A Rational Cosmology: The Euclidean Line

This is Essay XVI 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.

The work of the ancient Greek mathematician Euclid has been perhaps the greatest leap in human history toward the understanding of real spatial relationships among entities.

The geometry that Euclid laid the foundation of (today known as Euclidean) functions perfectly as a model to study the dimensional qualities of entities, provided that it is always remembered that the tools used by the Euclidean model, as by all mathematics, are just aides for the human cognition, and do not represent things in themselves.

The sum total of Euclid's findings and derivations need not be explicated here, as they are easily accessible in any elementary treatise on mathematics, and their systematic elaboration is not the purpose of cosmology. Rather, cosmology seeks to discover in what manner Euclid's system is capable of representing reality using constructs, such as points, lines, and planes, which cannot possibly represent any real entities qua points, lines, and planes.

Since the subject of points has already been extensively covered in "Coordinate Systems," we move now to the matter of lines, or one-dimensional constructs.

Though no entity could have only a single dimension (as this would deny it the quality of volume), it must be recalled that each of the dimensions is a quality representable by a linear measurement, a line being the shortest distance between two distinct locations.