Math Can Be Art, But Why Can't Art Be Math?

"......when I look at a mathematical equation I see a piece of art in a way. Usually there are numbers and letters and various kinds of symbols arranged in a specific order just like a picture to decipher and understand."

-Mark Graham

It seems obvious that math can be art. There are many examples that spring to mind; equations may be rendered into paintings or drawings, mathematical symbols may be used to create sculptures or panoramic images, or used as the basis for props in a theatre production, or any of a thousand other possibilities one could imagine. The quote above which is from a reader comment on a story I published recently is yet another example. On a more esoteric level it is possible to argue that any and all things created by man which have a mathematical basis (e.g. anything created by science and/or technology), and that anyone, anywhere considers to be beautiful or ugly or interesting or creative in any fashion, could be considred math as art. It reallydoes not matter how narrow or how broad of a definition of art one uses, examples of math as art (defined that way) could be made to fit any of them. That is an interesting observation in its own right, but, to me at least, it is not nearly as interesting as the question of why the reverse is not true, and seemingly can't be true, ever. So, why exactly is it that math can be art, but art can't be math?

The answer to this question greatly depends on what one's particular philosophy of math happens to be. Many believe, and they have much evidence and real wold examples to muster in support of their position, that math is foundational to the structure of the universe and ourselves as sentient beings living with it. Math 'works' (note: I will use the term math throughout in its broadest sense to encompass any and all branches of mathematics from basic arithmatic, geometry, algebra, and calculus to the most advanced such as triple integrals and math theorem discovery), and is what it is because the universe 'works' the way we observe that it does. This is the way we believe it should work, or must work, at least how it must work for it to have eventually given rise to ourselves as sentient conscious beings living within it. Those who hold this position generally go even further then that, and suggest that math goes deeper than observation or belief, and that, in fact, even if human beings never came to exist, math would still work the way it does for us, and still describe the universe exactly as it does for any users of it. They would say that math would and does 'work' the same for any being, sentient or not, that knows how to make it work, or knows of its principles. Knowing may not mean consciously knowing, but even knowing in the sense of an animal knowing that two pieces of food are 'more' than one piece of food and that more food is a good thing, to give just one example. (Note: concepts like greater than, less than, fall under the rubric of the laws of logic, or laws of thought as they are often called. Traditionally, these include the law of contradiction, the law of excluded middle (or third), and the principle/law of identity. Mathematics takes the laws of thought as base axioms for all of its principles. Art does as well. Everything does, by its very nature. This is why they are universal laws, which to our knowledge, can never be violated. In stronger terms, they cannot be violated by anything, or any one, any where, at any time. Much like with Math, if the laws of thought would exist/apply in the absence of thinking entities is debatable. However, I think most, and I include myself in this group, believe they would. They have always applied and will always apply in any and all universes that we could ever hope to recognize as such. A universe in which the laws of thought did not apply, is not a concept the human mind is capable of understanding. In my opinion even a God could not operate in a universe without the laws of logic, but of course my puny mind is constrained by the yoke of the laws of thought which effectively prevent me from even imagining other possibilities. In case you were wondering while certain quantum phenomenon may appear to violate the laws of thought, they do not actually. After that long winded and highly debatable digression what I intended to emphasize was that the laws of thought and math share very many similarities and for purposes of this discussion could be thought of as essentially interchangeable, though they are not.)

The fact that math is foundational is what allows persons doing math to make use of theorems, unlike scientists like myself, who must rely on hypotheses and theories to advance our ideas. I have written previously about the difference(s) between a theory and a theorem in one of my many attacks on data 'science' as science. Because data 'science' relies exclusively on theorems and does not hypothesize or theorize it cannot be science. For sure scientists use theorems and they use math but they are only used as tools, not as an end in and of themselves as in data 'science.' Data science itself is a tool of science, but it is not science. I veered off topic there for just a moment as I often do, particulary when given the opportunity to poke at a long time irritation, but let's move back to the topic at hand. If math is foundational than it is not possible for something else to be identical with it, otherwise it would the same as that thing. Think of a building foundation. One can replace it with a different foundation, but then that thing becomes the foundation, it is the foundation now. It is identical with what it replaced in function if not perhaps exactly in form. It is an imperfect analogy, as most are, because for something as foundational as math (if it is truly foundational), in order for a thing to replace it, that thing wold need to be identical in function and form. The nature of mathematics, foundational or not, hinges on the question of whether or not math theorems are invented or discovered. In my view, in order for math to be truly foundational math theorems must be discovered. They already must exist, they must work, and the mathematicans job is to find clever new ways of uncovering and using them. If math theorems are invented by man, or by any sentient conscious or even non conscious being, then they cannot be foundational, because they would created. Unlike a building foundation, a foundational aspect of the universe cannot be created (except maybe by God or a God) it must simply be.

Art, in contrast to math, is generally considered to be representational and relational not foundational. A universe could exist in which there was no art. For instance, it could be that art requires the existence of sentient conscious beings like ourselves that are capable of apprediating it. On the other hand, it could be that any sentient conscious being could appreciate art, and it could even be, though it would be a stretch to imagine, that non conscious beings are capable of appreciating art, at least in some fashion. The point is however that in each of those instances, there is some other thing that is needed for there to be a thing known as art. Something that can relate to it, and recognize it as such, even if unconsciously. Art is also invented or created, even if it is created by accident of nature or some other non intentionally controlled manner. Math, on the other hand, if one believes it is foundational, does not require any observer or anyone or anything, other than a universe for which it is a foundation (and maybe not even that), to exist.

Ultimately, this seems to be the answer to the question posed in the title of this piece. Math can be art because as a foundational thing it could always be incorporated into other representational things, art being just one example. However, math, since it is foundational can only ever be itself. It can only be what it is always for all time, and hothing else can be it, lest it would be identical with it.

I will end it there, but I did want to say a special thank you to to Mr. Graham, whose comment on a totally unrelated humorous article, was the jump start needed to get me thinking about this question. I love reading and replying as much or more so than writing original stories and I make it a point to try and respond at least in some manner to each and every one I get. Fortunately, or unfortunately, depending on your point of view, I do not get very many. LOL!