Most people think that mathematics is not spiritual or creative. My experience, however, is just the opposite. The one place I have found completely unbounded possibility and spiritual awe is in mathematics.
Did you know that there are different "sizes" of infinity? The natural numbers are infinite, but they are a "countable" infinity, meaning that each element in this infinite set corresponds to a natural number (1,2,3,4,5... and so on). However, as the mathematician Georg Cantor proved, the real numbers are an even LARGER infinity, an "uncountable" infinity. And there are larger, and LARGER infinities beyond that one: an infinite number of infinities, nested inside one another like an infinite number of Russian Dolls. Cantor gave each infinity a cardinality, designated by the the Hebrew letter Aleph. The infinite series of infinities he listed as...
Huh? What? Uh... How exactly is this spiritual or creative? Well, consider this...
Imagine God has a book with an infinite number of pages. He decides to put the name for every object, concept or action into this book, with each name having its own page. He calls this book, The Book of Names.
The Book of Names is has a "countable" number of pages (each page has a page number) that goes up to infinity. This should be enough for every possible name, right? But God discovers he has a problem.
Collections of names can be gathered together into subsets, some finite and some infinite, and all these subsets are called "Stories." God realizes that each of these stories will themselves have a title (or name), which will need to go into The Book of Names.
But (as the mathematician Cantor has proven), the book with an infinite number of countable pages is too small to contain all the possible stories made up of collections of the names (words) on it's own pages. As it turns out, God needs an infinite library filled with and infinite number of books, each with an infinite number of pages to contain the names of all these stories.
He calls this The Library of Names.
Is he done now? No, he is not. He soon realizes, as Cantor did, that this library itself has an "index" of all the books in it. In fact, there must be an index for every possible library filled with a subset of books from the main library. Each of these possible sub-libraries must have a name, and the index of this infinite number of sub-libraries is too large to fit in the original Library.
God needs a CITY with an infinite number of infinite libraries. The City of Names.
Which leads him to realize that this process naming, storytelling and indexing is never ending. He discovers he will need a PLANET of Names with an infinite number of possible cities, then a SOLAR SYSTEM of Names with an infinite number of possible planets, then a GALAXY of Names with an infinite number of possible systems, and then a UNIVERSE of Names with an infinite number of possible galaxies...
It goes on and on, with multiplicities stacked on multiplicities, until god realizes that there is no limit. No concept of infinity is large enough to contain itself and all possible names. Even God cannot possibly understand and name himself, for he would need an infinite number of infinite Gods just to name all of his own possibilities. God is not "one." God is pure multiplicity. God is an infinite number of infinite names, unknowable in its totality, even to himself.
Chew on that,
- Sean Hood
(P.S. If this subject blows your mind, read The Library of Babel by Borges, or The Library of Dreams in Neil Gaiman's Sandman, Being and Event by philosopher Alain Badiou, and of course the work of mathematician Georg Cantor)
(P.P.S. Oh and also try Arthur C. Clarke's "The Nine Billion Names of God." With the creepy ending, "Overhead, without any fuss, the stars were going out." This one was suggested by computer genius, Kai Lui.)