31–40 of 89 posts
Anyone else see the flaw in asking a gifted mathematician about the human brain, merely because they're a gifted mathematician? cperciva is certainly very smart, and may also happen to know a thing or two about the subject...but mathematical ability doesn't necessarily correlate with knowledge of how humans learn or cognitive development.
Precocity is overrated. To me, believing that genius is decided at age 0/5/10 whatever means that you are just rationalizing not working hard enough with "I am not a genius. I will not make it. Therefore no point in working hard". The primary test really is : a) Are you having fun (with maths in this case)? b) Are you willing to put time and effort into it? Note that the amount of time available may be one hurdle if…
Anyone else see the flaw in asking a gifted mathematician about the human brain, merely because they're a gifted mathematician? cperciva is certainly very smart, and may also happen to know a thing or two about the subject...but mathematical ability doesn't necessarily correlate with knowledge of how humans learn or cognitive development.
Can people who are not inherently 'gifted', start with an immense interest in math at a mid-point in their life, and still go on to make meaningful and significant contributions to the field? Probably not. In other words, is precocity a prerequisite to doing good work in Math? Maybe, depending on whether you by "precocity" you mean "demonstrated precocity". Intelligence is something you either have or don't have -- a…
"not because it's particularly suited to prodigies, but rather because mathematics prodigies tend to get noticed. Some fields, like mathematics or chess, have little knowledge required before intellect can be applied" it is not true. imo modern math requires years of study to reach the border of known. to topic starter: i know pretty good mathematicians who think that geniality exists and who think it does not. i tho…
You're right -- and modern mathematics requires more study than a field like computer science, simply because computer science as a field hasn't had enough time to accumulate very much content. (This is one of the ideas I mentioned as floating around but not fully crystallized earlier.)
But this doesn't contradict what I was saying: My point was not about doing original research, but merely about crossing the threshold to being recognized as a prodigy. A 13 year old attending university is certainly noticed -- but that doesn't mean he's doing original research (I didn't until I was 15).
Very great mathematicians are born. You're either born as Ramanujan or Erdos or you're never going to be Ramanujan or Erdos. No way around it. But, merely pretty damn good mathematicians can work really good and be a thousandth as useful as an Erdos or Ramanujan.
I'm pretty sure most people wouldn't want live the life of Erdos...
Come on... travelling the world and couch-surfing for years on end, while having no financial concerns at all? I think most people would love to live that life.
Can people who are not inherently 'gifted', start with an immense interest in math at a mid-point in their life, and still go on to make meaningful and significant contributions to the field? Probably not. In other words, is precocity a prerequisite to doing good work in Math? Maybe, depending on whether you by "precocity" you mean "demonstrated precocity". Intelligence is something you either have or don't have -- a…
What is "intelligence?" Can we separate it from society's conception of it? Can we state a computational definition rather than a definition in terms of satisfaction of cultural standards? We undervalue a lot of mental attributes - consistency of thought, sensitivity to subtle differences in concepts, patience, self-reflection, the ability to "go meta" etc. which cannot be detected by the rough and rigid abstract pro…
I find this notion rather peculiar. Do people get "highly turned off" that they can't "get tall"? I've known for my entire life that I could never become a professional athlete -- I simply don't have the physique.
What is it about intelligence which makes people get so much more upset than they get about physical attributes?
Earlier quoted context omitted.
"not because it's particularly suited to prodigies, but rather because mathematics prodigies tend to get noticed. Some fields, like mathematics or chess, have little knowledge required before intellect can be applied" it is not true. imo modern math requires years of study to reach the border of known. to topic starter: i know pretty good mathematicians who think that geniality exists and who think it does not. i tho…
imo modern math requires years of study to reach the border of known. You're right -- and modern mathematics requires more study than a field like computer science, simply because computer science as a field hasn't had enough time to accumulate very much content. (This is one of the ideas I mentioned as floating around but not fully crystallized earlier.) But this doesn't contradict what I was saying: My point was no…
I constantly witness failures in business because someone said, "It can't be done," or "He can't do that," or "She'll never be able to do that."
I love proving them wrong. I'm rarely disappointed.
Given the right resources, the opportunity, and most of all, genuine encouragement and support, it's amazing what the human brain, at any age, can accomplish. Sometimes, all it takes to discover it is a little more faith in another than in onesself.
Earlier quoted context omitted.
imo modern math requires years of study to reach the border of known. You're right -- and modern mathematics requires more study than a field like computer science, simply because computer science as a field hasn't had enough time to accumulate very much content. (This is one of the ideas I mentioned as floating around but not fully crystallized earlier.) But this doesn't contradict what I was saying: My point was no…
15? wow! may i look at your papers?
It turns out that those "loose ends" are rather mixed up with the problem of integer factorization, which might be why I couldn't manage to tie them up. :-)
Earlier quoted context omitted.
What is "intelligence?" Can we separate it from society's conception of it? Can we state a computational definition rather than a definition in terms of satisfaction of cultural standards? We undervalue a lot of mental attributes - consistency of thought, sensitivity to subtle differences in concepts, patience, self-reflection, the ability to "go meta" etc. which cannot be detected by the rough and rigid abstract pro…
I am highly turned off by the idea that we can't "become smart" after an early age. I find this notion rather peculiar. Do people get "highly turned off" that they can't "get tall"? I've known for my entire life that I could never become a professional athlete -- I simply don't have the physique. What is it about intelligence which makes people get so much more upset than they get about physical attributes?
My claim is even slightly deeper/more provocative than that - I don't think that efforts by a lot of academics (including a lot of my friends) to propagate an idea of "general intelligence" which solidifies at a young age are entirely benign. I think that they are largely founded in worry and attempts to create an elite academic class. Once you're in, you're in (since getting in means that you have a "good" brain which is not really subject to change). It's self-reinforcing and (in my experience) always based in self-doubt.
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As an aside, the idea that "people get so much more upset" about the intellectual than the physical is completely absurd. I know a ton of people (girls and guys) who freak out constantly about their appearance. I know like 3 guys (including myself) who are the least bit worried about our intellects. Admittedly, most of my friends are academics, but my interactions with people outside this sphere indicate that the trend is not peculiar to my social group (and is probably even more physical-attribute oriented, in general). Seriously, I can't believe that you wrote this. This isn't meant to be mean or like ad hominem - but seriously? Do you actually believe what you wrote? Do you know anyone who isn't an academic?
To answer what I think you might have meant (namely: why do _I_ get much more freaked out about my intelligence than my physical attributes - which is also presumptuous because you have -no- idea how much I care about my physical attributes) I would like to observe that in modern western society "we are our minds." Your mind is essentially the limit of your capabilities in the sort of world I'm sure both you and I live in (the quote unquote information world). The mind is connected with the ability to create beauty (art), the ability to connect with other human beings (sex), the ability to experience spirituality (love), etc. In the academic world, at least, our physical bodies are a burden. They wear out. They get cancer. They die.
Did you seriously ask this? Were you being rhetorical? I can't tell. I don't mean to be mean, but sheesh.
(1) and I accuse you of attempting to employ an underhanding rhetorical trick in making this implicit comparison, I might add.