**From:** Douglas P. Wilson (*dp-wilson@shaw.ca*)

**Date:** Thu 14 Nov 2002 - 08:22:31 GMT

**Previous message:**Kenneth Van Oost: "Fw: An Individualistic Step"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

forwarded copy of message posted to Virus (CofV)
mailing list -- please see e-mail links to possibly
interesting lists at the end of this message

dpw http://www.SocialTechnology.Org/dpwilson.html

----- Original Message -----
From: "Douglas P. Wilson" <dp-wilson@shaw.ca>
To: <virus@lucifer.com>
Sent: Thursday, November 14, 2002 12:16 AM
Subject: Fw: message layer cake: FFT of Sampling = Repetition, Graphics Needed, Origin of Universe ...

What, Joe & Co. want examples of creative thought.
Well, I don't suppose this really qualifies, but it might
be a refreshing change from To B or Not To B(omb).

dpw http://www.SocialTechnology.Org/dpwilson.html

----- Original Message -----
From: "Douglas P. Wilson" <dp-wilson@shaw.ca>
To: <digitalphysics@yahoogroups.com>
Cc: "Robert Neville" <rneville@telus.net>; "Douglas Hofstadter" <dughof@cs.indiana.edu>
Sent: Wednesday, November 13, 2002 9:28 PM
Subject: message layer cake: FFT of Sampling = Repetition, Graphics Needed, Origin of Universe ...

This is the preface, and table of contents for a
short sequence of messages to follow, including also
the three listed in in the Subject line, and a conclusion.

Preface -- this message layer cake, of (which this is
just the icing), reminds us that the (not-necessarily Fast)
Fourier Transform of the Sampling operator is the
repetition operator, then laments my inability to show
you this right now with a nice picture, and turns my
rough design for software to generate the graphics
into a theory of the origin of the universe, then concludes
by pointing out that imperfect sampling (leaky cells)
makes for a much more interesting OverAll Universe,
in which our neighbouring Local Universes are not
mere repetitions but actually the slightly different
parallel universes of science fiction.

Contents:

(F)FT of Sampling = Repetition -- if you sample a blob-like
function, one whose Fourier Transform is also a blob-like
function,since the Gaussian normal distribution is an identity
or invariant under the transform, then the FT of the result
is a sequence of blobs. The Fourier Transform of the
Sampling operator (or functor, categorically) is the
Repetition operator (functor). (In all this I am actually
thinking of the Power Spectrum, not the whole FT,
but the PS is the magnitude, and phase is irrelevant to this
discussion -- it is almost always better to work with
Mag/Phase rather than Real/Imag).

Graphics Needed -- at least a graph showing original
Gaussian curve, Fourier Transform (PS, or Mag, only)
of it, which is the same shape, then a sampled version
of the same curve,and the FT (magnitude, only) of the
sampled curve, which is an endless repetition of the
original unsampled blob-like FT. A nice two-D graphic
diagram of this would help a lot, and so would an
example showing the universe repeated over and over.

Origin of Universe -- while designing software to
illustrate the (well-known, often forgotten) point that the
FT (actually "Power Spectrum") of the Sampling
operator is the Repetition operator, I started with a
2-D cellular automaton, planned to 99% of the points
to 0, with just a handful of 1s, then added mass and
gravity to affect that mass, so nearby points would
gradually merge into one another. Then I planned to
add velocity, thus momentum, and conservation of
angular momentum to cause the points to swirl
around one another as they approach. Yes, should
look like the (Local) Universe. Hmmm. Maybe it
is the LU -- look I just reinvented Digital Physics!
But ... locally velocities would probably not sum to the
nice 0.00 that I assumed for graphics-generation
purposes, so locally we would expect to see

(depending on where we were), so we might (about
half the time) see what might look (locally), like a big
bang ...

Conclusion -- well, as long as we are talking Celluar
Automata anyway, for generating graphics, why not
go all the way to Digital Physics and suppose the
Universe is a CA? But a cellular model looks alot
like a sampling of the smooth ("no more than second
degree") functions of Classical Post-Classical-Physics.
Smoothed out, our Galaxy, seen from above the
principal coordinate plane, would look like a blob,
and many physicists of the Big Bang School seem
to think that the Smoothed-Out Universe would be
a blob too. Then the (2-D or 3-D) Fourier Transform
of the universe would look like a blob too, blobs
being invariant under rotation from Cosmological Space
into Spatial Frequence Space. But the FT of the

(rather obviously [somewhat irregularly]) sampled universe
would look not like a blob but like an endless repetition of blobs.
How boring. Unless the cells leak, in which case the
Parallel Universes are not identical, more like those of
Science Fiction.

dpw http://www.SocialTechnology.Org/dpwilson.html

FIRST Message ONLY -- for rest of sequence, visit website of
the Digital Physics mailing list, via http://www.DigitalPhysics.Org
or http://groups.yahoo.com/group/digitalphysics/

web site: http://digitalphysics.org
email list: http://groups.yahoo.com/group/digitalphysics
to post: digitalphysics@yahoogroups.com
to unsubscribe: digitalphysics-unsubscribe@yahoogroups.com

You might also consider:

AbstractElectronics-subscribe@yahoogroups.com

AbstractMachines-subscribe@yahoogroups.com

AppliedMemetics-subscribe@yahoogroups.com

CASApedia-subscribe@yahoogroups.com

FreeSoftwareRequests-subscribe@yahoogroups.com

FunctionOfMusic-subscribe@yahoogroups.com

GeneticFlowers-subscribe@yahoogroups.com

GlobalLearningGames-subscribe@yahoogroups.com

GradStudentProjects-subscribe@yahoogroups.com

InterpediaSoftware-subscribe@yahoogroups.com

MakeMcGuffinsMatter-subscribe@yahoogroups.com

MathematicalTheology-subscribe@yahoogroups.com

MemeticFlowers-subscribe@yahoogroups.com

MemeticTechnology-subscribe@yahoogroups.com

NonArbitraryLanguages-subscribe@yahoogroups.com

ShortWords-subscribe@yahoogroups.com

SocialTechnology-subscribe@yahoogroups.com

SoftwareFantasies-subscribe@yahoogroups.com

TechnologicalFantasies-subscribe@yahoogroups.com

dpw http://www.SocialTechnology.Org/dpwilson.html

===============================================================
This was distributed via the memetics list associated with the
Journal of Memetics - Evolutionary Models of Information Transmission
For information about the journal and the list (e.g. unsubscribing)
see: http://www.cpm.mmu.ac.uk/jom-emit

**Next message:**Chris Taylor: "Re: Fw: An Individualistic Step"**Previous message:**Kenneth Van Oost: "Fw: An Individualistic Step"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

*
This archive was generated by hypermail 2.1.5
: Thu 14 Nov 2002 - 08:26:01 GMT
*