"pi" is a constant used to express discrete reality
(events) in terms of continuous reality (space).
Auto-correlation is used to determine discrete reality
and cross-correlation is used to determine continuous reality.
Auto-correlation involves a set of events associated with
a single point or body,
cross-correlation involves a set of events associated with
two points or bodies.
Discrete reality is expressed in "N" counts of
cycles or events (Which are one point entities)
in a sample,
continuous reality is expressed in "N" counts of
cycles*x (Where x is a two point entity)
in a sample.
Note that x can be degrees, grads, mils, radians,
hertz seconds, etc. x can be any real number.
In other words,
if x is an integer you are expressing discrete reality.
if x is a real number you are expressing continuous reality.
The most fundamental two points
that can be equated to discrete reality (Cycles)
is the diameter of a cycle (Circle).
2 pi is a sort of Dedekind Cut
that separates discrete reality from continuous reality.
As can be seen,
2 pi is the math equivalent of physic's "c"
the so-called speed of light.
In other words, 2 pi is a constant used to
express discrete one point realities,
which are basically times,
in terms of continuous two point realities,
which are basically spaces,
just as "c" is used to express time intervals (discrete realities)
in terms of spaces (continuous realities).
That said, Conway's game of "Life"
is a better representation of reality than all existing models,
as the physical properties and their values
used in conventional models,
can be derived from auto-correlations, cross-correlations,
and the motions of the various "Life" populations.
In other words, at the most fundamental level,
reality consists of discrete populations
interacting in, and modifying, an environment,
an environment being a contiguous set of interacting populations.
Tom Potter
http://tompotter.us
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