To escape the ordinary, we must take not one, not two, not any countable number of steps. We must go beyond all finite values --- which lands us in a different world altogether. "Infinity" is an easy word to say, deceptively so, and that apparent simplicity lulls us into a false comfort. We imagine the infinite as something merely big. Big beyond description, huge, stupendous, colossal, gigantic, brobdignagian ... the list goes on and on, fooling us into thinking we understand. We're wrong.

The realm of the infinite is another universe, one in which our basic instincts fail utterly. Parts are no longer smaller than the whole; sequences become ambiguous. The most elementary operations, such as adding up lists of numbers, give wildly varying results depending on the order in which they are executed.

Truth itself slips away. Statements are no longer verifiable; they begin to talk about themselves, and to generate paradoxical contradictions. A computer with any finite amount of memory, however large, is a well-defined and predictable entity. There's no problem (in principle) determining which programs run forever and which ones halt. Give the computer an infinite amount of memory, a boundless Turing machine tape, and it suddenly escapes comprehension. The same applies to logic.

Infinity is where the ghost of ** meaning** sneaks its camel's nose into the tent of the mechanical universe.

Saturday, July 31, 1999 at 07:46:52 (EDT) = 1999-07-31

TopicScience - TopicPhilosophy

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