“The last computable infinity,” he said, “is the biggest infinity that we can work with. Beyond that is a host of infinities, infinitely incomputable and yet infinitesimally out of our reach. There are infinities greater than other infinities, ones that we can classify and construct and others that are a magical mess of numbers and bits, stretching on as far as the Turing Machine’s tape will.”
He means forever.
“Infinities render problems undecidable, unrecognizable even. We cannot know some things with certainty because we lack the patience, the practicality, the time to watch our machines run forever. We know not what it means to run forever, for you to press a button today and for the machine to never stop. Not before lunch, not by the time you grab your bag and head for the door, not by the time you return tomorrow morning, bright-eyed and hopeful. It will be running when you come back from the weekend and it will be running when you come back after New Year’s, not this one or the next one but the one a decade from now. You will look at your screen and wonder if it’s frozen or broken a quarter century from today, but it won’t be, it will just be running, trying a never-ending combination of inputs until it can be sure of the answer it gives you. But you give up, maybe not a quarter but perhaps a half-century from this moment- fifty golden years of your life gone, waiting on an answer, and the machine is still running. You stop breathing one day, and the machine goes on. Your great-grandchildren whom you haven’t met yet have great-grandchildren of their own that never knew them, and when they grow old and retire the machine is still working, tirelessly. The world ends, one day, and the machine dies like everything else, but it is not yet done. It will never tell you the yes or no that you had wondered, eons earlier.
“So the question I ask is not a binary one, for those are hard and our tools, no matter how fast, may never solve them.
“My question is, where did the infinities come from? Who created them, who overlooks them, keeps count of them, orders them? Who comprehends what the word means, the one that rolls off the tongue in four quick syllables but does not cease to unroll, when we try to make it stop?
I’m looking for the Entity that will be there, when all is gone, enfin.