An Incompleteness Theorem
by Josh Potter
If something were true, God would know it to be such. If something were false, likewise, God would know it. This is His omniscience – paramount rationality. It can be said that all rational beings believe in their own existence. Even those of a fictitious nature must believe in their own existence to be deemed rational. Therefore, in God’s omniscience He believes himself to be so, and so He is.
This, Kurt Godel will think, and then he will die.
It will not be on account of his weak heart, although he has feared this all his life. He will die of starvation. The skeletal structure of the man he had been will hardly test the springs in his mattress. A can of pureed beets will sit on his night stand unopened; he will not have touched a morsel in weeks. He will know it to be poisoned. By whom he will not know, but this will not change the inevitable.
He knows the conspiracy for his assassination won’t be proven, even by himself, but that it must be so outside his own sphere of comprehension. His enemies are many and yet he knows not who they are. His superior reason pit against another’s will not be enough to save him. His mind working is, alone, his mind working. The problem, he has determined, is in the other’s mind. His only hope is for a larger mind that may reconcile his with another. This is the first time in his life he has experienced hope and knows it not by name.
He will die in a type of peace. It is inaccurate to say he will take solace in the belief of a higher power. The power is not higher, and the action is not belief. Nor is it knowledge. It is a type of inference. It will not bring him comfort. He will die ill at ease but at peace. He will die with certainty. He will certainly die.
Kurt Godel is in the frozen food aisle. Clustered neatly in the corner of his cart is a stick of butter, baby food, and a bottle of laxatives. He is searching for pureed beets. Were the aisles arranged like the limbs of a tree, all sprouting off in rationally inferred directions from the central axiomatic corridor, he would have found them, without thought or judgment, next to the baby food.
He knows that this can never be the case. He knows that such a system, encompassing all of his grocery needs, will never be devised, can never be constructed. Noticing a block of frozen spinach, he knows that this system could never sort itself such that spinach in its fresh, frozen and canned form would be found down a singular branch-like aisle.
He is not discouraged. Survival, he knows, is a matter of following such secular symbolic systems regardless of their overarching whimsy. E=mc2; two rings + two signatures + two blood tests = marriage; judicial + executive + legislative = democracy. It’s true as long as it’s consistent.
In vain, he arrives at the checkout and counts his change.
Kurt Godel yawns. It is his wife, Adele, who has brought him to the opera. He has never cared for the opera. Scratching his ankle, he wonders why.
Upon the stage before him, people dressed as people they are not act out a story devised by another person not present before him. What they say is not what they think or feel but what they have learned to say. The story is an isolated incident beginning at 7:30 and ending at 9:00 with a short intermission during which the story does not exist because it is not being performed.
To him the story is not truth. It is artifice. He looks to Adele. Her eyes are wet with emotion. He opens his mouth to ask her why and she places a hand on his thigh.
Between 7:30 and 9:00 this fictitious story, written by an entity removed from the immediate scene and played out by people pretending to be others has the capacity to simulate a truth, however incomplete, true enough to illicit emotion in Adele and earn himself affection.
Kurt Godel rushes from the theater and home to his desk. He spends the rest of the evening writing equations.
Kurt Godel would walk with Albert Einstein on Sunday mornings. They both took great pleasure in this leisure activity. Often, Einstein would whistle full symphonic movements. Often it was Beethoven. Always it was the violin section.
Godel had perfect pitch and would be familiar with most of these tunes. He would have devised lengthy mnemonics to memorize the notes in the progression. He could recite them backwards. At Einstein’s request, sometimes Godel would accompany him. Always it was the cello line. Always he preferred to hum.
Kurt Godel became a US citizen.
He spent long nights pouring over the American Constitution, optimistic for a system that would not permit totalitarian fascism. The
English language gave him little trouble. Despite its irregularities, its logic was sound.
Albert Einstein, who often accompanied Kurt Godel on morning walks, agreed to go with him to the courthouse. They sat in the back of the car, Albert Einstein in his scarf and Kurt Godel in his ski mask. Albert Einstein advised Kurt Godel to remove the mask upon entering the building and not to speak of phantasms.
The judge was startled to meet two figures of such eminence and decided to keep the hearing short. He offered Kurt Godel a Danish but Kurt Godel declined. Cutting to the chase, the judge asked him if he was glad, after his years in Nazi-occupied Austria, to become part of a system incapable of producing an evil dictator.
“On the contrary,” he replied. “It is possible. I have found an inconsistency.”
The judge knew the truth in Godel’s words. He was not, however, amused. Einstein chuckled and countered his colleagues words with a very funny joke. Kurt Godel did not laugh. The judge knew also of the danger in Godel’s words but allowed himself to be diverted. This, to him, was a safe and reasonable response. Godel opened his mouth and Einstein raised an index finger to his own pursed lips.
Kurt Godel became an American.
Kurt Godel carried the one and paused. He felt the one may have already been carried. He checked back over the figures and found no redundancy. Instead he found a gap in the equation, a section not yet notated. This did not trouble him. He was content to wait for a future moment, an afternoon the following week, to fill the foundation in beneath the part on which he presently worked. Still there was the deja vu.
Kurt Godel exclaims that “X is not an MP number” and is kicked in the shin. He falls to the ground, but not for his logical theorem. The boys have mistaken him for a Jew. Adele Godel, his wife, is swift to smite the urchins with the handle of her umbrella, and they flee to a nearby alley. Arm in arm, Kurt Godel whispers his fears of what more could come his way at the hands of those who understand such a theory. Schlick, his mentor, has been dead for one year – assassinated.
He cannot make it all add up and this is why it makes so much sense. His is probably bleeding, although he dares not lift his pant-leg. The system is present and irrefutable. On the page, the numbers can be crunched. The logic is consistent. Within the system, the truth is self-evident. What results, though, is problematic. It is neither right nor wrong. It cannot be proven or disproved. In its incompleteness the formula is complete. For now he must feign Nazism. He must move to the US. There is no one he can trust. He clutches Adele tighter.
Kurt Godel looked out his window and when he looked back the equation was complete. A hummingbird had floated just outside the pane, sipping from one of Adele’s flowering trellises. He had been stumped for an hour and allowed for his attention to stray. When the bird flew on, he returned to the work he now found finished. It startled him, but only momentarily – no more than one is startled upon wandering into a dark room and flipping the light switch to find oneself staring at their own reflection. He looked back to the window but it was frosted opaque. When he looked down at the page again, he found it blank. This troubled him more. He rose and opened the window to let the cries of playing children inside. He could see a kite in the distance. When he returned to his seat there was a fat folder set deliberately upon his desk.
The hairs on his hands were white as chalk.
Kurt Godel will put down the phone and turn on the television. He will have invited Albert Einstein for a walk in the park but knows well that he will not meet the physicist at the old stone bridge. He will instead watch Snow White and the Seven Dwarves for the fifth time this week. He will proclaim it the most beautiful work of art he has ever known.
He will envy Snow White and wish she was there in his living room with him at that very moment. In his frail state he will know it is impossible for him to build the rocket capable of taking him to her. If she would only get her team of dwarves to build such a ship, he knows she could come to him. When she gets there he will kill her and fly back to capture her dwarves. Such a team, he knows, would make the perfect body guards, each with their particular skill and drive for the greater good of the team.
With such a team he would not need to make phone calls inviting his nemeses to meet him in distant places where he knows they cannot hurt him.
He will stare into the TV screen and know that she will come to him. It cannot be disproved. He will remember the revision he made to Einstein’s relativity and remember how Einstein scoffed. He will scoff himself at Einstein’s scoffing.
Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undermined in every possible universe.
If time travel is possible, then time itself is impossible.
Because the universe is spinning and not expanding, a sufficiently long trip in an adequately engineered rocket could land the traveler at any moment in the past.
If it cannot be proven untrue in this universe, he will know it cannot be untrue on the other side of his TV screen. Still, he will sweat in fear.
Kurt Godel peers down into his glass and knows not if what he sees is a memory. Tiny flecks of dust float in arbitrary patterns across the still skin of water. Everything is there and it all makes sense. They appear to him like people, bouncing into one another and proceeding onward to an indefinite destination. From above the microcosm he is brought to tears by its beauty.
His bedroom door swings open and Kurt Godel cringes. It would not be illogical for his distant, unborn, great-great grandson to walk into the room, now a similarly elderly man, and put a bullet in his ancestor’s frail chest. He closes his eyes to remain in uncertainty and only opens them after a pair of lips have been pressed to his forehead, a jar of something red placed on his night stand, and his door pulled shut once more.
About the author:
Josh Potter resides in the western half of the northern hemisphere where he tries to make himself useful. This is his first published piece.