Aesthetic Realism Asks Thirty-Five
Questions about Mathematics
By Eli Siegel
1. Does the fact that two diagonal lines can meet at the same point and seem to go out or rise from the same point, show a oneness of opposites?
2. May Roman numerals and Arabic numerals, in their difference, show a certain kind of rest and motion? (I mean by that, a Roman numeral seems stiffer than an Arabic).
3. Is 12 a whole and a part in so far as it is 12 × 1, but also 1/12 of 144; and does this show oneness of opposites?
4. Is the purpose of calculus to show a oneness of differential and integral—that is, of variable and part and of constant and whole; and is this in the field of the making one of opposites?
5. Is a function—that is, a relationship found between variables—a mode of making the differences in reality also orderly and continuous?
6. Does the Einstein theory of relativity, or any theory of relativity, go after the making one of space and time?
7. Is trigonometry involved, in its study of angles and parts of a circle, with the making one of the curved line and the straight line?
8. Does the fact that all triangles amount to two right angles, show a continuity and discontinuity in existence which say something of each other?
9. Does the fact that 12 is a oneness of 7 and 5, the result of 4 × 3, the result of 18 - 6, and the result also of 2x = 24—does this show that 12, in its numerical factuality, is also very much in motion; and is it in its mobility and immobility like a self?
10. Do integer and differential, constant and variable, say something of sameness and difference as we find it in ourselves?
11. Does the fact that any odd number multiplied by an even number comes to an even number, while every even number added to an odd number comes to an odd number—does this say something about reality, and even about the cause of reality?
12. Are quantities in music—that is, the length and depth, thickness and thinness of sound—still quantities as they make for emotion?
13. Does music, with its quantity becoming emotion, show or at least intimate that quantity and quality are two opposites which may be one?
14. Does the fact that in prosody—which is a study of quantity—the word family and the word persevere and the word happiness have a similarity of structure, with the first and third syllables larger and rising more than the second—does this show that quantities in the world are related to value?
15. Does the following quotation from a treatise on mathematics by James Rice (University of Liverpool) show that separation and junction in mathematics can approach each other?
It was from the Hindus that the Arabs learnt this system and brought it to the West. In the solution of equations, there is a well-known operation in which quantities on one side of an equation are brought over to the other side with a changed sign. This transposition was considered to be a reunion of separated quantities and was regarded by the ancients as an operation of great importance.
16. In Is Beauty the Making One of Opposites?,* Sameness and Difference are said to be one in art; how much is this true in mathematics?
17. Is a long algebraic equation a study in continuity and discontinuity the way a work of art is—a poem, a painting, a concerto?
18. Does the concerto in music show a relation of oneness and manyness which says something of unity and multiplicity, one and the multiple in mathematics, and of whole and part?
19. Is solid geometry a study of form and volume—very close to matter itself—the way sculpture is?
20. Do outline and color say something of a series of quantities enclosed by a parenthesis, as in algebra?
21. Does Shakespeare’s The Phoenix and the Turtle say anything valuable about mathematics?
22. Prof. A. Wolf ( University of London) says this in “A Philosophic and Scientific Retrospect” (1931): “In 1809, Gay-Lussac showed that gases reacted with each other in simple proportion by volume.”
When they react, they lose some of their volatility; they get proportion; and there is a cause for that. It has to do with art; and also, since it's simple proportion, it has to do with mathematics.
What is the mathematical meaning of this, and is it akin to an artistic meaning?
23. Is there mathematics in the phrase “You mean much to me”?
24. Do addition and subtraction, multiplication and division—in so far as any operation of these can come to the same quantity—have something in common, and stand for opposites like each other?
25. A thing that has made people wonder is how African art (which is still thought much of), while seemingly discordant and grotesque, can have some symmetry. Does the following quotation from Roger Fry—
In the figures, as in the masks, what strikes us is the expression of the inner life of the imagined being, and this again in spite of the most incorrect proportions and extravagant distortion of the actual human form. This vital reality is achieved by an instinctive sense of expressive form and by the coherence and inevitability of the plastic relations.
—show that art is a method of finding the coherent among the incoherent, of oneness among fractions, and of order in the discontinuous?
26. Is there anything in the world which is not both quantity and quality?
27. Is the world simultaneously a situation of no motion at all and all motion?
28. If motion and icebox can both be measured, what have they in common?
29. When a person is said to be “large”—meaning he has a good soul or heart or mind—is the use of the quantitative adjective just fortuitous or does it have a meaning?
30. What has calculation to do with quality?
31. What relation is there between the depth of an abyss and the depth of a symphony; and why is the first associated with pain, and the second so often with pleasure?
32. Does the fact that benefits and injuries can both be measured show a likeness between them; and is the word damages in law a study both in injury and benefit—that is, a making one of opposites?
33. Does the fact that the diameter of a circle is incommensurable with the circumference, show that the world is orderly and disorderly at once?
34. Is infinity in mathematics, as infinity elsewhere, a sign that the world is both rational and irrational; and that the world is an immediate situation of commensurable and incommensurable—that is, rational and irrational; and that perhaps this oneness of rational and irrational is not against beauty?
35. Does mathematics try to make, as in algebra, the known and unknown one; and does Aesthetic Realism also honor the relation of known and unknown?
Copyright ©1968 by Eli Siegel
Published in The Right of Aesthetic Realism to Be Known #605