Nobody's ever going to mistake me for an elite basketball player. I'm taller than average (about 6'6", a hair under 2m in SI units), but I'm not especially quick, or agile, or all that good a jumper. And I'm carrying at least 40lbs of extra weight above what a really good player my size would (in terms of mass, I'm closer to the dimensions of a really good (American) football player, though not nearly enough of it is muscle).
This doesn't stop me from playing basketball, though. I love the game, and I play a good deal, at least for a guy in his forties with a full-time job. I can hold my own against much younger players at least in the kind of casual pick-up games that happen on campus. If nothing else, I can generally be confident that I won't be the worst player on the court.
I bring this up because of a comment Kaleberg made over in one of the E. O. Wilson posts:
Maybe the problem revolves around the difference between being good at math and being good enough at math. Our culture puts a barrier around math, arguing that the ability to learn it is innate, so if you lack that talent, don’t even bother. There are other cultures where the attitude is that math might take a bit of work, but everyone can learn it well enough. (e.g. This is the case in much of Eastern Europe, China and India.) I’ve seen people who are actually fairly good at math simply choke when faced with a math problem.
I think this is an important point, and it's one of the many factors rattling around that led to the book-in-progress. In fact, I go into this at some length in the (current draft of the) introduction. I think we're far too quick to declare math and science aptitude to be innate talents, skills that only a tiny minority of people are capable of acquiring. This is certainly flattering to the vanity of science nerds, but I'm not entirely convinced that it's accurate.
The problem is that it's difficult to sort out the effects of innate ability from the effects of practice driven by interest in the subject. I recognize that I am vastly better at algebra than a randomly chosen person on the street (as long as that street is in a city that isn't hosting the APS March Meeting, anyway), but I don't actually think of myself as all that exceptionally gifted, mathematically, because I know too many theoretical physicists who blow me away. Some of these differences are undoubtedly attributable to talent, but a lot of them are due to practice. I'm good at algebra, relative to a non-scientist, because I've spent a good chunk of the last 20-odd years manipulating equations as part of my job. A theoretical physicist or a mathematician can prove circles around me, though, because they spend even more time engaged in manipulations of abstract math. I'm way better than they are at soldering wires together, though, or any of the other routine tasks of experimental physics.
(Incidentally, I should note that I am not without sympathy to a weaker version of Wilson's point in that original op-ed-- I'm acutely aware that my mathematical background is very limited relative to a lot of physicists. I've never had a class in group theory, for example, and as a result, I don't understand it very well. That hasn't hurt my career, though, because I picked a field where I don't need that stuff. Where Wilson loses me is the "don't worry about the math, you can contract it out" thing.)
The same holds for basketball. I'm not an elite player, but I'm way better than average, especially for my age group, because I've spent a lot of time over the last thirty years playing basketball. That counts for a lot, and because of it, I can out-play even people who are more physically gifted than I am. And there are plenty of people who, despite being in worse physical shape than I am, could kick my ass all over a golf course, because they play a lot of golf, and I don't.
I bring this up because, along with Kaleberg's point about being too quick to declare math and science to be innate talents, I think we have an aberrant attitude toward those talents specifically. That is, while I would agree that my innate physical abilities prevent me from playing basketball at an elite level, that doesn't keep me from playing basketball for fun. Even in academia, where any head-to-head competitive sport gets looked at askance by many faculty, there are even some social benefits from playing on a casual basis. I'm friends with faculty, staff, and students in some other departments primarily because of playing basketball at lunchtime. And when I came up for tenure, the then-Director of Residence Life sent a very nice letter to the committee, praising my engagement with students through basketball. If I were in a different work environment, it would probably be even more valuable for extracurricular bonding purposes.
Nobody thinks it all that odd for a 40-year-old without elite skills to play basketball for fun. And less aerobic sports like golf, even more so. In a lot of social circles, it's kind of odd for a 40-year-old man not to play golf, even if he lacks the ability to play at a very high level. And millions of other people who can't play sports at an elite level are passionately engaged with sports on a fan level.
When it comes to math and science, though, this kind of gets reversed. Not only is there no expectation that random people without elite math and science skills do science for entertainment, there's actually a bit of stigma to it. I talk to and sometimes get email from people who have read and enjoyed my book who tell me that in a bizarrely sheepish tone, as if there's something wrong with having an interest in physics as an adult who isn't a scientist. People will tell me that they enjoy hearing about physics in a tone that suggests they're confessing to some kind of minor character flaw, like a fondness for hair metal bands of the early 1990's, or trash cuisine. And frequently this is followed by a comment that they really don't have the math ability to understand science.
This is an attitude that really doesn't carry over to any other field. I've never heard anybody sound sheepish about admitting to reading popular books about history, say. In fact, a lot of the time, people are sort of surprised that I haven't read whatever the latest pop-history book is. But some of these same people find it hard to even consider reading a pop-science book, even one that is deliberately written for non-scientists, and features a cute talking dog as a hook. "Oh, I'd never be able to understand physics," they say, as if lacking the abilities and training to be a physicist were reason not to even take an interest in popular treatments of the subject. It's as if lacking the skills to play basketball at the college or pro level disqualified you from even watching an NBA game on tv.
I think that attitude is inextricably linked with the idea that math and science are innate talents, and not skills that can be picked up with a bit of effort. But it goes well beyond the corresponding situation for athletics, closing off even casual interest in the subject, in a way that is, I think, ultimately harmful to science and society as a whole.
There is a sense here where I'm agreeing with Wilson-- you don't need to have elite-level innate abilities to be interested in and involved with science, any more than you need elite-level innate physical skills to play basketball. What I disagree with is the notion that this is an inherent and unfixable state of affairs-- that students who don't believe that their math skills are up to snuff can't do anything about this, other than hiring math nerds as contractors to do the hard stuff for them. If you're genuinely interested enough in a subject to want to make it a career, you can almost certainly acquire the skills that you need.
The problem is of long standing. This country has a tradition of anti-intellectualism that goes back to at least the mid-19th century (a political faction of the time were proud to call themselves Know-Nothings). The problem is most acute in math and science, but other areas are affected as well: many Americans are proudly ignorant of foreign languages and see no value in studying them, for instance. (That some Americans are 2000 km or more from the nearest place where English is not the primary language is a contributing factor--but so are some Canadians, and even the ones in the back woods of British Columbia are expected to learn French.) The problem is particularly acute these days, thanks to a prominent political faction that rejects empiricism.
I don't see any solutions short of a cultural change that will take generations to play out.
I completely agree with you, math and science can be taught! You can have a great career in math related subjects and science without needing to be a Liebniz, Nash or Kutta or even knowing who those people are.
My dad (who is not a scientist) took me at age 12 to a presentation on astronomy which got me interested in science. I read "A brief history of time" which cemented the interest. This lead to me doing more science and math in high school and then an engineering degree. I thought I wanted to be a lawyer but I loved engineering.
Books on science that are geared towards people who are not scientists are really important. So to is outreach by scientists and engineers to people who are really young.
I look forward to reading your books.
I have a (not original) theory that some people (e.g. John Von Neumann) are simply born with exceptional math ability. And some people are born with "average" math skills but they become math geniuses due to intense fascination/obsession with math- so much so that they rewire their brains to be great at it. The question then becomes is math passion innate or something you can acquire :)
I think I agree with you much more on this aspect of the tangle.
Out of curiosity, did you get your height especially late in life, after you'd formed your sense of self, or did you get it while you were still figuring yourself out?
I ask because I'm 5'2", and basketball is always my go to concession for "ok, at some level, excellence here requires innate factors". To be *able* to come up with basketball (of all things) as something that is mostly about practice may be in part related to your height.
I wonder if, given our society as it is, the ability to think of things as mostly about practice depends in part on whether there is a default assumption that "someone like you can do this"?
In any event, I've consciously changed my patterns of thinking on innate ability, so I know it can be done under some circumstances (not sure what it would take for a broader cultural change). I didn't change my mind because I thought I had good *data* on nature vs. nurture questions. Instead, I changed my mind because there's some evidence it leads to better performance in e.g. math and also because I'm much happier this way than I was believing in "native gifts".
In other words, I have no idea if "excellence is mostly about practice" is a TRUE model. I know it's a heck of a lot more USEFUL model for me than "excellence is mostly about innate talent".
I ask because I’m 5’2″, and basketball is always my go to concession for “ok, at some level, excellence here requires innate factors”.
Well, OK, you'd be at a disadvantage taking and defending against jump shots and layups. But there is more to basketball than that. Nothing you have said rules out the possibility that, with sufficient practice (and this is key), you could be a formidable (at least in pickup games) point guard.
Certainly, to do something like basketball or math at the very top level takes some innate ability. Nobody who posts here was ever likely to be a serious threat to Michael Jordan or Richard Feynman in their heyday. But basic competence--getting good enough to play a decent pickup basketball game or calculate compound interest--is something that can be taught to almost everybody. If you can walk and you have functional hands, you can be taught how to throw, catch, and dribble. If you have enough brain power to memorize a few basic rules, you can be taught to do arithmetic, algebra, geometry, and even (though this may take a bit more work) calculus.
I have seen advertisements for books that claim you can teach algebra to a 7 year old by following the methods described therein (I am not qualified to opine on whether these claims are true).
Becca you speak the truth! It all comes down to what story we tell ourselves: Do we tell ourselves that with enough work and practice that we can achieve some level of proficiency, or do we tell ourselves that we can never do something because of our lack of an innate ability? I for one know it feels a lot better to tell yourself the former rather than the latter.
And Chad, I wholeheartedly agree with the sentiments of your post. In my own discussions with others I've found the athletic comparison a useful and easy-to-grasp comparison that lets most people understand the absurdity of thinking it all comes down to innate ability. I typically use triathlons instead of basketball though, because there are no body size factors that come into play - it's all about how much effort you put in to get in shape and get fast! Even very tall people can do a good triathlon.
And finally, if I may add, I think most people use the innate ability reasoning as an excuse for not trying something, even if they don't consciously know they are doing it. Learning anything new requires failure (i.e. being not very good) at the start and an acceptance of that failure, and I think most people fear that failure. They say they don't have some innate ability as an excuse for their failures in an area, when really it is only because they haven't put in the time/effort to move from bad to good. In almost all areas of life you must be bad before you can be good.
So are you proposing a pick-up math league?
"What I disagree with is the notion that this is an inherent and unfixable state of affairs".
I can only draw upon my own personal experiences as a student, and somewhat from observing other students - but I think that math skills often are, in fact, inherent - yet also extremely "fixable". That is to say, I very much agree with the general sentiments above.
That said, I also think a great deal more people are capable, commensurate with time and effort, to achieve a "professional" capability at math, in the sciences, than they would be at attaining a professional level of athletic performance. Obviously the problem inevitably lies with any given person's reluctance to put in the required "time and effort".
So perhaps the question is also, somewhat, are people frightened off by the math? or the work that might be necessary in order to achieve some level of success? By the same token, "innate ability" in the sciences can be a curse for almost the same reasons. It can breed a poor work ethic.
Its an interesting topic, really. I think the best people to ask about this are the ones who never went after it, even if they had some hidden desire for the Sciences. Or the people who gave up because it seemed too difficult when they first experienced it. Or maybe the person who just assumed - or worse, believed it when someone told them, that they "couldn't cut it".
Exploding the myth that there is innate mathematical talent - at least, enough to be decent at it, is the subject and purpose of John Mighton's book The Myth of Ability. It's primarily aimed at teachers, but I still recommend it for anyone, especially anyone who thinks they were born unable to do math.
Mighton created a program of math education based on his experiences teaching 'math-challenged' kids.
Sure I think 90% of the population could become what passes in our society as good at math. But, we are talking about becoming (or not) a professional scientists here. That requires elite or at least semi-elite level at math. Being the guy who breezed through college calculaus with straight A's and then quit (which is probably already top 1%) just won't cut it.
I can partially agree with Wilson. You can contract out the toughest of the tough math. But, you got to at least be able to understand the issues, even if you wouldn't have been able to come up with the solution on your own. That still requires a high math capability. I think a similar dynamic applies to being good at computer programming -especially regarding stuff like numerical methods. You can probably contract out (or use existing software), but you better have at least an inking of understanding of whats going on underneath. I think because science is a cutting edge activity performed by only a tiny fraction of the population, that the selective hurdles to becoming one are only going to get tougher not easier.
Eric, the Know Nothing name isn't related to anti-intellectualism as far as I'm aware. It was the intended response to questions about a semi-secretive anti-immigrant/Catholic organization.
Like other human traits there is a substantial genetic contribution to mathematical ability. In studies of identical twins raised apart mathematical ability has one of the highest correlations between the twins.
In the history of mathematics there are quite a number of examples of closely related outstanding mathematicans. Blaise Pascal's father Etienne Pascal was a well-known mathematician ( Pascal's Limacon is named after Etienne not Blaise), Euler's father was a professor of mathematics and one of his sons was a pretty good mathematician, Emily Noether's father, Max Noether, was a very eminent mathematician, There are the Cartan's - Elie and Henri, Emil and Michael Artin, the whole Novikov family. And of course there are the Bernouli's.
Another case that comes to mind is Markoff whose grandson was a very good mathematician. However Emile and Armand Borel are apparently not related.
The claim is not that there is no genetic contribution to mathematical ability-- that would be just as ridiculous as the claim that there is no genetic contribution to mathematical ability. The claim is that this is hard to sort out from other factors.
For every talented scientist or mathematician who had a famous scientist or mathematician for a parent, you can name at least one whose parents were not especially notable in science or mathematics.
@Jim: In a world where the son of a butcher is expected to become a butcher and the son of a baker is expected to become a baker, is it any surprise that the son of a mathematician would be trained in mathematics? Or that some fraction of the sons so trained would also have some innate ability which allowed them to become top mathematicians themselves? Emmy Noether, I'll grant you, is an exceptional case: it was rare in those days for any woman to be offered mathematical training.
Compare with the 20th century, where it was much more common for people whose parents were not in the math/science business to become scientists or mathematicians. There are scientist families out there, certainly, but the overwhelming majority of such cases (at least that I know of) are married couples. (You may have heard of the "two-body problem"--it refers to the difficulty such couples have finding jobs in the same city.) Certainly there are some father-son pairings: Werner Heisenberg's son was a professor of physics at my university (the son retired several years ago), and one scientist in my field is the son of another scientist who worked in my field but has retired. But it's relatively rare for an active scientist to be related by blood to another scientist.
There are certainly people who learn mathematics with remarkable speed and at a very young age. Selberg independently discovered the Rademacher Formula for the partition function when he was in high school. Shafarevic read the Zahlbericht when he was fourteen. He wasn't sure he totally understood a few items in it so he wrote a letter sending it off to about 20 top mathematicians asking them to clarify some points in it. At age fourteen he goes right to the top of the mathematical world to get enlightenment. Shafarevic and Selberg were so far ahead of anyone around them in their youth that they couldn't have learned much from them. Shafarevic commenced university study at age 16 and received his Phd in mathematics at age 20. His dissertation on the theory of central simple algebras became a standard reference in the subject.
This looks like innate ability to me.