Abstract

A first hint of the Differential Calculus was gave by Democrito, Before of Christ. The air, he thought, must be matter in a form so finely divided that it couldn’t be seen. This hint, this whiff of the existence of atoms was carried much further by a contemporary of Before of Christ named Democrito. Of all the ancient scientists, it is he who speaks most clearly to us across the centuries.

The few surviving fragments of this scientific writings reveal a mind of the highest logical and intuitive powers. He was the first to understand that the Milky Way is an aggregate of the light of innumerable faint stars. Beyond campfires in the sky and beyond the milk of Hera.

He saw deep connections between the heavens and the Earth. Man, he said, is a microcosm, a little cosmos. Democrito understood that the complex forms changes and motions of the material world all derived from the interaction of very simple moving parts. He called these parts atoms.

All material objects are collections of atoms intricately assembled even we.

For example, when I cut an apple, the knife must be passing through empty spaces between the atoms, Democrito argued. If there were no such empty spaces, no void then the knife would encounter some impenetrable atom and the apple wouldn´t be cut.

Let´s compare the cross sections of the two pieces, are the exposed areas exactly equal? No, said Democrito, the curvature of the apple forces this slice to be slightly shorter than the rest of the apple. If they were equally tall, then we´d have a cylinder and not an apple. No matter how sharp the knife, these two pieces have unequal cross sections. But why? Because on the scale of the very small, matter exhibits some irreducible roughness and this fine scale of roughness Democrito identified with the world of the atoms.

His arguments are not those we use today, but they´re elegant and subtle and derived from everyday experience and his conclusions were fundamentally right.

Adapted from the book Cosmos by Carl Sagan