Why do my fellow artists reject mathematics as a tool for art?

[Pixel_Outlaw]

This is an odd subject I'll admit but I find it very frustrating that artists sometimes think of their work as something created in a vacuum. I like art and tolerate math, that said many people hate one or the other. In recent years I've attempted to help many artists draw accurately only to be rejected and scoffed at. They seem to think that art and math should have no place together. They may be drawing a pixel art isometric scene and when  I give them formulae to draw things like isometric polygons and other such things they just ignore me. They will spend hours tinkering with shapes that will never be accurate yet reject mathematics that would lead to the desired result. I can accept organic art forms but when I try to show my works they are labeled cold or emotionless, even if I have fully expressed my thoughts. The most prominent example comes from a high school art teacher. I wanted to know how to draw real world shapes in 1 point perspective. Problem was that he only knew how to geometrically construct figures. I was sent to a drafting teacher who had never worked in artistic perspectives like the 1 point. I was then sent to a math teacher who had never really drawn and had no idea where to start. I feel that this lack of knowledge stems from compartmentalizing useful knowledge. Artists are scared of mathematics in their art and mathematicians are scared of "crazy artists". I think the men like Leonardo Da Vinci had it right. You must learn everything you can and see studies as a general knowledge rather than try to break bridges and links between subjects. This rejection of math in art really chaps my ass.

Your thoughts as artists or programmers?

Oh and props to relsoft for his work on a perspective tutorial. Good stuff there.

Link: http://rel.betterwebber.com/index.php?action=contents&item=Tutorials

[Jim]

I like to look geometric equations and imagine what they look like in 3d.  Also, to take 3d things and work out how that could be represented mathematically.  In my engine I have a raft of geometric shapes that I can stick together, though I've not done much with it yet.
I think I was lucky at school because I used to go to my maths teacher with problems I wanted to solve on my ZX Spectrum, and usually she'd come back with a diagram and some sums I could use.
I like the rigidity of maths, but I think that's what makes artistic people reject it.  There's no artistic license with maths; either you are right or you are wrong; with art there are many more shades of grey.  It's not really art if there's not a fallible human element to it.  Mathematical people like things cut and dried, and dislike the hand-waving of artists.  I mean, a Mandelbrot set is a beautiful thing, but is it really art?
It doesn't really surprise me that you're not having much luck.  It's like trying to make the cat be friends with the dog.
You're right, you have to go to Da Vinci or Escher to get a crossover.  Does anyone know other people who've crossed this divide?

Jim

[combatking0]

You are indeed correct - some of the finest works of art have mathematical properties, and some of the greatest mathematical problems have been solved by applying artistic talents - one needs only to observe Menger sponges and the matrix equations which apply to models of atoms.

If you stick to what you do, you can accomplish great feats - but only tell them how you did it after they applaud you. Only then will they begin to see the light.

[taj]

What a great question. Karma++.

I believe the cause of seperation of art and maths from a consumer point of view is meaning.  Try to look at any art, especially anything since about 1900 without asking yourself questions like "What is the artist saying?", "how does she feel?", "why are the shapes only in orange and gold?". It reduces down to a belief that each piece of art has some meaning, something to say. A message. Thats why a pile of bricks in the Tate gallery *is* art ... more accurately meta-art ... because it forces us, in a brutally powerful way, to ask ourselves "what the hell? Is this art? If so, what is art?" and the artist has done his job.

Mathematics and computers, we believe, have nothing to say. They are, they exist, they don't emote or believe. So looking at a perfect mathematical figure is no more nor less art than seeing the winning Petunias at Chelsea Flower Show. Thats how we feel. Else, what value art? Skill, be it mathematical, programming or flower growing, is not art.

In the converse, an artist feels they are saying something: conveying meaning, challenging ideas. By following strict rules, how can they be free to express emotion or ideas (unless that idea is a concept related to rules of course)?

This is the commonly held belief: maths is rule based with right or wrong and thus no room for artistic expression and art is free with no rules. This I think is at best a half truth. Art has rules, of course. Art college teaches styles, known techniques, formats, materials, media, history. These are the rules. What is known to work. For most of us its easiest to see this in movies. We refer to them as formulaic or cliched when they follow the rules of movie making. Similarly maths has interpretation, its is not so black and white. What is PI? 3? 3.1? 3.14? 4? 1? For all of the values there I can provide an argument of where PI could be used as that value (though, only someone with experience of astrophysics might accept 1 as valid for PI).

Jim asks: Mandelbrot - is it art? So I've said art must have meaning. I'll try to convey loneliness using the mandelbrot set by placing a tiny version in my electronic canvas, surrounded by vast areas of white. I'll use cold colours to render it and Ill fill it with white too, avoiding the contrast of black and white distracting the viewers attention. I'll place it off centre but not by much, not at the golden ratio area, just disconcertingly off-centre to enhance the feeling of sadness and loneliness. Now its art. Not sophisticated. But art. Yet, its all mathematically rendered. So context, canvas, colour, scale, position may all be mathematical but can be used to express mood and hence create art. But the mandelbrot set itself, no , thats not art.

Then there is judicious use of rules. One can alter the fundamental rules of mandelbrot to produce something similar but different. However this is less successful a technique. Usually this results in "beauty" (see my flow2 1k) but its not art. Why? Altering rules of maths in order to express an emotion is a bit like using slightly different oil based procedures to produce a canvas for painting. Yes, it may be valid, yes it may enhance the colours, but no, nobody in the world is skilled enough to chose a chemical combination that will result in a more "happy" or a more "lonely" feeling. Similarly breaking the rules of mathematics to express ideas is nigh on impossible. Interest and beauty yes, but beauty is not art. I may see a beautiful childs face but it doesnt come to my mind that it is art - precisely because it has no meaning. I may admire in an abstract sense the beauty of nature or marvel at the "artistry" of nature but its words only.

So here we have it. Maths in context can be art. Breaking the rules of maths can intensify the beauty and interest of the art, but not (usually) create art in and of itself. This is why separation exists. The mathemetician strives for beauty (how many times have you heard it?) the artist focuses on meaning. The two are not the same.

Bringing this back to demoscene. How sad then that so many people in the demoscene say dull things like "nice colours" (beauty) or "too slow" (perhaps it was supposed to be?) or "interesting effect" (technical beauty). So few comment "why red?" (meaning) or "the pace was exactly like a heartbeat" (meaning).

And to prove I can still laugh about maths and rules and art:

Whats two plus two?
(Mathematician) Four
(Astrophysicist) As close to 1 as makes no difference
(Artist) Nothing without meaning...
(Philosopher) Perhaps we would best serve ourselves by asking why, not what
(Psychologist) The numbers suggest the social structure of family
(Psychiatrist) What do you feel two plus two is?
(Computer Scientist) 0x04
(Real Estate Agent) That an awful lot of room, but I'd knock a wall through from room 3 to room 4
(Pouet Troll) BASS
(Internet Troll) FIRST!
(Slashdot Troll) 1. Add two plus two. 2. ? 3. Profit!
(Dr Who) Two plus two, eh? Certainly not four, way too obvious. Aaahh such a great question. Aha! I have it! Quickly! This way, I'm not going to explain this sudden running but it will increase viewer retention figures and artificially increase tension.
(Buffy) Hey! Ask Willow. She's the scooby-Spock , I just kick and stuff.

[relsoft]

I remember someone (an artist) scoffing at my use of scale2x in Marvelous Twilight.  Told me it's not supposed to guess what's on the artist's mind when he painted the sprites. LOL

Look at Van Gogh, killed himself.

[Jim]

When we did the skateboarding game, the PS1 models were derived from the PC/DC models.  We needed to come up with a way of making the PS1 lighting look like the PC lighting.  The long and the short of it was, we added up all the light directions and re-normalised, we added up all the light colours and re-normalised, and then we lit the scene with one, averaged, light.  It looked ace.
Is that maths, or art?

Jim

[relsoft]

What skateboarding game?   

[taj]

When we did the skateboarding game, the PS1 models were derived from the PC/DC models.  We needed to come up with a way of making the PS1 lighting look like the PC lighting.  The long and the short of it was, we added up all the light directions and re-normalised, we added up all the light colours and re-normalised, and then we lit the scene with one, averaged, light.  It looked ace.
Is that maths, or art?
Jim

Maths. You have no meaning, no message, just a simple straight forward presentation goal. Compare for example mixing paints to achieve a certain colour, that someone else has defined for you. Its a skill to be sure, but its not art. It has no meaning.

Don't get me wrong though Jim. I'm not suggesting something is one or the other. Its possible to use maths as art of course but its not in the way most people think (which normally resolves to beauty).

[combatking0]

Programming can be yet another type of canvas on which a skilled artist may create works of fine art.

I consider Jim's Halloween demo where the black cubes combine to form various shapes a fine example of this.

A piece of paper with some paint on it has the same cognitive capabilities as your average computer - it is the person beind the brush/keyboard which supplies the artistic talent.

Anybody with a clear vision, and a good understanding of maths, can produce a mathematically driven piece of software which draws a fine, intricate work of art.

Such as my very own Black Sponge (named after myself, as it differs slightly from the classic Menger Sponge), seen here represented in four shades of grey, black and white, in an isometric view, best viewed at full resolution.

There are better examples though, I'm sure.

[Pixel_Outlaw]

This has turned into a delightful discussion. I think that the product of art must stem from personal choices in the creation process. I feel there needs to be a pre creation process filled with choices. If we were to go by the rejection of math as art draftsmen would not be artists. It seems that art is forced to be something that is held on a pedestal and isolated from all areas of study. Some of my favorite styles of art are purely functional, look at machines and buildings from the early 50's. People are often hesitant to welcome functional design styles because they lack embellishments. The original designer could have included such embellishments but chose a purely functional style. Frank Lloyd right has some really pretty buildings that are very ridged and functional. I did a great deal of drafting in school and felt that I was creating and expressing my ideas for new buildings. This wasn't really looked at as art because I was using CAD. I found this funny because paintings and drawings of buildings (considered art) could be produced with compasses and rulers. Was I making art by tying in commands? I would say so, I was making conscious choices regarding style and form during the creation process. It would be quite amusing if canvas artists had to tell their hands what to do with such commands as "move hand LEFT two inches". It would be like art LOGO. I guess art arises from conscious choices during the creation process.

That said, should schools offer hints of math in art for the precision artist? I know that teachers are working hard in my state but art teachers should receive some training in mathematical art. Ideally this would be nice but again the art teachers may be like their calculation rejecting students. Everyone plays with one two and maybe three point perspectives but they are never taught how to accurately plot objects. My math teacher always wanted to know how to draw a perfect cube in one point perspective or how to prove that a shape was a perfect cube. Well to make a long story short this question was taken through three branches of study and nobody knew the answer. It went through 2 art teachers, a drafting teacher (1 point perspectives are rarely used it seems isometric is preferred), and a math teacher that was crippled because it wasn't in the math book. I feel that our schools here require regurgitation of known facts rather than application in difficult situations. This may be fair in some way because the average math student will never have to do constructive geometry. I get the feeling that some teachers are not really interested in pursuing their trade, their trade is not an interest or passion. I think people give up on their questions rather than taking the time to pursue the answer. Had my math teacher found out how to represent a cube he would have opened up even more possibilities. Imagine new polyhedra he could have drawn, just geometrically truncate a few corners and new shapes can be made. Mr. Octahedron could be invited to the cuboid-only party. And that is my point, in one point perspective you can imply 3D shapes but without a rule to plot points, you can only guess at shapes' tactual sizes you just putter around until it looks right without geometric and algebraic construction algorithms. If my memory serves me correctly point (X,Y,Z) can be plotted as (X/Z,Y/Z) assuming that Z is never negative.

More discussion welcome, this is really a nice thread.

I don't want to seem arrogant but it is frustrating, I see a whole field of answers and possibilities in mathematical art and they are focused on a 1x1 foot patch of flowers. There is sooo much more out there that is just being ignored so many new artworks that will never get created. I feel like a stick bridge between two areas of study that are not masterable.

[taj]

This has turned into a delightful discussion. I think that the product of art must stem from personal choices in the creation process. I feel there needs to be a pre creation process filled with choices.

Agreed. But I would add, not all processes filled with choices are art. What shall I eat today? Should I phone for pizza or look in the fridge? etc.

If we were to go by the rejection of math as art draftsmen would not be artists.

I would argue, that like a surgeon or a formula1 driver they are skilled craftsmen - not artists. They have elevated skills, the like of which I do not have, to be admired for sure, but not held as art. Not because art is above them but because it is different to them.

It seems that art is forced to be something that is held on a pedestal and isolated from all areas of study. Some of my favorite styles of art are purely functional, look at machines and buildings from the early 50's. People are often hesitant to welcome functional design

No, I'll re-iterate that I don't think art is above, its equal but seperate. You use the term design. Why do we have two words - design and art? Because they are the same? No. Design I normally associate with form and function. Form of fine design is normally beautiful, but not necessarily artistic. However, there are certainly forms of design that reach as far as art for sure (one form of design is known as art deco right - and with good reason).

styles because they lack embellishments. The original designer could have included such embellishments but chose a purely functional style. Frank Lloyd right has some really pretty buildings that are very ridged and functional. I did a great deal of drafting in school and felt that I was creating and expressing my ideas for new buildings. This wasn't really looked at as art because I was using CAD. I found this funny because paintings and drawings of buildings (considered art) could be produced with compasses and rulers. Was I making art by tying in commands? I would say so, I was making conscious choices regarding style and form during the creation process. It would be quite amusing if canvas artists had to tell their hands what to do with such commands as "move hand LEFT two inches". It would be like art LOGO. I guess art arises from conscious choices during the creation process.

I think the reason such work is not considered art is because the choices made in the desiion processes you describe are not guided strongly enough by ideas like expressing deep emotions or causing others to think and question. They are guided by conveying information (what the building looks like in essence). That said, again its a grey space. A fine piece of architecture designed to harness light and create images of the outside world in an interior space, borders on art. But a drawing meant to represent it does not. Why? The drawing conveys the information of what this building will be, the building though conveys the feeling once in it. These are two different intents and results.

That said, should schools offer hints of math in art for the precision artist? I know that teachers are working hard in my state but art teachers should receive some training in mathematical art. Ideally this would be nice but again the art teachers may be like their calculation rejecting students. Everyone plays with one two and maybe three point perspectives but they are never taught how to accurately plot objects. My math teacher always wanted to know how to draw a perfect cube in one point perspective or how to prove that a shape was a perfect cube. Well to make a long story short this question was taken through three branches of study and nobody knew the answer. It went through 2 art teachers, a drafting teacher (1 point perspectives are rarely used it seems isometric is preferred), and a math teacher that was crippled because it wasn't in the math book. I feel that our schools here require regurgitation of known facts rather than application in difficult situations. This may be fair in some way because the average math student will never have to do constructive geometry. I get the feeling that some teachers are not really interested in pursuing their trade, their trade is not an interest or passion. I think people give up on their questions rather than taking the time to pursue the answer. Had my math teacher found out how to represent a cube he would have opened up even more possibilities. Imagine new polyhedra he could have drawn, just geometrically truncate a few corners and new shapes can be made. Mr. Octahedron could be invited to the cuboid-only party. And that is my point, in one point perspective you can imply 3D shapes but without a rule to plot points, you can only guess at shapes' tactual sizes you just putter around until it looks right without geometric and algebraic construction algorithms. If my memory serves me correctly point (X,Y,Z) can be plotted as (X/Z,Y/Z) assuming that Z is never negative.

Should a painter know how to make paint brushes or the chemical processes required to create paint thinner? Or should he just understand how to apply them? I am a driver - I drive cars. I dont know how the engine works except at the most basic level. I could still be a great driver though. Until the day my car breaks. So I think the answer is an artist needn't necessarily know about maths but should know how to use mathematical tools. Where is maths a tool and just maths for the sake of maths - I dont know. Do you need to know how to rasterise triangles to write a great game? No. Does it help? Debateable, certainly.  That said, maybe we need a specialised field (as quantum physics is to physics) taught at a very high level to all, but delving into depth for others.

More discussion welcome, this is really a nice thread.

I don't want to seem arrogant but it is frustrating, I see a whole field of answers and possibilities in mathematical art and they are focused on a 1x1 foot patch of flowers. There is sooo much more out there that is just being ignored so many new artworks that will never get created. I feel like a stick bridge between two areas of study that are not masterable.

I've hunted mathematical art for about a year now on the internet and found some remarkable things. There are people out there trying to do this stuff but I suppose its hard. You need two very different skills and there arent many DaVincis around who can master maths and art. I know I cant master either :-(.

http://3drecursions.com/forum/   this is a good place to start: its a mathematical art forum. But here again, I find people produce beauty not art in the main.
http://www.processing.org/ here is a programming language designed in the mina for designers and artists. I know a professional designer who swears by it. I looked at the book and it seems to describe many of the basic mathematical principles I think you are frustrated are not being spread wider.
http://www.bathsheba.com/ is a mathematician who manufactures art sculptures and designer objects from pure maths. Again I see beauty here, but not yet true art. However given the right context I think his stuff could be stunning.
http://www.3d-gfx.com/fractals/3d.html definitely not art , you just have to read the text of each image to see why, but certainly beautiful - and for some people thats enough I guess.

Taj

[taj]

http://news.bbc.co.uk/cbbcnews/hi/newsid_4110000/newsid_4112000/4112048.stm

:-) now then...theres a spanner in the works...

[Jim]

->rel http://www.google.com.au/search?hl=en&q=mtv+sports+skateboarding&meta= Unfortunately not Tony Hawks!

Jim

[relsoft]

Whooa Jim! That looks rad!!!!


You know what they always say...

"Beauty is in the eye of the beholder"

[rain_storm]

it is extremely difficult to excell at both art and maths due to the fact that they are powored by different sides of our brains such that someone who is right side oriented is more likely to posses better spatial abilities whereas those who are left side oriented are more likely to be greater at reasoning and logic. Artist tend to be right sided whereas mathemeticians tend to be left sided. creativity however comes from the base of the brain just above the stem. Leonardo was an oddity in that he was one of the worlds greatest artist as well as one of the worlds greatest invertors. However his inventions fell short of his artistic abilities. Most people who are good at music are also quite good at maths due to a natural appreciation of rythms and timing. This is quite at odds to those who paint. Painters usually excell at spatial awareness but suck at maths. We now have computers to compensate for our lack of mathematical prowess. This gives artist a great advantage over artist of old. But then again you still have to convince those that view your pixel art and convince them that it is truely art

[taj]

it is extremely difficult to excell at both art and maths due to the fact that they are powored by different sides of our brains such that someone who is right side oriented is more likely to posses better spatial abilities whereas those who are left side oriented are more likely to be greater at reasoning and logic. Artist tend to be right sided whereas mathemeticians tend to be left sided. creativity however comes from the base of the brain just above the stem. Leonardo was an oddity in that he was one of the worlds greatest artist as well as one of the worlds greatest invertors. However his inventions fell short of his artistic abilities. Most people who are good at music are also quite good at maths due to a natural appreciation of rythms and timing. This is quite at odds to those who paint. Painters usually excell at spatial awareness but suck at maths. We now have computers to compensate for our lack of mathematical prowess. This gives artist a great advantage over artist of old. But then again you still have to convince those that view your pixel art and convince them that it is truely art

Bloody hell well said.

[Pixel_Outlaw]

I've just signed up for a drawing class at my college and am wondering if I should explain the mathematical properties of perspective? I've had her before and she is the kind of person who likes to hear from everyone. I'm debating if it would be out of place and how I might present the very simple formula for plotting in perspective. I don't want her to feel like I'm teaching but she is often open to new ideas from everyone.

I convert points like this (x,y,z) in 3D space can be plotted as (x/z,y/z) with some limitation on the z value. This sets the center of the picture at (0,0).

[combatking0]

I always had difficulty calculating some of the lines in perspective, though it is very possible.

Maybe a program can be coded which can do this to either one or two point perspective or both (or even the theoretical three point perspective, which I can imagine in my head, but not realise on paper).

I'll have a go in PHP.

[Xone]

A piece of paper with some paint on it has the same cognitive capabilities as your average computer - it is the person beind the brush/keyboard which supplies the artistic talent.

Great topic, and a fascinating one to comment.
I started to write that code should not be classed as art, and then I ended up deleting the post before finishing my argument.
I'm finding this very difficult to answer because I do both and I can see reasons for math/code to be classed as art.

What mandlebrot produces is a perfect structure (as random as it may appear in places)... it can always be replicated
by following an initial rule. So I was going to say that mandlebrot is not Art. But art is largely about aesthetics, and the
mandlebrot pattern has no shortage of this.

It is because that mandlebrot can be replicated that I would say no... its not art. It's a mathmatical structure and should be
placed in the same category as the circle, triangle, hex etx.

For an artist to paint the mandlebrot is impossible, because of the endless structure of which is can retain at magnification.
So it could never be acheived by an artist on paper.
If an artist paints a picture using Artist tools (via a programmers algorithm) on a computer (using brushes etc), this
pixel painting (as I like to call it) method I would consider as Art. As the user is applying a colour palette to a
specific size of canvas which is impossible for any other user to replicate through experimentation with math.
I doubt a programmer could replicate what an artist can do in Photoshop with an algorithm (IF they could, the amount of
code required would be.... intense to say the least!)

The only thing I conclude, they are sepperate forms of art whereby code form is the odd one out imo.
[REAL] Traditional art - (painter with a paintbrush and paper or a sculptor with clay)
[REAL] Digital art - (Software program made for art, like photoshop with art tools)
[SIMULATED] CPU/Math art - (Driven by algorithms and equations and executed entirely by number with reproducable results)


Only when a computer is capable of generating something from nothing, will I class a CPU/Math image as Real art 

[Pixel_Outlaw]

All raster digital art is replicatable.

I too thought about this argument that art arises from the human element of inaccuracy. However, I noticed that all of my sprites could be reproduced in a single copy command by somebody else or by following the same inputs into the same program I used. I still think that art comes from the pairing of human deliberate decision coupled with the need to express something to other people. I don't feel that art is an algorithm. You can use concrete algorithms in art however the art in it's whole cannot be a single algorithm. If you were to choose an l system tree and then choose a position and make a special texture or algorithmic coloring description you have made personal choices to help describe a unique vision. I must persist that I feel that drafting is an art. It is a precision art but is based purely on choice function and aesthetics. Things like shading and hatching can be done at an algorithmic level but when I'm designing a building I'm also looking to express a feeling or notion to the people inside. If draftsmen were not artists (this is the assumption that draftsmen are DESIGNING and not just visualizing concepts) then we would all live in cuboids with no windows and no external shapes. It would be similar to the Borg ships from Star Trek. The fact that buildings are not completely utilitarian (having windows that lose heat and roofs that are not always optimized for rain and snow) means that there was some other reason for these decisions. That decision is driven by aesthetics at a personal level. Art for me arises from choice on a personal and meaningful level.

I've noticed that the students with whom I share an art class have started to warm up to my methods. My portfolio case has a calculator,rules and compass in it. They thought I was crazy at first but now they like the exactness of my work. I felt the need to express myself with precision in a largely "organic" field. Art can exist with and without precision it is up to the individual to set the accuracy of their work. I guess I don't like to show much of the human element in my work because everyone else is so concerned with it. I show some through color choices and lighting and such but the shapes in my work are usually ridged and precise. Even the Masters used math heavily. The forerunners of perspective were mathematicians and people wholeheartedly accept the notion of forced perspective. I must say that my art teacher has taken my stance on the subject and has encouraged me to show what is in my mind and accepts my view of underlying math in art. She is no mathematician but she still thinks the mathematical approach is valid.