Supplement: Nicole Oresme and the ergodicity of rotations

Summary

Nicole Oresme lived from approximately 1325 to 1382. He was a philosopher, mathematician and churchman. We shall here be interested in a very particular aspect of his work: the incommensurability of celestial motions. In many ways, though, it was at the center of his achievements. As background for the discussion of Oresme's mathematical results, let us review the elements of Ptolemaic astronomical models. Ptolemy, the greatest of the applied scientists of antiquity, in his astronomy assumed the Earth to be immobile, with the planets, the Sun and Moon orbiting around it in a motion consisting of several (up to three) uniform circular motions. There is a great circle, the epicycle, on which is attached the center of another circle, the deferent. On this circle, finally, is located the mobile object. Spatial coordinates are determined against the ‘sphere of the fixed stars.’ It of course rotates once a day around the Earth. Different combinations of sense and speed of rotation of the circles are able to account for phenomena such as the retrograde motion of a planet.

THE QUESTION OF THE PERIODICITY OF THE UNIVERSE

Starting with the Greeks, who are said to have invented the geometrical representation of the motions of celestial bodies, there has been a debate about the character of such geometric models. The crucial issue was, whether the models pertained directly to reality, or whether they were to be taken just as instruments for prediction.