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By Douglas R. Hofstadter

Readers of past works via Douglas Hofstadter will locate this e-book a typical extension of his kind and his rules approximately creativity and analogy; moreover, psychologists, philosophers, and artificial-intelligence researchers will locate during this difficult net of inventive rules a deep and tough new view of brain.

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Extra resources for Fluid Concepts and Creative Analogies

Example text

3,4,2,4,2,2,4,2,4,2,4,2,2,4,2, ... To my disappointment, there didn't seem to be much more clarity in this sequence than in the original sequence - it seemed equally irregular and chaotic. I tried replacing the initial "3" by a "2": 2,4,2,4,2,2,4,2,4,2,4,2,2,4,2, ... It was a pretty trivial change, but it at least made all the terms even, for what that was worth. And at some point, that suggested the slightly simplifying idea of dividing everything by two, which I did, getting a new sequence that started out as follows: 1,2,1,2,1,1,2,1,2,1,2,1,1,2,1, ...

And yet it is completely innocuous. There is no division by zero implied in this expression; what appears to be a zero denominator is actually added to a nonzero quantity to make the true denominator on that level. So much for the legality of the new expression - but what does it gain you? Well, to tell the truth, at first I couldn't see any gain at all. Horizontally, the sequence now ran this way: 1,0,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,1,14, ... , To my eye, it still seemed as blemished as ever.

Nonetheless, I pressed on, and derived more and more of the lower sequence - 15 terms or so of it, for which I needed about 100 terms of the upper one. ) 3,4,2,4,2,2,4,2,4,2,4,2,2,4,2, ... To my disappointment, there didn't seem to be much more clarity in this sequence than in the original sequence - it seemed equally irregular and chaotic. I tried replacing the initial "3" by a "2": 2,4,2,4,2,2,4,2,4,2,4,2,2,4,2, ... It was a pretty trivial change, but it at least made all the terms even, for what that was worth.

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