I'd like to comment on how math is utilized in art. I think we have done a poor job so far exploring the aesthetic possibilities of higher dimensional geometries. That is how art can be mathemathical and use math to represent what ever its purpose or intent may be. Mathematics, geometric figures, etc. appear in art for their symmetries, for their imposed order (or rather an order built upon a base set of axioms to so that something can be seen of a chaotic system) etc. . . . and so on. Art uses everything, but isn't everything. It's more the representation of everything, and frequently the most mathematical art was produced by the artist without intending to portray mathematical concepts to his audience but to convey messages through the math.
Obviously, this is a math class, and we should take the advantage to examine the math in these arts in light of what we can learn from the math but without losing the art. Studying the math should tell us more about the art, get us closer to the concepts and ideas which drive art, and utlimately life (if art is a worthy pursuit)
With this in mind, I'd like to comment on Dali's The Crucifixion. I find it hard to believe that Dali's statement is inherently mathematical. I think of it as: the depiction of the Crucifixion that Dali would paint--Rich in its classical underpinnings it is more a renaissance church painting than a surrealist document, but it utilizes a modern iconography distintly Dali. The perfect hypercube, unfolded, is a cross for the future, pure and transcendental--it is also in the shape of a cross in profile. What else is there to say: Jesus is depicted as a giant, there are mountains on the dark barely discernable horizon, the landscape is a wasteland, in the foreground it is a checkerboard tile, Mary looks up (not in grief but as if she is looking at a piece of art)--it is Dali's wife that is the model (she almost always is the model for women in his art). . ., the four cubes serve to hold Christ to the crucifix, replacing the stigmata and wounds of the sufferer for all mankind--there is no blood. . .
I'd like to call to attention another artistic, but "non-mathematical" piece: Petersburg by Andrei Bely. It is a novel which is considered the masterpiece of Russian symbolism witten in the early years of the twentieth-century and first published in 1913. Vladimir Nabokov ranked it among the four greatest novels of the twentieth century. . . Anyway, Bely was a mathematician and uses geometric figures prominently as symbols in his books: squares and parallelepipeds represent imposed order and structure, man-made, artificial. . . pyramids and points and spheres have their roles, but his symbology is too much to mention here. The plot is essentially this: there is a plot to kill a Russian official who is responsible for keeping all action from happening in the entire empire--he is partly responsible for it when he sees the thought of thisscenario in the pupil of a stanger on the street; his son ultimatly becomes the planter of this time bomb hidden in a round sardine can which grows from a point and expands into a sphere and explodes and consumes all of Petersburg down to a point. . . sort of, it's a very strange book. I wanted to bring a quote to the attention of those interested in the aesthetic, "cosmic" ramifications of higher-dimensionality. . . There are really thousands of good quotes, but there are only two in which the fourth dim. is explicitly mentioned:
"Petersburg is the fourth dimension which is not indicated on maps, which is indicated merely by a dot. And this dot is the place where the plane of being is tangential to the surface of the sphere and the immense astral cosmos. A dot which in the twinkling of an eye can produce for us an inhabitant of the fourth dimension, from whom not even a wall can protect us. A moment ago I was one of the dots by the windowsill, but now I have appeared. . . "
Anyway, Bely is hard to put in context. . .When Nikolai, the son, imagines the bomb exploding, killing his father:
"Bloating into an immensity, out of the fourth dimension, very likely, it was penetrating the YellowHouse, and it was rushing throught the rooms. Its surfaces were sticking to his soul, and his soul was bcoming the surface of a huge, rapidly growing bubble, which had swollen into Saturn's orbit. Oh, oh, oh! Chills ran through Nikolai Apollonovich. Winds wafted into his forehead. Everything--was bursting."
There is little math to be taken from this in a way that will get you very far, but I feel that as a writer Bely is accomplishing a great deal and is worth anyone's looking at him.
If people are looking to put themselves in a 3-d maze click here.
To look at some nice maze art.The artist amazing fills an entire space without leaving the cavities that are in every crossword puzzle and in many mazes with an irregular path design that more conveys an image than depicts it.