Ever since discovering in the fifth grade that a standard coffee mug is topologically identical to a donut, I’ve been fascinated with the study of space and the relationship of points in three-dimensional space. It is the combination of my combined interest in rocks and topology, in fact, that led to my studies in rock deformation. Track the points and their velocities under varying pressure, temperature, stress and/or time. (I trust this satisfies my parents’ curiosity as to why I purchased and played with tubs of Play-Doh well into my grad school years, as well as what Play-Doh has to do with the visualization of objects using a computer. Pixels don’t get your hands dirty and can be easily saved.)
A rock is a beautiful thing unto itself, but looking at a deformed rock and seeing geometry in it is even more mind-blowing. That there is an underlying material pattern in the visible overprint of entropy. For example, the Pacific coast bears formation after formation of mangled rock thanks to its active tectonic plate boundary. Take a closer look at, say, a schist from that locale. The first thing a stratigrapher will wonder is who took a nice, neatly-deposited sand and shale package and, through myriad geological processes, made it look like this piece of garbage. The structural geologist instead discerns the patterns of stretching, squeezing, and the physical and chemical reconstituting of minerals, while the petrologist makes a thin section of the rock, places it under the microscope and sees the most breathtaking array of minerals in all of their colorful glory. Following this, the object of the investigation is to deconstruct and simplify — turn the coffee mug into a donut — in order to understand what happened between the deposition of a grain of quartz and its eventual exhumation in a chunk of schist. Here’s the most lovely rock you’ve ever seen. Now calculate x. It’s a fine job, let me tell you. (Fine? Get it, get it.)
Schist: Hand sample (Top); Under the microscope (Bottom)
This is also why I love art in which you can see mathematics.
