Re: [ontolog-forum] randomness and information

[Pat Hayes <phayes@xxxxxxx>]

At 9:46 AM +0800 2/13/08, Rob Freeman wrote:

> On Feb 13, 2008 5:19 AM, Pat Hayes
> <phayes@xxxxxxx> wrote:
> >
> > But OK, let me accede to my own strictures. You are right, any
> variable
> > which incorporates a degree of chance may be called 'random'; and
> Sean is
> > right that a sampling of such values may well provide
> statistical
> > information about likelihoods. Nevertheless, my original point
> still holds.
> > When we are talking about what is usually called a 'random
> sequence' of
> > numbers or bits, as spoken of in Kolmogoroff theory, what makes
> such a
> > sequence have maximal information density is that there is no way
> to compute
> > any one of its values from all the others.
>
> I think that's right Pat. But, with respect to you all, I'm not
> talking about extracting information about the next bit.

What then do you mean by 'random'?

> Let's try another approach. Given a
> sequence random by this
> definition. How many distinct patterns
> can you find in it?

The question is meaningless. What counts as a 'pattern', and what makes one distinct from another?

More seriously, its based on a misunderstanding. Any particular sequence can be viewed as a determinate sequence, and once generated it can be reproduced exactly. The randomness inheres in the process which generated it in the first place. It's random when the only way to generate it again is to store it and read it back out: no shorter algorithm is possible (Kolmogoroff again).

Pat

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