Abstract
Contemporaneous comparisons of the Moscow mathematicians with the Pythagorean School, as reflected in Petersburg, contained contradictory political allusions. The Moscow “school” was considered both conservative, just as Pythagoreans had been, and radical, owing to the reputation of Pythagoras as the founder of Freemasonry.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
See Chapter 2, Section “Arithmology.” Pythagoreanism is evoked in some studies on the Moscow “school” but only vaguely. See the preface by S.S. Demidov, S.M. Polovinkin, and P.V. Florenskii to: P.A. Florenskiĭ, “Chernovik vystupleniîa na otkrytii studencheskogo matematicheskogo kruzhka pri Moskovskom matematicheskom obshchestve,” IMI 32–33 (1990), 468;
S.M. Polovinkin, “Moskovskaîa filosofsko-matematicheskaîa shkola (Obzor),” Referativnyĭ zhurnal. Obshchestvennye nauki v SSSR. Seriîa 3. Filosofiîa 2 (1991), 62;
M.A. Prasolov, “‘Tsifra poluchaet osobuîu silu’ (Sotsial’naîa utopiîa Moskovskoĭ filosofsko-matematicheskoĭ shkoly).” Zhurnal sotsiologii i sotsial’noĭ antropologii 10: 1 (2007), 45–46;
Lena Szilard, Germetizm i germenevtika (Sankt-Peterburg: Izd. Ivana Limbakha, 2002), 298–299.
A valuable discussion of Florenskiĭ’s interpretation of Pythagoreanism is to be found in Anke Niederbudde, Mathematische Konzeptionen in der russischen Moderne: Florenskij—Chlebnikov—Charms (München: Verlag Otto Sagner, 2006), in particular, 25.
I attempted to tackle this problem in the above cited article “Moskovskie pifagoreĭtsy,” in S.N. Zenkin, ed., Intellektual’nyĭ îazyk épokhi: Istoriîa ideĭ, istoriîa slov (Moskva: Novoe literaturnoe obozrenie, 2010, 117–141.
See, in particular, Andreĭ Belyĭ, Simvolizm (Moskva: Musaget, 1910), 126, 516 n. 5, 546 n. 5; Belyĭ’s notes on Pythagoreanism which were most probably taken around the time of his work on Symbolism are held in RGB (f. 25, k. 31, ed. khr. 19, L. 19).
The convincing argument against this belief is to be found in L. Zhmud, Wissenschaft, Philosophie und Religion im frühen Pythagoreismus (Berlin: Akad. Verl., 1997), 261–279.
Sergeĭ Nikolaevich Trubetskoĭ, Metafizika v Drevneĭ Gretsii (Moskva: Mysl’, 2003), 216;
Andrei Belyi and Ivanov-Razumnik, Perepiska (Sankt-Peterburg: Atheneum; Feniks, 1998), 435, 442 n. 82.
P.A. Nekrasov, “Moskovskaîa filosofsko-matematicheskaîa shkola i ee osnovateli,” MS 25: 1 (1904), 6.
P.A. Nekrasov, “Logika mudrykh lîudeĭ i moral’ (Otvet V.A. Gol’tsevu),” VFiP 70: 5 (1903), 902.
P.A. Nekrasov, Teoriîa veroîatnosteĭ (S.-Peterburg, 1912), XV.
Cf. P.A. Florenskiĭ, “Pifagorovy chisla,” Trudy po znakovym sistemam, V (1971), 504–506.
Mikh. Ferd. Taube, Sovremennyĭ spiritizm i mistitsizm (Petrograd, 1909), 229. The comparison of Moscow “school” with Pythagoreans was drawn not only by its members. The mathematician Dmitriĭ Dmitrievich Mordukhaĭ-Boltovskoĭ (1876–1952), who criticized their philosophy, called the “school” the “revived Pythagoreanism [vozrodivshimsîa pifagoreĭstvom]”: “O zakone nepreryvnosti,” VFiP 87: 2 (1907), 174; cf. M. Men’shikov, “Zvezdy i chisla,” Novoe vremîa, No 9990, December 25 (January 7), 1903, 7.
Bugaev had Lewes’ History in his library (ORK i R NB MGU, f. 41, op.1, ed. khr. 252, L.72 ob.) Evoking Pythagoras in his Mathematics as a Scientific and Pedagogic Instrument, N.V. Bugaev referred to Lewes (Matematika kak orudie nauchnoe i pedagogicheskoe (Moskva, 1869), 18–19.
It is probably not irrelevant that Pythagoras assuming the powers of a senator turns up in Bulwer Lytton. See Edward Bulwer Lytton, Athens: Its Rise and Fall, Vol. II (Leipzig: Bernard Tauchnitz, 1843), 239;
cf. Lewes, Istoriîa filosofii ot nachala ee v Gretsii do nastoîashchikh vremen (S.-Peterburg, 1865), 21. One of the preliminary versions of the title of the novel, “Laquered carriage [Lakirovannaîa kareta],” is perhaps another sign of the link between Apollon Apollonovich and Pythagoras. The principal character of the story A Carriage [Kolîaska] by Belyj’s favorite, Gogol, was called Pifagor Pifagorovich.
Mikh. Ferd. Taube, Svod osnovnykh zakonov myshleniîa (Petrograd, 1909), 29, 133. Cf. on Nekrasov’s conception of epistemological “harmony” above. See also Taube’s characteristics of “Western” and “Eastern” (that is Russian) mathematics: “Dualizm Zapada i triedinstvo Vostoka,” MT 10 (1910), 114–118.
See also Michael Hagemeister, “Wiederverzauberung der Welt: Pavel Florenskijs Neues Mittelalter,” in N. Franz, M. Hagemeister, and F. Haney, eds, Pavel Florenskij — Tradition und Moderne. Beiträge zum Internationalen Symposium an der Universität Potsdam, 5. bis 9. April 2000 (Frankfurt am Main, Berlin, Bern, Bruxelles, New York, Oxford, Wien: Peter Lang, 2001), 30;
Michael Hagemeister, “Pavel Florenskij und der Ritualmordvorwurf,” in Michael Hagemeister and Torsten Metelka, eds, Appendix 2. Materialien zu Pavel Florenskij (Berlin u. Zepernick: Kontext, 2001), 71.
In the course of the 1930s campaign against the Moscow mathematicians Pythagoreans were not forgotten. The Soviet mathematician Mikhail Khrisanovich Orlov (1900–1936) devoted most of his Ukrainian booklet on mathematics and religion to a severe critique of the Moscow “school” (I have found this booklet following the quoted article by Eugene Seneta “Mathematics, Religion, and Marxism in the Soviet Union in the 1930s,” Historia Mathematica 31: 3 (2004), 349–353).
Before addressing the subject of the “school,” Orlov writes of the “reactionary mathematics” of earlier times, and in particular, of Pythagoreans characterized as a conservative political group. See M. Orlov, Matematika i religiîa (Partvidav “Proletar,” 1933), 12.
“Nebol’shogo rostochka sukhaîa figurka,” “malen’kiĭ,” “legkaîa” i “nesolidnaîâ” pokhodka, “netopyr”’ (Andreĭ Belyĭ, Nachalo veka (Moskva: Khudozhestvennaîa literatura), 1990, 157–158). As indicated in the commentaries to Petersburg, the similarity with a bat links Ableukhov to Konstantin Pobedonostsev, who was then widely regarded as a symbol of the strong state and reaction (in the contemporary press he was frequently compared with a bat and caricatured as one; S.S. Grechishkin, L.K. Dolgopolov, and A.V. Lavrov, “Primechaniîa; in Andreĭ Belyĭ, Peterburg (Sankt-Peterburg: Nauka, 2004), 651, n. 58). What was still more important for Belyî, the bat, as well as geometry and speculative thought in general, was traditionally associated with Saturn. It should be emphasized that Belyî’s portrayal of Petersburg, above which the senator (a close anagram of Saturn) soars like a bat (see Appendix 1), is permeated with Saturnian imagery. Petersburg is represented as the very embodiment of the “reign of Saturn” which had occupied Belyĭ’s thought since at least 1909. See Spiritus [Bugaev], “Sem’ planetnykh dukhov,” Vesy 9 (1909), 71; see also n. 69.
A.V. Repnikov, “Predislovie,” in Dnevnik L.A. Tikhomirova. 1915–1917 (Moskva: ROSSPĖN, 2008), 10. See also A.V. Repnikov and O.A. Milevskiĭ, Dve zhizni L’va Tikhomirova (Moskva: Academia, 201), 446. Interestingly, long before the “mystical anarchism” was launched by G.I. Chulkov, Tikhomirov, already a monarchist, warned of its future emergence. Discussing “social mysticism,” which informed radical thought, he discerned “in present some outlines of the future mystical anarchism,” a dangerous outcome of a distorted religious feeling. See Lev Tikhomirov, Bor’ba veka, 2nd edn (Moskva, 1896), 11 (italics are by Tikhomirov). Tikhomirov was widely read, so it is probable that he may have actually put the thought and the name of “mystical anarchism” in the mind of Chulkov, whether the latter remembered of this source or not. If that was the case, we have a curious— even if comical, for the actual movement did not live up to Tikhomirov’s expectations—example of the latter’s alleged subversive activities.
Ippolit Tèn, Napoleon Bonapart (Moskva: Musaget, 1912).
H. Taine, Les origines de la France contemporaine. V. La Révolution. La conquête jacobine, T. 1 (Paris: Librairie Hachette et Cie, 1904), 23–24.
In the aftermath of the revolution of 1905, Taine’s work was translated both by the Black Hundred (and published as the supplement of the journal Mirnyĭ trud, since the middle of 1905 up to the last issue in 1914), and the famous member of the People’s Will Herman Lopatin (Ippolit Tèn, Proiskhozhdenie obshchestvennogo stroîa sovremennoĭ Frantsii, T. 1 (S.-Peterburg: Izd. M.V. Pirozhkova, 1907).
In 1910, while traveling in Sicily, Belyĭ was meditating on the European “geometrical” spirit exemplified in Robespierre and Napoleon. See Andreĭ Belyĭ, Putevye zametki, T. 1. Sitsiliîa i Tunis (Moskva-Berlin: Gelikon, 1922), 101.
E.A. Gopius, “Filosofiîa ‘moskovskoĭ filosofsko-matematicheskoi shkoly’ i ee otnoshenie k intellektualizmu filosofov XVIII veka i èkonosmicheskomu materializmu K. Marksa,” VFiP 79: 4 (1905), 554–586.
Andreĭ Belyĭ, Na rubezhe dvukh stoletiĭ (Moskva: Khudozhestvennaîa literatura, 1989), 171.
V. Egorshin, Estestvoznanie, filosofiîa i marksizm (Moskva: Gosizdat RSFSR, Moskovskiĭ rabochiĭ, 1930), 44. The portrayal of the Moscow “school” offered by Egorshin sounded like a police report. He did not forget to make references to the interest in arithmology on the part of Men’shikov (45 n. 2, 47), who had been shot in 1918 and had an established reputation as an extreme reactionary. What must have been especially dangerous for the contemporary mathematicians was the emphasis on Bugaev’s wide influence. Egorshin noted that almost every Russian university had Bugaev’s pupils teaching in them, and that all Moscow professors had been his pupils (46). Curiously, however, Egorshin seems to have been acquainted with his subject only superficially. Born in 1898, his knowledge of the ideological context of the “school” was limited. Although he described the “school” as the “Black Hundred,” he does not appear to have been aware of the extent to which it was really “Black Hundred.” His analysis of political implications of arithmology is very inadequate.
The following fragment from Élisée Reclus may serve to illustrate this: “Les formules proverbiales sont fort dangereuses, car on prend volontiers l’habitude de les répéter machinalement, comme pour se dispenser de réfléchir. S’est ainsi qu’on rabâche partout le mot de Linné: ‘non facit saltus natura: Sans doute ‘la nature ne fait pas de sauts,’ mais chacune de ses évolutions s’accomplit par un déplacement de forces vers un point nouveau. Le mouvement général de la vie dans chaque être en particulier et dans chaque série d’êtres ne nous montre nulle part une continuité directe, mais toujours une succession indirect, révolutionnaire, pour ainsi dire.” See Élisée Reclus, L’évolution, la revolution et l’idéal anarchique, 6-ème éd. (Paris: P.-V. Stock, Éditeur, 1914), 18. This book ran to several Russian editions after the revolution of 1905.
In his other works of the Soviet period Belyĭ tried to convey the same impression of the revolutionary character of arithmology. Thus, he called it the “sociology of numbers (a doctrine of number community [sotsiologiîa chisel (uchenie o chislovykh kollektivakh)].” See Andreĭ Belyĭ, Ritm kak dialektika i “Mednyĭ vsadnik” (Moskva: Federatsiîa, 1929), 34. Belyĭ was keen to draw a parallel between arithmology, which he also called a “doctrine of primacy of the number complex [uchen’e o primate chislovogo kompleksa]” (Belyĭ, Ritm kak dialektika, 34), and his treatment of verse. Intending to demonstrate that rhythmical studies of verse were more adequate than metrical ones, the latter were likened to a primitive arithmetical addition, whereas the former to tackling arithmological problems. In studying rhythm one was faced not with simple elements of metric feet, but with a “complex which configures its elements [kompleks, konfiguriruîushchiĭ èlementy]” (Belyĭ, Ritm kak dialektika, 34) On the other hand, rhythm transmitted the “social command,” the “sound” sent to poets by society (Belyĭ, Ritm kak dialektika, 29–30, 225–232). Thus, rhythm was dictated by a “community,” and not by its “elements.” Reading this, one gains the impression, which must have been calculated, that both arithmology, as the “doctrine of number community,” and Belyĭ’s rhythmical studies were a perfect representation, in mathematics and in poetics respectively, of the new spirit of collectivism.
This obituary was first referred to in S.M. Polovinkin, “Psikho-aritmo-mekhanik (filosofskie cherty portreta P.A. Nekrasova),” Voprosy istorii estestvoznaniîa i tekhniki 2 (1994), 112;
cf. Oscar B. Sheynin, “Nekrasov’s Work on Probability: The Background,” Archive for History of Exact Sciences 57 (2003), 339.
S. Uritskiĭ, “Prof. Pavel Alekseevich Nekrasov: Nekrolog,” Izvestiîa 294 (2329), Decembre 24, 1924, 7.
Vladimir Nabokov, Sobranie sochineniĭ v 4-kh tt., T. 4 (Moskva: Pravda, 1990), 293. There is another curious indication of Nekrasov’s success in establishing a good reputation with the new authorities. According to a local newspaper of Sergiev Posad, two streets to be found in this town neighboring Moscow—Nizhne-Nekrasovskaîa and Verkhne-Nekrasovskaîa—owe their names not to the famous Russian poet, but to our mathematician. In August 1924, when Nekrasov was still alive, Komsomol members of Sergiev, which, before the revolution of 1917, had been an important religious center with Troitse-Sergieva Lavra and Moscow Theological Academy situated there, initiated a renaming of streets of their town. Newly chosen names had to be compatible with the new revolutionary culture. See Aleks Rdultovskiĭ, “Zdravstvuĭte, Pavel Alekseevich!,” Vpered. Munitsipal’naîa obshchestvenno-politicheskaîa gazeta Sergievo-Posadskogo raĭona. Kraevedcheskiĭ vestnik, July 23, 2011, http://wwwvperedsp.ru/statyi/kraeved/?ID=3745.
Andreĭ Belyĭ, Mezhdu dvukh revolîutsiĭ (Moskva: Khudozhestvennaîa literatura, 1990), 283;
Mikhail Bezrodnyi, “O ‘îudoboîazni’ Andreîa Belogo,” Novoe literaturnoe obozrenie 28 (1997), 113, 124 n. 98; cf. Szilard, Germetizm i germenevtika, 261–263.
Aleksandr Selîaninov, Taïnaîa sila masonstva (S.-Peterburg, 1911), 284–285. An interesting document records the reaction of an important functionary and probably a Mason, Ėduard Nikolaevich Berendts (1860–1930) to this propaganda. In 1911 he published a brochure entitled Masonstvo ili velikoe tsarstvennoe iskusstvo vol’nykh kamenshchikov kak kul’turoispovedanie [Masonry or the great royal art of the free Masons as a cultural creed] (S.-Peterburg, 1911). (The copy that I have consulted in the Russian Public library was previously held in the library of Duma). The Masonry is represented here as a profoundly Aryan phenomenon (17); the core of its program is claimed to be purely cultural, its political object being limited to the struggle against the Jews and Jesuits.
Echoes of this view could even be found in the history of mathematics. Thus, Ferdinand Hoefer called Pythagoreans “ces antiques francs-maçons” (Histoire des mathématiques: depuis leurs origines jusqu’au commencement du dix-neuvième siècle (Paris: Librairie Hachette et Cie, 1874), 92). Cf. in Bulwer Lytton (to be quoted by Lewes): “the political designs of his [Pythagoras’] gorgeous and august philosophy, only for a while successful, left behind them but the mummeries of an impotent freemasonry, and the enthusiastic ceremonies of half-witted ascetics” (Edward Bulwer Lytton, Athens: Its Rise and Fall, Vol. II (Leipzig: Bernard Tauchnitz, 1843), 240),
Lewes, Istoriîa filosofii ot nachala ee v Gretsii do nastoîashchikh vremen (S.-Peterburg, 1865), 22). If, as suggested above, the political activity of Pythagoreans was better remembered at that time, this must have contributed to their “Masonic” reputation, and vice versa.
See, for example: E-T. B.-Clavel, Histoire pittoresque de la franc-maçonnerie et des sociétés secrètes anciennes et modernes (Paris: Pagnerre, Éditeur, 1843), 172.
A certain Karl Oppl thus admonished his fellow Masons: “Ne soyons-nous jamais inférieurs aux nobles Pythagoriciens!” See Karl Oppl, Pythagore et la Fran-Maçonnerie (Francfort s.M.: Ferdinand Bosell, 1861; reprinted: Nîmes: Lacour, 2000), 47.
See M. Vashutin [M.F. Taube], K Vozrozhdeniîu Slavîano-Russkogo Samosoznaniîa (Petrograd, 1912), 113–118.
RGALI, f 53, op. 1, ed. khr. 100, L. 123; Belyĭ and Ivanov-Razumnik, Perepiska, 341. Belyĭ was working on Istoriîa from the middle of the 1920s till the early 1930s. For the details concerning his work on this treatise, see Monika Spivak, “Andreĭ Belyĭ v rabote nad traktatom Istoriîa stanovleniîa samosoznaîushcheĭ dushi,” Russian Literature 70: 1/2 (2011), 1–19.
RGB, f. 167, k. 18, ed. khr. 9, L. 31; the same is repeated in RGB, f. 167, k. 18, ed. khr. 12, L.17. Cf. Houston Stewart Chamberlain, The Foundations of the Nineteenth Century, trans. John Lees, and ed., Vol. I (London — New York: The Bodley Head; John Lane Company, 1912), 47, 54–57.
This observation was common knowledge at that time. One encounters it, either accepted or refuted in works concerning various subjects. See, for example, Camille Flammarion, L’inconnu et les problèmes psychiques (Paris: Ernest Flammarion, Éditeur, 1900), 2–3; ÎA. Veĭnberg, Nikolaĭ Kopernik i ego uchenie (S.-Peterburg, 1873), 10–16.
Ilona Svetlikova, “Kant-semit i Kant-ariets u Belogo,” Novoe literaturnoe obozrenie 93: 5 (2008), 74.
Belyĭ refers to this story in his memoirs (Belyĭ, Nachalo veka, 70). A detailed analysis of this theme is to be found in I. ÎU. Svetlikova, “‘Edinorog, probodaîushchiĭ rytsarîa’: iz kommentariev k ‘Peterburgu’ Andreîa Belogo,” in A.F. Nekrylova, ed., Zelenyĭ Zal-3: al’manakh / Rossiĭskiĭ institut istorii iskusstv (Sankt-Peterburg: RIII, 2013), 73–79.
Andrei Bely, Petersburg, trans. Robert A. Maguire and John E. Malmstad (Bloomington — London: Indiana University Press, 1978), 20.
Maria Carlson pointed out that, following the European iconological tradition, the unicorn on the Ableukhov coat of arms symbolized Christ; it promised the spiritual rebirth occuring at the end of the novel. See “The Ableukhov Coat of Arms,” in Boris Christa, ed., Andrey Bely Centenary Papers (Amsterdam: Verlag Adolf M. Hackert, 1980, 157–170. In the above mentioned Sem’ planetnykh dukhov the “reign of Saturn” is to be ruined by the “Lamb” (see n. 20). Both killing and reviving, the unicorn placed on the Ableukhov coat of arms (and, in a sense, on that of Belyĭ himself) is an appropriate emblem of the dialectics permeating the novel and Belyĭ’s thought.
Conan-Doyle, Strannoe prividenie, in his Polnoe sobranie sochineniĭ, Kn. 3 ([Sankt-Peterburg]: zhurnal “Priroda i Lîudi,” 1909), 241–256.
The image of Mongol hordes frightening anti-Semitic Dudkin was inspired by Rightist propaganda (see Chapter 3, Sections “1911 in the history of the extreme Right,” and “1911 in Petersburg”; it will be recalled that Lippanchenko looks like a Mongol). In some contemporary sources familiar to Belyĭ the worship of the sun was perceived as essentially Aryan. Here is what Schuré wrote in the chapter on Pythagoras: “L’adoration de l’homme aryen se porta dès l’origine de la civilisation vers le soleil comme vers la source de la lumière, de la chaleur et de la vie.” See Édouard Schuré, Les Grands Initiés: Esquisse de l’histoire secrète des religions (Paris: Perrin et Cie, Libraires-Éditeurs, 1889), 293.
In the first version Dudkin’s words were slightly different: “And on that day the final Sun will rise in radiance over my native land: this will be our Lord, Christ [to Gospod’ nash, Khristos]” (L.K. Dolgopolov, “Tekstologicheskie printsipy izdaniîa,” in Belyĭ, Peterburg, 630). Having removed this precision on the meaning of the sun, which, as Dolgopolov correctly pointed out, rendered the whole passage more polysemantic, Belyĭ’s aim was rather to make a clearer hint at the Pythagorean constituent of Dudkin’s character, than to create a vague allegorical message. As a visual counterpart of Dudkin’s prayer, one may refer to the painting by Fedor Bronnikov The Hymn of Pythagoreans in Praise of the Rising Sun (1869),
in which Pythagoreans look like early Christians, which reflects an old tradition of considering the former as the precursors of the latter. For the scholarly expression of this tradition, see Isidore Lévy, La Légende de Pythagore de Grèce en Palestine (Paris: H. Champion, 1927).
See, in particular, Andreĭ Belyĭ, “Krugovoe dvizhenie. (Sorok dve arabeski),” Trudy i dni 4–5 (1912), 51–73; id., Putevye zametki, 100–102. The fact that Belyî attached geometrical emblems to different outlooks and manners of thought confirms that the ideological use of geometry in the novel was not a chance and semi-conscious artistic device; it was fully deliberate.
Copyright information
© 2013 Ilona Svetlikova
About this chapter
Cite this chapter
Svetlikova, I. (2013). The Pythagoreanism of the Moscow “School”. In: The Moscow Pythagoreans: Mathematics, Mysticism, and Anti-Semitism in Russian Symbolism. Palgrave Pivot, New York. https://doi.org/10.1057/9781137338280_6
Download citation
DOI: https://doi.org/10.1057/9781137338280_6
Publisher Name: Palgrave Pivot, New York
Print ISBN: 978-1-349-46399-2
Online ISBN: 978-1-137-33828-0
eBook Packages: Palgrave History CollectionHistory (R0)