i know this is not what your post is really about, but you're wrong about math aptitude, and i suspect about other endeavors. i was always good at math. it was very easy and took little or no effort. i never memorized much. during exams i would re-derive the theorems that were needed.
i can only think of 2 times i had to think hard about math. once was in 11th grade when i was trying to prove that an axiom in our textbook was really just a theorem. [i eventually learned that i needed dedekind cuts or something similar to do the proof- i couldn't prove it, but found it in a book in columbia's math library.] the other time was in analysis class in college when our take-home final consisted of proving a single theorem. i was the only person in class to eventually prove the theorem [it took a couple of weeks], but i found the process so unpleasant that it made clear that i didn't want to pursue math as a career, although i graduated as a math major.
i've studied a lot of neurophysiology, neuroanatomy, logic and a bit of automata theory. there is no reason to think that peoples' brains have "more or less" the same hardware. [though i guess this idea depends on just how much "less" you're willing to sweep under that rug.] in fact, given the complexity of brains, the variability of genetics and the contingencies of embryology, the idea is preposterous. given that brains vary, so will their skills.
my guess is that your son has a better skill at certain kinds of pattern recognition, and certainly more pleasure in it, than you do. experiencing pleasure is also something brains do, and what you call "will" must in fact be significantly influenced by differences in what is pleasurable.
my wife is a photographer and sees things i overlook. she is bothered by dirty windshields which i don't even notice. she easily finds objects that i think are "lost." obviously she is processing visual data better than i can. and it is clearly not an effort for her to do this. it's just part of who she is, of how she's wired.
If I’m being honest about it, I do know a few people who have exceptional processing power and exceptional natural intelligence and ability. And the one thing every single one of them have in common is the humility to never say anything remotely like your comment.
i don't think i'm so wonderful. i think i hit the wall; i could go so far, but not farther. i think i might have become a mediocre mathematician, a journeyman. we have our skills, and our skills have their limits. i occ come across a reference to some branch of math that is foreign to me. i used to think i could probably master it if i tried but now i think that it is likely that i could not. i think it is likely your son is just a better chess player than you. saying i could master something if i had enough "will" is a way of avoiding recognition of one's limits.
I like your other writting but I strongly agree with Jeff Klugman. you probably don't spend much time with ordinary people , to remember, how vast is the spectre of (dis) abilities ....
On re-derive and writing, epic! Similar here, it works and very useful! You guys rock!
Cheers!
What an honor. Huge Cliff fan. Will enjoy this I am sure!
Thanks Squirrel
i know this is not what your post is really about, but you're wrong about math aptitude, and i suspect about other endeavors. i was always good at math. it was very easy and took little or no effort. i never memorized much. during exams i would re-derive the theorems that were needed.
i can only think of 2 times i had to think hard about math. once was in 11th grade when i was trying to prove that an axiom in our textbook was really just a theorem. [i eventually learned that i needed dedekind cuts or something similar to do the proof- i couldn't prove it, but found it in a book in columbia's math library.] the other time was in analysis class in college when our take-home final consisted of proving a single theorem. i was the only person in class to eventually prove the theorem [it took a couple of weeks], but i found the process so unpleasant that it made clear that i didn't want to pursue math as a career, although i graduated as a math major.
i've studied a lot of neurophysiology, neuroanatomy, logic and a bit of automata theory. there is no reason to think that peoples' brains have "more or less" the same hardware. [though i guess this idea depends on just how much "less" you're willing to sweep under that rug.] in fact, given the complexity of brains, the variability of genetics and the contingencies of embryology, the idea is preposterous. given that brains vary, so will their skills.
my guess is that your son has a better skill at certain kinds of pattern recognition, and certainly more pleasure in it, than you do. experiencing pleasure is also something brains do, and what you call "will" must in fact be significantly influenced by differences in what is pleasurable.
my wife is a photographer and sees things i overlook. she is bothered by dirty windshields which i don't even notice. she easily finds objects that i think are "lost." obviously she is processing visual data better than i can. and it is clearly not an effort for her to do this. it's just part of who she is, of how she's wired.
brains vary a lot.
If I’m being honest about it, I do know a few people who have exceptional processing power and exceptional natural intelligence and ability. And the one thing every single one of them have in common is the humility to never say anything remotely like your comment.
i don't think i'm so wonderful. i think i hit the wall; i could go so far, but not farther. i think i might have become a mediocre mathematician, a journeyman. we have our skills, and our skills have their limits. i occ come across a reference to some branch of math that is foreign to me. i used to think i could probably master it if i tried but now i think that it is likely that i could not. i think it is likely your son is just a better chess player than you. saying i could master something if i had enough "will" is a way of avoiding recognition of one's limits.
I don’t think so. Our limits are self imposed based on perception.
I like your other writting but I strongly agree with Jeff Klugman. you probably don't spend much time with ordinary people , to remember, how vast is the spectre of (dis) abilities ....