Re: Turing Machines Have no Real Time Clock (Was The Game of Life)

From: David Lloyd-Jones <>
Date: Tue, 25 Jan 2000 06:36:10 -0500

Hal Finney writes:

> Russell Standish, <>, writes:
> > Why do you think the only possibilities are that the universe is
> > either discrete or continuous? For example, the space Q^4 (4-D space
> > built from rational numbers) is neither.
> Rational numbers are continuous, by the typical definition. Between
> any two rational numbers there is another (and therefore, an infinite
> number of others).

Hunh? This is certainly true, but on the other hand between any two rational
numbers there are also an infinite number of irrationals.

But even if this were not the case, the fact that any two rationals have
other rationals in between would not make Hal's claim of continuity true;
rather it would prove the opposite, discontinuity.

Seems to me we have here a demonstration that, as in physical reality,
continuity cannot exist. What could it possibly mean?

Received on Tue Jan 25 2000 - 04:43:27 PST

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