I’ve been following E=mc^2’s string theory thread all day, and for the past hour I’ve been poking around on the link that Ring provided in post # 24 of that thread. My wife is getting thoroughly pissed at me right now because she just came home with her hair and makeup fully done and she wants me to take her out to dinner, and I refuse to budge from the computer. I’m wondering what percentage of the population would be capable of understanding this stuff. I’m looking at the descriptions of supersymmetry and supergravity mathematics and wondering if it would be possible to study this material without suffering from a complete loss of all hair, teeth, and sexual function. I’ve made fun of my mathematical capabilities on this message board before, but the truth of the matter is that they’re not all that bad. I’ve gotten A’s in honors college level math courses, albeit with difficulty. And the vast majority of people that I know are incapable of handling any mathematics beyond arithmetic. Most adults I know can add, subtract, multiply, and divide and that’s it. But I seriously doubt that I could ever come anywhere close to understanding this stuff, no matter how hard I applied myself. How high are the IQ’s of the people who understand string theory? I would guess that an entry level genius IQ of 130 (two standard deviations from the mean) would hardly be enough to cut the mustard. Are the people who understand this stuff basically intellectual demigods who possess IQ’s which are three, four, or even five or more standard deviations above the mean? Are there only a handful of people in the world who are capable of understanding this, or can a guy like me get this stuff if he tried hard enough?
Just from self studying physics texts I’ve managed to pick up the math required for some classical mechanics, special relativity, quantum mechanics and a little general relativity.
I don’t know what my IQ is but I do know that I would have no chance whatsoever to understand the math required for string theory. At least not without a full time math tutor that could explain very sophisticated stuff to a very unsophisticated person.
Well, Richard Feynman, whose talent spoke for itself, and who was really more an applied mathematician than a physicist, gloried in his unspectacular IQ of 121. I’ve never known a top-notch mathematician who wasn’t fairly above-average in terms of general intelligence, but I’ve certainly known top-notch mathematicians who wouldn’t be able to carry on a discussion of, say, the differences between Stalinism and Maoism.
One thing peculiar to mathematics is that you usually can’t learn concepts superficially at first, the way you can in some other fields. You either get it or you don’t, and to get it, you have to build it up from its logical foundations. You start studying eigenvalues, and after a few days, weeks or months, suddenly you understand what an eigenvalue is, and you can’t even remember what it was like not to know what an eigenvalue is. At least that has been my experience. Because of this, when you first encounter a new branch of mathematics, it’s just meaningless glyphs on a page. In comparison, an intelligent layman could read an article from the latest issue of a leading academic history journal and probably understand superficially what was being discussed. I have a doctorate in engineering with a heavily mathematical orientation, but if I pick up a pure mathematics journal, it might as well be written in Sanskrit.
It’s not a matter of IQ so much as it is math aptitude and interest.
http://www.unknowncountry.com/news/?id=2009
The campus doctor at the University of Sheffield in the U.K. was treating a math major, when he noticed that the student’s head was a little larger than normal. He referred the student to neurology professor John Lorber, who gave the student a CAT scan and discovered he has virtually no brain at all, despite having an IQ of 126 and doing well in college.
I’d really like to see documentation about that from a site that doesn’t mention Whitley Streiber in its title.
I this speaks more to the limitations of IQ tests in measuring “applied” intelligence than to Feynman’s meanness of intellect. Feynman also enjoyed deprecating himself, intellectually, in the same sort of “Aw shucks,” manner than a Southern politician likes to relate to his voters. Not that it’s a bad thing; his explaination of his “master safecracking skills” is quite amusing and serves to highlight how a simple oversight in security can allow even an amateur to penetrate the most secure system, and it’s far more honest than the political types who like to lay an exaggerated claim to every idea and innovation that they may have been within vague proximity of (Al Gore, we’re talking about you).
That being said, as ultrafilter points out, becoming adept at math is more of a combination of the aptitude for visualizing or sorting out the complex language of math in your mind and having the interest to pursue it in a disciplined fashion. I’m fairly good at math–I passed my basical calculus course with ease, and managed A’s out of introductory differential equations (second time…I think better’n half the class was flunking with the first instructor) and partial differential equations, but then, except for a couple of computational math classes, went no further. I’ve delved into M-Theory slightly, but just don’t have the patience to develop the particular (and, for me, otherwise useless) math skills to gain a mastery of the theory. I think, though, anyone who can genuinely comprehend calculus and linear algebra can, with sufficientt devotion, obtain a working comprehension of the requisite math; not enough to start cranking out original and innovative work, mind you, but sufficient to follow the footsteps of those before.
That echos my experience exactly. It’s one thing to grasp the mechanics of, say, integral calculus enough to knock out a few integrals, but gaining a true understanding requires gathering together enough information and letting it matriculate, while going thorugh the mechanics of solving problems or applying the methods until something just clicks into place. I specifically remember Fourier transforms being like this; for about a year I cranked away, coming up with Fourier transforms for various classes (A-bomb, PDQ, signals analysis) and then one day was working on a problem in Vibrations and it just…clicked. Mind you, I understood that you were taking a function in one domain and converting it to a “frequency” representation, but the process was just crank and push until I was solving a problem and it all became clear. (I figured out Laplace transforms at the same time…beautiful things, they are.)
Anyway, you need to be smart enough to, say, read Greek characters and think that Reinmann functions are sexy, but not so smart as to realize that women (typically) don’t think the same and furthermore don’t think that of you either just because you understand them. It takes, then, a certain type of intelligence…the kind that isn’t really dedicated to procreation, which is therefore of rather questionable long-term value. 
Stranger
The essential thing about advanced mathematics is that it isn’t (contrary to popular belief) about numbers. It’s about logic, and the ability to make a completely rational deduction. Humans work a lot on intuition and analogy, which can get a good idea rolling, but they really need to be trained to think absolutely logically. I’d say it’s analogous to the notion that anyone can (in theory) run a marathon, but only so many people have bothered to put in the effort to train for it.
I realize you’re speaking metaphorically and in shorthand–even though I’m uncertain as to what you mean by “general intelligence”–but the inabiliity to distinguish between Stalinism and Maoism could be corrected by a 15-minute seminar at any third-rate university in the world. For perhaps 99 percent of the world’s population, however, the ability to comprehend the finer points of string theory would never happen even after 15 years of patient tutoring.
The marathon analogy is good, because you also have to take into account the fact that some people have the cardiovascular edge and will find the training easy, while others are going to have to work a lot harder. It’s the same for higher math.
I think that using I.Q. tests to determine whether you’re going to be able to understand math of a given level is a poor idea. The only way to find out if you’re going to be able to understand math of that level is to take a course or read a book on the subject by yourself. If you want to learn some given piece of mathematics, find out what the preliminaries are that you need to learn. Then go ahead and start learning them. If, after some determined work, you find that you can’t understand them, then you can give up. Be sure that you don’t try to jump ahead and try to learn something without learning the preliminary courses. I think that anybody can eventually learn anything. In some cases, it would take longer than their expected lifetime to do it, but eventually they could learn it.
How true it is. The biggest difficulty in learning advanced math is mastering the symbolism, notation and terminology.
I tried educating myself in Linear Algebra using an old 1960s textbook and the notation left me without a clue. Later I bought a modern text that actually explained stuff and I found it to be both accessible and interesting. If textbooks were specifically written for self studiers I thing most people could at least get a good idea as to what it was all about. Unfortunately they’d probably weigh 80 pounds.
BTW. Thank God for posters like Chronos who keep the esoteric jargon to the minimum.
I expect you will get a lot of grief from your beloved over this behaviour, so perhaps you’re not being ‘smart’ in ignoring her? :eek:
Credit me with a little common sense here, OK? I knew damn well that if I intended to have sex anytime this decade that I had better get my quantum mechanical ass out of that chair and take her to dinner. We made it to the restaurant about half an hour before it closed. My wife is a redhead, fer chrissake! Hell hath no fury like a redheaded Dope Widow. 