eli_sennesh comments on Is Scott Alexander bad at math? - LessWrong

31 Post author: JonahSinick 04 May 2015 05:11AM

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Comment author: IlyaShpitser 04 May 2015 02:44:30PM *  14 points [-]

Let me take a stab at my (not OPs) views on math:

(a) A single number model of intelligence is toxic and silly. IQ is a single number proxy for a complex multidimensional space.

(b) Effective test taking has very little to do with math ability. Many excellent mathematicians are bad test takers (e.g. do not think quickly on their feet): this means basically nothing.

(c) Brains are complicated, and there is a huge amount of heterogeneity in how people process information and think about mathematics (and indeed all topics, but it is clearer in mathematics perhaps). Some are very visual, some are big on calculation.

(d) There is no separate magisterium called "math," there is a gently sloping continuum from common sense to "novel math work." When someone says "I am bad at math," I am not sure if they mean "I can't think carefully at all," "math notation scares me," "I can't think abstractly," [something else].

(e) If you haven't engaged with math beyond high school, you probably don't have enough information to evaluate the counterfactual "would a hypothetical me that pursued a math education make a good mathematician?" A lot of people's current trajectories in life are based on contingent things like what sort of teachers you had, social situation, etc.

(f) There is a skill component to math that needs practice and repetition, as with anything else. I call it "taking the time to insert metal struts into your brain."

(g) I think a non-trivial % of college-educated population can have a non-trivial engagement with mathematical topics, if they get over their panic. A smaller % can do novel work, if they wanted to put in the time.

(h) There is an enormous overlap between doing math properly and doing rationality properly. Math gives you quite a bit of good rationality habits for free (e.g. "I am notice I am confused.."), and (?conversely?) you can't engage with rationality without a bit of math.

Comment author: [deleted] 04 May 2015 07:53:16PM 0 points [-]

Brains are complicated, and there is a huge amount of heterogeneity in how people process information and think about mathematics (and indeed all topics, but it is clearer in mathematics perhaps). Some are very visual, some are big on calculation.

And importantly, brains are more heterogeneous at the extremes than at the means. A person of average intelligence might not have much difference between their verbal and calculation abilities; a person of great verbal or calculative intelligence may have a large gap between their stronger and (comparatively) weaker cognitive abilities.