Here is the English translation of the previous picture, for those of us who do not read Braille:

This is also my attempt to re-integrate the three-dimensional mathematical replica with the abstract information which generated it.

The Hyperbolic Paraboloid as a physical object may contain no abstract information to someone unfamiliar with the mathematics of it. The captions on the surface supply information about the surface specific to the region on the surface being read. The title gives the full equation of the surface. The curves traced on the surface contain text of the rearranged expressions for the curves resulting from holding one of the parameters to a constant value.

The reader's hand, passing over the line of text on the surface is constrained to a three-dimensional point in space, specified by the mathematics being read at that point. The reader's hand is also constrained to the tangent vector -- the first directional derivative -- of the mathematical curve in the direction of the line of text. And it also constrained to the normal vector to the surface, thus the reader's hand must follow the Gauss map of curvature for the surface.

This is an example of a higher-dimensional integration of information space. It is also physical mathematics. I assert that the experience of reading the captions on the surface is a corporeal awareness of the mathematics of the surface. But, this assertion remains to be proven by actual classroom experience.

So, what does this have to do with art? Well, the problem I have stated is the "hard" problem. This is the obvious problem which can be logically formulated -- a solution to an obvious particular need. But this is only the beginning. Further aspects of the situation -- such as my theory of a corporeal awareness of mathematics -- are far more subtle and are more difficult to prove. But I believe there is precedent for a path of action leading to the proof.

The emphasis in computing is on the Virtual -- to immerse the imagination in this plastic, abstract space -- to further disembody the mind. This is simply the continued tendency of writing and literature.

Copyright 1999 (c)