I was in a flat somewhere in Edinburgh, Scotland when I got into a conversation about Euclidean geometry. My fellow undergraduate was studying mathematics (I was getting a Bachelor’s in chemistry), and had just learned a system of mapping three dimensional space using circles. This meant that what we had all been taught as children – x, y and z axes that were straight lines – was merely a particular way of looking at things. It had come from Euclid‘s approach to describing shapes mathematically. Instead of looking at space as being made of cubes and straight lines, you can look at it as circles and spheres. What we’d been taught as the way to map 3D space was actually just one way, based on one man’s theory. Whoa.

Then there’s the theory of light. First Newton said rays of light were made up of a series of particles or corpuscles (the corpuscular theory of light). My memory gets a little sketchy here but I believe this competed with a wave theory of light for a while. Sometime in the nineteenth century, someone set up an experiment to test which theory was correct. The wave theory correctly predicted the results of the experiment and won the day until Einstein came along. I can’t tell you what is happening on the pioneering edge of physics today but I do know that as recently as when I was in high school (or not so recently) quantum physics helped us to equate the corpuscular nature with the wave-like nature of light. Whenever I solved problems in Advanced-level physics, I knew how to choose which equations to use based on which aspect of light I was dealing with.  Continue reading →