Laird Robert Hocking

Statement

As a kid, I grew up exploring coastal British Columbia, sometimes bringing home treasure that I found. I would sometimes feel an intense need to find out what the view is like from a mountain visible in the distance. Similarly, as an adult I find myself intensely curious about, for example, "What do 3D cross-sections of 4D Menger sponges look like?". In both cases, an answer exists - I just have to go out and find it (either by climbing the mountain, or by doing the math). In this spirit, I see mathematical art less as a creative process and more one of exploration and discovery. Just like when I was a kid, I rarely find anything interesting. However, I occasionally stumble up a treasure which I want to take home (with a 3D printer).

Artworks

A 1972 result by Stephen Hawking rules out the existence of black holes with nonspherical topology in spacetimes with three spatial dimensions, provided, among other things, that "reasonable" energy conditions are met. In this work, the first step was to create a 3D black hole with the topology of a torus by violating these conditions. A toroidal event horizon allows one to "entangle" the black hole with a second, physical torus by joining them like two links in a chain—this was the second step. The physical torus is a hollow shell with star-shaped holes and light emanating from within. This is the sole light source illuminating a virtual environment in which the two tori are placed, leading to intricate patterns of illumination.

A 1972 result by Stephen Hawking rules out the existence of black holes with non-spherical topology in spacetimes with three spatial dimensions, provided that certain conditions are met. In another work, I violated those conditions to get torus-shaped black holes in 3D.  This work instead explores hypertorus-shaped black rings in 4D, where no such violations occur. 3D black holes have a 2D shadow - a black region in the viewer's 2D field of view.  Similarly, 4D black rings cast a 3D shadow.  Here I have etched in glass the 3D shadows of two black rings.  Instead of a torus, we obtain a surface with genus at least two.  However, more holes appear as the resolution increases, making the true genus unclear for the time being.