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Sunday, May 3, 2009

Differences in the aesthetics between math and art

Difference #1:
Mathematical truths are discovered Artistic truths are mediated.

Difference #2:
Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.

Difference #3:
Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure.

Difference #4:
Science reveals the body of "God" and Art reveals "God's" mind -- or is it the converse?

Difference #5:
Pure Mathematics has no expression for metaphor however; it does provide us a structure that can be used for it.

Difference #6:
In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is.

Difference #7:
The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.

Difference #8:
Artists have an insouciant tendency to get lost in their imagination Mathematicians have an attentive tendency to 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.

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

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

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

Please feel free to add any other difference you can think of, and also to question the proposed ones.

This thoughts where originally written by Kaz Maslanka, in his blog called Mathematical poetry.

30 comments:

martyn said...

nice post. thought-provoking. i have a nagging issue with #1 (lol), which i'm sure will seem dumb after a night's sleep. but, can we define 'artistic truth'? i'm not sure i could (or at least, not without a lot of words)

Mariana Soffer said...

Hello and Txs martyn for the compliment. I do not know if we can define artistic truth. I consider it as something that happens, that somtimes causes a sensation in the artist or in others that makes them know that that is it. Do you have any other definition? Hegel metions interesting stuff, but I think it is to long and complicated for this short post, although I can write it if you want me to.

Mariana Soffer said...

Here you can check martyn post and comments.
http://breuddwydion.org/?p=1769

jinjir minjir said...

Hmmm, is it sad (I wonder) that you had to get to No 9 to mention "constructions"...??

Just joking. Here's something related and which you may find interesting.

Mariana Soffer said...

I was just trying to hide that is all an invention (construction), so we can live our life thinking we know the truth.
TED, I usually walk some of the talks, but I havent seen this,txs, we can comment later about it.

Mariana Soffer said...
This comment has been removed by the author.
Stu said...

"Mathematical creations are not unique in the sense that they could be discovered by anyone.
Artistic creations are uniquely invented by individuals." This could be proposed as the most 'essential' difference. However, procedural (e.g. Oulipo) and 'mechanistic' forms of art seem to blur this distinction somewhat.

Mariana Soffer said...

I was thinking while I was reading the beginning of your post what about warhol serial stuff, but mostly about duchamp's ready mades , and then you mention the mechanistic form of art.
I have the sensation that art can be unique even dough it is mechanistic, but I do not have a rational explanation for this.

Uncle Tree said...

Hello, Mariana!

The only form I use as a tool for creation is language. I have a major amount of respect for those people who can draw, paint, sculpt, etc., but I can't speak for them. I will opine from my own experience, although I do not consider myself to be an artist. That may change, but as of now, no. A wannabe poet, or a novice in training sounds good enough to me.

#1: The truth is already here for the hard sciences. They uncover it. Or discover, if you please. Realism may come close to the truth, if the representation is spot on. There is no abstract truth. A writer deals with humans, and tells people what they already know. The reader wishes they could have put it that way...in so many words. "Ah-ha!" moments are completely personal. I don't take my own word for it.

#2: True. With art, one can sometimes follow precedent. "That famous artist got away with it. Why can't I?" Nevermind the grammar teacher.

#3: Over my head, but you made it sound good.

#4: There's really no distinction when you can't tell where one leaves off, and the other begins. Mind, body, and spirit work together for the whole. If my toenail could talk, he'd say all the rest of the body is there to support him.

#5: What?

#6: True nonsense is best when it gets a laugh. If it works, it's truly comical.

#7: If you read something and it 'hits home', it was already true. You just didn't want to admit it to yourself.

#8: That's the excuse I use for being absent-minded.

#9: Theorize? Intuition brings me an idea, or a title, or a first line. Then I elaborate.

#10: I agree 100%! Everything else is pure imitation. Consciously done, or not.

#11: True

#12: My answer for #1 will suffice.

#13: Oh! We're done.

A mathematical truth: once it's done, it's done. Otherwise, it's still a theory, or just plain art.

Mariana Soffer said...

I think you are a poet, an as a real one you are going to keep
seraching for what is it that you are really searching to express
all of your life.

1. I liked your comment, actually I am completelly confused
about that, I need someone to clarify for me what I think about it.

3.I do not understand what over my head means

4.Nice, its true.

5. Means that everything is what it is, but based on that isness you can
create metaphors (it is a bit twisted, sorry)

6. I love nonsense, Like in alice in wonderland

7. So true

8. I use the same (we have a logical problem here)

9. So true

uncle I miss you sorry, I have been busy

Uncle Tree said...

"Over my head", means: Outta my league. No comprende'! Or, "I have not been informed whatsoever, and any attempt to explain it to me would be fruitless."

How can you miss me when I'm right here, Mariana? That is complete nonsense.

Mariana Soffer said...

Not only you tought me something, but you also made me happy.

poeticgrin.com said...

It is so interesting that you posted this, because such a conceptual battle has been on my mind since I wrote the poem "Of My Science and Her Poetics" - in which a man battles what he interprets as an internal pull between science and poetry (math and art) - and in the end, the two cannot co-exist and he commits suicide. Now, of course I don't believe that the two cannot co-exist. I think they can be good friends, art and science... especially if one has the patience and talent to use one to enhance the other. Unfortunately, most of us are only talented in one area or the other and don't explore the possibility of combining the two.

Great post, again, Mariana. You make my head hurt - in a GOOD way! (you make me think!!!!)

:)

Mariana Soffer said...

pretty intreting poet, what you posted is what we are talking about here, is it a coincidence? maybe we have the same intrest
so it is not that suprising.
I liked your story a lot, It seemd like some plot that could came out of myself, I like it cause I feel identified with you.

I agreee that most people are only gifted on one aspect, I am gifted in the math part of the spectrum, so for me is a challenge to
write, paint, and many other things. I think you have to fight in order not to be limited, for example I might never be the best writter or poet, but I do it, I do not avoid it or discard it automatically cause I think am not excelent at it.
Just do not limit yourself, if you do not want to do something make sure that you are not doing it cause you do not care about it, not cause you do not dare to.
You are so kind poet, thanks to you, you are the kind of people that makes me wanna go on thinking.

Stu said...

Actually Mariana, I'm not sure why I used the term 'mechanistic', as this wasn't quite what I meant. I was thinking more of process art and indeed Warhol, whom you mentioned. Duchamp's readymades and appropriative works are an interesting case. And not forgetting that some art (visual, music, poetry, etc) is mathematically based.

Mariana Soffer said...

I think I got you from the beginning, you met things that where not exactly unique. That is what I mentioned. those artists.
That is a whole world and you are absolutely right. Too long to discuss right now, but for example did you know that they did some research on Polock's work and discovered that in his paintings there where fractal patterns?just a comment. Have you read the book Godel Escher and bate, there you have 1.000 pages where Hofstadter (the author) plays, explains, connects the math from the mathematician with the music from the musician and the art from the artist, which by the way has his work done based on math concepts.
Anyway, I still wouldn't know how to explain this clearly to you, or to me, but I am trying to understand more.

theperceptionpoint said...

I don't have one to add, but I really like the list.

Cheers

Paul said...

Eight million and sixty two. 3,678. I could write down numbers all day and it wouldn't have any meaning at all. 6.89. It's not until you add words to them, give them a context that they gain meaning. Eight million and sixty two dead people. 3,678 lovers. Numbers are a means to an end, art is an end in itself, it is meaning.

Mariana Soffer said...

Percepcionist, thank you very much, you are always welcome to comment anything you want to.

Mariana Soffer said...

Paul: Excellent
"Numbers are a means to an end, art is an end in itself, it is meaning."
Numbers are suppose to provide us a shortcut for modeling reality without having to depict the whole of it. About art I have my doubts, first, is it an end in itself? yeah, I think so, but I can not justify it. Is it meaning, probably, but it unrelated with the fact that it is a mean in itself.
IT is funny because when I was a kid for me just writting numbers, adding them, finding relations between them, it made a lot of sense to me, much more than language or history. Playing with numbers felt like I was discovering the most real of the realities. Besides I was not expecting for anything else, I did not need an equation to plug in my numbers, and I did not need a mean to and end, because to me it was already there.
Anyway now I do not believe it is like that anymore.

Jonathan said...

for me, science is beauty through truth, art is beauty through truth.

funny that you @jonone100 on twitter today. someone randomly mentioned Keats on facebook today. My favourite words by Keats are 'truth is beauty, beauty truth'.

i'll be back !

Mariana Soffer said...

You perfectly described the difference!Txs!

You know what else is crazy, I followed you cause of this guy harris that did the Ifeelfine project, and then realized it wasn't him, but I got intrested in your stuff. All by chance.

drodbar said...

Yes.

Mariana Soffer said...

Drodbar:I am, assuming that you agreed to the sentence .Am I wrong?

Mayer Spivack said...

You have a valuable knack for provoking thought in others (American fortune cookie?).

Difference #1:
Mathematical truths are discovered except for those that remain undiscovered. The undiscovered amount will always be greater.
Artistic truths are mediated by other mathematicians, artistic decisions are judged, evaluated, and sadly, mediated by critics and the media. The amount of art undiscovered is infinite.

Difference #2:
Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.
Well, kind of…,This is especially true for young growing artists who make the mistake of trying to make ART!. As artists mature, and few do, they begin to develop idiosyncratic ideals of structure, form, meanings, and something that might best be termed ‘honesty or artistic integrity’, this is all quite personal and relative. But it turns out that artists often recognize these qualities in each other’s work, perhaps by the smell.

Difference #3:
Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure.
The “structure” and the “wind”, parts of the thought move in the mind, whatever and wherever that is. These structures are in nature and in the nature of our minds.

Difference #4:
Science reveals the body of "God" and Art reveals "God's" mind -- or is it the converse?
If one ignores “God” as a revealed idea and replaces it with the words ‘nature’ or ‘universe’, nothing changes in the meaning of this sentence.

Difference #5:
Pure Mathematics has no expression for metaphor however; it does provide us a structure that can be used for it.
Lovely! But how can mathematics express metaphor if it contains no mathematical expression for it? “Used” in what way? To provoke thought? Einstein claimed to think in pictures. So do some artists. He also, obviously thought in words and the dynamics of number. So do some artists.

Difference #6:
In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is.
Many mathematicians have been fond of nonsense “Alice In Wonderland” and the tradition of Victorian Nonsense. Artists and mathematicians have equal reverence for the absurd. ‘Truths’ often masquerade as obsurdities.

Difference #7:
The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.
…. And IS us.

Difference #8:
Artists have an insouciant tendency to get lost in their imagination Mathematicians have an attentive tendency to map their imagination.
If one is mapping new territory one may either carefully navigate one’s way into it from within known coordinates, and thereby have the illusion that one is not lost because the way back is known, or leap off the edge of the world and find a ‘new world’. In either case both the mathematician and the artist, and the rest of us are always ‘lost’ because we cannot see the largest and smallest contextual frames around and within our existence.

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.
What then is an “artistic theory”? Do you mean the meaning of a work of art or it’s organizing principles? When I work on sculpture sometimes I may work for a year or more without any idea of where I am going with the piece that occupies both my studio space and my mindspace. In this long time I am truly in a kind of wilderness, trusting that eventually I will find my way to organizing meaningful principles. This is a silly, frightening and wonderful state of mind, a real adventure.

Difference #10:
Mathematical creations are not unique in the sense that they could be discovered by anyone.
Because they are intrinsic to reality? Out there? To be stumbled on or to be hit on the head by?
Artistic creations are uniquely invented by individuals.
Over and over and over again by different individuals for millennia.

Difference #11:
Mathematics, among other things, is a language.
Art, among other things, uses language.
Both create new language elements at their edges, language pseudopods to extend their reach and grasp, as if locked within in an expanding fractal bubbleverse.

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
Who could argue better?

/t. said...

mariana,

fascinating
&
i recognize that i am late
to this party but offer the following thots

• it is possible that all things exist already in Creation
• with the possible exception of some formal methods, artists and scientist have more in common than differences

great blog!

/t.

Mariana Soffer said...

You are never late, this things are never closed of finished, we can go on luckyly

This is my opinion of the day (cause I change):
I think art and science are not very far apart at all. Art gave birth to science but now science doesn’t want to acknowledge link. In time it will.
It makes me happy that you came by.
Now I am going to check your new artworks.
M

Anonymous said...

Easily I agree but I about the brief should have more info then it has.

Anonymous said...

"Mathematical truths are discovered Artistic truths are mediated."

Not true. See, for instance, non-standard(infinitesimal) analysis vs standard analysis. They both produce statements which are true, but they are not the same.

The deeper you get, the clearer it becomes that certain mathematical truths that were "discovered" may very well have gone undiscovered for all time if it weren't for their particular discoverers. A mathematical truth is not some fact like, "The capital of France is Paris."

A mathematical discovery is a new UNDERSTANDING. If a scientist discovers a new element, that's something that, in theory, anyone could have done, and which doesn't constitute (or require) a new understanding.

"Mathematicians generally agree on what is mathematically correct."

Totally false. Sure, once someone's proven a theorem, other competent mathematicians will accept it as long as the reasoning is valid. But as far as mathematical IDEAS go, history is full of examples of controversy. So-called "imaginary numbers" went mistrusted and misused for generations before Gauss "discovered" a geometrical interpretation for them which made them comprehensible. Spatial dimensions higher than three were resisted for decades. Hell, the simple idea that the Euclidean geometry of three-dimensional space wasn't the end-all-be-all wasn't accepted without intense controversy. Or consider Cantor's ideas about the infinite, which were referred to by a leading contemporary as a "disease"!

The proposition that mathematicians generally agree on what is mathematically "correct" is absolutely false.

"Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure."

Uh, quantum mechanics? Chaos theory? Mathematics is hardly some static edifice of rational thought: it is the bleeding edge of rationality, a realm of sublime metaphor and creative energy.

"Pure Mathematics has no expression for metaphor however; it does provide us a structure that can be used for it."

This is just too ridiculous to comment on seriously. "Mathematics has no expression for metaphor"? Get a clue.

"In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is."

Actually, absurdity and paradox are where new mathematics is born. Zero is that something which is nothing. Negative numbers are "less than nothing". Real numbers identify an infinite series of terms with a single concept. Non-euclidean geometries reject the idea that two parallel lines will never meet and ask, "What then?" Game theory confronts the idea that sometimes it's in our best interest to be UNABLE to do something. The list is endless, and these aren't even the most interesting examples (just the most accessible ones).

"The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us."

Mathematics HAS a language, but it is more than a language.

"Artists have an insouciant tendency to get lost in their imagination Mathematicians have an attentive tendency to map their imagination"

...whatever that's supposed to mean. Lots of mathematicians get lost in their imagination. (Higher) math is probably the single activity which requires the most imagination.

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

I've already touched on this, but this is truly absurd. No new mathematical idea will be framed, presented, and elaborated the same way by two different mathematicians. It sounds like you're trying to belittle mathematics.

Mariana Soffer said...

Anonymous: I agree that you have a fairly amount of valid points, which we could discuss in more detail, at least the one I do not agree exactelly with what you say. This post for me was just a kind of game which I thought It would be interesting to do a brainstorming based on something I wrote before, but it does not have rigor at all. I do many things just for fun, and to open other people's mind, being able to share ideas with them.
By the way have you checked the official post regarding this:http://apperceptual.wordpress.com/2009/05/08/math-and-art-differences-and-similarities/
You should compare it with mine.
By the way I am really curious who you are, do you have anythig in the web I can check, are you involved in math/arts, I would like to find out more so I can reply to the person that is talking to me in a language that we can both understand.
Thanks for taking the time of posting this.
M