I must admit that finding the inspiration to write this blog post has been difficult, which is likely why I’m writing this on the last possible day. To be completely honest, I’m a mathematics major who has been taking English electives because they are relatively easy to get through, and they are much more interesting that history classes. Because of this, my literary knowledge outside of what we have done in class is somewhat…. uh, limited. So I figured it made the most sense to write about something I actually know, math.
The basic concept behind the sublime — attempting to represent the unrepresentable — immediately got me thinking about the concept of infinity in mathematics. When first formally introduced to infinity it is convenient to think of it as a really big number, or, the biggest number. Doing this makes applications with infinity easier to understand. For example, the limit of 1/x as x approaches infinity is 0, because 1 divided by any really large number is a really small number. Make the divisor big enough, and the result can be considered to be close enough to 0. In reality, infinity is not a number, but an abstract concept of something without bounds. Basically, using infinity is a way of acknowledging that there is no biggest number, and instead seeing what happens when something gets bigger and bigger forever.
So back to the example of evaluating 1/x at infinity, we aren’t dividing 1 by a really big number and deciding that our result is close enough to 0. Instead we are seeing what happens to 1/x as x gets bigger and bigger:
1/10 = 0.1
1/20 = 0.05
1/5462 = 0.00018308
1/10,435 = 0.00009583
As you can see, our result keeps getting closer and closer to 0, so we say that 1/x converges to 0 as x approaches infinity. So infinity is a concept that is impossible to quantify or visualize, yet can be somewhat trivially applied to math in certain ways. Not only is this interesting to think about in relation to the literary definition of the sublime, it is interesting how extremely important such an abstract concept is to something as huge as mathematics. So, how do we represent the unrepresentable concept of infinity, well…. Just: ∞. Yeah that’s it.
A cool visual example of the sublime in mathematics is a fractal. Fractals are never-ending patterns that are self-similar. Meaning you can zoom in on a point and end up with infinitely many copies of your original image as you zoom in further and further. Here’s a cool video with some weird music.
Anyway I just thought it was neat how a concept from studying literature can be applied to mathematics. Thanks for reading, bye.