I met up with Kolya, Austin, and Ethan today. We ate out at this Ramen place, where we chatted mostly about light math, mathematicians, and intelligence related topics. I remember telling Austin about how the brain doesn’t peak in many until mid-late 20s or so, with rapid growth spurts often occurring in one’s early and mid twenties. This is consistent with the precipitous dip in car accident rates at age 25-26, the age when the prefrontal cortex matures, according to various online sources I’ve seen. So if you are struggling with things and not past that age, you still have plenty of hope! As for math, I asked Austin, who is entering a math PhD program next year, about the proof of Rolle’s theorem, which an old friend had asked me about a week earlier. It goes as follows. The hypotheses are continuity from and differentiability on . As for the extreme value, it can occur either at an endpoint, in which case the function is constant, or in between, in which case the left and right derivatives are less than or equal to zero and greater than or equal to zero, which combined necessitates a derivative of zero at that point.
Afterwards, we played some piano with some singing alongside, and following that, I played a game of chess with Ethan after he asked if I had a chessboard, which I did. Chess has basically not crossed my mind for almost 10 years, and I have probably not played a single game in the last 3 years or so. I would sometimes observe the live 2700 to see changes in rankings, but there was no actual chess content in my head whatsoever. I still have nostalgia for when I played in chess tournaments in 6th grade. I remember at the end, I had some state rating of only a little above 1200, having placed in the top 30 in the state tournament that year. Needless to say, the level of chess going on between those little kids, of which I was one, was quite low. I stopped in junior high as there was no chess club there. Nonetheless, I always had a mix of fascination and awe with the game. At that time, I was, to put it bluntly, quite clueless about it; I simply had not the requisite intellectual maturity.
I obviously lost to Ethan, who is rated at 2200 something, but to my great pleasure, I didn’t lose in a pathetic way. I was very calculating and rational in every move, to the extent that my level of knowledge and experience permitted. At the end, I lost with a reckless sacrifice where I forwent a minor piece for two of the pawns that covered his kingside castle, hoping to launch an attack. I did not calculate far enough and it was not successful, and seeing that all hope was lost, I resigned. The biggest contrast between this time and when I played long before was that I had much better positional sense, which I suspect is derived from a substantially higher level of qualitative reasoning, the aspect of intelligence captured by the verbal side of IQ tests, relative to before. I believe this because position is all about how different pieces to relate together and about thinking of the pieces in a high level of coherence. In every move, I took into account positional considerations. Unlike before, when I could make moves recklessly, without thorough calculation, I would think carefully on what exactly I gained from making such a move, as well as thinking how the opponent could respond. It is just like how in writing, every word you use must be there for a good reason, and how in social interaction, one needs the cognitive empathy to predict how the other party is likely to respond. I will not go much into the details of the game, which I am not confident I could easily reconstruct. I do remember it began with the Caro-Kann, the name of which I still remembered well, and that in the early middle game, it felt like there was little that could be done that made sense. Then, I had said, “I feel like I’m in a zugswang right now.” Ethan responded with a why, along with a remark this game appears more positional than tactical.
Back on the car, Ethan and Austin played some blindfold chess (or at least it seemed like that), which I don’t think I could do. Austin thought that blindfold chess required visual spatial, but I told him that chess viewed properly is not visual spatial at all. The state of a chess game in essence is entirely qualitative, representable as an array of states, each of which is empty or of some piece, along with states for castle and enpassant. The board is nothing but visual distraction. This is akin to how blindness did not interfere much with genius mathematicians like Euler and Pontryagin; the math exists independent of the visual representation through text.
While they were playing, I brought up Mikhail Botvinnik, who I was reading about on Wikipedia in both English and Russian (okay I still know very little of that, but enough to get *something* out of glancing through texts). He was a Soviet Jew who was one of the top chess players during the Stalinist era and a world champion. He characterized himself as “Jewish by blood, Russian by culture, and Soviet by upbringing.” On a victory in a great tournament in Nottingham, he sent an effusive telegram to Stalin. He also became a committed communist, whatever that means. Speaking of which, could it be a coincidence that both Kasparov and Fischer became political radicals notorious for opposing their home countries in an obnoxious manner, especially Fischer, who behaved as if he had developed some form of schizophrenia? Will Magnus Carlsen become the same? (I think not.) Anyhow, chess is a crazy world, with the people at the top most definitely not normal, and the politics, viewed superficially by me, not qualified to discuss the matter intelligently, can be intense as that pertaining to the Olympics, which can, as we all know, also go quite out of hand.
I’ll conclude by saying that if I were take up chess again, I could probably do much better than before with my much bigger brain, though of course, I have matters of higher priority. In any case, I’ll probably keep a casual interest in chess, and perhaps read more about the lives of and culture amongst the top players of the world, as well as studying the game itself.