Abstract
The comparison of how Sol LeWitt and Donald Judd refer to mathematics and use the ‘mathematical’ reveals not only a historical development of New York art, but also shows varied intentions and thus the individuality of artistic positions of so-called Minimalists. The ‘mathematical’ in the form of a combinatorial rule, is an essential component used by LeWitt to analyse how art is seen and perceived; with reference to Judd’s work, the concept of production could interpreted as a phraseology of arithmetic for reckoning with Europe. Similar to Michael Baxandall’s concept of the ‘period eye’, knowledge of the visual culture of mathematics enabled the observer to recognize the mathematical in the works. This process was supported by the concept of ‘structure-seeing’ within the theory of perception, characterized by mathematics and structuralism. To Judd, problems of formality and aesthetics of effects such as wholeness were important in his recourse to numeric ‘schemes’; LeWitt, however, puts the formal aspects of a work of art, the formalism into question.
This essay is written in context of my doctoral thesis ‘Geometrien, Zahlen, Diagramme. Die New Yorker Kunst um 1960 im Spiegel der Mathematik’ (Geometries, Numbers, Diagrams. Fine Art in New York Around 1960 in the Mirror of Mathematics) submitted at the Freie Universität Berlin.
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
Notes
- 1.
It was traditionally believed that the concrete material execution and the meaning had to be firmly coupled.
- 2.
With the broad format Judd wanted, among other things, to dissociate himself from the painting and its typical formats.
- 3.
The application of arithmetic had been discussed in 1966 in reviews, in articles by Robert Smithson, Mel Bochner Lucy Lippard and Rosalind Krauss, and in the following years by art critics such as Elizabeth C. Baker, John Coplans and William C. Agee. See for example [8].
- 4.
Robert Smithson had refered to this manual of mathemactics located in the library of Judd as one of the sources for the Progressions; see [36, p. 37]. In this manual alternating harmonic series (72) ‘\( 1-1/2+1/3-1/4+1/5-\dots \infty \)’ is indicated, which was used in Untitled 1965 (DSS 84); see [19, p. 14].
- 5.
Kynaston McShine mentioned in the catalogue Primary Structures: ‘Contemporary art, inevitably, will be influenced by new intellectual concepts, and it is not surprising that many of the sculptors [Sol LeWitt, Donald Judd, Robert Smithson, Carl Andre and others] have found the new physics and the new mathematics as a source of ideas which open new possibilities for them’ [30].
- 6.
The idea of the visual culture shall be regarded here as the totality of visual media of a community or required for a discipline and the related experience; see [35: p. 9].
- 7.
In contrast to the Renaissance artists mentioned by Baxandall, New York artists like Judd didn't aim at the mathematical pre-knowledge of their observers in the context of an intellectually stimulated game. The concept is nevertheless applicable.
- 8.
Linda Dalrymple-Henderson suggested the consideration of the Cuisenaire rods.
- 9.
After their introduction in the United States in the 1950s, the Cuisenaire rods were reviewed in many popular journals and magazines such as New Scientist, Scientific American and Life Magazine, as well as in the first edition of Whole Earth Catalog (1968), which was very popular among artists.
- 10.
Furthermore, the mathematical content of the Progressions was reviewed in publications and explanatory material presented at exhibitions.
- 11.
This statement of Sol LeWitt refered to the concept and the realization of his work Incomplete Open Cubes (1974). See interview of Russell Bowman with Sol LeWitt, VHS-Video, Museum of Contemporary Art Chicago 1979. Transcription by the author.
- 12.
A single form can take three steps of height and be respectively open and closed. This produces respectively 3 x 2 = 6 possibilities. The arbitrary combination of the conditions of inner and outer form generates 6 x 6 = 36 configurations.
- 13.
This can be depicted ‘with the help of artificial symbols’, and this depiction fulfills the qualities of the ‘typographical, schematic and use of symbols without interpretation’ [23: p. 1f].
- 14.
It is worth noting that years earlier Sol LeWitt already started to paint the parts of the series Structures white to neglect the materiality which was unimportant to him. In contrast, the research field Schriftbildlichkeit focuses on the aesthetic dimension of documents; see [25].
References
W.C. Agee, Unit, series, site: a judd lexicon. Art in America 63, 3 (May/June 1975), pp. 40–49 (1975)
L.B. Alberti, De Re Aedificatoria—Zehn Bücher über die Baukunst, ed. by M. Theuer (Darmstadt, 1975)
L.B. Alberti, Della Pittura—Über die Malkunst, ed. by O. Bätschmann, S. Gianfreda (Darmstadt 2007)
R. Arnheim, Art and Visual Perception. A Psychology of the Creative Eye (University of California Press, Berkeley, CA, 1954)
R. Arnheim, Visual Thinking. (Berkeley, CA, 1969)
M. Baxandall, Painting and Experience in Fifteenth Century Italy : A Primer in the Social History of Pictorial Style, 2nd edn. (Oxford, 1988)
E. Bippus, Sol LeWitt. Serial Project No. 1 (ABCD), ed. by M. Dobbe, E. Schmidt. Schriften des Museums für Gegenwartskunst Siegen, vol. 3 (Siegen 2005), pp. 8–61
M. Bochner, Primary Structures. A Declaration of a New Attitude as Revealed by an Important Current Exhibition. Arts Magazine 40, 8 (June 1966): pp. 32–35 (1966)
J. Coplans, Don Judd. An Interview With John Coplans. Artforum 9, 10 (June 1971), pp. 40–50 (1971)
P. Cummings, Oral History Interview With Sol LeWitt, 15 July 1974. Transcription, no page numbers (Archives of American Art, Smithsonian Institution, Washington, DC, 1974)
F. de Saussure, Course in General Linguistics, ed. by C. Bally, A. Sechehaye (New York, 1966)
F. de Saussure, Grundfragen der allgemeinen Sprachwissenschaft, 3rd. edn, ed. by C. Bally, A. Sechehaye (Berlin, 2001)
G. Didi-Huberman, Was wir sehen blickt uns an. Zur Metapsychologie des Bildes, herausgegeben von Gottfried Boehm und Karlheinz Stierle. (Munich, 1999)
R. Dubisch, I.P. Rucker (eds.), Mathematics I. (New York, 1969)
L. Fietz, Strukturalismus: eine Einführung, 3rd edn (Tübingen, 1982)
M. Fried, Art and Objecthood. Artforum 5, 10 (Summer 1967): pp. 12–23. (1967)
B. Glaser, Questions to Stella and Judd. Interview von Bruce Glaser, published by Lucy R. Lippard. in Minimal Art. A Critical Anthology ed. by G. Battcock (Berkeley, CA, 1995), pp. 148–164
J. Held, Minimal Art—Eine amerikanische Ideologie, in Minimal Art. Eine kritische Retrospektive ed. by G. Stemmrich (Verlag der Kunst G+B Fine Arts, Basel, 1995), pp. 444–470
L.B.W. Jolley, Summation of Series, 2nd edn (Dover Publications, New York, 1961)
M.L. Keedy, R.E. Jameson, P.L. Johnson, Exploring Modern Mathematics, vol 1 (New York, 1963)
G. Kepes, Thing, Structure, Pattern, Process. in The New Landscape in Art and Science, 3rd, ed. by G. Kepes (Cambridge, 1963), pp. 204–207
G. Kepes (ed.), Structure in Art and Science (George Braziller, New York, 1965).
S. Krämer, Symbolische Maschinen. Die Idee der Formalisierung in geschichtlichem Abriß. (Darmstadt, 1988)
S. Krämer, Gibt es eine Performanz des Bildlichen? Reflexionen über ‘Blickakte’, in Bild Performanz. Die Kraft des Visuellen, ed. by L. Schwarte (Munich, 2010), pp. 63–90
S. Krämer, E. Cancik-Kirschbaum, R. Totzke (eds.), Schriftbildlichkeit. Wahrnehmbarkeit, Materialität und Operativität von Notationen. (Berlin, 2012)
K. Kunkel-Razum (ed.), Entry ‘Regel’, in Duden. Deutsches Universalwörterbuch, vol. 5 (Mannheim, 2003)
S. LeWitt, Serial Project #1. Aspen Magazine 5/6 (Herbst/Winter 1967): no page numbers (1967)
Life Magazine (unsigned): Captivating Key to Math. Life Magazine 50, 6 (10 February 1961): pp. 47–49 (1961)
L.R. Lippard, Sol LeWitt: Non-Visual Structure. Artforum 5, 8 (April 1967): pp. 42–46 (1967)
K. McShine, Introduction, in Primary Structures: Younger American and British Sculptors, ed. by K. McShine, Exhibition catalog, no page numbers, Jewish Museum (New York, 1966)
E. Meltzer, The Dream of the Information World. Oxford Art J. 29(1), 115–135 (2006)
J. Meyer, The Minimal Unconscious. October 130 (Herbst 2009): pp. 141–176 (2009)
G. Pólya, R.E. Tarjan, D.R. Woods, Notes on Introductory Combinatorics. (Boston, MA, 1983)
K. Sachs-Hombach, Das Bild als kommunikatives Medium. Elemente einer allgemeinen Bildwissenschaft (Köln, 2003)
S. Schade, S. Wenk (eds.), Studien zur visuellen Kultur: Einführung in ein transdisziplinäres Forschungsfeld. (Bielefeld, 2011)
R. Smithson, Quasi-Infinities and the Waning of Space, in Robert Smithson: the Collected Writings, ed. by J. Flam (Berkeley, CA, 1996a), pp. 34–37
R. Smithson, Entropy and the New Monuments, in Robert Smithson. The Collected Writings, ed. by J. Flam (Berkeley, CA, 1996b), pp. 10–23
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Rottmann, M. (2015). Donald Judd’s Arithmetics and Sol LeWitt’s Combinatorics. On the Relationship Between Visual and Mathematical in New York Art Around 1960. In: Emmer, M. (eds) Imagine Math 3. Springer, Cham. https://doi.org/10.1007/978-3-319-01231-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-01231-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01230-8
Online ISBN: 978-3-319-01231-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)