A Rational Cosmology: Differences in Paths of Motion

Essay XXXVI

This is Essay XXXVI of Mr. Stolyarov's series, "A Rational Cosmology," which seeks to present objective, absolute, rationally grounded views of terms such as universe, matter, volume, space, time, motion, sound, light, forces, fields, and even the higher-order concepts of life, consciousness, and volition. See the index of all the essays in "A Rational Cosmology" here.

Thus far our discussion has concerned itself with an explanation for motion trends' variation with time and the manner in which the model of calculus elucidates these. However, if these variations were the sole ones possible in motion, all of them could occur with respect to an entity moving along some particular path, such as a straight line.

However, it is ubiquitously observable that an object moving between some two points, A and B, can conceivably follow one among an indefinite variety of paths, be they curved, looped, bent, or any conceivable combination thereof.

Having merely the entity's points of arrival and departure as our reference frame, we cannot adequately describe its particular path. Thus, other considerations are necessary.

As with motion trends with respect to time, a narrowing of reference frame will result in a more accurate understanding of the entity's path, and, if the path between the chosen two points happens to be perfectly linear, the approximation mirrors reality precisely, and net displacement, combined with an understanding of the object's velocity and changes therein, will suffice for a true description of its motion. However, if the path is not linear, it would be necessary to refer, again, to the model of Newtonian calculus.

Newtonian calculus may be applied as a model for the description of entities' precise paths in a similar manner to its ability to describe their rates of motion. However, instead of relating a coordinate of spatial position to a coordinate of time, calculus used in the description of paths relates a coordinate of spatial position to another coordinate of spatial position.