Visual Geometry: El Lissitzky and the Establishment of Conceptions of Space–Time in Avant-garde Art

Abstract

The development of new spatial and temporal conceptions in twentieth-century art is examined through the prism of the ideas of El Lissitzky’s text “Art and Pangeometry.” A comparative analysis of space–time models in art, mathematics and physics indicates that at the beginning of the twentieth century, artistic experiments “had fallen behind” in the intensity of their conceptual construction of space. This text analyzes the ways in which irrational spaces were modeled in the theory and practice of El Lissitzky and the avant-garde in tandem with the move towards an artistic image of space–time.

KEYWORDS:

• space–time conceptions
• avant-garde
• space in art
• time in art
• perspective
• developments in mathematics
• relativity

Notes

1. I.N. Dukhan, “Filosofiia klassicheskogo v iskusstve i proektnoi kul’ture modernizma,” Voprosy filosofii, no 6 (2009): 47–56.

2. Kazimir Malevich, Sobranie sochinenii v piati tomakh (Moscow: Gileya, 2003), 4:308.

3. Gino Severini, Du cubisme au classicisme (Esthétique du compas et du nombre) (Paris: J. Povolovzky & Cie., editeurs, 1921).

4. K.S. Malevich, Ot kubizma i futurizma k suprematizmu. Novyi zhivopisnyi realizm (Moscow, 1916); reprinted in Kazimir Malevich, Sobranie sochinenii v piati tomakh (Moscow: Gileia, 1995), 1:69.

5. Malevich, Ot kubizma i futurizma k suprematizmu. Novyi zhivopisnyi realizm, in idem, Sobranie sochinenii, 1:51.

6. Malevich, Ot kubizma i futurizma k suprematizmu. Novyi zhivopisnyi realizm, in idem, Sobranie sochinenii, 1:44.

7. Kazimir Malevich, “Suprematizm. Mir kak bezpredmetnost’ ili vechnoi pokoi,” ms, 1921; reprinted in Malevich, Sobranie sochinenii, 4:282.

8. Kazimir Malevich, Sobranie sochinenii v piati tomakh (Moscow: Gileia, 2003), 4:324.

9. A. Belyi, “M. O. Gershenzon,” Rossiia, no 5 (14) (1925): 4 and 255; emphasis added.

10. Ibid., 256.

11. For the evolution of El Lissitzky’s creative vision from Unovis to his active participation in the international avant-garde movement while he was staying in Berlin and Switzerland, 1921–25, see: Susan Marten-Finnis and Igor Dukhan, “Transnationale Öffentlichkeit und Dialog im Russischen Berlin. Die Avantgarde—Zeitschrift Vešč—Gegenstand—Objet,” Osteuropa (March 2008): 37–9; and I.N. Dukhan, El’ Lisitskii 1890–1941. Geometriia vremeni (Moscow: Art-Rodnik, 2010), 30–62.

12. El Lissitzky, “K. [Kunst] und Pangeometrie,” in Carl Einstein and Paul Westheim, eds., Europa-Almanach (Potsdam: Gustav Kiepenheuer, 1925), 103–13. English translation: “A. and Pangeometry,” in Sophie Lissitzky-Küppers, El Lissitzky, Life. Letters. Texts, trans. Helene Aldwinckle (London: Thames and Hudson, 1968), 348–53.

13. Cited by Éva Forgács, “Definitive Space: The Many Utopias of El Lissitzky’s Proun Room,” in Nancy Perloff and Brian Reed, eds., Situating El Lissitzky: Vitebsk, Berlin, Moscow (Los Angeles: Getty Research Institute, 2003), 70.

14. Erwin Panofsky, “Die Perspektive als ‘Symbolishce Form,’” in Fritz Saxl, ed., Vorträge der Bibliothek Warburg 1924–5 (Leipzig: B.G. Teubner, 1927), 258–330.

15. Ibid., note 75.

16. See, for instance, Pavel Florenskii, “Obratnaia perspektiva,” in Pavel Florenskii, Ikonostas: Izbrannye trudy po iskusstvu (Saint Petersburg: Russkaia kniga, 1993), 175–283; and Fritz Novotny, Cézanne und das Ende der wissenschaftlichen Perspektive (Vienna and Munich: Verlage der Anton Schroll, 1938).

17. Concerning this type of understanding of space, see Maurice Merleau-Ponty, “Eye and Mind” (1951), in The Merleau-Ponty Aesthetics Reader: Philosophy and Painting, ed. Galen A. Johnson and trans. ed. Michael B. Smith (Evanston, Il.: Northwestern University Press, 1996), 121–50.

18. Concerning the connection of “Art and Pangeometry” with avant-garde theory and practice, see: A.G. Rappaport, “El’ Lisitskii i ideia pangeometrii,” in I.E. Danilova, ed., Rossiia-Frantsiia. Problemy kul’tury pervykh desiatiletii XX veka (Moscow: GMII im. A.S. Pushkina, 1988), 32–57. For the essay’s significance within the context of systems of spatial representation, see Yve-Alain Bois, “From – ∞ to + ∞: Axonometry, or Lissitzky’s Mathematical Paradigm,” in Jan Debbaut, ed., El Lissitzky, 1890–1941: Architect, Painter, Photographer, Typographer (Eindhoven: Stedeijk Van Abbemuseum, 1990), 27–33. See also I. Dukhan, “El Lissitzky—Jewish as Universal: From Jewish Style to Pangeometry,” Ars Judaica, no 3 (2007): 53–72.

19. Leon Battista Alberti, Della pittura e della statua (Milan: Società tipografica de'Classici italiani, 1804).

20. Ibid.

21. Lissitzky, “A. and Pangeometry,” in Lissitzky-Küppers, El Lissitzky, 348.

22. Lissitzky, letter to Sophie Küppers, 21 March 1924, in Lissitzky-Küppers, El Lissitzky, 46.

23. Sophie Lissitzky-Küppers, “Life and Letters,” in Lissitzky-Küppers, El Lissitzky, 19.

24. Lissitzky, “A. and Pangeometry,” 349.

25. Ibid.; original emphasis.

26. D.A. Stroik, Kratkii ocherk istorii matematiki (Moscow: Nauka, 1990), 37.

27. Lissitzky, “A. and Pangeometry,” 349.

28. Ibid.

29. Ibid.

30. Ibid.

31. As is known, historically, the natural sequence of numbers (based on the criteria of the nature of quantity and order of objects), was initially amplified by fractions and negative numbers. Complete numbers, fractions (positive and negative) and “zero” form the aggregate of rational numbers, which allow the performance of spatial measurements to any required degree of accuracy. The system of rational numbers became inadequate for investigating constantly changing shifts in size. As is known, even in ancient geometry it was observed that not all segments of exactly defined length were commensurate; that is, that the relationship between two segments could not always be expressed by a rational number (e.g. the relationship of the sides of a square and its diagonal cannot be expressed by a rational number). The investigation into the uninterrupted processes and methods of converging calculations led to a more dynamic understanding of numbers, not so much as units of quantity, but more as relationships of size. It is precisely in this way that Isaac Newton understood numbers. This definition already contains the idea of the active number—rational or irrational. As Lev Pontriagin observed, “the move from rational numbers to active numbers occurred because of the inner logic of the development of mathematics rather than because of practical requirements, because with the aid of rational numbers it is possible to effect any measurement with any degree of precision … Active numbers represent a limitless medium, in which rational numbers are positioned.” See L.S. Pontriagin, Oboshchenie (Moscow: Editorial URSS, 2003). The definitive formulation of the idea of active numbers occurred in mathematics in the nineteenth century, in connection with thinking about constancy and abstract real infinity in the work of Georg Cantor, Karl Weierstrass, and Richard Dedekind. The development of the idea of numbers led to the notion of complex numbers. The concept first appeared in mathematics in the sixteenth century, particularly (as Lissitzky recalls) in the work of Girolamo Cardano, although the systematic theory of complex numbers was developed by Leonhard Euler and Carl Gauss. Complex numbers became particularly significant in nineteenth-century mathematics in connection with the development of the theory of the function of complex changes, although they retained an element of uncertainty, which was manifest in the definition of a complex number as “imaginary.” For an everyday understanding, they are best understood, in so far as they represent themselves, in the form of the number x + iy, where x and y are active numbers, and i is an imaginary unit (a square which is equal to a negative entity).

32. The iconic image of Kazimir Malevich’s Black Square appears in this place in the text. Lissitzky was referring to Girolamo Cardano and Niccoló Fontana Tartaglia.

33. Once again, the iconic image of Kazimir Malevich’s Black Square appears in the text.

34. Lissitzky, “A. and Pangeometry,” 350.

35. Ibid.

36. Ibid.; original emphasis.

37. Erwin Panofsky, Perspective as Symbolic Form, trans. Christopher S. Wood (New York: Zone Books, 1991), 63.

38. A.G. Barabasheva, Beskonechnoe v matematike: filosofskie i istoricheskie aspekty (Moscow: Ynus-K, 1997).

39. “Wir kommen in ein Gebiet, das nicht vorstellbar ist, das keiner Anschaulichkeit fähig ist, das aus der rein logischen Konstruktion folgt, das eine elementare Kristallisation des menschlichen Gedankens ist.” See, Lissitzky, “A. and Pangeometry,” 351. German text reprinted in Sophie Lissitzky-Küppers, El Lissitzky: Maler, Architekt, Typograf, Fotorgraf. Errinerungen, Briefe, Schriften (Dresden: Verlag der Kunst, 1967), 70.

40. Lissitzky, “A. and Pangeometry,” 351.

41. Ibid., 352.

42. Ibid.

43. See facsimile reproduction in: Lissitzky-Küppers, El Lissitzky: Maler,Architekt, Typograf, Fotorgraf. Errinerungen, Briefe, Schriften (Dresden: Verlag der Kunst, 1967), plate 90.

44. Kazimir Malevich, letter to El Lissitzky, 17 July 1924; reprinted in Malevich, Sobranie sochinenii, 4:297.

45. Lissitzky, “A. and Pangeometry,” 351.

46. Concerning the space–time aspects of El Lissitzky’s photography, see Leah Dickerman, “El Lissitzky’s Camera Corpus,” in Perloff and Reed, eds., Situating El Lissitzky, 153–76.

47. Margarita Tupitsyn, Ulrich Pohlmann and Matthew Drutt, El Lissitzky: Beyond the Abstract Cabinet: Photography, Design, Collaboration (New Haven and London: Yale University Press, 1999), 86, illus. 18 and 19.

48. Dickerman, “El Lissitzky’s Camera Corpus,” 159.

49. Ibid., 160.

50. See Mark Antliff, Inventing Bergson: Cultural Politics and the Parisian Avant-Garde (Princeton, N.J.: Princeton University Press, 1992); and I.N. Dukhan, “Kubizm i dlitel’nost’: filosofiia vremeni Anri Bergsona v zerkale avangarda,” Iskusstvoznanie 10, nos 1–2 (2010): 455–72.

51. Julia Kristeva, Le temps sensible: Proust et l’expérience littéraire (Paris: Gallimard, 1994), 1–36.

52. Lissitzky, “A. and Pangeometry,” 352.

53. Ibid.

54. Ibid., 353.