As I work through the problem sets about imaginary and complex numbers, a generous commenter to Electron Blue has explained i to me in a way which disperses the mist of mysticism with which I surrounded it in my previous posting. What a relief! And there I was waxing lyrical when I didn't have to. The commenter (as usual, all commenters to the Electron are "name withheld") showed me that i and other "imaginary" numbers actually correspond to quantitative things which almost all of us can experience in ordinary life.

The square root of a negative number will occur in the calculations of removing an area from another area, for instance. The commenter quoted this aphorism: "Imaginary numbers are not mystical. Your doorway is 2i meters tall." Similarly, as I read a little about the history of i, the reference text explained that i was implied even as early as ancient Egypt, when geometers wished to find the volume of a truncated (incomplete) pyramid.

Basically, i is involved in the measure of a negative area, that is, an area that is taken away. To put it simply, if you have a measured flat area, and you take away a square area from that area, then the measurement of the side of that removed square will be an "imaginary" number, the square root of a negative number. The area of a doorway removed from the plane of a wall is an i number, too.

This is, then, about "negative space," not some mystical imaginal world. (Alas.) Most artists are familiar with the concept of "negative space," either instinctually or because they had to sit through lectures about it in art school. "Negative space" in the context of art composition, is the space around a figure, the shape or shapes that are formed not by the figure itself but by the remaining space on the plane it occupies. Especially with geometrical or abstract art, "negative space" becomes as important as "positive space." You don't just fill negative space with a background. The example I quoted about the area of a square removed from a plane is a very simplified version of this "negative space." Either the figure (square) or the ground (remaining space around the square) could be "negative," and described with an i -number. I'm glad to have received some background on this matter.

Posted at 2:14 am | link