Examples of my Visual Numerical Art

Leonardo, Vol. 10, pp. 39-41. Pergamon Press 1977. Printed in Great Britain EXAMPLES OF MY VISUAL Richard Kostelanetz* 1. The graphic works that I shall describe are both visually and numerically organized and they were made to give aesthetic pleasure. Their ‘meaning’ is primarily, though not exclusively, in terms of numbers. (The mysticism of numerology does not concern me.) In my art, the numerical relationships are those of simple arithmetic; and since these relationships are not arbitrary, the works might be considered systemic. Though at first viewing they * Artistand writer, 141 Wooster St., New York, NY 10012, U.S.A. (Received 2 Mar. 1976.) I024 512 512 I28 1% I 2 8 128 128 I28 128 I28 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 3232323U23US323UUUU~~~~UU~U~~UUUUU232323U2 I616161616161616161616161616161616161616161616161 616161616161616 161616 1616161616 16 1616161616161616161616161616161616161616161616 Fig. 1. ‘1024’, numerical art, silkscreened print on Arches paper, 56 x 78cm,1974. Fig. 2. ‘Indivisibles’, numerical art, silkscreened print on Arches paper, 56 x 78 cm,1914. might appear rather elementary, further contemplation reveals a complexity of relations that is nonetheless empirical. I think of my antecedents as being the constructivists, Mondrian [I] and van Doesberg in particular, Moholy-Nagy (cf. my documentary monograph [2]) and the composer John Cage (cf. my documentary monograph [3]). From the former, as well as the serial composers, comes my interest in rigorous structure; from the latter, the realization that one can try to make art of anything. Other texts of mine are listed in Refs. 4 and 5. 2. The four examples of my numerical art that 1 shall discuss were all made in 1974. ‘1024’ (Fig. I) This array consists of 9 sections, each containing repeated numbers that add up to 1024, and first o r topmost section containing only the number 1024. 39 40 Richard Kostelanetz p r h on Arches paper, two images, each 56 x' 78 cm. 1974. 34781256903 670145119236 7812sci90347 01 4~8923670 n 9 ~ ~ 6 7 0 1 4 s n 347x125~903 12569034781 458992367014 56903478125 90347812569 23670145892 56903478125 90347812569 3478125690.3 67014589236 78125690347 01458923670 I2569034781 56903471125 x 9 m 7 0 1 4 s n 2367014~892 45892367014 .-. .. . . . .. 45L192367014 56903478125 90347812569 347x1256903 n92367014sn 2.1t.7014~1192 670 I 4sn9?.36 7x I 2 5 6 ~ 0 4 7 014 ~ n 9 2 J b 7 0 I25690.147XI ~~. .~ 55892367014 6 7 0 I45XY2.16 9OJ47XI 2569 014SXY2.1h7Il .I47X I 25hYO.I 45x923670 I 4 'XI 2ShY0.347 X92.1h70145X I ? ; I ~ I . 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Also, the number 1024 is obtained when the following multiplications are performed, where the multiplicands are selected consecutively from the top and from the bottom of the array, and concluding with 32, which is multiplied by itself: 1024 x I : 512 Y 2: 2 5 6 ~ 4: 128 8: 64 v 16: 32 Y 32. subtracted from the previous number. The system works vertically also. It is further possible to perceive in the diagonals both numerical regularities in the intervals and visual bands of parallel diamonds that are produced by repeating numbers. 'Inclivisihles'(Fig. 2) This visually haphazard arrangement is a collection of prime numbers. (A prime number is a whole number that can be divided only by I or by itself.) It follows that they are all odd numbers with the exception of 2, which seems incongruous. I chose a haphazard arrangement to indicate that there is no other recognizable relation or pattern in the sequence of prime numbers. 4 'TwoIntervals' (Fig. 3) I call these arrays of numbers 'Two Intervals', because each number in them is related to the four numbers immediately surrounding it, vertically and horizontally, by adding or subtracting the numbers I or 3. A qualification is that since there are no two-digit numbers in the array, the number 1 functions as both I and 1 I simultaneously, and 0 as both 0 and 10. For example, the top horizontal row in the upper-left-hand array reads 1256903478I. When going from left to right, the next number in the row is obtained by adding 1 (1 + I = 2) and then 3(2+3 =5) and soonalternately,remembering that 9+1 = 10 = 0 and 8 + 3 = I 1 = 1. When going from right to left, I and 3 are alternately Fig. 4. 'Parallel Intervals', numerical art, silkscreened prints on Arches paper, 56 x 78, 1974. Examples of My Visual Numerical Art 41 ‘Parallel Intervals’ (Fig. 4) This array has been constructed so that: (1) All pairs of numbers in geometrically opposite (mirror) positions to the right and left of the vertical line of zeros add up to 10. (2) If the numbers in the horizontal rows are added, starting at the bottom, the sums obtained are 0, 10, 10, 20, 20, 30, 30, 40, 40, 50; and the sums are then repeated in inverse order continuing upward. (3) The ten numbers in any slanting line add up to 45. (4) Any four numbers forming a diamond shape have the same sum for two opposing numbers; for esample, for the fournumber diamond at the left the sum is 5 or (4+I =5 ; 8+7 = 15 =5). (5) All slant lines of numbers parallel with the topright edge, beginning with a number at the top-left edge, have the same sequence of intervals or differences between two successive numbers: +4, +1, +2, +4 (11 = I), +I, +6, +1, +4, +3. This set of numbers appears in the first vertical column of numbers to the right of the zero axis, when read downwards (e.g. 412416143). I have found several other similarly systemic properties in this rich numerical array and there are probably more yet to be discovered. References 1. A. Hill, Art and Mathesis: Mondrian’s Structures, Leonard0 1,233 (1968). 2. R. Kostelanetz, Moholy-Nagy (New York: Praeger. 1970). (Out of print, but available from the author.) (Also, London: Allen Lane, 1971.) R. Kostelanetz, John Cage (New York: Praeger, 1970). (Out of print, but available from the author.) (Also, London: Allen Lane, 1971, and, in German, Cologne: DuMont Schauberg, 1973.) R. Kostelanetz, Numbers: Poems 1 3Stories (New York: Assembling, 1976). R. Kostelanetz, ConstructivistFiction, Tracks, 1/3 (Fall, 1975). 3. 4. 5. ...