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Goethe's thought in the Light of his Pronouncements on Applied and Misapplied Mathematics

Published online by Cambridge University Press:  02 December 2020

Martin Dyck
Martin Dyck*
Affiliation:
University of Michigan, Ann Arbor
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Extract

The clarification of Goethe's concept of mathematics is important not only for an exact delineation of the extent and limits of his thought, but also in defining the relation between the humanities and the sciences. Again and again his spirit is invoked by humanists and scientists alike to define their relative positions. When the peculiar characteristics of the humanities and the sciences are brought into sharp focus, mathematics is usually the separating ingredient, and frequent reference is made to Goethe's supposedly negative attitude toward this science with a resulting unjust classification of his science as unscientific. Such arguments usually terminate upon application of two ancient remedies for deadlocked thought, the sets of supposedly logical alternatives-quality versus quantity, intuition (Anschauung) versus logic. Based on these criteria, Goethe's thought is securely if unilaterally embedded in the realms of quality and intuition, but at all costs immunized against the sinister demons of quantity and logic, which to some humanists are irritating symbols of aridity and vacuity, or even eternal foes of poetry, art, and life.

Type
Research Article
Information
PMLA , Volume 73 , Issue 5-part1 , December 1958 , pp. 505 - 515
Copyright
Copyright © Modern Language Association of America, 1958

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References

* Part of this paper, entitled “Goethe's Concept of Mathematics,” was presented in the Goethe section of the MLA at the 1957 annual meeting at the Univ. of Wisconsin.

Note 1 in page 505 “Über Mathematik und deren Mißbrauch,” Werke, Weimarer Ausgabe (1887-1912), Zweite Abteilung, xi, 78— hereafter cited, mainly in original spelling and punctuation, as WA plus Abteilung, volume, volume section, if any, and page.

Note 2 in page 505 “Metaphysische Anfangsgriinde der Naturwissenschaft,” Werke (Leipzig, 1922), vii, 193.

Note 3 in page 505 To Eckermann, 20 Dec. 1826. See F. v. Biedermann, ed. Goethes Gesprdche (Leipzig, 1909-11), iii, 304—hereafter cited as Biedermann.

Note 4 in page 505 “Die Goethesche und die Newtonsche Farbenlehre im Lichte der modernen Physik,” Geist der Zeit, xrx (May 1941), 267-268.

Note 5 in page 505 A bibliography of the most important previous research on the subject of Goethe and mathematics is to be found in my article, “Goethe's Views on Pure Mathematics,” GR, xxxi (Feb. 1956), 49-69. Numerous articles and speeches dealing with Goethe's relation to science, and not infrequently dealing incidentally with mathematics, were published on the occasion of the 1932 and 1949 Goethe anniversaries. They cannot be listed here. Mention should be made of the excellent notes to Vol. xii of the Hamburger Ausgabe and Vols, xvi and xvii of the Gedenk-Ausgabe of Goethe's works. The Leopoldina edition of Goethe's Schriften zur Naturwissenschaft, which is currently being published as a replacement of the Zweite Abteilung of the Weimar edition, is to include in the second part of the edition commentaries on the texts contained in the first part. The following titles may be added to my GR bibliography: Louis Locher-Ernst, Mathematik als Vorschule der Geist-Erkennlnis (Zurich, 1932; 2nd ed. Basel, 1945); Andreas Speiser, Die mathematische Denkweise (Zurich, 1932); Max Bense, “Exkurs iiber Goethe und die Théorie des Impressionismus,” in Konturen einer Geistesgeschichte der Mathematik, ii (Die Mathematik in der Kunst) (Hamburg, 1949), 156-165; H. Honl, “Goethe und die mathematische Naturwissenschaft,” Gestaltende Kràfte des neunzehnten Jahrhunderts (1954), pp. 85-114. I was unable to inspect this last article.

Note 6 in page 506 See Hermann von Baravalle, “Goethes Prinzipien von Urbild und Pflanze in der Mathematik,” and Louis Locher-Ernst, “Die moderne Entwicklung der Geometrie und Goethes Idee der Metamorphose,” in Goethe in unserer Zeit: Rudolf Steiners Goetheanismus ah Forschungsmethode, heraus-gegeben von der Naturwissenschaf tlichen Sektion am Goethe-anum Dornach durch Gunther Wachsmuth (Dornach-Basel, 1949).

Note 7 in page 506 Die Welt als Wille und Vorslellung (Wiesbaden, 1949), i, 222 f.

Note 8 in page 506 “Goethe und die Metamorphose des Menschen,” Goethes Weltanschauung: Reden und Aufsätze (Wiesbaden: Insel-Verlag, 1949), p. 73.

Note 9 in page 506 For details and documentation see Dyck, “Goethe's Views on Pure Mathematics.”

Note 10 in page 506 “Die ersten Erzeugnisse der Stotternheimer Saline. Überreicht zum 30. Januar 1828” (WA, 1, rv, 286).

Note 11 in page 507 Morris Kline, Mathematics in Western Culture (New York, 1953), p. 238.

Note 12 in page 507 Otto Spieß, Leonhard Euler: Ein Beitrag zur Geistesge-schichle des achtzehnten Jahrhunderts (Frauenfeld and Leipzig, 1929), p. 20.

Note 13 in page 508 “Der Versuch als Vermittler von Objekt und Subjekt,” Werke, Hamburger Ausgabe (1948 ff., not yet completed), xiii, 18-19—hereafter cited as HA.

Note 14 in page 509 See Dyck, pp. 5S-S6, 58, for passages indicating Goethe's preference for geometry. Goethe at times groped for geometric coordinates, as is evident in his following observation: “Urn sich aber von solcher Gestaltung der Steinmassen den

Begriff zu erleichtern, so fingiere man, dafi ein Gitterwerk durch sie durchgehe, und zwar vierseitig, wodurch so viele einzelne Kôrper abgeschnitten werden, kubisch, paralle-lipedisch, rhombisch, rhomboidisch, sâulen- oder platten-fôrmig, welcher Art es auch ware. Hiebei mufi man sich abei sagen: diese Trennung sei anzusehen als ideell, als potentia der Moglichkeit nach…“ (Die Schriflen zur Nalurwissen-schaft, Leopoldina ed., i, 340).

Note 15 in page 510 Cf. Walter Silz, Early German Romanticism (Cambridge, Mass., 1929), pp. 173-174.

Note 16 in page 510 See, e.g., Louis O. Kattsoff, A Philosophy of Mathematics (Ames, Iowa, 1948) for a discussion of various definitions of mathematics.

Note 17 in page 510 Opera Omnia, Series Prima (Lipsiae et Berolini, MCMXI) I,9.

Note 18 in page 511 Leland R. Phelps claims in his study, “Goethe's Meteorological Writings,” Monatshefte, xxviii (1956), 321: “It was just as difficult for Goethe to think of the dynamic phenomena of the atmosphere in terms of numbers, symbols, and graphs as it was for him to think of colors as being reducible to numbers. Such an approach to natural phenomena was, in Goethe's opinion, false.” In view of Goethe's numerous statements to the contrary, I fail to reach the same conclusions as Phelps. He bases his assertion on a misinterpretation of the following words by Goethe: “Den ganzen Complex der Wit-terungskunde, wie er tabellarisch durch Zahlen und Zeichen aufgestellt wird, zu erfassen und daran auf irgendeine Weise teilzunehmen, war meiner Natur unmbglich” (WA, 2, xn, 7). This means that Goethe himself was unable to follow up all tabular data on meteorology, and that it was against his nature to carry out the laborious task of compiling them. There is no implication that he considered such an approach to be false. On the contrary, Goethe advocated the use of tabular matter, especially in graphic form, as we just have seen. An attentive reader of Goethe's writings on natural science could not possibly have overlooked the graph entitled “Vergleichende graphische Darstellung der Barometer-stânde verschiedener Orte im Monat Dezember 1822. Ge-zeichnet von Ludwig Schrôn” (WA, 2, xii, 79) and Goethe's positive attitude toward it. It was not so difficult for Goethe to think of colors as being reducible to numbers. Several times he discusses and advocates measuring the color of the sky.

Note 19 in page 513 Heinrich Henel, “Goethe und die Naturwissenschaft,” JEGP, XLViii (1949), S12; B. Bavink, Ergebnisse und Problème der Naturwissenschaft, Sth ed. (Leipzig, 1933), p. 246; Karl Viëtor, Goethe (Bern, 1949), p. 408; Friedrich Gundolf, Goethe (Berlin, 1918), p. 471; Martin Losche, Goethes geislige Welt (Stuttgart, 1948), p. 315; Wilhelm Lorey, “Goethes Stellung zur Mathematik,” Goethe als Seher und Erforscher der Natur, ed. J. Walther (Weimar, 1930), pp. 140 ff.; Werner Danckert, Goethe: Der mythische Urgrund seiner Weltschau (Berlin 1951), p. 308.