The Fourth Paper
‘The year 1904 was one for the history books — literally. It was the year of what almost didn’t happen. A young and essentially unknown physicist by the name of Albert Einstein was at the time a patent clerk in Bern, Switzerland. He had some big ideas about the universe, and the notions of space, time, and gravity within it.
Young Albert would efficiently and diligently carry out his work and be done by late morning. This then allowed him to work on his physics ideas for the rest of the day. One Tuesday morning in July of 1904 Albert — or Nootsie as he was affectionately known to his friends — finally completed the third of three absolutely groundbreaking papers that within a few years would take the young physicist from an unknown to one of the most celebrated scientists in the world.
But on that particular Tuesday morning Nootsie was struggling. It was understandable. The guy was about to send out years of work to be peer-reviewed by other physicists who would determine if his papers were sufficiently important and mathematically rigorous enough to be published.
Nootsie was worried. He couldn’t make up his mind if he should send the papers off or not. His mind kept going back and forth on what to do, and the two fried eggs he had that morning were flopping around his stomach like unhinged gymnasts in a bouncy house.
It was too much to deal with. He needed to call Yaakov. Yaakov would know what to do.
Albert explained his dilemma to Yaakov. Yaakov listened and took it in, not interrupting. When he was done Albert waited. Only silence and the low steady crackling of background noise cut through the telephone line. Eventually, Yaakov broke the quiet.
‘Listen to me Nootsie. Publish the first three, and bury the fourth. No one will believe it. It’s too much.’
By 1905 the entire world knew who Albert Einstein was. Even as that fourth paper — the most astounding of them all by far — never saw the light of day.
When Kurt Godel, arguably the greatest mathematical logician that ever lived, met up with his close friend and intellectual equal Albert Einstein after his death in 1975. Or more precisely, with the transcendental essence of who Einstein had become. Godel had only recently passed away, and so was seeing it for the first time. He was taken aback.
‘Did you know it would be like this? Could you possibly have imagined?’ Godel asked his old friend, who died several years before him.
‘Yes, my dear Kurt. Or rather, a version of it in my equations.’ It had been a very long time since Nootsie thought about that fourth paper.
It isn’t clear exactly when Kathryn completed the mathematical proof of it. An analysis of her notebooks suggests that it was sometime in the fall of 2031. Possibly before the end of October. What is certain is that for two years after its completion, she didn’t tell anyone. Not her colleagues, not her family, no one.
For two years she struggled not with the technical construction of the proof, the mathematical structure that followed accepted rules of progressive logic to the final conclusion of what she proved given a starting set of assumptions — axioms. No, she struggled with something much deeper. Something of tremendous broad and far-reaching consequences that she knew would affect everyone. Literally everyone. Every human being that had ever been born, alive or dead. She struggled with the interpretations of what she had proved.
The contents of Nootsie’s fourth paper had been rediscovered. And it was no less unreal and astounding now as it was well over a century earlier. Who knows, for all we know Einstein had rediscovered it himself. It could have been discovered and rediscovered over many years potentially. Buried every time. Yaakov was right. No one would believe it. But yet here it was again. It just wouldn’t go away.
Mathematics is this beautiful and private world of pure thought and pure reason. There are no wars, no hunger, no pain. No suffering and no regrets. Only beauty. Beauty in its purest form without blemishes and without the messiness of the physical world. It is a product of thought and reason. It does not have any physical counterpart and it is not an approximation of anything. It is by its very construction and conception its own self, and does not rely on or need to be apologetic for being represented by a less than perfect bastardization of its true essence. Gregor Cantor, who discovered infinity, viewed his work as God’s work. He proceeded Albert by many years. It was a spiritual experience for Cantor not in a religious way in the sense of blind belief based on the teachings of others, but in the sense that if God is truly pure and perfect, mathematics is the manifestation of such purity and perfection in the universe and its imagination. In a transcendental yet very down-to-earth and tangible real way, mathematics allows us to feel and experience God, the term here meant as a label for such transcendental perfection, not by having to blindly believe in Him, i.e. by having ‘faith’, but by being allowed to actually ‘see’ Him through understanding and logic. No faith is needed. (That is the beauty that Katie and Albert had realized.) To the enlightened, God is not asking to simply believe in Him without cause, He is providing the tools necessary to experience Him, to ‘see’ Him, directly. Of course, such a gift (rightly so?) does not come easy, and the requirement for such enlightenment is a commitment to a labor-intensive, very deep, very prolonged introspective inward journey.
Before Albert and Kathryn, Gregor Cantor had discovered it. The fourth paper existed before it was ever a fourth paper. Cantor couldn’t take it. Infinity killed him as it was. Literally. He committed suicide. This would have tortured him before doing so. He burned it instead.
To exist as a stream of energy is to be integrated into parts of the universe in such a way that one’s consciousness is shared with those of others. In fact, there is no sense of self in this realm. No physical boundary that separates ‘you’ from everyone else. You are aware of your thoughts and feelings and your own imagination and creativity, but looking towards the horizon of your inner thoughts there is a seamless transition to the thoughts of others and everyone else. It is a bit like crossing the event horizon of a black hole. The individual crossing it notices absolutely nothing. There is no horizon. You don’t feel anything different. It is only from the perspective of a distant observer that at the horizon all time stops.
This is what existence means to a class of living beings that permeate the universe. That fill higher order dimensions that humans cannot detect and are aware of, at the same time that they surround us. But this is not a one-way street. These beings cannot see, feel, experience or detect the finite and self-contained existence of human beings. Or any similar life for that matter, on this plant or others. We are like shadows passing in the night. A physical event that passes without perception or consequence.
The one commonality humans have with these beings is mathematics. The universal and transcendental language. They communicate their thoughts with one another by synchronizing their energy. The integration of pure thought and reason.
At approximately the same time that Kathryn completed her own proof, one of these beings completed theirs. They shared it with another being, a cosmic energy version of Yaakov.
‘The proof is real. It’s complete.’
‘Listen to me. Listen carefully. Burry it. It can’t be correct. It is impossible for such physically constrained and limited beings to exist. We would collectively know if they did. They just aren’t real.’
The fourth paper. To be rediscovered.
