There Is No Magic(deconstructinggenius.wordpress.com)
deconstructinggenius.wordpress.com
There Is No Magic
http://deconstructinggenius.wordpress.com/2011/04/22/there-is-no-magic/
6 comments
HN's founder, pg, has done something to promote this idea.
http://www.paulgraham.com/hs.html
"I'm not saying there's no such thing as genius. But if you're trying to choose between two theories and one gives you an excuse for being lazy, the other one is probably right."
It is indeed a good idea for people who are trying to solve hard problems not to ask, "How good is my ability?" but rather to ask, "What use am I making of all my ability and all my other resources to solve this problem?"
http://www.paulgraham.com/hs.html
"I'm not saying there's no such thing as genius. But if you're trying to choose between two theories and one gives you an excuse for being lazy, the other one is probably right."
It is indeed a good idea for people who are trying to solve hard problems not to ask, "How good is my ability?" but rather to ask, "What use am I making of all my ability and all my other resources to solve this problem?"
Agree! Another example of this that my old music teacher used to give all the time was John Coltrane. Everybody agrees that he was a great player, but he wasn't a prodigy. He was notorious for practicing day and night to continue improving his craft.
Even Miles Davis thought he was a bit boring because all he (John) wanted to do was practice. :)
Even Miles Davis thought he was a bit boring because all he (John) wanted to do was practice. :)
>"I am somehow less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops."
not. There weren't people of equal talent in cotton fields and sweatshops. It is possibly that there were people who at the age of 2 had the brain with the same potential as Einstein's brain at the age of 2 (though not likely as Einstein's brain seems to have unique basic biological parameters like smaller size of neurons and greater ratio off energy generating cells to neurons). Brain development is reflected in its biological structure. The brain of a 30-40 years old is the _biological_ result of the 30-40 years of development of that organ. Different experiences, like intensive studies and intensive manual labor create different brains - different sets of neurons wired differently. Silicon waffers look the same before being lithographed and frequently look the same after, yet they may be lithographed with completely different CPU/chips/etc...
not. There weren't people of equal talent in cotton fields and sweatshops. It is possibly that there were people who at the age of 2 had the brain with the same potential as Einstein's brain at the age of 2 (though not likely as Einstein's brain seems to have unique basic biological parameters like smaller size of neurons and greater ratio off energy generating cells to neurons). Brain development is reflected in its biological structure. The brain of a 30-40 years old is the _biological_ result of the 30-40 years of development of that organ. Different experiences, like intensive studies and intensive manual labor create different brains - different sets of neurons wired differently. Silicon waffers look the same before being lithographed and frequently look the same after, yet they may be lithographed with completely different CPU/chips/etc...
Yes, I think that is a profoundly powerful belief.
At the same time, my impression is that things have actually gone in the other direction in the last twenty years - the popular press credits genes for a laughable variety of behaviors specific to civilized humans.
At the same time, my impression is that things have actually gone in the other direction in the last twenty years - the popular press credits genes for a laughable variety of behaviors specific to civilized humans.
In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the “ordinary” and the “magicians.” An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon, in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students because they cannot be emulated and it must be terribly frustrating for a brilliant young mind to cope with the mysterious ways in which the magician’s mind works. Richard Feynman is a magician of the highest caliber.
--Mark Kac
I think it's probably best if we don't deify too many geniuses, but I think it's fair to say that there are a handful in history where, even had we been exposed to all of the diverse experiences they had, we still wouldn't hope to equal.
--Mark Kac
I think it's probably best if we don't deify too many geniuses, but I think it's fair to say that there are a handful in history where, even had we been exposed to all of the diverse experiences they had, we still wouldn't hope to equal.
The impression I got on reading Feynman's "Surely You're Joke...", was that Feynman was a magician in the ordinary sense of the word; he liked to produce results in a fashion that was maximally dramatic and maximally inexplicable (whether those results involved opening safes or calculating complex formulas).
And consider. The first sleight-of-hand magicians were village shamans who used the wonder the "magic" produced to leverage the power of suggestion for healing. But we know that the effect of superstition on society as a whole is detrimental.
Similarly, the belief that Feynman really had "magic" ways to unlock safes or solve math problems is less-than-useful.
Edit: I think that it is true that some fraction of scientists operate as "magicians" but some of this can come from a remarkably selfish position - the desire maintain their colleagues in awe and ignorance. I don't think Feynman in particular was in this unfortunate category but I've seen some folks whose approach was basically abusive.
And consider. The first sleight-of-hand magicians were village shamans who used the wonder the "magic" produced to leverage the power of suggestion for healing. But we know that the effect of superstition on society as a whole is detrimental.
Similarly, the belief that Feynman really had "magic" ways to unlock safes or solve math problems is less-than-useful.
Edit: I think that it is true that some fraction of scientists operate as "magicians" but some of this can come from a remarkably selfish position - the desire maintain their colleagues in awe and ignorance. I don't think Feynman in particular was in this unfortunate category but I've seen some folks whose approach was basically abusive.
I read "Surely You're Joking..." and "What Do You Care..." with the idea that he's probably underselling himself.
Didn't Feynmann said that he sometimes seemed magical because he just had 'different toolbox' than his friends? As far as I remember these words regarded calculus. Probably I am more wrong than Mark Kac in this matter, but I think that this kind of orthogonal thinking can be somehow learned by looking in the directions that at first glance doesn't look like they lead to any solution or even unrelated. Also it seems that great knowledge of two seemingly disconnected areas allow to actually find some connections between them - which may seem magical for spectators.
I disagree. It's like debugging -- at some point, bugs are just too slippery and difficult to find, so we give up and say "I can't hope to solve this" ?
No.
No.
Multiple studies have shown that beyond a certain point (around two to three standard deviations), further IQ is not particularly helpful.
Is this true? I'd wager that the average IQ of top-rank mathematicians (say, the top 100 as judged by their peers) is at least three standard deviations above the mean, and more likely closer to 4. In fact, it wouldn't surprise me if the average IQ of said group is well over 160.
Is this true? I'd wager that the average IQ of top-rank mathematicians (say, the top 100 as judged by their peers) is at least three standard deviations above the mean, and more likely closer to 4. In fact, it wouldn't surprise me if the average IQ of said group is well over 160.
Is this true?
You are to be commended for asking whether the statement is true. I'd like to check that author's references, but I have reason to believe that he is on the right track.
I'd wager that the average IQ of top-rank mathematicians (say, the top 100 as judged by their peers) is at least three standard deviations above the mean, and more likely closer to 4.
You have indicated your view of the sources you have read by proposing a wager. I'll gladly stake a large amount of money on that wager, because you would surely lose. There have already been studies of the issue, after all. Definitional problems here for settling the wager among you, me, and our seconds would include defining just who the top 100 mathematicians are (I'd expect a lot of debate on that point), and which brand of IQ test should be taken to be the most definitive, as each IQ test battery disagrees with each other IQ test battery. But I have no doubt I would win the bet.
For one thing, four standard deviations above the population median (IQ score of 160 by current standard scoring conventions) is the very peak of reliable scoring on any currently normed brand of IQ test. Commenting on the higher numerical scores found in the scoring tables of the obsolete Stanford-Binet Form L-M IQ test, Christoph Perleth, Tanja Schatz, and Franz J. Mönks (2000) comment that "norm tables that provide you with such extreme values are constructed on the basis of random extrapolation and smoothing but not on the basis of empirical data of representative samples." "Early Identification of High Ability". In Heller, Kurt A.; Mönks, Franz J.; Sternberg, Robert J. et al.. International Handbook of Giftedness and Talent (2nd ed.). Amsterdam: Pergamon. p. 301. ISBN 978-0-08-043796-5. Lewis Terman recognized the core problem with IQ scores at the high end a long time ago:
"The reader should not lose sight of the fact that a test with even a high reliability yields scores which have an appreciable probable error. The probable error in terms of mental age is of course larger with older than with young children because of the increasing spread of mental age as we go from younger to older groups. For this reason it has been customary to express the P.E. [probable error] of a Binet score in terms of I.Q., since the spread of Binet I.Q.'s is fairly constant from age to age. However, when our correlation arrays [between Form L and Form M] were plotted for separate age groups they were all discovered to be distinctly fan-shaped. Figure 3 is typical of the arrays at every age level.
"From Figure 3 it becomes clear that the probable error of an I.Q. score is not a constant amount, but a variable which increases as I.Q. increases. It has frequently been noted in the literature that gifted subjects show greater I.Q. fluctuation than do clinical cases with low I.Q.'s . . . . we now see that this trend is inherent in the I.Q. technique itself, and might have been predicted on logical grounds." (Terman & Merrill, 1937, p. 44)
Alan S. Kaufman has a great discussion of error of estimation in IQ testing and variance in scores between one IQ test and another in his recent book IQ Testing 101. For much, much more on this issue, see
http://en.wikipedia.org/wiki/User:WeijiBaikeBianji/Intellige...
for further reading suggestions.
A quotation, from an interview with Stephen Hawking in the New York Times:
"Q: What is your I.Q.?
"A: I have no idea. People who boast about their I.Q. are losers."
http://www.nytimes.com/2004/12/12/magazine/12QUESTIONS.html
You are to be commended for asking whether the statement is true. I'd like to check that author's references, but I have reason to believe that he is on the right track.
I'd wager that the average IQ of top-rank mathematicians (say, the top 100 as judged by their peers) is at least three standard deviations above the mean, and more likely closer to 4.
You have indicated your view of the sources you have read by proposing a wager. I'll gladly stake a large amount of money on that wager, because you would surely lose. There have already been studies of the issue, after all. Definitional problems here for settling the wager among you, me, and our seconds would include defining just who the top 100 mathematicians are (I'd expect a lot of debate on that point), and which brand of IQ test should be taken to be the most definitive, as each IQ test battery disagrees with each other IQ test battery. But I have no doubt I would win the bet.
For one thing, four standard deviations above the population median (IQ score of 160 by current standard scoring conventions) is the very peak of reliable scoring on any currently normed brand of IQ test. Commenting on the higher numerical scores found in the scoring tables of the obsolete Stanford-Binet Form L-M IQ test, Christoph Perleth, Tanja Schatz, and Franz J. Mönks (2000) comment that "norm tables that provide you with such extreme values are constructed on the basis of random extrapolation and smoothing but not on the basis of empirical data of representative samples." "Early Identification of High Ability". In Heller, Kurt A.; Mönks, Franz J.; Sternberg, Robert J. et al.. International Handbook of Giftedness and Talent (2nd ed.). Amsterdam: Pergamon. p. 301. ISBN 978-0-08-043796-5. Lewis Terman recognized the core problem with IQ scores at the high end a long time ago:
"The reader should not lose sight of the fact that a test with even a high reliability yields scores which have an appreciable probable error. The probable error in terms of mental age is of course larger with older than with young children because of the increasing spread of mental age as we go from younger to older groups. For this reason it has been customary to express the P.E. [probable error] of a Binet score in terms of I.Q., since the spread of Binet I.Q.'s is fairly constant from age to age. However, when our correlation arrays [between Form L and Form M] were plotted for separate age groups they were all discovered to be distinctly fan-shaped. Figure 3 is typical of the arrays at every age level.
"From Figure 3 it becomes clear that the probable error of an I.Q. score is not a constant amount, but a variable which increases as I.Q. increases. It has frequently been noted in the literature that gifted subjects show greater I.Q. fluctuation than do clinical cases with low I.Q.'s . . . . we now see that this trend is inherent in the I.Q. technique itself, and might have been predicted on logical grounds." (Terman & Merrill, 1937, p. 44)
Alan S. Kaufman has a great discussion of error of estimation in IQ testing and variance in scores between one IQ test and another in his recent book IQ Testing 101. For much, much more on this issue, see
http://en.wikipedia.org/wiki/User:WeijiBaikeBianji/Intellige...
for further reading suggestions.
A quotation, from an interview with Stephen Hawking in the New York Times:
"Q: What is your I.Q.?
"A: I have no idea. People who boast about their I.Q. are losers."
http://www.nytimes.com/2004/12/12/magazine/12QUESTIONS.html
I have no doubt I would win the bet.
Awesome. I love betting at ∞:1 odds. I wager $ε.
Awesome. I love betting at ∞:1 odds. I wager $ε.
Here are just a few of the many results for an easy Google search:
http://www.google.com/search?q=infinity+is+not+a+number
http://nrich.maths.org/2756
(I particularly like this one, as the author is a top mathematician, here seen writing in her younger days.)
http://mathforum.org/library/drmath/view/62486.html
(Ask Dr. Math pages are generally good for answering elementary questions from students.)
http://scienceblogs.com/goodmath/2008/10/infinity_is_not_a_n...
(Of course the Good Math, Bad Math blog has a page on this issue.)
http://www.physicsforums.com/archive/index.php/t-65355.html
(A discussion on Physics Forum illustrating how some of the confusions about infinity arise.)
http://www.jimloy.com/algebra/two.htm
(Jim Loy's page on this is interesting too.)
http://www.google.com/search?q=infinity+is+not+a+number
http://nrich.maths.org/2756
(I particularly like this one, as the author is a top mathematician, here seen writing in her younger days.)
http://mathforum.org/library/drmath/view/62486.html
(Ask Dr. Math pages are generally good for answering elementary questions from students.)
http://scienceblogs.com/goodmath/2008/10/infinity_is_not_a_n...
(Of course the Good Math, Bad Math blog has a page on this issue.)
http://www.physicsforums.com/archive/index.php/t-65355.html
(A discussion on Physics Forum illustrating how some of the confusions about infinity arise.)
http://www.jimloy.com/algebra/two.htm
(Jim Loy's page on this is interesting too.)
It is true. Multiple attempts have been made to measure the IQs of clearly gifted people. They tend to be 2-3 standard deviations out.
IQ is imperfectly correlated with the intellectual abilities needed to be a good mathematician. So top mathematicians are, in the abilities that they need to have, indeed probably several standard deviations over the mean. But in the other abilities (I say abilities loosely here - the luck of how you are feeling that day is surprisingly significant) tested in an IQ test which they don't need for what they do, they are all over the map. Average those two factors together on an IQ test, and they consistently have good IQs, but not stellar ones.
IQ is imperfectly correlated with the intellectual abilities needed to be a good mathematician. So top mathematicians are, in the abilities that they need to have, indeed probably several standard deviations over the mean. But in the other abilities (I say abilities loosely here - the luck of how you are feeling that day is surprisingly significant) tested in an IQ test which they don't need for what they do, they are all over the map. Average those two factors together on an IQ test, and they consistently have good IQs, but not stellar ones.
Feynman's I.Q. was reputedly 125. He was a genius.
There definitely is Magic, at least as it's defined here.
This is plain to see in anyone who has worked with children. These kids are too young to have had very varied experiences, and they come from bad homes, good homes, and everything in between.
Yet, a very small percentage of them are an easy order of magnitude 'better' at understanding and communicating complex ideas.
There is no doubt that hard work, and smart work begets better brains.. but the idea that brilliance and genius is 'something you earn' just doesn't hold up when you look at kids.
This is plain to see in anyone who has worked with children. These kids are too young to have had very varied experiences, and they come from bad homes, good homes, and everything in between.
Yet, a very small percentage of them are an easy order of magnitude 'better' at understanding and communicating complex ideas.
There is no doubt that hard work, and smart work begets better brains.. but the idea that brilliance and genius is 'something you earn' just doesn't hold up when you look at kids.
The way I like to look at it is: even if I am not particularly smart, I am not going to let that fact get in the way of anything I wish to do [n]. I say don't underestimate the power of concept reframing, perspective changes, weaknesses leveraging, tenacity and plain not caring whether or not you are smart.
[n] So long as it is not stupid and without being stupid about it.
[n] So long as it is not stupid and without being stupid about it.
When I was young I sailed and raced dinghies and skiffs.
This is a fairly cerebral sport that usually requires a great working knowledge of the physics invovled in making boats with sails go fast.
Most of the champions I observed were really smart kids in other regards, but every so often I would see regatta winners that were not 'smart' people in any academic sense, but who had what appeared to have an inate ability to rig and sail a boat as fast as possible. This is not a trivial thing, and I am talking about people who would have likely failed a highschool level physics class on the same topic.
Is this a type of genius too?
This is a fairly cerebral sport that usually requires a great working knowledge of the physics invovled in making boats with sails go fast.
Most of the champions I observed were really smart kids in other regards, but every so often I would see regatta winners that were not 'smart' people in any academic sense, but who had what appeared to have an inate ability to rig and sail a boat as fast as possible. This is not a trivial thing, and I am talking about people who would have likely failed a highschool level physics class on the same topic.
Is this a type of genius too?
[deleted]
I generally agree with this, however it doesn't explain the "Rainman" aka Kim Peek, geniuses; this level of mental strength can't be gained purely from hard work.
this level of mental strength can't be gained purely from hard work.
Actually, research shows that it can, and has been.
http://www.cambridge.org/gb/knowledge/isbn/item1172019/?site...
An interesting historical study of calculating prodigies turned up evidence that the famous nineteenth century idiots-savants with powerful calculating ability were often no better at calculation than department store clerks from the era when store clerks had to do calculations mentally or by pencil and paper (without any help from a cash register or other machine). Years of drudgery, steadily doing arithmetic in a variety of contexts, can turn into "chunking" ability that speeds mental calculation and results in apparently magical feats of mental arithmetic.
Actually, research shows that it can, and has been.
http://www.cambridge.org/gb/knowledge/isbn/item1172019/?site...
An interesting historical study of calculating prodigies turned up evidence that the famous nineteenth century idiots-savants with powerful calculating ability were often no better at calculation than department store clerks from the era when store clerks had to do calculations mentally or by pencil and paper (without any help from a cash register or other machine). Years of drudgery, steadily doing arithmetic in a variety of contexts, can turn into "chunking" ability that speeds mental calculation and results in apparently magical feats of mental arithmetic.
Didn't he have savant syndrome - ie. his brain was wired differently than ours? I am not a neurologist, and I can't explain how his mind worked (I doubt if anyone can) - but I think that question 'how to gain mental abilities of Kim Peek' is similar to 'what can I do to get autism'. I know it sound harsh, I just want to say that you probably can't gain this kind of abilities from any amount of hard work.
Exactly, but autism doesn't excuse the fact that it is a humanly possible level of intellectual capacity.
Well, we don't know how many 'brain resources' does 'normal' skills that autistic people lack require - and in my opinion they may require as much computing power and memory as Kim Peek's genius skills. We don't know how much of our potential is spent on everyday tasks, like parsing converstaions with other people.
You seem to suggest that the brain is a zero sum game. It may be so, but it is a mere assumption.
I don't have a source for this, but I remember reading about how the "autistic" brain dedicates more of its capacity for more intellectual, rather than using it for social purposes.
I hope it's true, because we currently focus our resources and attention on those who are labelled "gifted" early on, instead of building on the idea of life as a constant process of re-imagination and education. If this is true, then there are geniuses the world over, and we just need to tap their potential.
"I am somehow less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." - Stephen Jay Gould