Paul Auster , whose eyes burn with the intensity of a star gone supernova, was staring me down, and not in a seductive manner. More like I was threatening his children.
Auster, a writer whose work I admire, was taking questions following a reading at my graduate school, and I’d asked him about his apparent obsession with money in his fiction. I imagine he was so sick of addressing this particular issue that he turned into a literary anti-superhero and tried killing his questioner with laser beams springing forth from his pupils.
Funny, I don’t mind being asked about my obsessions—in fact, I can talk obsessively about them.
They are broad and minuscule, sublime and ridiculous: The Mayor of Casterbridge, the Cubs, Rachmaninoff’s Piano Concerto No. 3, Elvis (Presley and Costello), certain unknown bands from my hometown, the nature (and unfaithfulness) of memory, Jackie Chan, evolutionary psychology, Spinal Tap, certain movie stars, astrophysics, criminalizing Bud Light.
Also, big numbers. Not the kind of numbers used in counting money, or grains of sand, or even atoms in the universe. Larger than that. Numbers like Graham’s number, considered the largest number ever used in a mathematical proof. (And if you will stick with this mess, I’ll actually show how this relates to writing. Or fiction. Or Paul Auster’s glare. Or all of them.)
Graham’s number is named after one R.L. Graham, who used it in a proof dealing with an really, really hard mathematical problem. What is fascinating about Graham’s number is despite the fact it was actually put to use, it is beyond human comprehension.
Yes, you can use it but not comprehend it.
The only way I can explain Graham’s number is via exponentials. (And if I mess up the math, please feel free to correct me).
Starting with: 33 = 3x3x3 = 27, which you already knew. But add another 3 to the top of the exponential string–just one–and you get the following: 333 =327=7,652,600,000,000 (That’s 7.65 trillion).
By adding an additional three to the stack, and it’s: 3333 = 3327= 37,652,600,000,000.
Don’t try this at home
Which means multiplying 3 by 3 more than 7.6 trillion times. In other words, stacking four 3s on top of each other creates a really, really big number. So big you can’t calculate it—3^3^3^3 is by far more than all the atoms in the observable universe (1070).
Simply stack “3″s that another 61 times (yes, for a total of 64 times) and you get Graham’s number, which is so far beyond the realm of human comprehension that it beggars the imagination.
Compare it to something most of us are familiar with: the googol (the number, not the site engine that deposited you here in search of pr0n-o-graphic pictures). A googol is 10100—a 10 with 100 zeros behind it.
A googolplex is 1010100—a googol a googol number of times. A googolplex is so enormous that if you tried writing out the number, and put each “0″ on an atom, there wouldn’t be enough material in the entire universe to do so.
Now consider this: Graham’s number is far, far, far larger than a googolplex, which is to Graham’s number as an electron is to the Milky Way.
In a sense, Graham’s number bigger than infinity, for infinity is at least comprehensible. To me, Graham’s number is another way of saying that numbers, which are a human invention, exist in their own dimension independent of comprehension. We understand the universe in ways that we cannot understand. Is that the coolest, most amazing, facinating thing ever?
What, you say that it’s not?
The most humbling thing in the universe
OK, so I’m a nerd. In a different life, I would have been a mathematician, if that life actually included aptitude with mathematics. Instead, I became a writer, but one of my preoccupations is describing the cool, the offbeat, the indescribable—like Graham’s number or Elvis Presley or the Cubs.
Like Paul Auster’s fixation with money, I am obsessed.
And if we aren’t obsessed with something, we really shouldn’t be writing.