Dr. Dobb's Python-URL! - weekly Python news and links (Mar 17)

Robin Becker robin at jessikat.fsnet.co.uk
Thu Mar 20 01:15:48 CET 2003

In article <mailman.1048105833.20269.python-list at python.org>, Tim Peters
<tim.one at comcast.net> writes
>[Robin Becker]
>> I assume absolute normality excludes the case where one expresses the
>> number in itself as a base or am I being more than usually stupid.
>It has to do with digit distribution in conventional positional notation in
>positive integer bases (>= 2).  Google will lead you to a precise definition
>faster than I can regurgitate one.

well in base pi, pi has a a value which isn't exactly random.
>> Also I suppose that being non-random implies finiteness (in some sense)
>> so are we just talking 'symbol' count or information.
>Sorry, I couldn't parse that -- but digits is digits, and the requirement
>that all k-digit subsequences appear equally often, for each k >= 1, is
>intuitively simple.  See Knuth (Volume 2) for an entertaining argument that
>piles on more intuitive requirements, until he ends up with a definition for
>randomness that (it turns out) no number can meet!  Intuition isn't always
>enough -- or maybe it is, and randomness doesn't exist.
Well lets use sin.

sin pi/2 = 1

so in math speak

pi = 2 * sin^-1(1)

ie pi is a very small number of symbols. Digits are also symbols. Can
you parse this? I guess what I am getting at is that randomness/entropy
is an observational opinion. How much information is actually in pi?
Does it really encode the universe or is it just an anthropomorphically
distinguished symbol?
Robin Becker

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