Date: Tue, 03 Sep 2002
The Unbounded, Finite Universe
Thomas M. Miovas, Jr.
Regarding Alex Silverman's essay "The Unbounded, Finite Universe,"
www.geocities.com/rationalphysics/Unbounded_Finite.htm
I think there are flaws in Alex Silverman's arguments. Assuming he intends
for the essay to stand alone, in the sense of not having the necessity of
referring to another article for clarification of terms, it lacks a
definition of "time" and "bounded" so the reader isn't sure what he is
referring to by those terms. In other words, he is relying on floating
abstractions -- ones that aren't concretized or reduced in any manner
whatsoever -- and thus it comes across as rationalistic and circular.
For his discussion of "bounded" he refers not to an object one can readily
hold in ones hands, say a ball, and therefore encompass it with something
larger, our hands, but rather to our own galaxy, the Milky Way, which can't
even be viewed by us as a whole. He then asserts that the Milky Way has
spatial boundaries, as if space instead of an entity is the fundamental
unit for consideration. The concept "space" is a high level abstraction
arrived at by observing entities and differentiating them from other
entities, with the realization that one ends and another begins. But this
can't occur with the universe as a whole, because by definition the
universe is everything that exists, and therefore there is no other
existing thing from which to form such an abstraction from; so the concept
of "bounded" (by what?) doesn't apply to the universe as a whole.
Alternatively, "bounded" means "here versus there," and since there is no
not-in-the-universe thing, there is no "here versus there" possible with
regard to the universe as a whole.
He makes a similar mistake with the concept of "time," treating time as a
physical existent, rather than an abstraction arrived at by observing
entities moving. When we observe one entity moving while another is at
rest, say a ball rolling towards a wall, we observe that the ball doesn't
suddenly wind up at the wall once it is released from our hands -- other
events can occur before the ball gets there (we can clap our hands
together) and the ball is still rolling; or once we release the ball, the
pet cat pounces on it before it gets to the wall. So, after we roll the
ball, other events can occur before the ball reaches the wall -- i.e. the
concept "time" is based on observations of events with regard to "before
and after." However, such an abstraction cannot apply to the universe as a
whole, because there is no not-in-the-universe thing that can move towards
the universe (nor the universe towards it). Therefore, the concept "time"
cannot be applied to the universe as a whole.
For those who insist "time" is fundamentally a psychological concept,
rather than a physical concept, a similar argument can be made. It is
asserted that we are aware of the passage of time via some internal,
psychological mechanism (which does exist) such that we can compare the
inner workings of our clock mechanism to events we observe (internally or
externally). However, for the psychological aspects of time to be applied
to the universe as a whole it would be necessary for us to be outside the
universe in order to observe it as a whole, which is impossible. Therefore
even the psychological aspects of time are not applicable to the universe
as a whole.
His discussion of "quantity" and "number" are a little better than his
discussion of "bounded" and "time," though it lacks concretization and
reduction to make his points more clear. To have a concept of the quantity
of something, it is necessary to differentiate these entities from those
entities -- i.e. the quantity (or number) of marbles in my bag versus those
outside my bag. In other words, quantity is an abstraction requiring a
specific type of differentiation of these versus those, whether or not they
are physically separated out or mentally separated out. However, there can
be no separation (differentiation) of these things in the universe versus
those things outside the universe, since by definition there is no "outside
the universe" from which to form the abstraction. Therefore the concept of
"quantity" (or "number") of entities or existents in the universe cannot be
applied to the universe as a whole.
