all of this nonsense to the tendency of the high-AH brain to fixate upon its interests, potentially at the expense of non-interesting subjects. Whereas a highly intelligent brain will acquire knowledge indiscriminately, and a conscientious brain will prioritize knowledge according to group norms, an inductive brain will prioritize knowledge according to its own value system. The inductive brain is saying “I think this bit about Green’s theorem is important and interesting and I’d enjoy fixating on it some more, and this multiple integral stuff is tedious and useless and I can’t stand it long enough to finish my homework, no matter how much the upcoming test is worth”.
This observation-induction style is obviously maladaptive in social species with narrow bounds of conformity, but I think it could be adaptive in situations where knowledge is either scarce or untrustworthy. In modern times, we have a nice mix of trustworthy and untrustworthy information to analyze. The PC malaise is much deeper in some subjects than others; anthropology is tainted more deeply than psychology, and biology moreso than physics. An anthropologist may as well throw out his textbooks, dig up his own facts, and try to formulate his opinions according to patterns he has guessed at himself. On the other hand, a physicist can put more trust in the opinions of authorities because there is less outright deception within the field.