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Ask cperciva: Are great mathematicians born or made?

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Re: Ask cperciva: Are great mathematicians born or made?

#51

Post by thaumaturgy »

yelsgib wrote: post #47
thaumaturgy wrote: post #43

Earlier quoted context omitted.

Or, you had a certain innate intelligence to begin with, and are only now practicing with it. At this point it's impossible to know one way or the other. Genetic intelligence versus developed intelligence is something that the top scientists of several fields are still investigating.

I don't think that we can really investigate "genetic intelligence" until we have a definition of intelligence which makes -any sense at all-, which we don't. I find a lot of the opinions of neuroscientists I've talked to/read articles from to be really dogmatic in their interpretation of intelligence (probably because they aren't regularly faced with Very Hard Problems in the sense that mathematicians/computer scien…

Just because people disagree on exactly what constitutes intelligence doesn't exempt the brain from the same general limitations that we see elsewhere in physiology.

Take fast-twitch muscle tissue for one example. Different people have a genetic predisposition towards developing more or less fast-twitch muscle fibers, which gives them the potential to be faster runners or have faster reflexes. Now, that's not to say that someone without that predisposition can't train hard and also be fast; likewise, if someone with that predisposition doesn't make use of it on a regular basis, then they're not likely to be any quicker than anyone else in reasonably good physical condition.

However, assuming the same training regimen, the person with the beneficial genetics will always have an advantage.

There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way. Yes, someone of average intelligence can work very hard and produce the same results as someone who's more intelligent and less motivated. But, you're comparing someone who's operating at their peak potential against someone who isn't.

I think cperciva's original point was merely that due to the nature of the field of mathematics, there's a huge barrier to entry where that genetic advantage becomes necessary. I disagree with that point only a little bit; if I worked really hard at it, I might be able to produce a small handful of exceptions against the very large body of evidence in cperciva's favor.

Re: Ask cperciva: Are great mathematicians born or made?

#52

Post by yelsgib »

yummyfajitas wrote: post #45
yelsgib wrote: post #17

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…

"Intelligence" is a hidden variable g, which comes out of statistical tests of various mental examinations. Basically, give a bunch of people a french test, a math test, a physics test, a driving test, etc. Run statistical tests for hidden variables, and you will discover this mysterious hidden variable 'g'. It is relatively independent of cultural knowledge: i.e., french is nearly independent of g (1), while physics…

I agree with this point, but I think that what you run into is that there are certain important cross-cultural trends which might cause g to be pertinent. What I mean is that perhaps the set of tasks which we "regularly perform" are governed by g - these tasks usually involving "problem solving" of the you-give-me-a-well-defined-problem-and-I'll-solve-it variety. It's a kind of reciprocal process - society will produce lots of jobs/roles which fit mass statistics it can determine, and it will also screen for that mass statistic.

What interests me, and what I'm worried that focus on this sort of gross statistic deprives us from thinking about, is the non-regular. I'm interested in the philosophical, the revolutionary, the artistic. I'm interested in what made Einstein Einstein. I don't think it's "g."

Slightly more abstractly/hypothetically: The way I kind of see intelligence is that we can function within contexts (e.g. functioning within the "Math context" would be doing math problems) and "g" corresponds to our ability to manipulate symbols generally, so that we are generally good at working within contexts. This is a really abstract way of saying g corresponds to our ability to solve problems. However, I don't think g says anything about long-term problem solving (involving abstraction, self-reflection), novel content creation (involving cross-context thinking), etc.

Does this make sense?

Re: Ask cperciva: Are great mathematicians born or made?

#53

Post by yelsgib »

thaumaturgy wrote: post #51
yelsgib wrote: post #47

Earlier quoted context omitted.

I don't think that we can really investigate "genetic intelligence" until we have a definition of intelligence which makes -any sense at all-, which we don't. I find a lot of the opinions of neuroscientists I've talked to/read articles from to be really dogmatic in their interpretation of intelligence (probably because they aren't regularly faced with Very Hard Problems in the sense that mathematicians/computer scien…

Just because people disagree on exactly what constitutes intelligence doesn't exempt the brain from the same general limitations that we see elsewhere in physiology. Take fast-twitch muscle tissue for one example. Different people have a genetic predisposition towards developing more or less fast-twitch muscle fibers, which gives them the potential to be faster runners or have faster reflexes. Now, that's not to say…

"There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way."

I agree if what you mean is that there's no reason to believe that there is no fixed, genetically-determined components to intelligence. I disagree if you are making any sorts of claims about what these components are (as I said, I don't even think we can make gross claims like people are born with "good memories").

I also agree with the point that cultures look for certain intellectual traits in young children. I cannot say whether these particular traits are determined genetically because it is highly possible that we learn a great deal (and abstractly) even from the first day of our lives.

The thing is that (as another poster pointed out) there IS a salient statistic (g - for general intelligence) which we can be "better" or "worse" at - but its value in a field like math which requires highly specialized mental strategies is questionable.

---

I think that you should look at the example of the polgar sisters - they were raised to be grandmasters in chess and 2/3 of them did (the other one become an international master). I think this puts a bullet in at least one interpretation of your theory.

Re: Ask cperciva: Are great mathematicians born or made?

#54

Post by thaumaturgy »

DaniFong wrote: post #10

I would strongly suggest that you read the biography of Erwin Schrodinger. Empirically, it seems to be quite possible to pick up mathematics and science at a later stage. But it doesn't happen too often. I cannot tell if this has to do with society's influence (there are many pressures keeping people from switching fields) or something to do with natural talent. But I do think that success in science, mathematics, or…

| I cannot tell if this has to do with society's influence ... or something to do with natural talent.

Both. Those with natural talent are more likely to produce notable work at an earlier age. Likewise, for male scientists, testosterone seems to drive creativity, and in later ages that has a tendency to get channeled into marriage and family instead (http://www.timesonline.co.uk/tol/news/world/article1149615.e...).

Re: Ask cperciva: Are great mathematicians born or made?

#55

Post by whacked_new »

cperciva wrote: post #36
yelsgib wrote: post #17

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?

I don't have an answer to this question, but this seems to be the same attitude that got Lawrence Summers into trouble!

My guess is that "intelligence" can be largely hidden, whereas your physique is immediately apparent even if you just sit and do nothing. That it is hidden then, gives it a mysterious feeling of potential, and nobody wants that put in a box. I think it is a cultural phenomenon that necessitates something like unconditional encouragement.

Re: Ask cperciva: Are great mathematicians born or made?

#56

Post by thaumaturgy »

yelsgib wrote: post #53
thaumaturgy wrote: post #51

Earlier quoted context omitted.

Just because people disagree on exactly what constitutes intelligence doesn't exempt the brain from the same general limitations that we see elsewhere in physiology. Take fast-twitch muscle tissue for one example. Different people have a genetic predisposition towards developing more or less fast-twitch muscle fibers, which gives them the potential to be faster runners or have faster reflexes. Now, that's not to say…

"There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way." I agree if what you mean is that there's no reason to believe that there is no fixed, genetically-determined components to intelligence. I disagree if you are making any sorts of claims about what these components are (as I said, I don't even think we can make gross claims like people are born with "good memories"…

I now think you're allowing your own prejudices on this subject cloud what you're reading, and what you're saying in response. I think I was fairly clear in my position that genetics plays an important role in intelligence, specifically because we have no indication that the brain is exempt from the same physiological rules that the rest of the human body obeys.

| I think that you should look at the example of the polgar sisters...

I specifically covered edge cases in mentioning the impact of training on innate ability.

Re: Ask cperciva: Are great mathematicians born or made?

#57

Post by whacked_new »

yelsgib wrote: post #52
yummyfajitas wrote: post #45

Earlier quoted context omitted.

"Intelligence" is a hidden variable g, which comes out of statistical tests of various mental examinations. Basically, give a bunch of people a french test, a math test, a physics test, a driving test, etc. Run statistical tests for hidden variables, and you will discover this mysterious hidden variable 'g'. It is relatively independent of cultural knowledge: i.e., french is nearly independent of g (1), while physics…

I agree with this point, but I think that what you run into is that there are certain important cross-cultural trends which might cause g to be pertinent. What I mean is that perhaps the set of tasks which we "regularly perform" are governed by g - these tasks usually involving "problem solving" of the you-give-me-a-well-defined-problem-and-I'll-solve-it variety. It's a kind of reciprocal process - society will produ…

You are aware that Einstein's brain had some very unusual features, right? I don't pay much attention to this, but I remember it is unusual enough that it is safe to say most people's brains don't have those features.

Relativity was not a well-defined problem when Einstein came up with it. You can analyze this intelligence in however many ways, but it is highly possible that "quantum leaps" in scientific advancement come from unusual thinkers -- unusual in a way that you can't just train very hard in and attain.

Re: Ask cperciva: Are great mathematicians born or made?

#58

Post by maurycy »

Few notes.

The whole discussion whether intelligence is born or made, misses the fact that motivation to work hard for years is unfrequent. Most people give up quickly, and are not able to commit themselves without immediate reward.

I easily imagine a mathematican without great intelligence, yet with high motiviation and ability to stay focus for hours. I can't imagine a mathematican who is smart, yet is not able to concentrate.

Another thing is that what seems to upset most people about genetic intelligence is limitation of our free will. It goes something like this: "I realize I want to become a mathematican and environment limits me; I can't afford this thought."

The problem is that between born and made there is a lot of grey area. What if, for instance, you do not realize it?

You might grew up in a suburbia environment that encourages you to become a MBA or a lawyer. If so, non-zero chances are you'd simply don't want to become a mathematican, or a quant. (no money, no chicks). Is your free will limited, or no? In different environment you'd dream about becoming an Erdos.

You might think that you made the decision, while, actually, the socialization process made the decision, and if you want to change it, you have to overcome the defaults. A non-trivial task.

I also feel that, besides the intelectual curiosity, there is something more behind this question. It seems, at least to me, that most people asking it, actually ask whether chances are their effort will be rewarded.

There is nothing wrong with it. One wants to minimize her risks. If investment of 10 years would be known to give 0 output (here: becoming a great mathematican) in some cases (here: lack of genetic intelligence), then, under given circumstances, it doesn't make sense at all.

The point is that intellectual work is highly non-linear and if there are any constant factors, they are highly more complicated than born vs made.

Re: Ask cperciva: Are great mathematicians born or made?

#59

Post by yelsgib »

thaumaturgy wrote: post #56
yelsgib wrote: post #53

Earlier quoted context omitted.

"There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way." I agree if what you mean is that there's no reason to believe that there is no fixed, genetically-determined components to intelligence. I disagree if you are making any sorts of claims about what these components are (as I said, I don't even think we can make gross claims like people are born with "good memories"…

I now think you're allowing your own prejudices on this subject cloud what you're reading, and what you're saying in response. I think I was fairly clear in my position that genetics plays an important role in intelligence, specifically because we have no indication that the brain is exempt from the same physiological rules that the rest of the human body obeys. | I think that you should look at the example of the po…

What does it mean that the brain "obeys the same physiological rules" that the body obeys? This point is incoherent.

My point is that yes, there is a genetic aspect to intelligence (duh), but that doesn't mean that there is a genetic component to how "fast" your brain is or how much "memory" you have. These could be emergent phenomena - not directly determinable.

Please tell me more specifically how my prejudices are clouding what I'm reading/saying. You didn't follow this point up.

Re: Ask cperciva: Are great mathematicians born or made?

#60

Post by Retric »

yelsgib wrote: post #40
cperciva wrote: post #36

Earlier quoted context omitted.

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?

I think you're being presumptuous. I'm not saying that I'm "turned off" by the -fact- that I can't get tall(1). I'm saying that this is not a -fact- at all. Even if it -is- a fact, it certainly is much more uncertain/open for debate than the question of whether you can get tall at a late age. I'm saying that the fact that you -claim it is a fact- is what turns me off. Perhaps I was slightly imprecise. I should have s…

There are basically 3 requirements for intelligence that surpass the basic need to survive:

DNA, Diet, and Stimulus.

DNA limits what structures can develop which is the basic foundation of intelligence.

Diet provides the raw materials to crate the structures that DNA is trying to build. Poor diet causes DNA to sacrifice specific objectives to insure survival. Specific toxins like lead also limit the body's ability to create structures. At the same time short term diet inhibits performance.

Experience refines specific structural elements. Without early experience in specific areas it becomes harder to develop efficient systems for dealing with those situations. It's not impossible to learn French at 50 if you only know Spanish, but it's far easer to learn it at 5 than 50. Part of this has to due with the brain ignoring sounds that it finds unimportant.

All of the above statements are well supported by a huge body of research being annoyed by them is like getting pissed off at gravity while building rockets.

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