And by extension metaphors, stories, pictures, and math. During my lunchbreak today, I read about Kurt Godel, a mathematician close friends with Einstein. The story was about Godel's discovery of a flaw in the US Constitution that would allow the government to shift to a dictatorship--this flaw he began to explain during an interview for US citizenship. This fun historical nugget led me to learn other things about Godel, the most intriguing of which was his mathematical "God proof."
Before we go on, let me explain that my lunch break is often filled with a sort of random and fragmented search for entertainment and knowledge, and one never knows where one will end up. This takes just enough of the mundanity out of the day to make it bearable. This mathematical (ontological) proof was succeeded by a YouTube video explaining Graham's number, inexplicably larger than the inexplicably large googolplex.
Mind effectively blown, this was followed by a quote found via Wikipedia while attempting to understand the ontological proof better, a quote by mathematician Georg Cantor that in such a strange way tied the other two discoveries together. What follows below was a quickly typed up explanation to myself so as to make the connections. It rambles a bit, and likely the logical leaps are perilous without being in my head or without the proper time to pound it out. It became for me a kind of validation of my path choices, of my obsession with words and symbols, and thus a validation of my choice to be a writer and storyteller. Explaining to yourself on paper is something I suppose writers do.
The explanation to myself begins with the Cantor quote. I make no guarantees as to the accurateness of the newly discovered information, nor as to the tightness of my logic. I'm not sure I even vouch for the sanity of it.
“The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.” -- Georg Cantor, mathematician
Mathematicians struggle with infinity because math doesn’t work so well outside of finite (created) bounds. This led Blaise Pascal to say some crazy shizznit like: "Nature [God] is an infinite sphere whose center is everywhere and whose circumference is nowhere.” This fries his mathematical noodle and he is launched into the metaphysical abyss (see Borges's "The Fearful Sphere of Pascal"); you just can’t do good, end-game math in a world like this.
For example, a googolplex is so large a number that there isn’t enough space in the observable universe to write it out one number per atom.
Graham’s number is crazy bigger than that, rendered in certain ways, like below, though these aren’t the only ways because nobody can find the right symbol to represent it. Graham's number hold's the world's record for largest number used in real math.
The number's so big we only know the last 10 digits, and we know it ends in 7--the rest is a mystery, or as I render it:
…2464195387
In Graham's language, it looks like this:
In another, similar language, like this:
Naturally, there are in infinity higher numbers, existing currently only in computer science and apparently represented as TREE(n). TREE, it appears is magnitudes larger than G (Graham’s number) and also larger than another computer number magnitudes larger than G: AA(187196)1. Whatever that means.
You see the absurd symbolization difficulties we get into when we try to stretch our chimpanzee math out into infinity, then, right? Once we reach certain numbers—which certainly are real if incomprehensible—we reach equivalent god planes that must be rendered in other absurd symbols like G-O-D. Real but inconceivable. Expressible, but not.
Now, this Godel character, Einstein’s pencil-neck buddy, wrote in weird math logic Greek symbols what translates as the following:
"God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist."
Just happens to be a nearly exact match of the argument of an 11th Century Catholic Saint named Anselm of Canterbury.
Anyway, you might say we can’t conceive of a bigger number except within contexts we have created, and even though the context is imaginary, the bigger number is real because we must be able to count into infinity. God exists in our minds, but we could conceive of a greater existence than just in thought, which is in reality, and God existing in reality would be the limit of how we might conceive him, the inconceivable and real number. Bang, thanks to the holy semantics of ontological word play and the laws of argumentation by definition, God exists within this weird paradox, one where imagining God to exist creates the existence in perpetuity represented by inadequate symbols, one where God is composed literallyof everything, and the standard scientific requirement that a demonstration of a posteriori negative proof is necessary to prove an existence—if indeed existence can be proved--is moot because a thing that is everything naturally encompasses its impossible opposite, which is nothing, because even the tiniest essence of nothingness is immediately a somethingness and God; circular as it is--with a finite circumference arrived at via infinite constant, i.e., pi), here we are again at the limit of that which we might conceive, which is where God and some absolute infinite lives.
In other words, see John 1:1, which says in the beginning was the Word, and the Word was with God and the Word was God; and note the Genesis is brought forth with (not literally) speaking the universe into existence, in essence telling a story, in essence slapping symbols (metaphors) on that which is beyond symbols, which is what writers, poets, storytellers, musicians, artists, and mathematicians do in pathetic and plastic imitation. John used a generic symbol, "word," to stand in for what cannot be expressed. Before and after him, thinkers, storytellers, and mathmaticians have done the same by substituting their own symbols.
And that, my friends, is perhaps for me the incarnation of Borges's "Vindication," of which he wrote the probability of finding was zero. I write because stories and symbols are how we find God, who lives inexplicably within and without us.
