Stephen P. King (stephenk1@home.com)
Mon, 03 May 1999 08:23:05 -0400
Dear Lester,
Lester Zick wrote:
>
> Hello to All,
>
> There are additional considerations relevant to the nature of material
> time and spatial dimensionality. Space in general is not laid out on any
> universal grid. The dimensionality of space is Euclidean in geometric
> terms, but this circumstance is simply a categorical implication of the
> ability to think and act. It is nothing more than a recognition of
> geometric necessity analogous to the application of principles of plane
> geometry to flat surfaces. Nor is it an exclusive aspect of conscious
> being because it applies equally to all aspects of being in space
> although obviously the knowledge involved is reserved to conscious
> beings.
I remember Kant's discussions of categories... ;) It is obvious that we
must never forget that our ideal models are *not* the finite objects of
perception, but, on the other hand, if we were to be Platonists for a
while and forget about the implicit unknowability of infinite absolute
Forms, the ideal case is seen to be the bound of the limit of finite
percepts! ;)
> Time on the other hand is not a geometric category. Time exists because
> the present cannot be what the past was, nor can the future be what the
> present is. This is how we come to recognize the ideas of past and
> future. Everything that ever happens happens in the present. There is no
> graph of past events nor of future events waiting to happen. We only
> know of the past and future not because knowledge of either exists or is
> capable of existing in general but because the present cannot be as it
> has been nor remain as it is. And what knowledge can be had of the past
> or the future is really only knowledge of the present in the context of
> various properties associated with present phenomena.
We see that each observer has its own unique hypersurface of events
that it perceives as a *now* or "present". We must not forget that it is
only in the very special case of synchronous co-moving observers can
agree on what events make up this Now! :)
It is possible, then, to make sense of gravity in these terms: the
inability to smoothly shift from one perspective to another without
changing local gauges of clocks, rods and orderings parametrizes (?) the
curvature of the space-times involves.
I am conjecturing that there is no absolute space-time for all
observers; there is only superposition/overlap of individual
space-times, one per observer...
> Consequently, time is not a geometric adjunct, nor is geometry the
> adjunct of time. Time has no commensuration with spatial dimensionality.
> The three dimensions exist as they do because each has some form of
> commensuration with the others. This is the only reason we can know the
> dimensions at all, because each is capable of being measured in exact
> geometric terms in relation to the others. The difference between points
> is a line, the difference between lines a plane, and the difference
> between planes a volume. And all are mutually commensurable.
We denote this commensurability with inner products and orthogonality.
The algebraic properties of associativity and commutativity are brought
to the forefront...
> However, at the fourth dimension this is no longer true. The difference
> between volumes corresponds to some form of shell and is incommensurate
> with the three universal dimensions. The reason for this is that the
> integrand for the ratio between differences in volumes must include the
> natural logarithm of a non transcendental number, meaning there can be
> no exact correspondence between the volumes of shells in geometric terms
> since the natural log of a non transcendental number must itself be
> transcendental.
Perhaps this number is Phi, the golden mean? ;)
> In any event, time corresponds to no geometric dimension because it is
> simply a logical construct, the necessary implication of change in the
> context of a static spatial geometry. Space is Euclidean only in the
> sense of being subject to Euclidean concepts applicable to geometry in
> general. And that geometry can only be three dimensional in nature
> because the difference between volumes corresponds to no volume exactly
> for the reason stated.
I would say that time is a flowing bisimulation, computed by the
interactions of the LSs, much like a cross between a surprise 20
questions game and a soap opera. Suffice it to say that the objects of
perception are not "out there" waiting to be experienced, like some
people assume. The continuing acts of observation act contructively via
cooperation and competition to render the local reality we can the
world.
> Thus I submit it is incorrect to speak of space-time or of the geometry
> of space-time or of time as some form of geometric concept. Whatever
> time may mean in ultimate terms and however it may be measured, it
> corresponds in no sense to geometric dimensionality because that
> geometry necessarily exists and can only exist whereas time measures and
> is measured by change.
:) Agreed!
> Regards - Lester
Onward to the Unknown!
Stephen
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