Re: Question about random numbers
From: Unruh (unruh-spam_at_physics.ubc.ca)
Date: 6 Jul 2005 19:34:18 GMT
firstname.lastname@example.org (Rob Warnock) writes:
>Unruh <email@example.com> wrote:
>| Bryan Olson <firstname.lastname@example.org> writes:
>| >Unruh wrote:
>| > > Bryan Olson writes:
>| > >>"A string of zeros 64-characters long," is a specific string;
>| > >>nothing random about it.
>| > >
>| > > All strings are specific strings.
>| >The next 64 bits to be produced by hotbits is a random string.
>| Nope. Once produced it is a specific string. You have in fact
>| characterised it in your sentence.
>I disagree, since (if HotBits is truly random) his sentence
>carries *no* prediction [information] whatsoever about the
>values of those next 64 bits.
That is not the question. Once produced he has a string. That string is
characterised by the statemnt "the next 64 bits produced by hotbits"
together with the time at which it was said.
It is true as I said, that one CAN characterise a string by the process
which produced it, and call any specific string random if it was produced
by a random process. HOwever, once produced it is some specific string. For
any specific string, randomness or not becomes more difficult. What one
means often is not "this was produced by a random process" but "this has no
discernable pattern." That is encompassed by the Kolmogorov-Chaitin
characterisation that the string is "random" if the minimal computer
program required to produce it, in some given language, is at least as long
as the string itself.
Under this defn, a long string of 0 is clearly not random, since the
for (i=0;i<100000000;i++) fprint("0");
is much shorter than the 100000000 characters long.
r said another way, "The next 64 bits to be produced by HotBits" is
>a description of a (hopefully-random) *process*, as contrasted to
>some particular instance of some specific 64 bits produced by HotBits
>at some time in the past, which would contain no randomness at all
>once the particular 64 bits were specified.
Yes, this is one definition of randomness.
>Rob Warnock <email@example.com>
>627 26th Avenue <URL:http://rpw3.org/>
>San Mateo, CA 94403 (650)572-2607