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gjm comments on SciAm article about rationality corresponding only weakly with IQ - Less Wrong
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Comments (28)
I think there's a better way to think about the Jack-Anne-George problem, which generalizes more readily. You've got a chain with "married" at one end and "unmarried" at the other: so of course at some point along it there has to be a transition from the former to the latter, QED.
That is a very tidy analysis.
Easier than enumerate and evaluate, but much less general.
It instantly gives you the answer to cases that look like A->B->C->D->...->Z where enumerate-and-evaluate requires you to consider 2^24 possibilities.
Let's think a moment about further generalization. So you have an arbitrary directed graph where a->b means a is looking at b; some vertices are coloured white ("married") and some black ("unmarried"), and the question is: is there a way to colour all the vertices black and white that has no instance of white->black?
Well, if there is any chain of arrows starting at a white vertex and ending with a black one, then the reasoning I described tells you that in any colouring there must be a white->black edge.
On the other hand, if there isn't then we can start at every white vertex, walking along arrows and whitening every vertex we reach; since there is no W->...->B chain this will never produce a clash. At this point we have whitened every vertex reachable from a white one, so now we can colour all the rest black; we've coloured the whole graph without any W->B edges.
So we have our (maximally generalized) answer: the answer to "must a married person be looking at an unmarried person?" is "yes, if there is a married->...->unmarried chain somewhere; no, otherwise". And (so it seems to me) this is just following the path of least resistance using the approach I described. So I'm going to stand by my claim that it "generalizes more readily".
Assuming the only states are married and unmarried. I'm not sure if I would call a widow unmarried, in the same way I'm not sure if I would call a man with a surgically reattached foreskin uncircumcised.
Sure. (I think it's pretty obvious in the "puzzle" context that you're supposed to take "married" and "unmarried" as exhausting the possibilities, though.)
I'd call a widow unmarried if she wasn't currently married.
I suppose the language usage might get complicated.
Is she still a widow, in the present tense, after she has remarried? Looking at a few definitions, it appears so, but the archtype of widow is one who has yet to remarry.
Marriages vows are "Till Death Do Us Part".