Godel, Escher, Bach: an Eternal Golden Braid

I’m reading this Pulitzer Prize winning novel; it describes itself as: a metaphorical fugue on minds and machines in the spirit of Lewis Carroll. Here is a thought provoking quote:

People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a windowpane merge; does one plus one make one? A cloud breaks up into two clouds – more evidence for the same? It is not all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably find a statement such as, “there are 17 languages in India, and 462 dialects.” There is something strange about precise statements like that, when the concepts” language” and dialect” are themselves fuzzy.

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