Genius, in the popular conception, is inextricably tied up with precocity—doing something truly creative, we’re inclined to think, requires the freshness and exuberance and energy of youth.
It is also tied up with the idea that "geniuses" are fast. It was nice to see profiles of Maryam Mirzakhani indicate that she was a deep thinker, not a fast thinker. Maybe we can start changing some of these popular mis-conceptions.
I thought this was mostly a myth. Do you have source for that?
Einstein to Feynman: "Please explain things slowly"
You could call Schwinger "slow", but he "saw" very deeply. After all, he found and corrected problems with the Dirac equation.
Also, Darwin:
"At no time am I a quick thinker or writer: whatever I have done in science has solely been by long pondering, patience, and industry." [2]
On a personal note, I entirely relate to the slow thinker. Most smart peers of mine are fast thinkers and I'll usually lose to them on puzzles and tricky math problems when it is a matter of speed, but then I'll solve problems that these same people give up on and claim too difficult if I can sit in a quiet room with my fists on my head.
I have a suspicion that fast thinking involves a developed ability to filter out (quickly) what seem like dead end avenues -- so the fast thinker can hone in on the promising avenues and get to a local maxima solution faster. But for some problems -- especially ones that require very non-traditional paths to solutions -- this filter fails and prunes away avenues that actually lead to a solution to that "impossible" problem or global maxima solution.
I realized a long time ago the danger in pruning away the "obvious" dead ends, so I think my slow thinking comes from a refusal to categorize anything as a dead end until it is provably so -- because of a worry I'll prune away the solution. A bunch of avenues will present and I'll need to consciously sort through them. So my filter is slow and requires me to retreat to that quiet room to go sort through all the possibilities. But then I'll come up with gold.
I have a theory that I'll put out here... that slow and fast thinking are developed tendencies not innate qualities. In my experience most of the smart people I know are fast thinkers. Which makes sense if this is developed, because there's an ego reward involved -- especially in our educational systems -- for developing that way. And the only reward for slow thinking is solving a hard problem, but as a kid in school, where's the external reward in that? And how often is the opportunity for solving really hard problems given? Basically what I'm saying is that I'd like to see more slow thinkers in the world. (I'm not kidding.)
[1] http://www.unmuseum.org/einstein.htm [2] http://www.criticalthinking.org/pages/the-questioning-mind-n...
As for whether it's a developed vs innate quality, I don't remember ever thinking differently and being trained to think the way I do because of my environment. I would agree that in our system fast thinkers are rewarded more, but that doesn't mean that our system develops fast thinkers at the expense of slow thinkers, or that its any less innate. It just means that slow thinkers have more difficulty being recognized earlier (hence "late bloomer" or missing the "precocious" label.
"Upon starting high school, Feynman was quickly promoted into a higher math class and an unspecified school-administered IQ test estimated his IQ at 125—high, but "merely respectable" according to biographer James Gleick;"[2]
I think people with extremely high IQ tend to be "fast thinkers" and they seem to rely more on logical thinking while those who have sufficient IQ tend to be "deep thinkers" and rely more on intuition/epiphanies.[3]
John von Neumann would the "fast thinker" type of Genius.
[1] http://c2.com/cgi/wiki?FeynmanAlgorithm
[2] https://en.wikipedia.org/wiki/Richard_Feynman#CITEREFGleick1...
[3] “I never made one of my discoveries through the process of rational thinking” ― Albert Einstein
First of all, most IQ tests do not go above 140. So anything anywhere near 140 may only be telling you the person is at about the limits of what the test can measure. Even for those tests that do go above 140, it requires a qualified assessor to interpret it properly. The smartest kids often do not measure as being all that smart by standard measures. "Genius" is, basically by definition, someone who thinks differently from others. So measuring the kid who is radically different by standard measures has a track record of missing a lot.
In recent years, there is increasingly research into and available literature on the idea that gifted kids have different minds. They are not merely "more" of something, they are fundamentally different. The correlation of "speed = intelligence" is a rubric which assumes gifted kids are simply "more" of something. Yes, they do tend to be faster than average, even if they are slow compared to other gifted students, but it's really a lot more complicated than that and I think the emphasis on speed does a huge disservice to the gifted community.
The "fast = smart" paradigm is a really major metaphor for giftedness in the world. For example, Stephanie Tolan's essay "Is it a cheetah?" is very popular: http://www.stephanietolan.com/is_it_a_cheetah.htm I once wrote something of a polite rebuttal to that which used redwoods and gazelles as other metaphors. I am not terribly important in the world and it did not become popular (and is no longer online, unless it got captured on The Way Back Machine). I think the cheetah metaphor does a disservice to the gifted community in part because of the unstated assumption that smart people are all dangerous predators. Gazelles are just as fast and are not predators. Why not use that as a metaphor?
Anyway, I am quite busy today so I don't plan to argue this or dig up detailed supporting links. If you really want to look into it, HN's member who goes by the handle tokenadult is a good resource on the topics of intelligence and education. I believe his profile contains links to resources and his posting history, both comments and articles, is likely to be enlightening. (Though I have no idea if he would agree with any of my views above. He and I are not close. We haven't talked in quite a long time. But I have reason to believe he remains far more current on these subjects than I am.)
Deep thinkers tend to be more original and there is actually a negative correlation between extremely high IQ and creativity.
Extremely fast thinking is the name of the game in the IMO and similar competitions. In fact, the emphasis is so much on speed that there are often doubts as to whether the medalists will also be good at research.
An IMO takes place over two days. On each day the candidates get a question paper with three questions on it. They have 4.5 hours to attack the questions. The threshold for getting a gold medal might be roughly equivalent to getting five of the six problems more or less completely solved.
The questions are always of the form "prove X" -- maybe occasionally "prove or disprove X, whichever is possible" or "find quantity X, with proof"; but it's always a matter of finding proofs -- where X is something no more than a few lines long.
So it's "speed math" in comparison with actual academic mathematical research, which typically takes place on a timescale from weeks to years and where there's no guarantee that any human-accessible solution exists. But it's a whole lot slower than pretty much anything else these (roughly) 16-19-year-olds are being asked to do in mathematics.
And, empirically, it does turn out that people who do well in IMOs tend to do pretty well in mathematical research, and in other mathematical things they put their minds to. (But yes, of course there are kinds of genius that have nothing to do with mathematics, and kinds of impressiveness that have nothing to do with genius; and there are plenty of first-rate researchers who never took to IMO-like problem-solving.)
(Random example of an IMO question, from this year's IMO, to give an idea of what a typical X looks like: "For each positive integer n, the Bank of Cape Town issues coins of denomination 1/n. Given a finite collection of such coins (of not necessarily different denominations) with total value at most 99+1/2, prove that it is possible to split this collection into 100 or fewer groups, such that each group has total value at most 1.")
There is a skill component to those things although. You could practice them a bit and improve your scores significantly. But is that really intelligence or just skill? It will always be a combination.
It is a detailed 900 page exploration if a lifetime of research from the famous behavioral economist Daniel Kahneman on the topic
As elsewhere mentioned, our educational system often ties success to fast thinking. I've always known I am not a fast thinker and, in fact, had often been the slowest thinker in my classes. This made school difficult and I struggled accordingly. Ultimately, I offset this by studying harder than my peers. For me, it has never been about reading the material and repeating, for example, some mathematics system from memory, but in truly understanding that system.
I consider myself a deep thinker that can easily connect concepts, graph relationships, and see the big picture. This is why I prefer to work as an architect, on security projects, and inevitably play the right stocks on the market. I suppose, anecdotally, if I'm any model, that deep thinkers might be better suited to certain roles and might naturally gravitate toward them.
Finally, and now a bit off-topic: The fact that deep thinkers might be equated with "late-bloomers" might have to do less with "figuring out what they're good at", and more to do with a society and a system which is prejudiced against them. If deep-thinkers were better nurtured and led through the educational system, they may not spend their thirties, or even 40's, learning how and where to apply their talents.