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Analogy analysis : comments.
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
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
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
in my thinking.
at 08:41pm on 19/03/2014
This is interesting, as your answers were among the more "Mitchelly" of the answers given - I think I would have guessed that you were one of the people less biased by the initial example, more willing to update your rule to take account of new information rather than to stay consistent with the first rule you thought of.
Feynman - if you're doing science, then arguably by definition you get to test your hypotheses, and the smart-aleck hypotheses have
to be worth testing.
at 09:13pm on 19/03/2014
Feynman - if you're doing science, then
*nods* Yes, I had that thought shortly after hitting send. Perhaps if you're approaching the analogy problem with the mind of an experimental physicist, you treat the premise abc → abd as an
, and the question becomes, 'Given that observation, what law of nature is most likely?' And then you take the Occam's Razor approach, and pick the simplest one that fits the observations – until, of course, further experimental results are obtained and the explanations that are
simple begin to be ruled out.
Perhaps Feynman's position, though on the surface it had what Hofstadter called a 'village idiot' nature about it (a curious contrast to your characterisation as 'smart aleck'!), would have revealed huge depths of subtlety had Hofstadter only thought to add one or two
exemplars to his analogy problems: 'If abc → abd
def → deg, what does this or that go to? Do your answers change if it is later revealed that abd → abc? Or dba → cba?'