A Rational Cosmology: Instantaneous Velocities as a Means for Describing Motion

Precisely what an instantaneous velocity describes is no mere technicality -- it is essential to our knowledge of what motion is and how to take account of it.

The human perception of time is analog: men view time's accumulation as a continuous flow rather than a series of discrete instants -- all the better for it, of course, because there is an inexhaustible number of temporal coordinates between any two points on a linear time scale, and, were we to perceive time in discrete quanta (as some empiricist-positivist devotees of that twentieth-century doctrine known as "quantum mechanics" suggest), it would take us an infinite amount of time to perceive any finite span of time, however small, which would result in an evident logical contradiction.

Because we cannot perceive any single instant of time, or what happens during it, we can only explain an entity's state during said instant by the model of Newtonian calculus, which extrapolates that behavior onto an analog interval of time, an interval that is accessible to human comprehension.

This is the reason why the graph of a function's derivative at a given point is the straight line tangent to that point. The tangent line most often does not correspond with the graph of the motion itself, as rates of motion tend to change for most moving objects, but it allows us insight into what course the object follows at the point along the graph to which the tangent line is drawn.

In the real universe, fundamentally, all that exists is entities, for without entities there cannot be any other kind of existent. Entities have measurements in all four dimensional qualities. The human mode of perception, absolutely and undeniably correct, indeed fathoms entities as having measurements in all four dimensions, and, in the case of time, accumulating age in a uniform, analog fashion.

The Euclidean model of geometry, however, further verifies the accuracy of the human ability to comprehend these properties by allowing, through the use of points, a description of any part of an entity's spatial position.

Similarly, Newtonian calculus reinforces the correctness of human perception of motion by allowing, by means of instantaneous velocities, and, by extension, accelerations, changes in acceleration, and even changes in those changes, so on indefinitely, the observation of any part of an entity's motion. Due to the discoveries of Euclid, no point comprising an entity need be unaccounted for, and, due to the ideas of Newton, no time interval during which an object moves need be left unexplained.

But it cannot be overemphasized that, however indispensable in mathematics and human cognition, points and instants are not real existents. Entities are real existents, and entities can never be confined to points, nor their behaviors to instants. Whatever special tools and techniques its analysis might require, reality remains, and shall always remain, analog and four-dimensional.

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