Re: Lexicons

From: Timothy Little (tim-via-n.i.net_at_little-possums.net)
Date: 01/01/05 

Date: 1 Jan 2005 04:06:16 GMT

R3769 wrote:
> Is there an algorithm for computing the shortest representation of a
> given sequence of digits?

No, there is not.

> Or is it possible that there is some real number x, whose digits
> have no short explanation, and yet x is not normal?

It is not only possible, it is certain. The set of non-normal reals
is uncountable. The set of "explanations" is countable.

Normality is not necessarily connected with randomness, except in the
sense that if X is a random real variable from a uniform distribution
on a given interval, then P(X is normal) = 1.

Pi itself is not random; no number considered by itself is random.
Even an algorithmic complexity definition does not say that any number
in itself is random, it only defines randomness in the context of a
given labelling system.

- Tim

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