What made the computer seem
like a reasonable possibility for this kind of search?
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
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
You mean that you never would have thought of.
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.
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. ...
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.