While browing the Dictionary of Philosophy, on my way towards Hobbes, I stopped at Hegel, and noticed a comment about his “orbits of the planets”, something to the effect that the view that he proved, from first principles, that there are seven planets, is an error of translation. Odd, I thought: Hegel I know little about, other than a vague disrespect and a lack of interest in finding out more. But I didn’t know he was up to astronomy or maths; and… he isn’t. You can read it here if you like.
It looks to me like nonsense, along the lines of the modern french philosophers stuff that Sokal shredded. Lots of it is words that could mean anything; the first obvious error is in his analysis of book 1, section II, prop 1 of the Principia, which Hegel thinks shows that both the arcs and the areas are proportional to time. This is wrong, clearly: in an elliptical orbit, the body moves faster at apogee, and traces out less arc in unit time than when at perigee. Or if you prefer the geomerical view, in an elliptical orbit the arcs *must* be smaller when the radii are larger, because the areas remain the same. There follows some confusion about the physical meaning of he parallelogram of forces… he seems to think that the mathematical resolution represents some physical reality. Hegel appears to be following the failed Greek idea of deducing the world from pure though, disdaining tedious experiment: Perhaps philosophy itself can deduce a priori what the experimental method, which assumes the name of philosophy, tries to discover with false and fruitless success from experiments, seeking therein with a sort of blind enthusiasm after the shadows of true philosophical concepts in sense perceptions. This doesn’t seem likely, when Hegel manages to decide that the tangent to the ellipse represents centrifugal force (I may have got that wrong because the entire thing is so badly garbled its hard to understand. I *think* it may partly be the standard “does centrifugal force exist”, garbled, but its hard to be sure). On the plus side, he notices that in the famous application of the law of centripetal force to the motion of the moon and to the planets with their satellites, there is no reference to any relation between the masses. Clearly this gravitation law is a law merely of the phenomenon of motion and not a force law at all but alas he misses his chance when he decides It would be tedious to discuss the distinction. Fairly soon after he discovers that law can be inverted which says that the gravitation force stands in inverse ratio to the square of the distances, so we can say instead that it stands in direct ratio to the square of distances. How he got there I don’t know, but we may as well skip lightly onwards from this point.
Ah. Suddenly I’m at the end. The seven-planets stuff is just the standard attempts at numerology to find a pattern in the planets orbits which isn’t there (he should have stuck to his first sentence: relations of planetary displacements, which appear to be a matter of experience alone); he certainly doesn’t say there are only seven, assuming the translation is honest. What a let down.
A brief googling doesn’t point me at any interesting commentaries on this text. Is it now regarded as uninteresting juvenilia, to be quietly ignored? In conclusion I suppose I should note that being wrong about area A doesn’t mean you’re wrong about area B: Hobbes, who I was heading for, made any number of embarassing maths errors, which don’t touch Leviathan.
[Update: Gauss wasn’t impressed – see comments -W]