@jay I honestly don't think you need to stress over Riemannian geometry and manifolds. All they're talking about is the use of the inner product to define the gradient, as I already said.
@robjohn ( or someone else) can you say why the velocity field of the curve $\gamma$ is plugged into the metric tensor at minute 34:10 of this really cool video youtube.com/…
jay outside of the riemannian context, how would you compute the speed of a space curve in R^3? it's the same formula, just generalized.
maybe three times. it's cheaper than you'd think until you realize that most people don't need it even once in a given year. also if someone in your family has it, you might already have it even if you drive different cars.
One thing I have learned to do is to make the way I engage with the world fault-tolerant, because I make a lot of silly mistakes. For this case, that solution is "have a car with auto headlights", though that's kind of a non-starter as practicable advice goes.
I also had one time where I forgot to turn on my headlights coming out of a place. A cop pulled up next to me and shouted, "Hey, dude, turn your [redacted] lights on!"
The mean being so close to the true answer (even for a ~1000-size data set, the mean was <1 away from the integer minimizer) just made me bark up a bit of a wrong tree. My suspicion is that the problem was formulated in such a way as to force someone not to shortcut.
My 1971 Saab turned off the headlights automatically when you turned off the ignition. Modern cars aren't so civilized; they just beep at you to warn you.
@TedShifrin I can think of several instances in my life where I've thought, "Why wasn't I warned about <x>?" and immediately my brain, like a diligent stenographer, pulls up the record of me seeing/hearing whatever warning. Funny how people work.
I really like algebra, but I can't say I'm good at it. I find I need to refresh myself a lot, and my last adventure in doing so was something like two years ago. Now a couple of years of stochastic nonsense, financial math, and hobbyist programming have pushed that all out of my head...
@amWhy Of course, Magnus's game was crazy, 7 hours or so but it was a great game. He is very humble despite being the best in my opinion. However, Nepo's game was very clean. What do you think?
Different strokes, as they say. I think I come down mostly rejecting firm classifications like "everyone's either an algebraist or an analyst" or whatever, but that people come to math with proclivities (however they get them) seems undeniable.
I had a colleague at UGA who, even in his forties, could not remember anyone's names — not just students, but colleagues just down the hall from him.
It does trouble me that I'm probably somewhere around my cognitive peak; alive long enough to know how I think best, and young enough to still be sharp.
@Fargle That's not true. People tend to see what they believe, more often than believing what they see. People absorb such myths, and look for evidence to confirm it.
@amWhy From what I read it seems that Nepo used to play other games apart from chess. I guess at the moment he's the closest opponent to Magnus. I'm curious if Magnus can perform about 25 movements in his mind. It is incredible!
@copper.hat Does eidetic memory really exist? I have read that some people manage to develop strong memory techniques. My memory does not work well for me, I must have my notes at hand or show at every moment that I forget something. A problem
My memory is strange. I have extremely good memory for, say, strings of digits, or other similar small chunks of information, and I have a decent memory for technical or narrative information (thinking, like, basic physics, or stuff in history), but my social memory---remembering bits of conversations, putting names to faces---is exceptionally poor.
I apparently surprise people in my life for the details I remember from childhood. Highschool, College, Grad School, family, birthdates, dates of death. It's likely numerical, but also experiential.
I used to know my work phone numbers (I had a few when I was associate dept head). I guess I still remember those. But among my friends, I know only my own. Everything else is in the phone.
I remember I once spooked my high school teacher who took us all out for dinner one time. For whatever reason, his card was passed around (I think to take the checks of all the students who couldn't pay, myself included).
I walked by him near the end of the night and said the whole number to him. He looked at me and said "come on, man". (I was much more of a gremlin back then.)
Which she really should have done three or four years ago, but (a) she is a little abrasive and (b) her committee doesn't seem to be able to get its act together.
@TedShifrin He has a pretty broad background. I think that he is thinking English, but he is also qualified to teach mathematics (to a high school level), history, sociology, etc.
My Ph.D. student trained previously to be an elementary teacher in Poland. She took a Rudin analysis course for calculus, just like all the Europeans we see in here as math majors.
I grew up on Easy Street. Literally! It was at the top of hill, and it was only "easy" going down hill! By literally, I mean that was the actual name of the street.
i used to live in iowa avenue in iowa city, iowa. i never tested whether mail would get to me if someone addressed it to my name, followed by a couple of iowas.
i expect it would have, because of my high reputation
