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You probably shouldn't use Chomsky as an example. Chomsky is the ultimate outlier. He's got a superhuman intellect and it's actually exceeded by his superhuman patience. I will tell you a Chomsky story. One night in grad school I was wandering the library stacks looking for anything other than what I was supposed to be working on. I found myself in front of Emerson's complete works, picked out, let's say, Volume 18, and stumbled on Emerson's critique of the Mexican-American war. I noticed that he was saying exactly what Chomsky was to say about the Vietnam war 120 years later. I thought hey maybe Chomsky hasn't seen this, so I wrote him a letter: Dear Chomsky, you don't know me and I'm just a grad student in an unrelated field, but I thought you might enjoy this quote from Emerson. Love, me. A couple weeks later, I was surprised to find that Chomsky had written me back: Dear Daniel, I wasn't aware of that quote and found it very interesting. Thanks for writing. Love, Chomsky. Well, that was nice of him. End of story. Not quite. Two years later, I got another letter: Dear Daniel, I was at your university last week and had been looking forward to giving you a call and meeting you. Unfortunately, blah blah blah came up and there was just no way. Hopefully next time. Chomsky. This one flabbergasted me. By that time I had learned enough about academia to realize that in the star professor system, star professors never do that. They talk to students maybe after class or if they sign up for an appointment. Other than that, they avoid you because they don't want to lose star power. One guards one's fraternizations very carefully, and there are quite fine and quite strict lines demarking the various equivalence classes. Probably most celebrity systems work that way. It's the same reason Hollywood actors date each other. Anyway, the fact that Chomsky would write a letter like that to a nobody of a grad student, the lowliest of the low, really touched me. It also convinced me that, among star academics at least, the man really is a mutant. A decent mutant. Who would remember something like that after two years? |
I think most academics do.
My own story: When I was an undergraduate student, I wrote a paper which gave sharp bounds on the round-off errors resulting from computing FFTs using floating-point arithmetic; and I noticed that my bound was much better than the bound given by Higham in his Numerical Analysis textbook (which is, by quite a wide margin, the most widely used textbook in the field). I sent him an email -- "Dear sir, I noticed that in section X.Y of this book, you prove a bound of N sqrt(N) log(N) instead of N log(N); if you change foo to bar in your argument, you'll get the stronger bound which I prove in my paper (see attachment)" -- and he wrote back to thank me and tell me that he would make sure the improved bound was in the next edition of the textbook.
A year later, a copy of said textbook arrived in the mail, "compliments of the author".
Two years after that, when I was a graduate student at a different university, I went to a talk by Higham; and at the end when we were asked for questions, I introduced myself (by name, no mention of FFTs) and asked a question. Higham answered my question, and then went on -- in front of most of the department -- to announce that I had found an error in the first edition of his textbook, and that when I wrote to him he had assumed that I was a professor rather than an undergraduate student.
I think "star professors" are actually more likely to remember things like this, simply because someone pointing out something they didn't know, or a mistake they made, is so unusual. It's people like Chomsky, Higham, and Knuth who remember such contributions and can afford to send out free books -- or $2.56 cheques -- to those who provide them.