I recently attended probably one of the strangest topics for a church to offer a lecture on: The Structure of Infinity. I have to say although odd, it was fascinating as it was a primarily secular, or perhaps I should say mathematical exploration of the idea of infinity.
The discussion started simply enough with a review of Calculus, discussing limits and such but quickly jumped to mathematicians such as Cantor and Dedekind. Of particular note was Dedekind’s discovery of the “purpose” of irrational numbers – to separate rational numbers from each other without breaking the continuum of rational numbers. This set the stage for the main thrust of the talk that delved into set theory and essentially the characteristics of infinite sets.
Having done fairly decent in math in high school and university, I followed the discussion well enough but our minds get easily blown when trying to map the discussion to the real world. Even Cantor and his exploration of infinite sets led to both wonderment and depression. It is likely that his wonderment led to his conversion to Catholicism while his depression resulting from a sense of failure to prove all his theories and therefore also successfully dissect and prove the properties that he found.
One point that definitely caught me was the idea that the infinite is isomorphic, that is, can be corresponded one to one, with both lesser and greater infinite sets. In the smallest distance, there is an infinite number of points. In an entire galaxy there are an infinite number of points in space. The sets correspond perfectly if you were to number each of those respective points. I’m reminded of the idea that we could all be tiny specks on a much larger snow globe, like the recursive sequence at the end of Men in Black.
Discussing infinities of infinities remind us that we cannot attempt to grasp God’s personhood and feel that the box we build for Him is sufficient to contain Him. At the same time, we should realize how sensible it is to see our limited selves and creation around us and see that infinity is contained within the finite, the created. I see how in a scientifically-minded world this can still help to build our sense of respect for the infinite dignity of others and our stewardship for creation. Sacramentally we see how God can exist in a simple piece of bread and drop of wine. The finite not only can contain the infinite, but mathematically speaking must contain the infinite! Understanding this should do nothing less than restore our sense of awe and wonder in God’s greatness in all His infinites – His power, His creativeness, and His Love.