# Hegel does maths

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 slower at apogee, and traces out less arc in unit time than when at perigee. Or if you prefer the geometrical 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 the 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]

[2020 update: this got referred to at Slate Star Codex (What The Hell, Hegel? under the “inexcusable scientific errors” text) alas, that’s a pointer to the ScienceBlogs version, so doesn’t get the correction.]

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## 8 thoughts on “Hegel does maths”

1. Didn’t Hobbes make a lame attempt at squaring a circle? I think he also tried to redefine the numerical value of pi to something else.

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2. TomS says:

You may be interested in this from Engel’s “Anti-Duhring”:

In contrast to the deification of Newton which was handed down from the French of the eighteenth century, and the English heaping of honours and wealth on Newton, Hegel brought out the fact that Kepler, whom Germany allowed to starve, was the real founder of the modern mechanics of the celestial bodies, and that the Newtonian law of gravitation was already contained in all three of Kepler’s laws, in the third law even explicitly. What Hegel proves by a few simple equations in his Naturphilosophie, Â§ 270 and Addenda (Hegel’s Werke, 1842, Vol. 7, pp. 98 and 113 to 115), appears again as the outcome of the most recent mathematical mechanics in Gustav Kirchhoff’s Vorlesungen uber mathematische Physik, 2nd ea., Leipzig, 1877, p. 10 and in essentially the same simple mathematical form as had first been developed by Hegel.

[Interesting. I’ve read the thing myself (ie the dissertation; I’m assuming the Naturphilosophie is little different; though if he repudiates his earlier mistakes, that would be nice to know), and its clear that Hegel is wrong. Now I’m faced with Gauss agreeing, and Engles disagreeing; its not a hard choice: I’ll take Gauss on science any day. This looks to be like the continuation of the Newton-Leibniz wars, with the Germans, oddly enough, taking Leibniz’s side, and by extension knocking Newton whenever they can -W]

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3. Newton made a balls up of chemistry.

[Another fine example, which I’d also thought of. In the case of Newton and Hobbes, we’re pretty sure the rest of their work has great value. As I understand it the case is less clear. His writing is so obscure that unless you take years working into, it looks like gibberish. For the moment, I’m going with Russell and Popper on the non-maths bits -W]

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4. Kapitano says:

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.

That’s Hegel all over. He’s what’s known in philosophical circles as an Idealist. That doesn’t mean he has lofty ideals, it means he believes physical objects and events are poor reflections of the ideas of these things, and which predate them. Plato and Berkeley are also idealists.

Marx said he was pruning away the mysticism and idealism from Hegel, revealing the rational core. I think Marx could have got along perfectly well without Hegel.

It’s interesting though that Hegel got his geometry wrong. It suggests that his reputation as a polymath (even among those who detest his work) may be, shall we say, an exaggeration.

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5. Burntend Russell says:

Marx can be described, in my opinion, as Hegel minus 90% of Hegel. Marx was a materialistic version of the Mystical Hegel which is as absurd as a mystical version of Karl Popper.

But there is some truth, known only to the most careful and non-partisan historians, that British political-economic-nationalistic forces have shaped the way english speaking history has been written. There is a subtle enough disgust for the Kepler-Leibnitz-Hegel Platonic tradition to artifically exalt the Newton-Hobbes-Popper (Peripatetic?) tradition. Read both sides as if you belonged to neither and you will open your eyes to the mature world of German mystical philosophy and metaphysics that allowed them to carry the torch for at least 200 years while England remained in the dark world of Newtonian fluxions. Gauss was not part of this tradition, but a fair middle ground.

But there is much truth in that Leibnitz owed nothing to Newton but Newton may have owed much more than the politically correct version of the tale indicates.

Regards,
Burntend Russell

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6. I seem to be unable to edit this at the moment, so I’ll note in the comments that “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” is, ironically, wrong. Not wrong in principle, but in detail. So, in principle: since the body moves at different speeds at different points in the orbit, the arcs traced out cannot be proportional to time; this is just the definition of speed. However, “moves faster at apogee” should read *slower*, since apogee is the distant point.

And, having now regained edit privileges, I’ve now fixed the post, leaving this as the only reminder of my shame.

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