Marx & Engels on elliptical motion & dialectical contradiction

We saw in a former chapter that the exchange of commodities implies contradictory and mutually exclusive conditions. The differentiation of commodities into commodities and money does not sweep away these inconsistencies, but develops a modus vivendi, a form in which they can exist side by side. This is generally the way in which real contradictions are reconciled. For instance, it is a contradiction to depict one body as constantly falling towards another, and as, at the same time, constantly flying away from it. The ellipse is a form of motion which, while allowing this contradiction to go on, at the same time reconciles it.

SOURCE: Marx, Karl. Capital, Volume I; Chapter Three: Money, Or the Circulation of Commodities, Section 2 — The Medium of Circulation, A. The Metamorphosis of Commodities; translated by Samuel Moore and Edward Aveling, edited by Frederick Engels (1887).

Thomas Weston [pp. 5-6] finds the above translation misleading and provides his own:

a) The Metamorphosis of Commodities

We saw that the process of exchange of commodities includes relations that contradict and exclude one another. The development of the commodity does not overcome [aufhebt] these contradictions, but creates a form within which they can move themselves. This is in general the method through which real [wirkliche] contradictions solve [losen] themselves. It is a contradiction, for example, for one body to continuously fall into another, and just as constantly fly away from it. The ellipse is one of the forms of movement in which this contradiction is actualised [verwirklicht] just as much as it is solved [löst].

The German original:

a) Die Metamorphose der Waren.

Man sah, daß der Austauschprozeß der Waren widersprechende und einander ausschließende Beziehungen einschließt. Die Entwicklung der Ware hebt diese Widersprüche nicht auf, schafft aber die Form, worin sie sich bewegen können. Dies ist uberhaupt die Methode, wodurch sich wirkliche Widersprüche lösen. Es ist z.B. ein Widerspruch, daß ein Körper beständigin einen andren fällt und ebenso beständig von ihm wegflieht. Die Ellipse ist eine der Bewegungsformen, worin dieser Widerspruch sich ebensosehr verwirklicht als löst.

English translation of the French translation [p. 27], which is different from the German original:

The exchange of commodities cannot, as one has seen, take place without fulfilling contradictory conditions, which exclude one another. Its development, which makes commodities appear as something with two aspects, use-value and exchange-value, does not make these contradictions disappear [ne fait pas disparaitre], but creates the form in which they can move themselves. This is in any case the only method for resolving [resoudre] real contradictions. It is, for example, a contradiction that a body should fall constantly toward another, and also constantly fly away from it. The ellipse is one of the forms of movement by which this contradiction realises itself and resolves itself [se resout] at the same time.

The French translation:

L’echange des marchandises ne peut, comme on l’a vu, s’effectuer qu’en remplissant des conditions contradictories, exclusives les unes des autres. Son development qui fait apparaitre la marchandise comme chose a double face, valeur d’usage et valeur d’echange, ne fait pas disparaitre ces contradictions, mais cree la forme dans laquelle elles peuvent se mouvoir. C’est d’ailleurs la seule methode pour resoudre des contradictions reelles. C’est par example une contradiction qu’un corps tombe constamment sur un autre et cependant le fuie constamment. L’ellipse est une des formes de mouvement par lesquelles cette contradiction se realize et se resout a la fois.

How does motion present itself in the interaction of attraction and repulsion? We can best investigate this in the separate forms of motion itself. At the end, the general aspect of the matter will show itself.

Let us take the motion of a planet about its central body. The ordinary school textbook of astronomy follows Newton in explaining the ellipse described as the result of the joint action of two forces, the attraction of the central body and a tangential force driving the planet along the normal to the direction of this attraction. Thus it assumes, besides the form of motion directed centrally, also another direction of motion or so-called "force" perpendicular to the line joining the central points. Thereby it contradicts the above-mentioned basic law according to which all motion in our universe can only take place along the line joining the central points of the bodies acting on one another, or, as one says, is caused only by centrally acting forces. Equally, it introduces into the theory an element of motion which, as we have likewise seen, necessarily leads to the creation and destruction of motion, and therefore presupposes a creator. What had to be done, therefore, was to reduce this mysterious tangential force to a form of motion acting centrally, and this the Kant-Laplace theory of cosmogony accomplished. As is well known, according to this conception the whole solar system arose from a rotating, extremely tenuous, gaseous mass by gradual contraction. The rotational motion is obviously strongest at the equator of this gaseous sphere, and individual gaseous rings separate themselves from the mass and clump themselves together into planets, planetoids, etc., which revolve round the central body in the direction of the original rotation. This rotation itself is usually explained from the motion characteristic of the individual particles of gas. This motion takes place in all directions, hut finally an excess in one particular direction makes itself evident and so causes the rotating motion, which is bound to become stronger and stronger with the progressive contraction of the gaseous sphere. But whatever hypothesis is assumed of the origin of the rotation, it abolishes the tangential force, dissolving it in a special form of the phenomena of centrally acting motion. If the one element of planetary motion, the directly central one, is represented by gravitation, the attraction between the planet and the central body, then the other tangential element appears as a relic, in a derivative or altered form, of the original repulsion of the individual particles of the gaseous sphere. Then the life process of a solar system presents itself as an interplay of attraction and repulsion, in which attraction gradually more and more gets the upper hand owing to repulsion being radiated into space in the form of heat and thus more and more becoming lost to the system.

SOURCE: Engels, Friedrich [Frederick]. Dialectics of Nature; III. Basic Forms of Motion. (First published in Russian and German in the USSR in 1925, except for Part Played by Labour, 1896 and Natural Science and the Spirit World, 1898.)

Marx’s physics and astronomy readings go back to his dissertation in the late 1830s and early 1840s (Marx, 1976a, 111–12). There is evidence that he was studying the theories of Kepler, Leibniz, Newton, and Hegel in the 1840s and 1850s. When reading Newton’s Principia, he noted: “Well said, old Isaak Newton” and “Bravo, old Newton!” (Kaiser and Werchan, 1967, 127). It is evident from a 1842 newspaper article that he was well-informed about the Leibniz-Newton controversy (Marx, 1975, 178). In The German Ideology, he claims that Newton “completed mechanics” (Marx, 1970, 49). In a 1853 column he mentions “the law of contact of extremes” which is related to “the laws of Kepler” and “Newton’s great discovery” (Marx, 1984, 147). Two years before Capital’s publication, Marx (1987b, 529–30) informs Engels that he “‘took the opportunity’ to ‘take up’ a little astronomy again.” This time he was focused on “Laplace’s theory of the formation of the celestial Systems and how he explains the rotation of the various bodies around their own axis.”

SOURCE: Kangal, Kaan. “Carchedi’s Dialectics: A Critique,” Science & Society, vol. 81, no. 3, July 2017, p. 431.

Note: These passages play a role in the debate over Marx’s notion of contradiction, his view of the dialectics of nature, the methodological relationship between natural sciences and political economy, Marx’s mathematical manuscripts, and Marxʼs relation to Engels and the relation of both to Hegel. Historically there are two extreme camps on the dialectics of nature issue, summarized by Kangal and Weston.

Marx links dialectics of nature and political economy in passing analogies—quantitative change becoming qualitative change, elliptical motion and commodity exchange. I do not see him making as strong and elaborate claims as does Engels.

It appears that while both Marx and Engels were influenced by Hegel, there are differences between the two, and Engels tends to sharply devalue Newton, while Marx praises Newton in various places. In my view, Engels is more likely to go off the rails, especially when he writes about ʽrepulsion’.

Weston covers Marx’s view in the greatest detail. I cannot see how gravitation and inertia constitute a dialectical contradiction. — RD

Essential references:

Dale, Russell. “Guglielmo Carchedi on Marx, Calculus, Time and Dialectics,” Science & Society, vol. 75, no. 4, October 2011, pp. 555–566.

Kaiser, Bruno; Werchan, Inge. Ex Libris. Karl Marx und Friedrich Engels. Schicksal und Verzeichnis einer Bibliothek. Berlin: Dietz, 1967.

Kangal, Kaan. “Carchedi’s Dialectics: A Critique,” Science & Society, vol. 81, no. 3, July 2017, pp. 427–436.

Weston, Thomas. “Marx on the Dialectics of Elliptical Motion,” Historical Materialism, vol. 20, no. 4, 2012, pp. 3–38.

Karl Marx on commonsense, unity, & distinction

Marx on good & bad abstraction in political economy

Marx’s mirrors

Marx & Engels on the Science of History

V.I. Lenin: Their Abstraction & Ours

Note on the Poznan School

Marx and Marxism Web Guide


Friedrich Engels and Mathematics (1948)
by Jean van Heijenoort

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