There's Geometry Involved...And Sociopathy?

Today I had to deal with the most annoying calculus homework section I have encountered thus far, "geometric applications" of the integral, beginning with a part called "Some Pointers on Drawing" that included some fine examples of "terrible solutions" (aka bad drawings) and some "reasonable solutions" that I found much less of an improvement than the authors did. They looked nicer, no question, but the comprehension of the fundamentals of the three-dimensional figures was not immediately forthcoming.

After beating my head against the wall much of the day until it was a useless, bloody pulp, Robert and I looked at the problems together after dinner. After a lot of discussion and attempts at translation, I realized that the reason I was getting nowhere on the first problem was wholly because I did not understand what they meant by "planes parallel to the plane that passes through the horizontal diameter of the base and the axis of the glass." (I knew I was unsure of its meaning, but did not realize that this was the primary hurdle.) But once I got what the hell that was supposed to mean, I clicked (even quicker than Robert) to the general shape of the cross-sections and felt this great sense of relief that the whole problem was conceivable now, though Robert patiently waited for me to screw up the algebra/geometry of the dimention of the cross-sections a couple times before I figured it out. On a later problem, Robert kept getting the shape of the wedge cut out of a theoretical tree backwards while I kept plugging away at the development of a formula to integrate.

The take away of this is that although I feel like I am pretty much incompetent when it comes to visualizing these shapes, that may not be as true in a relative sense as I've thought before. Maybe I'm just incompetent at it because it is kind of weird and difficult for most people, not because I am an especial moron in this area.

I mentioned to Robert that one IQ test I took had two subsections, a Performance IQ and a Verbal IQ and that oddly enough, I had scored higher on the PIQ than the VIQ (about 175 PIQ and 155 VIQ - I found these results in with some papers recently and the discrepancy surprised me all over again). In googling the test to determine whether each of the subscales was normed at 100, one of the first results was about PIQ>VIQ findings amongst a group of sociopaths, which made Robert laugh. Sociopathic?! Me?! Surely not.

Ahem. A little additional research indicates that the Performance/Verbal IQ discrepancy amongst sociopaths - "the most outstanding single feature of the sociopath" is linked to diminished (low-normal) VIQ, which is not my problem, rather than high PIQ. Robert teased me that my lower VIQ score was due to difficulties with the "16 questions which focus on issues of social awareness." I did note that my immediate internal response to the sample social awareness question "What is the thing to do if you find an envelope in the street that is sealed and addressed and has a new stamp?" was to see whether the stamp was one missing from my stamp collection. Fortunately, every piece of mail (gas bill, credit card bill, etc.) that a park visitor accidentally tucked into a survey they mailed to me has had a boring stamp on it, so I have simply put it in the mail for them without having to go down the other branch of the decision tree.