gwern comments on The Correct Contrarian Cluster - Less Wrong

38 Post author: Eliezer_Yudkowsky 21 December 2009 10:01PM

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Comment author: komponisto 22 December 2009 03:26:57AM *  28 points [-]

Along with 99% of humanity my IQ isn't high enough for me to ever understand the math behind quantum physics

This may be a tangential point, but I need to say this somewhere: claims like this are quite likely false. (Notice how rarely they're accompanied by justification.)

Quantum mechanics is new (in the scheme of things). So, of course, we see right now that the only people who understand it are very smart people: the ones who first thought of it and their students and associates. But that doesn't mean that no one else can understand it; it just hasn't had time to trickle down into everyone's general education yet.

300 years ago, you could have replaced "quantum" by "classical" in that sentence, and it would have seemed reasonable: at that time, only a few dozen people in the world understood the differential and integral calculus. Yet now this kind of mathematics is taught regularly to hordes of IQ 110 college freshmen, and (I expect) is considered elementary and routine by a majority of LW readers. Taking an Outside View approach here, I don't see any reason not to expect that the same trend will continue into the future, with quantum mechanics eventually being considered a grade-school subject (even without recourse to transhumanist solutions such as intelligence enhancement, which will immediately come to the minds of many readers).

Going back further, once upon a time literacy was an elite skill. Now we take it for granted, but how much do you really think our IQs have improved in the last couple thousand years?

And let's not forget that even now, we already know that the fundamental mathematical ideas behind quantum mechanics are actually quite simpler than you would have thought from listening to physicists -- little more than linear algebra over complex vector spaces.

Comment author: gwern 14 October 2010 03:37:17PM 6 points [-]

Yet now this kind of mathematics is taught regularly to hordes of IQ 110 college freshmen, and (I expect) is considered elementary and routine by a majority of LW readers

This seems factually false to me. For starters, the average IQ of college freshman (all colleges, all majors) is more like 115 or 120 (choose the reference you please from Google). And math or physics majors are a cut far above that average, with GRE scores indicating an average around 130. (Prospective grad students, yes, but the ranking fits with high school SAT scores.)

I don't think very many schools make relativity-level mathematics (or even just multi-variate calculus sufficient to solve Newtonian problems) a core requirement rather than major-specific...

Comment author: komponisto 14 October 2010 04:54:20PM 2 points [-]

The number 110 was just a guess, of course, but the point clearly stands even if the average IQ of people taking business calculus is 120.

The 17th-century counterparts of these folks would have been illiterate peasants or possibly, in a few cases, local merchants; they would not have been Newton and Leibniz.