Charles:
Well... it's the potentiality that is offered by mathematics that is of special interest to me. ...The type of mathematics one can use, say, doing hand pictures-if you will excuse the expression-is restricted by how much time it takes to solve a problem, that is, normal methods of working are too slow. I think that if I were to deal with that question in a sightly different way it might be better.

I am saying that the artist can now use complex mathematics and the digital computer in his work because its structure and characteristics may suggest different approaches to problems than would otherwise be considered, and this is especially true of problems involving the repetition of data and iterative procedures which can take advantage of the computer's speed of operation. That gets a little technical.

What I might be saying is that mathematics offers new possibilities in the realm of the arts. One can use things like N-dimensional geometry or like a hundred-dimensional geometry rather than a three-demensional geometry... which might give you a different idea of a form, a different idea of a structure. You can make use in a much more systematic manner of random-number generators that give certain kinds of distributions of points or lines that may be of great interest.

Arthur:
You mean that you never would have thought of.

Charles:
Right. I think when you deal with so-called structures or distribution of points, values, lines, or whatever, that you have a certain bias. This bias is based on past experience, pre-conceptions of what is structure in art, and one way of breaking away from this is to introduce a mathematical system that can't depend upon that kind of conception. This is a way of breaking the bias and perhaps getting to an interpretation that you ordinarily would not think of.

Arthur:
Let me try out this analogy and see if this makes sense to you. You can think of some of the highly mathematical forms of art that some of the renaissance masters worked with in developing geometric perspectives, as being essentially systems dealing with two or three dimensions, and in a sense, modern developments in mathematics which can handle not only more complex problems but handle them more rapidly are really opening up another realm of possibility to the artist just as Euclid's geometry made perspective possible. ...

Charles:
Well, I think this is particularly true when you move into dimensional geometry. It is not ordinarily described as dimensional geometry but is called vector spaces. You have for instance thirty directions rather than three directions that you think of as ordinary dimensions. It's not a real space-it's a theoretical space.