1) I once scored 800 on GRE Math and 730 on GRE Verbal. This was around the year 2000. More recently I got a score of 476 on the MAT. The mean (of MAT takers, presumably) is 400, the standard deviation is 25.
2) Like attracts like.
So what are smart folks like?
1) Extremely conflict-prone. And we can't even use the excuse of being surrounded by idiots - smart people feud with each other like crazy. Of course, we don't do it exactly like morons. Physical aggression is very rare. But angry denunciations, finger-trembling hate, humorless spite, frivolous lawsuits - all of that is typical. It seems that the moderately smart - the 100 IQ to 130 IQ brigade - are less conflict-prone than either idiots or brainiacs.
2) It's typical of very smart people to hold political views that are very far out of the mainstream. Racial supremacism, religious fundamentalism, communism, anarchism, unusual conspiracy theories, extreme liberalism (not the kind of stuff you'd see on MSNBC, much worse), fundamentalist libertarianism, violent environmentalism, other stuff that's so far out that there aren't even any terms in the dictionary to describe it succinctly. The only thing that's rare in these circles is being a moderate Democrat or Republican, or some foreign equivalent.
Unlike the propensity for conflict, this feature of the high IQ world is easy to explain. The range of currently-respectable political positions is determined through violent political struggle. Opposing interests clash, striving to silence and, often, to eliminate each other. Their titanic efforts frequently move the front line of debate. At any particular time the "moderate" position is the one right along this front line. The map can provide an analogy: why does Germany end and France begin at some particular point? Because of how the last war ended. Wait a century (or maybe less) and the line will move. But to a person with limited information and understanding, to a person who has not read much history, the line will seem to have more meaning than that.
The current political front line, the current set of moderate positions, will seem to him not a result of a hastily-hashed-out, self-contradictory, uneasy truce between opposing forces bent on each other's annihilation, but an obvious outcome of the universal principles of common sense and decency. Or, if he is less secular, of divine revelation. Why? Because that's how political actors have to describe their gains to the public (and likely even to themselves) if they don't want to drown in cynicism. The full, sausage-making truth of the thing can be too demoralizing, even to politicians themselves. The motivations behind their activity appear to often be subconscious.
A person with a bit of historical perspective (in other words, a man who reads a fair amount) knows that the "moderate" line has been all over the place many times. All (not even most) of the things that are being used to define morality now were used to define evil not very long ago, and will be used so again. To a curious, informed observer the range of currently acceptable political positions is like the visible light section of the electro-magnetic spectrum - a tiny thing whose only remarkable feature is that it can be noticed with the naked eye.
So why don't most smart people congregate in some different, but similarly small part of the spectrum, one whose features can be shown to conform to the universal principles of common sense?
Well, first, humans are inherently tribal. Even if some political position could be proven beyond the shadow of a doubt to make sense for tribe A, it probably wouldn't make sense for tribes B, C and D, for the same reason that no position on interspecies violence could simultaneously make sense for sheep, wolves and ticks.
But that doesn't come close to explaining all of the variance. People from identical backgrounds who have very similar and very high levels of intelligence are still likely to differ wildly on politics. Why? Politics is hard. You can't make controlled experiments in it. An uncountably large number of variables affects it. Ceteris is never paribus. It may well be that a satisfactory proof of what makes the best political sense for a single man, a family, a tribe or the world, is beyond the capacities of even the smartest man who's ever lived.
What about smart mainstream politicians? Bill Clinton was a Rhodes Scholar. Chuck Shumer, the senior senator from my state of NY, scored 1600 on the old SAT. Eliot Spitzer, our former governor, got 1590 in the SAT and a perfect score on the LSAT. There are lots of other certifiably smart people in respectable politics. All of them, by definition, have to hold moderate political positions. Are they all simply lying about that? I doubt it. Their careers depend on them having internalized conventional beliefs. I suspect that conscious Machiavellianism is rare - human beings aren't set up to handle it. Normally we have to deceive ourselves before we can become effective at deceiving others.
But yes, these people's political stances are atypical for high-IQ folks who are not professionally involved with respectable politics. My own views aren't as far out as Ted Kaczynski's or Bobby Fisher's, but neither am I as intelligent as those two. Which brings me to my next point.
3) The IQ spectrum appears to be extremely fine-grained to the naked eye. What do I mean by that? Let's say I'm very sure that person A is smarter than I am. I always feel like a boring, childish mediocrity talking to him or reading what he's written - that's usually a sure sign. Well, in my experience there's almost always a person B who's just as obviously smarter than A. And then there's C who is obviously (not just to me, to everyone who knows them) smarter than B. And on and on. These ladders of ability can be very long. I remember reading about some early 20th century explorer who studied the IQ of a primitive tribe - these may have been Bushmen. The tribesmen told him which members were smarter than others, and then his tests independently confirmed that information. It's amazing when you think about it, but differences between IQ 65 and IQ 70 can be noticed with the naked eye. And so can differences between 150 and 155, between 155 and 160, 160 and 165, etc. Here's something on this topic by Eugene Wigner, a Nobel laureate in physics, as quoted on Steve Hsu's blog:
"I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed me."
4) Women are largely asymptomatic carriers of high IQ. This is because they're congenitally bored by every topic to which high intelligence can be usefully applied. I've known women who performed better on tests than I do, but whose biggest interests were gossip, shopping, celebrity news and touristy travel. There have been one or two (very!) partial exceptions. Sure, a woman can pretend to be interested in topic X if she thinks that's expected of her. But female physics professors typically don't like talking about physics off work - it bores them. Same for female literature professors, female software engineers, etc. Ability minus enthusiasm will rarely equal achievement. It's a bit like macromastia - I'm sure that men are perfectly capable of carrying the genes that lead to buxomness in the next generation. But one can't tell by looking at them which men exactly will do that.
5) The very smart are definitely more honest than idiots (let's define the latter as under-85s), but are we more honest than the 100 IQ - 130 IQ group? I don't think so. Same thing for objectivity. I'm sure there is a large ethno-racial component to both. If we corrected for it, if we made strictly within-ethnicity comparisons of honesty and objectivity, I still doubt that the smart would outscore the average. This has political implications. W.F. Buckley famously said that he'd rather be governed by people randomly selected from a Boston phone book than by the Harvard faculty. There's wisdom in that. There were political systems, both in ancient Greece and Renaissance Italy, in which officials were selected by lots.
6) Addiction seems to be the one moral failing that the smart are less likely to display than people of average or moderately-above-average intelligence. Yes, I've heard about very smart addicts, but it's very rare. And I'm not just talking about drugs. Obesity is rare too. There seems to be a greater amount of self-control.
7) Real idiots are, without exception, ugly, but starting with the 90 IQ - 100 IQ group, attractiveness seems to become uncorrelated with intelligence, at least in within-ethnicity comparisons. I don't have any data on this, by the way. But impressions have value.
8) Not all smart people are nerds. This is actually painful for me to admit. I'm a nerd, so in many situations I've wanted to believe that nerdiness is the price of intelligence, that you can't get that particular piece of frosting without the fiber. But it's not true. Nerds are overrepresented among the smart, yes. Yet a lot of very smart people (a quarter? a third?) are even more outgoing than your average person. Obviously, these sorts of smart people are more likely to go into business or politics than into math, hard science or engineering.