Mariana Soffer has made a list of some differences between math and art. In a contrarian mood, I will go through the points in this list and discuss the similarities between math and art.
Note: The original source for the following twelve quotations is Kaz Maslanka, Delineations Between Aesthetics of Math and Art. Kaz cites Proceedings of the 2002 Bridges Conference on Mathematical Connections in Art, Music, and Science, page 256. (Note added December 5, 2009.)
Difference #1: Mathematical truths are discovered. Artistic truths are mediated.
The nature of truth in math is a difficult philosophical problem. Truth in art is perhaps even more problematic. But one lesson we have learned from Doug Lenat’s AM (Automated Mathematician) is that interestingness is arguably more important than truth. It is easy to write a program that generates an endless stream of mathematical truths (1+1 = 2, 1+2 = 3, 1+3 = 4, …); it is much harder to write a program that generates an endless stream of interesting mathematical truths. In this respect, art is much like math: It is much harder to make interesting art than to make true art. In both art and math, truth is (arguably) required for interestingness, but interestingness is more interesting than truth. (Computers can generate art, but is it interesting art?)
It might be said that math is discovered, whereas art is created, but discovery and creation are both aspects of evolution. Mathematical knowledge evolves. Artistic techniques and methods evolve. In both cases, differential fitness is determined by the degree of interestingness.
Difference #2: Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.
The first difference concerns the origins of math and art (where does truth come from?). The second difference concerns validating math and art, after the act of discovery or creation is complete (is it really true?). There is more consensus about truth in math than about truth in art, but, again, truth is relatively trivial, in contrast with interestingness. Arguably, the level of agreement among mathematicians about what is interesting in math is similar to the level of agreement among artists about what is interesting in art.
Difference #3: Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure.
Mathematics is heavily metaphorical. This is the lesson of Where Mathematics Comes From (Lakoff and Núñez). Art and math are both based on analogy-making. Meaning (semantics) in both math and art is based on analogy. There is an illusion that math is purely structural, that the interpretation of math is outside of math itself, but this is only an illusion. Math without interpretation is not interesting. Mathematicians, when actually doing math, are always working with interpretations, assigning meanings to the symbols. The formalist view of math misses completely the key role of metaphor in the human enterprise of discovering (creating, evolving) interesting mathematical truths.
Difference #4: Science reveals the body of “God” and Art reveals “God’s” mind — or is it the converse?
Math is grounded in perception (Where Mathematics Comes From), just as art is grounded in perception:
One of the great findings of cognitive science is that our ideas are shaped by our bodily experiences — not in any simpleminded one-to-one way but indirectly, through the grounding of our entire conceptual system in everyday life. The cognitive perspective forces us to ask, Is the system of mathematical ideas also grounded indirectly in bodily experiences? And if so, exactly how? — Preface of Where Mathematics Comes From
If you insist on the body-mind duality, then art and math are equally of the body or of the mind.
Difference #5: Pure Mathematics has no expression for metaphor however; it does provide us a structure that can be used for it.
Formal mathematics separates the symbolic structure of math from the interpretation of math, but the two really belong together. Math can only be interesting when it is interpreted.
Difference #6: In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is.
Many mathematical discoveries were made by asking questions that seemed nonsensical at the time. For example, what if the parallel postulate were false?
Difference #7: The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.
Art is a form of communication between the artist and the audience. Creative art pushes the boundaries of that communication and extends the language of art. Creative math extends the language of mathematics. In both cases, language evolves, communication evolves, new metaphors evolve (are created, are discovered).
Difference #8: Artists have an insouciant tendency to get lost in their imagination. Mathematicians have an attentive tendency to map their imagination.
Mathematicians get lost in their imagination. Artists map their imagination.
Difference #9: A mathematical theory seems to come in a flash of intuition before the final product is rigorously constructed. An artistic theory seems to come much after the artwork that has been constructed in a flash of intuition.
In both cases, something rough, incomplete, and vague becomes smoother, more complete, better understood over time. Both math and art evolve. The apparent difference here is perhaps due to the ambiguity of the word theory. A closer examination of what is meant by theory may show that there is little difference between math and art in this respect.
Difference #10: Mathematical creations are not unique in the sense that they could be discovered by anyone. Artistic creations are uniquely invented by individuals.
Artistic creations are no more unique than mathematical discoveries. This difference is the myth of the hero.
Difference #11: Mathematics, among other things, is a language. Art, among other things, uses language.
The symbolic system of math is a tool for expressing metaphors. The heart of math is the metaphors. Art is the same in this respect.
Difference #12: In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite. —Paul Dirac
Poetry can tell us new things, to the same degree that science and math can tell us new things. In both cases, we can learn new metaphors, new analogies, gaining a new perspective on the world.
Filed under: Evolution, Philosophy of Mind, Philosophy of Science, Semantics | Tagged: analogy, art, interestingness, math, metaphor, truth
This seems absolutely right.
I really appreciate all the work you took in analyzing the differences, I feel
honored.
Here are some new reflections induced by your commentaries:
1.I am doubting about the difference between discovering and
creating, They might be the same thing done in a different way.
If you do not know somethig exists, discovering it implies creating
that notion.
I think that the concept of evolution might be altered while considering that
intresting is more important than true.
2. The fact that the level of agreement among aritst about what is intresting art is
similar to the level of agreement about among mathmaticians about what’s true in math
can be related to the facts that:
-the value of art is based on the level of intrestingnes
-the value of math is based on its notion of truth.
3.Nothing without interpretation is intreting, maybe it does not even exist. There
is an interesting theory that says that metaphors are the way to get to the root/most
basic part.
4.We percive the word according to our perception model.
6. True, maybe we can call it a game.
7.We can think of Mcluchlan here
8, Why?
10. Good point. I agree with you.
11. Methaphors are at the root of every system
12. There I am stating just what most people think, not what I think
Thank you very much, I found it exiting, fun, entretaining and even
enlighting this kind of exchanges. They make me happier.
Thank you for making this discussion ever the more interesting, Dr. Turney.
I tend to think in the terms of the archaeologist or a miner searching for gold. New discoveries peak my interest. Digging around in one’s own mind can also be a tedious procedure. It doesn’t produce satisfaction until the treasure is completely uncovered and cleaned up a bit.
If someone then admires the final product, it is due to the spit and shine, or the work ethic. The discovery can stand on it’s own. I don’t have to lay claim to it. I can just say that it was right there all the time, and when I found it, it was ripe for the picking. I may be going bananas here.
No interest charges will be allowed. If I take the credit, I’ll also have to account for my fair share of the blame. So be it. Uncle Tree
I have been thinking about this a lot since Mariana’s first post. As an artist I trust my instincts a lot and my instincts were that there is a fundamental and important difference between maths and art. It has to do with (as you both have acknowledged) the idea of creativity. You make art, you do maths.
Ok, so art and maths both involve the discovery of interesting relationships between symbols, which, through interpretation, act as metaphors for… x? Is the ‘x’ different for art and maths?
Ok, so art and maths both involve the discovery of interesting relationships between symbols, which, through interpretation, act as metaphors for… x? Is the ‘x’ different for art and maths?
In general, art and math are concerned with different aspects of life, although there may be cases where they overlap.
Regarding the relation between analogy and metaphor:
The career of metaphor
Metaphor is like analogy
Regarding metaphor in poetry:
More than Cool Reason: A Field Guide to Poetic Metaphor
Regarding metaphor in math:
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being
Regarding metaphor in daily life:
Metaphors We Live By
Thanks for the links! :)
One of the texts which was formative in my thinking about metaphor is Nietzsche’s ‘On Truth and Lying in an Extra-moral Sense’.