The three spatial dimensions suffice in describing the constituents of a universe that are, in their entirety, absolutely static, and have not even a potentiality of being altered in their qualities.
A universe of entities exhibiting only mass, volume, length, width, and height would be a universe that subsumes only entities, qualities, and static relationships of position, which would remain constant in perpetuity and admit no effect of any entity upon any other.
Ubiquitous observation, however, informs us that, in the actual universe, such effects are made manifest unceasingly. The vast majority of actual relationships, the reader will recall, are interactions between two or more entities that affect some change in those entities' qualities.
We note that A=A, and a certain magnitude equals that magnitude, and no other. Then, how do we account for the fact that the same dog, for example, may have mass X, and, upon eating a dog treat, increase its mass to X+1? The fact that things are what they are cannot be denied or disproved. Thus, we must search for the answer within the framework of the axioms of existence and identity.
By the axiom of identity, it becomes self-evident that no entity can exhibit simultaneously different magnitudes of the same quality. Yet it is also self-evident, through ubiquitous observation, that a given entity can and most often does exhibit different magnitudes of the same quality. Thus, we are left to conclude that these magnitudes, to be mutually inclusive within an entity, must be non-simultaneous. To be non-simultaneous, they must be separated in some manner. This manner in which non-simultaneous measurements of the same quality in the same entity are separated is change.
The "separation" implied in the concept of change is not exclusively spatial, though, in almost every conceivable example, there is a spatial component to it.
For example, a sphere to which another entity of some mass is added thereby also becomes more voluminous. Nevertheless, to describe the sphere's transformation in terms of the three spatial dimensions alone would be insufficient. One would be left with the contradiction of having a sphere of mass X and that same sphere of mass X+1 occupying the same spatial position simultaneously!
These two states of the same sphere must be separated by some other dimension, a dimension that can be called time. It is separation through time, or temporal separation, that makes change possible and accounts for the ubiquitous observation of the same entities having different magnitudes of the same qualities.
Read other parts of "A Rational Cosmology" by clicking here.
Published by G. Stolyarov II
G. Stolyarov II is a science fiction novelist, independent essayist, poet, amateur mathematician, composer, author, and actuary. View profile
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3 Comments
Post a CommentForgive me for belaboring this. You said, "These two states of the same sphere must be separated by some other dimension, a dimension that can be called time. " I'll buy that as long as it's understood that the dimension we are inventing is being projected into existence, i.e. it is a product of our imagination. For contemplating the nature of change and to comprehend the ubiquitousness of it and the regularity and consistency of it, the dimension serves a conscious purpose. But the act of projection is a slippery slope and I mention it here because I think it bears consideration.
It takes an act of consciousness to know that change takes place. Without a consciousness to perceive change, there is only now. Past and Future exist only in the mind. And since time relates the two of them -in a mind - it is simply a concept of consciousness.
But time cannot be pointed to as an entity unto itself and therefore care must be taken to assure that it is not simply a concept of consciousness. Perception implies change. For a rock, time does not exist although everything else does: length, mass, and composition. A rock is what it is and although it does change, it is what it is now on the bleeding edge of existence.