The Apprentice was always unique, always distinct, although part of The Game. All Apprentice had to confront those who understood the structure of The Maze, the landscape of The Game to be infinite. The Maze was said to be infinite and The Apprentice knew that this was true – but the Apprentice also knew that it need not be infinite. There were always finite possibilities, he thought, even in infinite landscapes. How else could he explain the centuries of observation, where one idea and the next and the next were exactly as he had observed, down to the detail? His ideas were no mere experimental science, inexact and doddering, but knowledge of a precision so studied that it could scarcely be understood when you were playing The Game.
The Maze was a field of finite possibilities with infinite points, or so it seemed. Cantor had seen the dust of a million instances and more fit into a plausible space, and had claimed to have come close to the truth that there was an infinity. Cantor was in error, the Apprentice knew, about the presence of uncountable sets. Conjectures, but not in reality, he thought – nothing in his centuries of observation about the infinite landscape of even the finite had belied this belief. In another age, The Game’s structure was discovered in the popular paradox of the Tortoise’s infinite steps. In Athens, The Apprentice sought to deliver the philosophers from the truth, as if an affirmation of tangible power over intangible thought. Kronecker was later influenced by The Apprentice, and became the deliverer of Cantor’s insanity. Cantor’s work stood discovered, despite this. In our own time a more benevolent kind was prepossessed with this self-referential game of finding larger infinities, or greater infinities or smaller ones, when Rāmānujan had conjured infinite series upon infinite series as the landscape of his discovery emerged from his mathematical foundations (although inspired by his finite religious underpinnings).
The sundry infinite series, Mandelbrot’s fractals (for he too was a victim of The Apprentice) and Poincaré (and he too, were it not for his inchoate pondering on dynamical systems with infinitudes of possibilities) were some examinations of the field of possibilities, but there was nothing that could be conjured to explain human behaviours differently than The Apprentice had understood them. He was obliged to – it was his solitary activity in all existence to play The Game, in The Maze. He wasn’t the only player, and hadn’t been the only one. He knew not where the others before him were, if they existed – he existed in a strange solipsism, where his memories and observations were all he had, and he was otherwise, like a force of nature – ageless, although visibly middle aged, timeless, although seen amongst society in every age on Earth. His features were unremarkable but for his eyes, which seemed glazed over like a million fires had burned in front of his eyes, or multitudes of grand infinities had unfolded, doling out the sights that would make the mundane appear insignificant. He had a demeanour which was oft-dismissed as quirky, slavishly romantic, like a raconteur whose age belied his appearance. His stories were parables, were foundations that were created to elicit specific human behaviours, and chance was his weapon. The Apprentice was a game master, and he ran The Game. The Game was not a solitary game but a multitude of games, as The Maze was not a place, but an infinitude of points, with a creature or object at each turn, with shared potentials, shared histories and memories. The infinitude was only an instrument to help arrive at the true potential of the race, which, The Apprentice knew, was finite. The Apprentice was born of memories, as much as of people. He was not human, but post-human, co-existing with human civilization as it progressed through the ages. He was not a force of nature, but acted like one. He was an influencer, using chance and a foreknowledge of the probabilities of events to act upon a field of what he felt were limited possibilities. Every time humanity proceeded to discover the range of possibilities; they would be limited, as all limited species are, by their limited behaviors. Humans were incapable of infinite fields of possibilities, and only ever larger ones, he knew, and his calculations always revealed finite degrees of freedom for events in The Maze. The Maze was, of course, infinite, as hope was ubiquitous. And hope was what The Apprentice used when he was The Gamer.
The Gamer was a player in the field of virtue that is The Maze, a manipulator of an arena rife with possibilities. What is infinity to The Gamer was, in fact, finite, to The Apprentice. The Apprentice knew that there was finitude and that the infinitude was a myth, but when he was The Gamer, he hadn’t been sure. What kind of game but a game of chance, he thought, could incite the reactions of people who were fraught with the uncertainty that only numbers bring? What justice could such people do? What decisions could such people stand by? Was he too driven by hope, as much as he would have liked to think otherwise? The Gamer had asked himself this a few times, but was too fixated on The Game itself to answer these idle ponderings. He was happier when in the thick of the game, posing a problem, and observing his opponent’s solution. There were puzzles to partake of, there were conundrums driven by chance. With every game, The Game got more complex, with every solution, one more revealed itself. A few more revealed themselves similarly, and it would seem that there were no limits to The Game. But somewhere, he felt, these games would end in the same results. There were strategies that seemed to make these easier, but they were all like the warehouse keeper’s woe. The warehouse keeper needed to keep boxes as they came in within a limited space, and the warehouse would have different visitors, different customers, that needed the boxes when they came in. These visitors, these customers, arrived at different times, determined by chance.
The Gamer’s conundrum seemed to be that there were only a fixed number of visitors to this warehouse keeper’s conundrum. He had found evidence in observation that infinitude was a landscape for the finite to exist – that the infinitude was a canvas, upon which the limited degrees of freedom of human events and motivations provided a nominal chance of occurrence for any of many finite events. Thus convinced, he who became The Apprentice felt he had no need for The Gamer, and therefore was convinced that he should not field himself in The Maze. The Apprentice now looked to finality, for what was destiny undefined by finitude, despite these finite degrees of freedom squandering an infinite landscape? What was the future of humans that were, by him, deemed to have finite degrees of freedom, calculated in The Maze? Surely, he thought, there would be a conclusion to this. The Game was, in fact, multitudes of games and survival of the species, was not, of course, precluded. Games not only deemed victors and losers, but also survivors, whatever the species were. With practiced patience, The Apprentice lasted hundreds of generations, as humanity (and their finitude) evolved. The Apprentice was coeval to all these generations as he was to the older ones, perhaps as The Apprentice himself, perhaps as The Gamer, existing among them and like them, while being unique, even enigmatic, but never so much as to seem different from them. Influencing them as he went along, he found no indications to belie his interpretations that there were finite ends, however far away those were.
Finitude amongst humans evolved, and the Higher Species, as it were, were now cognizant of the field of possibilities. They didn’t know The Game, of course, because The Apprentice was the only one who was allowed to know it (by himself), over generations. However, many now knew that the post-human half of their species would deem the result of existence as being a finite point, as a hive-mind existing only to observe and know, or at some infinitude. (The infinitude, most on both sides of the species argued, existed only as an unknown finitude). The Apprentice’s calculations for the finality, the final finitude or The Singularity, as he called it, indicated a few generations more. Expectedly, one half had realized finitude (a different one) in a hive-mind, and another would continue till they reached their destiny, which he foretold, was a different finitude. The Game was still infinite, however, and there was room to do so much more in infinite spaces. The Higher Species and the evolving species also continued to play The Game in The Maze. The Game continued to be played differently, and newer and newer discoveries continued to suggest to the evolving species that there were infinities. Like Cantor, Mandelbrot, Poincare or Ramanujan or any of the myriad souls after them in The Apprentice’s seemingly infinite memory, they had all affirmed infinities at some level.
The Apprentice imagined the future landscape of the human universe with this beautiful cadence of finitudes that seemed to indicate finality, evolution, points rather than ranges, absolutes, perfection and constants. These would be as point lights dotted landscapes at night on ancient human planets. These were the final stages of human evolution. They represented knowledge – the aggregation, the elimination, the evolution and the distillation of it, over millennia. How would The Game now change? What would happen when the last humans became hive minds and reached finitudes in their degrees of freedom because they needed all to survive for one to survive? Would The Game itself evolve? (It had evolved, in the past). The Apprentice was now presented with a legacy. This music of finitude from the cacophony of human behavior was indeed his accomplishment. He had been The Gamer, who influenced multitudes of populations and affected The Game in myriad ways. He was then The Apprentice, who at first only had a hunch on the finitude of races, on finality. Over millennia (millennia appeared differently to them), he had confirmed his thesis, that the universe of human evolution ends at a point – the hive mind was indeed going to be The Singularity.
When the hive minds of multitudes of evolved generations united in The Game, the degrees of freedom each possessed dwindled significantly, and they converged to fewer and fewer distinct finitudes. In a few generations, only a few distinct minds existed, and the field of possibilities dwindled as they were limited to only two. The Apprentice had but one choice in The Maze – to let the two evolve as they became his grand vision – Singularity.
The Apprentice’s grand vision, The Singularity, was soon to be fulfilled. In one moment, The Apprentice found himself isolated, with The Singularity inhabiting one point on The Maze, which was of infinite possibilities. The Singularity, as The Apprentice called it, was not truly a Singularity, however, since The Apprentice existed independently of it. The last thought unique to The Apprentice, was that he had only one degree of freedom left.
With no degrees of freedom remaining, time stood still for It, the culmination of The Apprentice and The Singularity, as there were no more strategies possible in The Maze. It pondered The Game, now with knowledge of The Apprentice. The Game had come to an end because The Maze, that infinite field of possibilities, had no room for merely It.