Pythagoras's Oxen Revisited

Title: Pythagoras's Oxen Revisited. a RA A A | Authors: Albinus, Hans-Joachim Ros è Source: Mathematical Intelligencer; Summer2003, Vol. 25 Issue 3, p41, 3p Document Type: Article Subject Terms: *PYTHAGOREAN proposition MATHEMATICSin literature Abstract: Discusses literary work based on the pythagoras theorem which proves that in a right-angled triangle the squares of the smaller sides sum up to the square of the hypotenuse. Sacrifice made by Pythagorasin discovering the theorem; Translations of pythagoras theorem-based literary work. ISSN: 0343-6993 Accession Number: 10265702 Persistent link to this http://search.ebscohost.com/login.aspx? record: direct=true&db=afh& AN=10265702&site=ehost-live Cut and Paste: Database: <A href="http://search.ebscohost.com/login.aspx? direct=true&db=afh& AN=10265702&site=ehost-live">Pythagoras's Oxen Revisited.</A> Academic Search Elite The link information above provides a persistent link to the article you've requested. Persistent link to this record: Following the link above will bring you to the start of the article or citation. Cut and Paste: To place article links in an external web document, simply copy and paste the HTML above, starting with "<A HREF" If you have any problems or questions, contact Technical Support at http://support.epnet.com/contact/askus.php or call 800-758-5995. This e-mail was generated by a user of EBSCOhost who gained access via the UTRECHT UNIV account. Neither EBSCO nor UTRECHT UNIV is responsible for the content of this e-mail.

HANS-JOACHIM ALBINUS Pythagorass Oxen Revisited @ : is said that when Pythagoras discovered his famous theorem, in a right-angled triangle the squares of the smaller sides sum up to the square of the hypoteneuse, he sacrificed a hundred oxen to thank the gods. There is a poem in German describing this sacrifice: Vom Pythagordischen Lehrsatze Readers unfamiliar with German perhaps are aware of one of the two known English translations, one by the American biophysicist and biologist Max Delbrück (1906- Die Wahrheit, sie besteht in Ewigkeit, Wenn erst die bléde Welt ihr Licht erkannt; Der Lehrsatz nach Pythagoras benannt Gilt heute, wie er galt zu seiner Zeit. Ein Opfer hat Pythagoras geweiht Den Gotten, die den Lichtstrahl ihm gesandt Es taten kund geschlachtet und verbrannt Ein hundert Ochsen seine Dankbarkeit. Die Ochsen, seit dem Tage, wenn sie wittern Daf3 eine neue Wahrheit sich enthülle Erheben ein unmenschliches Gebrülle; Pythagoras erfüllt sie mit Entsetzen; Und machtlos sich dem Licht zu widersetzen Verschließen sie die Augen und erzittern. In the German vernacular there is a double meaning to the word Ochse, which constitutes the poem's essential irony: 1. an ox 2. a blockhead. 1981),! the other by Robert Edouard Moritz (1868-1940), an American mathematician, who had studied in Göttingen: Delbriick’s translation can be found in [7], p. 53; Moritz’s, in his book On Mathematics and Mathematicians* ([6), p. 309). Both translations are weak in various respects. Moritz's, for example, has lost the structure of rhyme in the first two verses, but it is in words and rhythm closer to the German text than Delbriick’s. Of course, there is no adequate translation for Ochsen covering both senses. It.is often believed (see for example remarks by Olga Taussky ([7], p- 53) or Mark Kae ([5], p. 98-99) that the poem is by the German writer Heinrich Heine. But this is definitely not true. The author of the sonnet is Adelbert von Chamisso (30.01.1781-21.08.1838), French by birth, whose family fled to Prussia during the French Revolution. There he grew up to become an officer in the Prussian army and later joined a circumnavigation of the globe as a natural scientist. After his return to Germany he worked at the botanical gardens in Berlin, where he became head of the herbarium. From his literary writings the most famous perhaps is the novel Peter Schlemihls wundersame Geschichte (published 1814) about the fate of a man who sells his shadow. 'He was the son of the German historian Hans Delbrück. In 1969 Max Delbrück (together with Salvador Edward Luria and Alfred Day Hershey) received the Nobel Prize far Physiology and Medicine for his basic research in molecular biology and bacteriological genetics. “Previous editions titled Memorabilia Mathematica or the Phitomath's Quotation-Book, © 200% SPRINGER VERLAG NEW YORK, VOLUME 25, NUMBER 3.2003.

Delbriick’s translation Moritz’s translation The truth: her hallmark is eternity Truth lasts throughout eternity, When once the stupid world its light discerns: The theorem, coupled with Pythagoras’ name, As soon as stupid world has seen her light Pythagoras’ theorem today is just as right As when it first was shown to the fraternity. Holds true today, as't did in olden times. The Gods who sent to him his ray of light To them Pythagoras a token sacrificed: A splendid sacrifice Pythagoras brought One hundred oxen, roasted, cut, and sliced Expressed his thanks to them, to their delight. A great burnt offering of a hundred kine, Proclaimed afar the sage’s gratitude. The oxen, since that day, when they surmise That a new truth may be unveiling Now since that day, all cattle [blockheads] when they scent New truth about to see the light of day, In frightful bellowings manifest their dismay; Forthwith burst forth in fiendish railing. Pythagoras forever gives them jitters— Quite powerless to stem the thrust of such emitters OF light, they tremble and they close their eyes. The gods, who blessed him with this ray divine; Pythagoras fills them all with terror; And powerless to shut out light by error, In sheer despair they shut their eyes and tremble. The sonnet Von Pythagoräischen Lehrsatze was writ- (1797-1856), as stated in the editor's note? to Taussky’s arten in August 1835 and first published in 1836 ([3], p. 765). ticle ([7], p. 53) and in Mark Kac's (1914-1984) autobiography Enigmas of Chance ([5], p. 98-99), too? One hint Cited above is the version found in a modern critical edition of Chamisso's complete works (for example [3], p. 536; there are identical editions by Carl Hanser Verlag, Miinchen, 1982, and Insel-Verlag, Leipzig, 1980); see [3], p. 679-682, for remarks concerning the punctuation and orthography,” which was left as close as possible to the original text. By the way, the source from which Chamisso was inspired to write the poem is believed to be an aphorism (no. 268, to be exact) by Ludwig Borne (1786-1837), who had already made use of the two meanings of Ochsen ([3], p. 765): could be Bérne, who was at first a close friend of Heine and later, in the days of their exile in Paris, became his intimate enemy (the so-called Heine-Börne controversy). Could this be the reason that Taussky and Kac and others remembered Heine's name instead of Börne's? Heine was more popular than Chamisso or Börne. And very likely they all remembered a passage in a text Heine wrote during a visit to the Frisian island of Norderney (see for example [4], p. 71), where he mentions Pythagoras and his hundred oxen in the context of the transmigration of souls (both human and animal) and possible funny incidents caused thereby: Als Pythagoras seinen bekannten Lehrsatz entdeckte, brachte er den Göttern eine Hekatombe dar. Seitdem ziltern die Ochsen, sooft eine neue Wahrheit an das Licht Wer weiß! wer weiß! die Seele des Pythagoras ist vielleicht in einen armen Candidaten gefahren, der durch kommt. das Examen fällt, weil er den pythagordischen Lehrsatz These sentences can be found in Börne’s complete works! (for example [2], p. 318); and again Moritz gives an English translation ([6], p. 308): nicht beweisen konnte, während in seinen Herren Examinatoren die Seelen jener Ochsen wohnen, die einst Pythagoras, aus Freude über die Entdeckung seines Salzes, den ewigen Göttern geopfert hatte. After Pythagoras discovered. his fundamental theorem he sacrificed a hecatomb of oxen. Since that time all dunces tremble whenever a new truth is discovered. A translation may read as follows: Who knows! Who knows! Perhaps Pythagoras’s soul is now in a poor candidate who fails his examination because he is unable to prove the Pythagorean theorem, while in Here he decided to use the second meaning of Ochsen. his evaminers live the souls of those owen which once, in Now, how has the belief arisen that the poem Vom Pythagoräischen Lehrsatze was written by Heinrich Heine the joy of the discovery of his theorem, Pythagoras had sacrificed to the eternal gods. A more modern spelling of the poem can be found in [1], p: 72, of which Moritz was aware. ‘Be aware that some other editions of Börne's works use a different numbering of the aphorisms and miscellanea. “The editor's question in The Mathematical Intelligencer for a hint to the poem's authorship or to a reference want unanswered at the time. THE MATHEMATICAL INTELLIGENCER

Thus, Pythagoras appears in the works of at least three prominent contemporary poets of the early 19th century: Ludwig Börne, Adelbert von Chamisso, and Heinrich Heine! REFERENCES [1] Ahrens, W.: Scherz und Ernst in der Mathematik. Geflügelte und ungeflügelte Worte. Teubner, Leipzig, 1904. [2] Böme, Ludwig: Sämtliche Schriften, vol. 2. Melzer, Düsseldorf, 1964. [8] Chamisso, Adelbert von: Sämtliche Werke in zwei Bänden, vol. 1: Gedichte—Dramatisches. Wissenschaftliche Buchgesellschaft, Darmstadt, 1982. [4] Heine, Heinrich: Säkularausgabe. Werke—Briefwechsel—Lebenszeugnisse, vol. 5: Reisebilder | 1824-1828. Akademie, Berlin, 1970, [5] Kac, Mark: Enigmas of Chance. An Autobiography. Harper & Row, New York, 1985. [6] Moritz, Robert Edouard: On Mathematics and Mathematicians. Dover, New ‘York, 1958. [7] Taussky, Olga: From Pythagoras’ Theorem Via Sums of Squares to Celestial Mechanics. The Mathematical Intelligencer, 10 (1988), no. 1, p. 52-55. HANS-JOACHIM ALBINUS Innenministerium Badlen-Württemberg Dorotheenstrasse 6 D-70173 Stuttgart Germany . 3 e-mail; hans-joachim.albinus@ien:bwl.id 5 RE a VASTE Hans-Joachim Albinus ‘ought perhaps to have been named for his famous ancestor Decimus Clodius Albinus, claimant to the Roman imperial throne untilhe was killed in 197 4.0: by his rival Septimus Severus. A ACER H.-J. Albinus did a master’s degree in mathematics and geography at Ruhr-Universität Bochum, then worked in com: puting centres. Progressively doing more and more management and less and less mathematics, he became deputy head - of electronic communication and management science: in the provincial Innenministerium. His interest in-history of mathematics and computingar: vived. Healso loves contemporary arts, fashion design, haute cuisine, and motorboats. He lives in ‘Leonberg. one of the| “Kepler towns”he invited us to in his MathometicatTouristar:- ticle, vol. 24, no. 8, 50-58, MAPELITIEETE VOLUME 25, NUMBER 3, 2003

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