Week 2: Mathematics, Perspective, Time & Space by Matthew Robertson

This weeks reading was about how artists incorporate a fourth dimension in their works. I got the impression from the article that there was a great disagreement to what the true fourth dimension is, which I found interesting. To me, this is similar to people arguing if the first dimension is length, width, or height. However, the way that the painters decided on a fourth dimension, be it temporal or spatial, is interesting.
Representing a scene which contains four spatial dimensions on a two dimensional media such as a canvas requires the artist to imply two extra dimensions in the painting. Thus, the challenge could be compared to representing a three dimensional scene on a one dimensional media such as a line. Thus it is no surprise that painters with interests in higher dimensional spaces have approached the problem in different ways. Part of the article centered around what different artists assigned to be the fourth dimension, with the third usually assumed to be scale.
The history of how mathematics integrated itself into painting was particularly interesting to me. While seeing the early examples of perspective I began to wonder how people who lived then and before perceived the world. Given that depth was never represented artistically, its possible that the notion of objects shrinking as they gained distance never occurred to them. Its possible that they perceived the world almost isometrically, with parallel lines never appearing to intersect (see http://en.wikipedia.org/wiki/Axonometric_projection). A few years ago, I received a certification in computer aided drafting. Part of that was viewing architectural models of houses. When viewed with an isometric projection, the houses became very difficult to look at and details seemed to fade. If indeed medieval man perceived the world that way, understanding the world must have been very difficult. Perhaps this contributed to the length of the dark ages; without understanding of perspective, spatial reasoning could be impaired, which would result in difficulties in mathematics and engineering.
A cool example of the fusion of math and science is the work of Dr. Taimina. She crochets models of hyperbolic spaces. See http://www.theiff.org/oexhibits/oe1e.html. Personally, I have a difficulty visualizing some hyperbolic surfaces. Perhaps if I’d been exposed to models like these from a young age thinking about and analyzing hyperbolic surfaces would not be very difficult.

The Upanishads idea of zero being the same as infinity was very strange to me. It reminded me though of the concept of indeterminate form from mathematics, or that zero multiplied by infinity cannot be evaluated. It also reminded me of the concept of integer overflow from computer science. If a number exceeds the largest size that its register width can support, it will wrap around and reach its smallest value. If there is no sign bit (meaning the number cannot be negative), the smallest value would be 0. Thus, zero would be one more than the largest number, and the largest number would be one less than zero.

- Thank you,

Matthew Robertson


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