simont: (Default)
posted by [personal profile] simont at 08:27pm on 19/03/2014
As I commented in the other post, I felt that the presentation of several of these analogy problems in sequence caused the first ones to bias my thinking on the later ones.

I'm quite inclined to think of the problem in a more holistic style, thinking of the whole space of transformations instead of one specific element of it: "if abc goes to abd, what (plausible-to-humans) mapping function might that be an individual element of?" And once you ask the question that way, you can imagine assorted generalisations of "abc → abd" that vary in their domain of applicability, and (at least along the Pareto frontier) vary in a precisely opposed fashion in their recognisable similarity to the original archetype element. In that spirit I answered 'EDOM' to one of your questions, because the idea of 'generalise abc → abd' I had in my mind at the time only went so far, which was the price it paid for feeling reasonably sensible in the areas it did reach. The Feynman answer of generalising 'abc → abd' to the function 'X → abd, for all X' is listed in your post as 'smart-aleck', but of course one advantage it does have is full generality! There's no input for which you can scratch your head and wonder how to best apply the underlying rule, and no input for which you give up and say 'no answer exists, try something actually in the domain of my function'.

So asking for several individual values in sequence caused me to repeatedly refine my idea of the mapping function I had in mind, and I probably didn't end up with there actually being a single sensible function that all my answers were consistent with. But that's an effect of the sequential presentation, not (or at least not obviously) of any genuine inconsistency in my thinking.

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