a galathaean theory of space

[ the following was rejected from sci.physics.foundations
for attempting to overstimulate interdisciplinary debate
through excessive cross-posting ]

i have learned that to be an effective usenet crank
one must have a crackpot theory of space to defend

whether mike gordge or henri wilson
or any of those fighting for or against various continua
or jack sarfatti evangelising the interesting models
connecting the zero-point to inertia and gravity
or robert israel on euclidean dynamics
( though of course not with the same existential commitments )
every name is throwing their hat in the ring

so i have decided to destroy all remnants of credibility
( meagre as they may be )
and describe some ideas on space i have toyed with over the years

when i first studied relativity
i became very impressed by the writings of ernst mach

i enjoyed the way he related properties of space
to properties of interaction

but both berkeleyan immaterialism
and einsteinian relativity
seemed to fall short of the machian interactionism

in particular in their notions of space

i began to think that models of space should know only
distance between two existents
that there was no good way to define a space of possible points
without introducing counterfactual existents
and other nonoperational existents
space could only be defined
in terms of properties on collections of existents
and i started simply with two-point distance relations

the observation that at the time "cinched" the model for me
was that none of the known forces had angular dependence
except in the presence of 3 or more particles
(and their higher multipole terms)

that all known forces decompose
to interactions between existents

models of space should be in the language of networks
with the edges of the interaction graph
colored by distances and other "interaction intensities"

to start
i used simple distance pairs

d , d , d , ...
12 13 23

for existents

e , e , e , ...
1 2 3

so that a succession of cases could present themselves for analysis

now i was drawn to first find a formulation
that would recapitulate the euclidean / galilean dynamics
so that i could understand better the translation
to this language of space

1 existent models
have no interactions and no notion of distance of pairs
they are very lonely and boring

2 existent models
can define d
12

there are several natural dynamics that i have studied here
but in general any H(d ) = C provides a dynamic
12

if
d = constant
12

this describes a completely correlated and combined state

there is no change with time
and we can see that if we map this to euclidean
we see the natural appearance of circles in this model

in particular
this model only has derived notions of angular arrangement
but not one innate to the two-point description

now if both existents are "inertial"
and i translate in the euclidean model
whose dynamics i want to emulate
i see a point and a line of locations for the other existent

d will decrease to a minumum and then increase
12

the constant of integration
can be taken as that minimum distance d
mu
and focus on the perpendicular d as the initial condition
|_
then

2 2 2
d = d + ( d - v t )
12 mu |_ 2

2
2 d /\ (d ) = - 2 d v /\ t + O( (/\t) )
12 -- 12 |_ 2 -- --

or as the first "fundamental" equation
in this formulation: