Open Thread, August 2010

NancyLebovitz

Open Thread, August 2010 — LessWrong

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I thought I'd pose an informal poll, possibly to become a top-level, in preparation for my article about How to Explain.

The question: on all the topics you consider yourself an "expert" or "very knowledgeable about", do you believe you understand them at least at Level 2? That is, do you believe you are aware of the inferential connections between your expertise and layperson-level knowledge?

Or, to put it another way, do you think that, given enough time, but using only your present knowledge, you could teach a reasonably-intelligent layperson, one-on-one, to understand complex topics in your expertise, teaching them every intermediate topic necessary for grounding the hardest level?

Edit: Per DanArmak's query, anything you can re-derive or infer from your present knowledge counts as part of your present knowledge for purposes of answering this question.

I'll save my answer for later -- though I suspect many of you already know it!

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[anonymous]16y00

"That is, do you believe you are aware of the inferential connections between your expertise and layperson-level knowledge?"

This is related to an idea that has been brewing at the back of my mind for a while now: Experts aren't always good teachers because their problem solving algorithms may operate at a level of abstraction that is inaccessible to a beginner.

0thomblake16y

Hmm... I'm not sure if I think of myself as an expert at anything, other than when people ask. But I'm pretty sure I have about the best understanding of logic I can hope to have, and could explain virtually all of it to an attentive small child given sufficient time. And I might be an expert at some sort of computer programming, though I can think of people much better at any bit of it that I can think of; at any rate, I am also confident I could teach that to anyone, or at least anyone who passes a basic test

6Oscar_Cunningham16y

I have a (I suspect unusual) tendency to look at basic concepts and try to see them in as many ways as possible. For example, here are seven equations, all of which could be referred to as Bayes' Theorem: =\frac{P(E%7CH).P(H)}{P(E)}\\[10]P(H%7CE)=\frac{P(E%7CH)}{P(E)}.P(H)\\[10]P(H%7CE)=\frac{P(E%7CH).P(H)}{P(E%7CH).P(H)+P(E%7C\neg%20\!\,H).P(\neg%20\!\,H)}\\[10]P(H%7CE)=\frac{1}{1+\frac{P(E%7C\neg%20\!\,H).P(\neg%20\!\,H)}{P(E%7CH).P(H)}}\\[10]P(H%7CE)=\frac{P(E%7CH).P(H)}{\sum%20P(E%7CH_i).P(H_i)}\\[10]%0Aodds(H%7CE)=\frac{P(E%7CH)}{P(E%7C\neg%20\!\,H)}.odds(H)\\[10]%0Alogodds(H%7CE)=log(\frac{P(E%7CH)}{P(E%7C\neg%20\!\,H)})+logodds(H)) However, each one is different, and forces a different intuitive understanding of Bayes' Theorem. The fourth one down is my favourite, as it makes obvious that the update depends only on the ratio of likelihoods. It also gives us our motivation for taking odds, since this clears up the 1/(1+x)ness of the equation. Because of this way of understanding things, I find explanations easy, because if one method isn't working, another one will. ETA: I'd love to see more versions of Bayes' Theorem, if anyone has any more to post.

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