Occam's razor

I have always been fascinated by the efficiency of Occam's razor. But what does it means exactly "use the simpler hypothesis"?

When Copernicus proposed the heliocentric theory he stated that it was a mathematical hypothesis allowed to greatly simplify the calculation of ephemerids. We usually believe that this statement was a cautionary note, but in fact heliocentrism is exactly that. In fact, if we set the origin of coordinates on the earth, the movement of the Sun and planets is perfectly described by the model of Ptolemy (epicycloids), apart from the fact that orbits are approximated by circles when they are actually ellipses. If we shift the origin of coordinates to the sun, the orbits become circles, and the description is greatly simplified. In fact, Copernicus simply changed the coordinates, and this was the simpler hypothesis.

In science we have theories that can be falsified, for instance the shape of the planets' orbits, and theories that cannot be falsified, for instance the choice of coordinates; a choice or the other depends only on the complexity of the resulting model - or, in other words, we choose the alternative models according to Occam's razor.

Many of the more important scientific revolution consistend actually in change of coordinates: Copernicus' heliocentrism, Einstein's general relativity, etc. Often, the simplicity is rewarding: it is possible to cope with more difficult problems. It would be imposible to calculate if epicycloids derive from circles or little excentric ellipses, whereas it is quite easy with circular orbits.

I suspect that this result is quite general: scientific revolutions are change of coordinates that are in accordance with Occam's principle.