Lester Zick (lesterzick@earthlink.net)
Sun, 02 May 1999 11:04:36 -0400
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.
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.
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.
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.
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.
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.
Regards - Lester
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