For the last few years ( I took two gap years before coming to UBC) I have been working as a high school Math tutor… not because I am particularly astounding at Math, but because under the circumstances it is a flexible job, there is a lot of demand and I somehow manage to do a good job of turning C and below students into A students. I don’t think it is necessarily a job that you need to have a degree to teach with.  While I know next to nothing about higher level Mathematics, I have completed grade 12 and that seems to be sufficient enough to teach it well. Depressingly I often see signs up for tutors who have degrees, even masters who charge about the same amount per hour. It makes me feel like even if I spend my next billion years in school, $30 per hour is probably the most I will ever be paid in my life…

Anyways in trying to explain sinusoidal functions and trig e.t.c. you come across a whole bunch of the ferris/bicycle/ anything wheel problems. That got me wondering about what would happen if you put a point on the base of a cylinder and rolled it along a plane. What shape would you get? My little brain can’t quite figure this sort of thing out on it’s own… So I decided to do my own little experiment to find out. I found a shot glass, taped a piece of pencil lead into the inside edge and rolled it along an old book. It turns out that you actually get semicircular shapes with a period of 2*pi*r… hmm not what I thought, but also not very exciting. Then I wondered what would happen if you rolled the shot glass around another shot glass of the same size. That was a little more interesting! The shape was somewhat like a circle but with an indent. I recognized the shape as being the main one in the Mandelbrot set. I wasn’t entirely sure though, so I went to check if it was the same shape on Wikipedia. Yes it was!!! Amazed by my discovery I started reading the article in a little more depth. Unfortunately upon reading the byline I found out that the shape already had a name: a cardioid and people had known about it hundreds of years ago.  And yes, they made it exactly the same way I did (ok perhaps minus the shot glasses) and there is a billion different wikipedia articles on pretty much every shape you could imagine… Don’t you just hate it when you figure something out, only to learn that in fact it is nothing new?

It seems to me that because we are essentially taught how to think, that we follow the same patterns over and over again. It seems like learning is just building upon those thought patterns that already have been established. And yet so many different thought patterns and things exist that a human lifetime is barely enough to understand anything at all. Sometimes I feel like we are only limited by what we already know. If we can go infinitely small and if we can go infinitely large, perhaps the smallest thing is also the greatest. <3