TheOtherDave comments on Rationality Quotes April 2012 - Less Wrong

4 Post author: Oscar_Cunningham 03 April 2012 12:42AM

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Comment author: Eliezer_Yudkowsky 05 April 2012 09:43:25PM 12 points [-]

Have you ever tried to teach math to anyone who is not good at math? In my youth I once tutored a woman who was poor, but motivated enough to pay $40/session. A major obstacle was teaching her how to calculate (a^b)^c and getting her to reliably notice that minus times minus equals plus. Despite my attempts at creative physical demonstrations of the notion of a balanced scale, I couldn't get her to really understand the notion of doing the same things to both sides of a mathematical equation. I don't think she would ever understand what was going on in matrix calculus, period, barring "teaching methods" that involve neural reprogramming or gain of additional hardware.

Comment author: Elithrion 05 April 2012 11:52:31PM 5 points [-]

No, I haven't, and reading your explanation I now believe that there is a fair chance you are correct. However, one problem I have with it is that you're describing a few points of frustration, some of which I assume you ended up overcoming. I am not entirely convinced that had she spent, say one hundred hours studying each skill that someone with adequate talent could fully understand in one, she would not eventually fully understand it.

In cases of extreme trouble, I can imagine her spending forty hours working through a thousand examples, until mechanically she can recognise every example reasonably well, and find the solution correctly, then another twenty working through applications, then another forty hours analysing applications in the real world until the process of seeing the application, formulating the correct problem, and solving it becomes internalised. Certainly, just because I can imagine it doesn't make it true, but I'm not sure on what grounds I should prefer the "impossibility" hypothesis to the "very very slow learning" hypothesis.