Leibniz and Fractals in a Theological Context
In my opinion, the intersection of Mathematics and Theology happens at infinity. The mathematical and the theological concepts of infinity are similar, mainly because we cannot comprehend the infinite—we are just aware that it exists.
"What would he not have said with that power of eloquence he possessed if he had gone further, if he had known that all matter is organic everywhere, and that, however small a portion one takes, it contains representatively, by virtue of the actual decreasing to infinity that it encloses, the actual increasing to infinity which is outside it in the universe. That is, each small portion contains, in an infinity of ways, a living mirror expressing the whole infinite universe that exists with it; so that a sufficiently great mind, armed with a sufficiently penetrating view, could see here everything everywhere"
-Gottfried Wilhelm Leibniz on Pascal
Leibniz spent much his time in Paris focusing on studying mathematics. In “Double Infinity in Pascal and Monad”, an excerpt from some of Leibniz’s unpublished writings, Leibniz discusses the idea of infinitely self-repetitive entities, posing the idea that the universe itself could be an infinite entity. He expands on this idea and uses it to explain how although God's infinitely greater than us, we too, are beings infinitely greater in the great scheme of things [1]. Despite the brilliant translation by Grua, Leibniz can be a difficult read. However, from my understanding, the self-similar nature of the universe leads to the idea of a kind of infinite zoom. In my understanding, Leibniz is arguing that god is the endpoints of the zoom. He is both the infintessimally smallest piece and the infinitely greatest piece. The point is, God himself is beyond self-similarity. We, being created in God's image, are spiritually similar in that our souls are endpoints as well.
In conclusion, self-similarity confirms the existence of God because he is the mathematical limit of infinity, which, unfortunately, we also do not understand.
