Thursday, August 18, 2016

Inside and outside

In The Last Battle, C. S. Lewis sketches a picture of heaven which is like an onion, with multiple layers, but with the inside of each layer bigger than the outside.

We can get a two-dimensional model by imaging a spherical space with an even bigger bubble sticking out of the sphere in one area.  A two-dimensional being could seamlessly transition from the original area to the bubble area. And of course we can enhance this by supposing bubbles on bubbles, larger and larger. The result would look like a snowman.

But even in the single bubble case, there is the question of the sense in which the bubble area counts as the inside and the rest as the outside. After all the bubble area is the larger one.

I think scenarios like C. S. Lewis's make us realized that the distinction between inside and outside may be rather arbitrary.

This reminds me of the joke about the mathematician who was given a rope and told he could have as much land as he could enclose. He made a small circle of rope around himself and said: "I stipulate that I am on the outside."