A Rational Cosmology: The Accuracy of Calculus in Describing Motion

Essay XXXVIII

This is Essay XXXVIII 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.

We have hitherto discussed the ways in which the Newtonian calculus can enable us to understand objects in continuous motion, their velocities and changes therein, and the paths they follow. Furthermore, the calculus can even account for special circumstances regarding motion, as when none of the derivatives of an object's position function are linear or when an object's trajectory of motion changes as it moves continuously.

Finally, the all-pervasive question of this exploration may be put forth: if the model of calculus may describe a moving object's trends through spatial points and temporal instants, and human beings cannot by nature perceive points and instants, does the model of calculus nevertheless describe precisely what humans perceive?

The answer is yes, for, indeed, all the inexhaustible variety of potential paths and rates of motion that calculus might account for can be perceived by the human eyes automatically, and needs not take an infinite amount of time to be thus fathomed.

Indeed, the model of calculus employs points and instants to narrow the field of human investigation from what is normally perceived rather than broaden it, thus maintaining the phenomena thereby described entirely within the realm of perception, with the realm of perception being the broadest possible domain as pertains to motion.