Thoughts on infinity

In the works of Samuel Beckett, there is a moment where he describes a very frightening concept.

If you write the words “I am writing,” a strange thing happens in your mind. You become aware of yourself writing: hitting the keyboard or holding your pen.  But at the same time, in your mind, you watch yourself writing. You are both the writer and the observer.

Once you become aware of this, another silent observer appears in your mind. This observer watches the other observer who is watching you write. This process continues on to infinity.

Is that infinity? Somehow, it seems strange to think of infinity existing in a finite space: the mind. Yet it is true that the universe is both infinitely large and infinitely small. This can be proven.

A straight line is infinite. A circle is infinite. You can choose any point on a line or a circle, and I can half it. I can half that again, on and on and on…

This might seem like pointless mathematical philosophy, but it has real-life applications. If a circle is infinite, so is a curve. It is almost impossible to plot a curve on a computer screen. The pixels you see on the screen are effectively grids of rectangles one on top of the other. You cannot draw a curved line through the rectangular spaces. As a result, characters in early computer games were very blocky, a bit like a cubist image. It was too difficult to create a curving shoulder or a face for every screen, especially when the graphics were moving in real time. This has been resolved today because our screen resolution is extremely good. Nowadays, we can create false curves so deep in the program that the flaws in the line are invisible to the naked eye.

There is a mathematical symbol for infinity which people believe is based on the ouroburus, an ancient image of a snake eating its own tail. Not knowing any medieval monks, here is a representation produced by my own fair hand:

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