A New Theory of Infinity

I am telling you this for what will follow, so that you really know where I am coming from. I am not prone to far-fetched nonsense. I think the moon landings were real and that the Earth is, roughly speaking, a sphere. I am not a crystal person and nor do I have a desire to attribute every mood to one of Jupiter’s moons or Mercury being in retrograde. I don’t even own a candle.

And yet, I am also a person who now realizes that our human understanding of the world is incredibly limited, and that there is a bias not to believe things that don’t fit our worldview. What I am saying is that sometimes we can’t accept the truth that is right in front of our eyes. And that sometimes the mad people of one era become the sages of the next.

I tell you all this because, over the course of the following pages, you may end up thinking I have lost my mind. So please consider the case of Georg Cantor.

As you are studying mathematics at university, I am sure you have heard of him. I think I even used to talk about him in class. The guy who came up with Set Theory at the end of the nineteenth century. Anyway, when he proved that there were, technically, different sizes of infinity, he was branded a heretic. He was criticized and ostracized and made a laughing stock. He couldn’t take it. He fell apart because of what he had discovered. He had his own belief system questioned. To stop believing in a single infinity was to believe the impossible. He had nervous breakdown after nervous breakdown and ended his days in an asylum. But he was right.

Mathematically, at least. There are different sizes of infinity. But it took a long time for everyone else to see what he was seeing.

Now, I am no Georg Cantor. But I too have had my worldview flipped on its head recently, and have felt a need to tell someone about it. I too have seen things that challenge me to my core. You emailed at just the right moment because I think my need to tell this story has coincided with your need for answers.

So, the question is, are you ready for a new theory of infinity?