Obnoxious

I was talking to Ed tonight about that famous psychology experiment where one person (the subject) is put in a room with a bunch of confederates and a researcher asks the group a question with an obvious answer and has them vote, at which point all of the confederates vote the wrong way, and the subject usually follows along despite the group being obviously wrong. (Sorry I don't have the details, but it's a widely known thing.)

My natural tendency is to scoff at the subject, but in truth, that's probably the right thing to do. It seems to me that that probability of a bunch of other people being wrong about something completely obvious is lower than the probability that you have misunderstood the question somehow. (And by "obvious" I don't mean like "It is obvious that rent controls only serve to make housing more scarce, thus exacerbating the underlying problem," but more like, "It is obvious that this line is longer than the other.")

Nevertheless, Ed and I are both the kind of obnoxious jerks who think we are right despite this kind of external evidence. When my mother taught me to write the numbers, right before Kindergarten, I argued with her that she was writing the 5 and the 6 backwards. I argued with my 5th grade teacher that "colonel" - one of our spelling words of the week - was clearly incorrect. I do not hesitate to argue with my professors now about factual issues within their areas of expertise, although I am not nearly as obnoxious now as I was as a kid. (To be clear, I don't argue with professors about matters of opinion unless it seems wanted.)

I am almost always willing to admit that I may be wrong, but I always actually believe that I'm right despite this theoretical possibility, and even in situations where the odds are against it. And I don't really mind being shown how I am wrong. (It occurs to me that this is similar to how I am with games - tending to be a bad winner, but nearly always a good loser.)

At any rate, this is probably why, when our linear algebra professor realized there was a lot of confusion over the question of whether the column space of an mxn matrix A was a subspace of Rⁿ or R^m, and had us vote, I was willing to raise my hand for m even though 17 or 18 of my 19 classmates had voted for n. (Reminder, for those who can be reminded: the column space of a matrix A is all of the vectors that can be formed of linear combinations of the columns of A, or in other words, all of the vectors b satisfying the equation Ax = b for some x.)

I thought that I must be wrong, because even though my classmates are often confused, that was an overwhelming majority against me, and yet, what I had on my paper sure made it look like m, so that's what I went with. I turned out to be correct.

She next had us vote on the same question pertaining to the nullspace of A. (The nullspace is the vectors x satisfying Ax = 0.) This vote didn't go against me quite as strongly - it was more like 17-3. But I was again correct.

(I should note that I was perfectly capable of getting either question wrong - this is not a question where the answer was obvious to me at the time, and this is the type of thing I am often wrong about, usually because I have made some simple mental error. This post is about my psychology, not about my besting everyone in feats of dimensionality.)

I suspect that I am different from most people in this non-majority-joining respect because I am not very bothered by being mistaken, and I see the possibility of being right (i.e., winning) as having a pretty big payoff. And although holding the minority position makes it more likely that I'm mistaken, it also raises the payoff for being right. (After all, being the only one who is right is much more awesome than being right in a crowd.) Also I am just unwilling to let things go until I see why I am wrong.