29 Jul '04 18:29

What number comes next in this sequence:

1 4 11 20 31 44 ???

-Ray.

1 4 11 20 31 44 ???

-Ray.

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Elsewhere30 Jul '04 05:15

I also get 536. As Wittgenstein pointed out (talking about IQ tests, I believe), a puzzle in this format has an infinite number of answers, each with logic to ack them up.*Originally posted by bbarr***Add 15 to 44 for 59.**

In particular, I could construct a polynomial whose output at consecutive integers is any sequence you give me, though in practice the algebra could get arbitrarily involved.- Joined
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Center of Contention30 Jul '04 05:20

Was he talking about IQ in particular? I don't have a copy of Philosophical Investigations handy (it's propping up a table somewhere, I'm sure), but I thought he was talking about rule-following in general, and he used the example of adding by two. He imagines that the person who was doing the adding suddenly switched after he reached one thousand, and seems to think that for any rule there are an infinite number of mutually exclusive applications of the rule consistent with any formulation of that rule.*Originally posted by royalchicken***I also get 536. As Wittgenstein pointed out (talking about IQ tests, I believe), a puzzle in this format has an infinite number of answers, each with logic to ack them up.**

In particular, I could construct a polynomial whose output at consecutive integers is any sequence you give me, though in practice the algebra could get arbitrarily involved.- Joined
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Elsewhere30 Jul '04 05:24

To be honest, I didn't read the quote--the place I saw it said something to the effect of ''This kind of thing pops up in IQ tests, but Wittgenstein said...''. I likely overlapped the contexts.*Originally posted by bbarr***Was he talking about IQ in particular? I don't have a copy of Philosophical Investigations handy (it's propping up a table somewhere, I'm sure), but I thought he was talking about rule-following in general, and he used the example of adding by two. He imagines that the person who was doing the adding suddenly switched after he reached one thousand, and se ...[text shortened]... r of mutually exclusive applications of the rule consistent with any formulation of that rule.**

Your citation is almost certainly more accurate, since I've never read PI, and it even seems to make sense.- Joined
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