From: sje@xylos.ma30.bull.com (Steven J. Edwards)
Newsgroups: sci.space
Subject: Somewhere in the decimal stream (Was: arbitrary precision)
Date: 16 Oct 92 17:11:47 GMT
	<1992Oct16.141153.4298@pixel.kodak.com>
Reply-To: sje@xylos.ma30.bull.com
Distribution: usa
Organization: Bull HN, Worldwide Information Systems, Billerica, Mass., USA

In article <1992Oct16.141153.4298@pixel.kodak.com> dj@ekcolor.ssd.kodak.com (Dave Jones) writes:
# Millard Edgerton (millard@eos.arc.nasa.gov) wrote:
#>  
#>  >In article <seal.719016011@leonardo>, seal@leonardo.Jpl.Nasa.Gov (David Seal) writes...
#>  >>Having been duly inspired by an episode of northern exposure i tried
#>  >>fiddling with ramanujan's and borwein and borwein's formulas for 
#>  >>computing pi on my mac.  however, the floating point accuracy
#>  >>for MATLAB (which i was using) isn't settable and i can't get past
#>  >>the sixteenth decimal place or so.  other mac programs or ways of computing
#>  >>pi?  thanks.
#>  
#>  
#>  The solution of 355/113 yields PI to with 10^-7.  Archemedies knew it close
#>  enough for our use today, beyond that it is an academic exercise.
#>  
# You're missing the point, guys.  The exploration of pi's digits as an
# end in itself is taken from Carl Sagan's "Contact" in which there are
# supposed to be messages from "the creators" hidden in transcendental
# numbers like pi, e etc.  At the end of the novel, the heroine finds a
# digital picture of a circle out in the jillionth place or so, indicating
# that there is indeed intelligence behind the structure of the universe,
# and that looking further will yield still more info.
#
# Of course, since pi has infinite digits, every sequence imaginable will
# occur there somewhere.  A significant sequence is one which is very unlikely
# given the number of digits computed so far.  8 consecutive 8's (10^8:1
# against) is not very significant given a couple million digits computed
# (which was the event mentioned in the show, I believe).

First, it is a common misperception that an infinite number of objects
(of a given type) must contain at least one of each possible variety
(of the same type).  For example, the decimal expansion of (1 / 9) is
infinite, yet contains only one of the ten possible digits.  On the
other hand, there are some transcendental sequences that do contain
every possible finite subsequence; for example:

0.0123456789101112131415161718192021 ...

not only contains every such finitely long subsequence, but contains
it an infinite number of times.

Second, Carl Sagan's suggestion that pi contain messages is thought
provoking, but becomes obviously incorrect after a certain amount of
thought.  The reason for this is because pi is a completely nonrandom,
totally deterministic number and so any embedded message can be the
only possible message.  A sort of superdeterminism, if you will.
There is no freedom for a creator to choose the message, at least as
long as said creator is bound by common logic.  If no such bound
exists, then further discussion by us is irrelevent.

Einstein had a comment about this.  Paraphrased from memory:

"As I learn to understand more about the order in the Lord's universe,
the more I believe that He had little choice in the way of His
creation."

 [The above opinions expressed are my own; not necessarily held by others.]
      == Steven J. Edwards           Bull HN Information Systems Inc. ==
      == (508) 294-3484              300 Concord Road         MS 820A ==
      == sje@xylos.ma30.bull.com     Billerica, MA 01821          USA ==
"That Government which Governs the Least, Governs Best." -- Thomas Jefferson
Newsgroups: sci.space