Sunday, February 04, 2007

Delineations Between The Aesthetics Of Math And Art

This page is dedicated to collecting ideas that describe the differences in the aesthetics of math and art.*

I would like to invite discourse into the construction of these ideas. Everyone is invited to comment. Making these delineations is not an easy task and I feel the statements may evolve. I will address any comments to these statements.

I feel it is very important to understand the differences in the disciplines of art and math so that we can join them in the most creative, clear and meaningful ways.

Delineation #1:
Mathematical truths are discovered Artistic truths are mediated.
Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.
Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure.
Science reveals the body of GGod and Art reveals GGod's mind -- or is it the converse?
Pure Mathematics has no expression for poetic metaphor however; it does provide us a structure that can be used for it.
In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is.
The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.
Artists have an insouciant tendency to get lost in their imagination Mathematicians have an attentive tendency to map their imagination
Delineation #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.

Delineation #10
Mathematical creations are not unique in the sense that they could be discovered by anyone.
Artistic creations are uniquely invented by individuals.

Delineation #11
Mathematics, among other things, is a language.
Art, among other things, uses language.
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

Delineation #13
Art is the expression of culture.
Pure mathematics is independent of culture therefore, cultureless.

Some of these were published earlier in Bridges proceedings 2002 “Sentences on the Aesthetics of Mathematics and Art” page 256


Kaz Maslanka said...

When I use the word GGod, I am not talking about an old bearded fellow in the clouds who throws lightening bolts at his distracters. I am speaking of a metaphor which points at the great mystery that is beyond all comprehension. I misspell it purposely to differentiate my different understanding of the transcendent from the traditional Judeo-Christian definition of God. (look east of Iran)


TransLorentz said...

Mathematics is a system that is not discovered, but is, being not a construct of human agreement but of truth. Then, mathematics is a system in itself, requiring intepretation only to be knowledge to humanity. On the other hand, art has a dependece on humanity, in that without humanity there exists in no way art or beauty in itself. For art is not a system, in fact it never claimed to be one.

thus, when you speak of the aesthetics of mathematics, you refer mainly to its elegance, and that fact that it is a truth. This is a human feeling towards mathematics, and is not what mathematics aims to achieve, for that would be truth and not aesthetics.

Perhaps then in using the term "mathematics" here, you are referring to "the discipline that discovers mathematics and her truths" and not mathematics per se.

Art on the other hand, cannot deny aesthetics as long as it wishes to be called art. Further, art would never claim to be truth, even if some artists and appreciaters of art do, for it firstly wasn't derived from truth as its origin, and secondly makes no claims.

Kaz Maslanka said...

Thank you TransLorentz I appreciate your comment.

Let’s look at your first sentence. You say that Mathematics is a system that is not discovered. If something is not discovered then it seems to me it must be invented, but yet you say that it is not a human construct. So how it is that mathematics can satisfy your first two statements which seem diametrically opposed? You talk of truth as if it is some sort of answer to this dilemma. Am I to accept this truth using some sort of faith? Am I to have faith in a thing like infinity or emptiness just because it makes some sort of linguistic sense? Faith is a difficult one for me on any level or context for I have little faith in faith. I can accept things to be true within a certain system however ultimately Truth with a capital ‘T’ is a ghost to me I have never been able to experience it without faith.
We are obviously treading on the ground of mathematical Platonism for which I have serious problems at this time (However, I am open). While I can believe in the mathematical characterization of ‘existence’ and ‘abstractness’ I have problems with the characterization on ‘independence’. I have not heard a argument that convinces me that Mathematical objects are independent of intelligent agents and their language, thought and practices.

It also appears that you wish to delineate the discipline of mathematical study from the mathematical objects themselves. This would imply that aesthetics is only in the discipline and not the object. If you want to separate the mathematical object from experience you must do the same with the art object and therefore the art object possesses no aesthetic either. It seems to me that either they both possess an aesthetic or neither possesses it.

As far as art and ultimate truth: I find no winners in philosophy furthermore, I find that artistic truth resides in the realm of philosophy. If there is no truth in philosophy then the can be no truth in art. I find in addition, mathematics also resides in the realm of philosophy one must have a philosophy to have mathematics. I remember reading a statement from the mathematician Father Magnus Wenninger: “Without philosophy there can be neither meaning nor logic, and without these there can be no rational thought or communication of ideas.”

Thanks again,

Mark said...

"There is no scientific discoverer, no poet, no painter, no musician, who will not tell you that he found ready made his discovery or poem or picture - that it came to him from outside, and that he did not consciously create it from within." William Clifford (From a lecture to the Royal Institution titled "Some of the conditions of mental development")

Clifford, a mathmatician, seems to think that the inspiration for math and art are external. I think he would say that their expression, how they are represented on the page, are analogous.

With respect to your Delineation #1, both are mediated in many of the same ways. I'm not a mathmatician, but I'm writing a math paper with collaborators I've never spoken with face to face. Our representations are different. They use the ideas and conventions from computer science (such as finite state automata), and I think in terms of number and group theory (such as multipication as an operation on a set). Clearly we're talking about the same thing, and come to the same conclusions (Delineation #2). But what we consider elegent, our aesthetic sense of the representation, is different.

Also, math isn't just about truth, it's about which truths are worth pondering and why. I think the same applies to art.

apperceptual said...

Hi Kaz,

I wrote a reply to these twelve sentences in May 2009, but I only discovered yesterday that the sentences came from your blog. See Math and Art: Differences and Similarities.


Kaz Maslanka said...

Hi Mark,
Thanks for dropping by. It sounds like William Clifford is a mathematical platonist ... I believe mathematics is purely a function of the mind and has no existence outside. There are some great books that address this but my favorite is "Where Mathematics comes from by George Lakoff"

Also I would like to say that you hit on the whole purpose of this list and that is that our considerations for beauty is very different.

Thanks again.

Kaz Maslanka said...

Hi Peter,
Thank you for responding to this list. I will address your response notify you and post it on my blog as soon as I can.

Anonymous said...

What is mathematics, for one to speak of it so knowingly?

What bothers me about (practically all of) your 'delineations' is that you speak exclusively from the standpoint of the bewildered bystander to mathematics, and make no attempt at grasping the actual underpinnings of the object to which you allude. Any monkey with a typewriter can spell the word 'mathematics' given enough time, but the true meaning of mathematical statements and equations is only apparent from years of training and conditioning spent in the pursuit of a comprehension of an extremely powerful lingual tool. There is no mysticism, no trickery. In this way, mathematics is the most candid of human endeavors, for if you were to study and learn, you too may arrive at exactly the same conclusions as Euler, Newton, et al. There's a reason why it's called "proof". It proves something! After having proven it, you believe it to be true, because it has been proven to you!

Ultimately, mathematics is a connection that humans make with the world around them. It gives them agency over the universe into which they were born, the ability to count and reason, and formulate synthetic statements which hold nontrivial information content.

It is only ironic that you purport your 'delineations' to speak about mathematics- many, if not all of them, have no information content whatsoever.

Kaz Maslanka said...

Dear Anonymous,
Thanks for your input. These statements not only address the aesthetics of math they address the aesthetics of art. Now I will certainly admit that I am limited in scope for both fields however, if you have something to help us with I would love to hear what you have to say. I am certainly open to change the delineations or delete them. Since there are many who believe that math is art, and you may be one of them, then you may help us out with illuminating some of the actual underpinnings of math; and while you are at it you would help us greatly if you balanced those underpinnings against the actual underpinnings of art. I am not trying to be condescending; I just think you should address both aesthetics if you would like to help in this discussion.
Thank you for dropping by.

Kaz Maslanka said...

For those who are not aware I responded to Peter's list at this entry.

Thank you Peter! I respect and appreciate your opinion.

jv said...

Dear Sir, A friend of mine sent me this link to your blog, she told me that what you do reminds me of myself. Curious as I am I had to check your blog out. I have had no true formal college education. Therefore; reading your blog is a tad confusing to me. Then again, I can not read between the lines, stay within the lines nor follow any pattern when it comes to my design and creativity skills. Makes me nuts to follow instructions, color wheels are of no use to me. If I take a class I would imagine I frustrate the instructor. I can learn a basic technique then I just do what I do. Some just say I have a natural intuitive creative mind. This I do not understand. That's my story and I am sticking to it! Thank you for reading my post.
JV Maslanka

Kaz Maslanka said...

Hi Vonna,
Education just helps with the technical stuff and has no bearing on the spirit. The only reason I went to the University was due to it being fun. Keep up your Jewelry and have fun. Good Luck!

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