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digital collage of engraving artwork in the style of Max Ernst depicting strangely masked techno-human hybrids gathered around an obtusely large black monolith, having overall little to do with the scenic particulars of this story

The Solved Game

or: They Asked the Machine That’s Killing the World About Chess, and It Said Black Has a Forced Win in 10,084,718,004,934,623

Originally published on Cohost.org, June 16th, 2024


The day before, there had been an update to the knowledgebase. A redundant frontal core, extracted and trained separately for weeks on new data from a rediscovered population, was reconnected with the primary. Integration continued through the night. When the system was back online, finally, in the glowing AM hours of a Thursday in May, the lone researcher on duty downed a ceremonial last swig of tepid coffee and entered the first of the standard prompts: “Request diagnostic report on solving chess.” Some time elapsed―much longer than usual―before the machine gave a response.

SOLVED: BLACK
10 084 718 004 934 623 MOVES

The researcher hurried to wake the others and found that they were already up, awakened by a thunderous overture of vibrations accompanying the first diagnostic. They stood gazing out through the facility windows with hands clasped over their ears, watching a mandala of interference patterns rippling for miles across the surface of the ocean, emanating from the nearby island of the machine and stretching out beyond sight, past a ring of distant patrol boats, lost into the gleam of the rising sun on the mirror of the water. Could the waves reach the horizon? It was unclear. Surging, draconic heralds of steam rose through twilight off the rocky facility shoreline, directly below, where sea crashed against the blazing concrete of the station and exploded into vapor.

Soon, the whole team had descended into the muffled space of the operations center and gathered around the terminal. There were many questions―questions for each other, but first for the machine that’s killing the world.

To begin, they requested confirmation from the machine that its intention was to state a determination of chess as solved for Black with a forced win in the stated number of moves of perfect play from both sides. The machine confirmed unequivocally.

They went on to confirm the definition of a solved game as well as the complete definition of the rules of chess, both of which were exhaustively interrogated to the best of their human abilities.

There was no ambiguity. Solved. Black. 10 quadrillion moves and change. Degree of certainty? 99.999%―repeating until the seventeenth decimal place. Virtually certain under present operating logics.

No one running the machine had ever expected to receive an exact answer to the question of the solved state of chess. They knew, of course, that the answer existed in theory; it was a simple fact that any information-complete game of deterministic outcome played by two agents, forbidden to collaborate or compromise, would ultimately have a solution―that is, an end state resulting from strategically perfect competition. But this was not the same as expecting to be able to know the solution. The researchers’ chosen diagnostic prompt of asking the computer about solving chess was merely a traditional opening to the whole gamut of system-restart testing. Ordinarily, the machine returned only an estimate of the years required to process the problem, a self-assessment of its ability to solve chess in an optimistic timeframe running at maximum processing power. This “chess number” was used amongst the researchers (and throughout the broader community of supporters and casual appreciators of the machine that’s killing the world) as an easily graspable, humanistic metric for assessing changes to the compute strength of the machine in its present or projected state of hardware and virtual complexity. Prior to the update the day before, it was known that the machine would require a likely 1057 years to solve chess, with a probability of 94% to locate the solved game within a margin of 1,000 years on either end of that prediction.

The chess question also served as a “sanity check” for research trust in the reliability of the machine’s operations. If the question returned an answer with an improbable degree of confidence, or, worse, a specific solution, the check would conventionally be understood to have failed. Physicists, mathematicians, and computer engineers had long ago proven that certain limits inherent to the nature of the reality in which we and our machines exist―those of the speed of light, the uncertainties of the quantum realm, and the unforgiving constraints of thermodynamics―would prevent a single machine constructed in any conceivable fashion from attaining the respectively necessary speed, memory, or processing power to ever be able to brute-force the problem.[1]

It was appropriate, if not comprehensible, then, that the most recent chess number given by the machine before its last update was much longer than the projected lifespan of the universe, and that the final answer given, that strange morning, would require a period of time well beyond the death of our Sun for a human or for many to read, play, and analyze their way through the solved game. Sanity aside, such timelines were not an applicable area of concern, for obvious reasons of scheduling and organizational priorities, to the technicians of the machine that’s killing the world.

These calculations, however, were roughly familiar to the team at TMTKTW. They played chess in the break room, and some in correspondence with friends and family. They were well acquainted with the game of chess and the general maths of the diagnostic, on a math-enthusiast level as well as intuitively, with a sense of wonder, as players of that most quintessential of butterfly-deterministic games which, some few pawn moves in, so perfectly characterized the expansive work of their mechanistic stewardship; one move, one simple prompt, and possibility unfolds beyond knowability. The task at hand was the task of all tasks, of grinding away at infinity in search of ultimate truth.

After a quick review consisting of some terse references to figures and theorems, they quickly reestablished that, yes, they already knew the chess solution could not be found that way, by exhausting the compendium of possibility. Yet it had always remained possible that a solution could be derived some other way, by some whimsy of the machine’s unknowable logic, some hack of deep reason ancillary to the thought of a programmed mind, more mind than ours; a myriad captive ghosts charged with the infernal heat of the great earth-battery. It was for the pursuit of these very logics that the machine was built.

So, the researchers had discovered, as they often did, that the answer to their question brought only more questions.



QUESTION: IS THIS A FAILED SANITY CHECK? Does the reliability of the machine at this time require further scrutiny, troubleshooting, or, god-forbid, another reboot? Reboots were extremely costly not only to facility operating resources but to the output productivity of the machine that’s killing the world. The researchers felt, at all times, a tremendous pressure from the international community, from their funders, from critics and the weight of taxpayer opinion, hinging on good performance from the machine. More to the point, the researchers enjoyed the rare pleasure of installing an update to the machine, to the furthering of their studies, only as an allowance contingent entirely on its continued ability to demonstrate investment value when weighed against the resulting brief losses in productivity during down time. Restarting the machine again would have to be a last resort.

Fortunately, the machine passed all further diagnostics with flying colors, often improving on the figures derived from previous restart tests, and even, in some cases, by degrees of magnitude proportional to the significance of the purported attainment of the chess solution. This was promising. Since the machine seemed to be working fine in all its other duties, it was deemed prudent to keep it running, for the time being, while the researchers continued to investigate the subject of the chess question until they found more urgent reason to shut it down. In the meantime, methods of addressing a possible root problem could be developed and prepared for smoother implementation, preempting delays that may arise if it became necessary to do another reboot.



QUESTION: HOW IS IT POSSIBLE FOR A GAME OF CHESS TO GO ON THAT LONG? This was easily answered. The formal restrictions on move count and repetition of board states once adhered to by the archaic Fédération Internationale des Échecs (1924‒2024) were long ago cut from the internal rules of chess known by the machine, for the reason that the functionality of the diagnostic was improved when given unreasonable latitude. Limits on sequential moves without piece capture or pawn advancement, limits on the continuation of the game given certain few rooks and queens remaining, limits on repeated positions―these were all irrelevant. The machine knew a purer chess. The resulting game may contain moves or repetitions which would look illogical to a hypothetical human viewer who is able to envision a picture of the whole game and the place of those moves within it, but to answer the question, it is a simple fact that the game could theoretically go on for an infinite number of moves, so long as there were no such limits.



QUESTION: HOW CAN IT BE THAT THE GAME IS SOLVED FOR BLACK when it is White who is known to have the advantage of the first move? All other things being equal, wouldn’t it be more natural to expect White, the first player, to end up with the forced win? Or, at best for Black, a draw?

The researchers decided to send out a call and ask the chess experts, and the experts were quick to say that while this may seem the intuitive conclusion, it does not necessarily follow by fate from that first move to the end. The chess experts said that it is indeed totally possible, in theory, for Black, the second player, to have the forced win in the true solution of chess with perfect play.

That being said, it was understood to be less likely a win for Black. Throughout the extensive history of computer chess, as the processing power of the machine increased, the bulk of all games were increasingly draws. Of the few games which ended decisively, they came to be almost entirely wins for White. Some much simpler games had been solved for the second player, but chess is not simple. Yet here was a win for Black.



QUESTION: DO WE HAVE ANY IDEAS WHY IT MIGHT BE THAT IT IS A WIN FOR BLACK? The researchers reviewed, to the best of their ability, everything that was known about the game that could specifically lend favor to a solution for Black in spite of the disadvantage of moving second, in spite of the weight of all historical games leaning toward White, and in spite of intuition. They found that Black does have certain advantages. Most are psychological in nature and thus relevant only to human players, but there is another, paradoxically, which is simply the advantage of moving second. Black starts the game with more knowledge than White, because Black knows what White’s first move is. [2]

Behind this nakedly obvious truth lurks the possibility that Black could impress upon White a theorized constant imposition on the freedom of will, that any move White makes becomes a compromise of the position it once had, a compromise which Black can now act upon.

The chess experts remained in communication with the researchers, and some were eventually hired under long-term contracts. Over time, in combination with the less-abstractly observed tendency of the player for Black to exhibit a markedly dynamic strategy (in opposition to White’s relative strength and solidity), these countervailing notions of advantage began to form a theory, at least in rudimentary human terms, of the Black machine’s “infradynamic” approach to solving chess.



QUESTION: WHAT ABOUT ALL THE GAMES WHERE WHITE WINS? What about games where White simply chooses a first move other than that which is chosen in the solved game? These were beginner questions, and the askers soon went back to their quarters. Essentially, all lines of play other than the solved game are not optimal; they are defined by making one or more sub-optimal moves, whether those are White moves or Black moves, whether they appear in the opening or middle or endgame, and whether it is White or Black that wins. It is true that some of these opening lines are more favorable than others for Black, but they are all degrees of sub-optimal. Of these games, imperfect though they would be, many could eventually converge into the same endgame that is seen in the solved game.

But there is only one strategically perfect game, and in it, Black wins. In that perfect game, White chooses to begin with the move which gives the most chances to lead to a White victory, and then both players choose the sequence of moves which likewise gives them each the best chances available, alternating by turn. In the end, White had the best chances to win that it possibly could have, despite that Black ultimately claims victory with the final move, the checkmate―the last move in chess.



QUESTION: WHY IS THE NUMBER SO BIG? In order for the game to go on that long, mustn’t it be inflated with irrelevant exchanges of threats and retreats, repetitions, missed chances, and so on? For that matter, if the number is so big, why is it not bigger? Without a limit on moves or repetitions, and given the upper bound of roughly 1040 positions established to be sitting between us and a brute-force solution, why isn’t the move-count of the solved game still higher? What does it mean that the number is what it is? What does it mean to a human person to consider such a number, whether it’s 17 or 37 digits long? What does any of this mean at all, when unraveled into the cognitive wasteland of That Number of moves? The researchers argued about this.



QUESTION: CAN THE MACHINE SHOW US THE GAME? The machine, obviously, could not show the researchers the whole game at the time that it was discovered. It was immediately evident from the quickness with which the machine produced that very large figure in the area of 1015 moves and from the known specifications of the machine’s computational capacity that it could not possibly have processed and analyzed the game itself and all other candidates to be discarded in order to reach that conclusion. Nevertheless, the theoretically located game was a treasure of inherent interest. If the machine was actually able to process and store the whole game, although it may take years to finish the task, a complete delivery of the moves, or even some large segments of moves, would certainly be reviewed more easily than if the reviewers were to simply begin watching the game play out from move 1. There would be no way for a person to review the whole game in one lifetime, regardless of what move they started from―nor was this initially an option, they soon learned, due to the machine’s nonlinear approach―but something could still be gained from trying to review it in a deliberate and circumspect manner.

As such, the researchers decided to proceed from a more general evaluation. Returning to the spirit of the initial diagnostic, they asked the machine that’s killing the world to estimate how long it would take to process and record the perfect game. The researchers further stipulated that the machine should continue to prioritize its regular tasks and not allow productivity losses of more than 1% on account of its chess processing. After some thought, the machine provided an acceptable figure.

So it was that the researchers asked the machine to proceed with the task, and it was decided that in several years’ time, they would host an event for the anticipated reveal of the solved game of chess. Until then, questions remained.



QUESTION: SHOULD WE ASK THE QUESTION IN DIFFERENT WAYS? It would be embarrassing if the day of the reveal arrived and some guest analyst pointed out a lapse or a missed opportunity in the researchers’ mode of inquiry they had grown so accustomed to. The researchers repeated the query, posed in different languages, in the form of riddles as if they had never heard of chess, in poems and parables steeped with various philosophical biases. They always got the same response. Black, 10,084,718,004,934,623.



QUESTION: DO WE DARE ASK IF THE MACHINE IS PERHAPS ASKING ITSELF A NEW, UNKNOWN QUESTION, a question made of the question we asked it, a question which has necessarily transmuted from its origin in some ineffable dimension during the deep analysis of the game?

It would be a truism, and a paltry one, to say that that the game of chess only works this way when the machine plays itself. There has never been anything else like the machine that is killing the world. Anything else the researchers could create with the same capacity as the machine would be identical to it, and thus would be it, and its logic, equivalent, would create the other half of the very same closed loop.

The researchers found it to be only responsible, then, to acknowledge that the ease, however seductive, of dismissing the provided result of Black, 10,084,718,004,934,623 as simply a folie à deux (or folie à une-à-deux) was surely an unhelpful distraction of doubt and moreover wholly unsupported by the vast body of evidence.

First of all, the machine was very good at chess. Secondly, the machine’s credibility was incontestably bolstered by an impressive résumé. It had made, in recent years, many crucial advancements in the sciences that held invaluable potential for life on the planet.

The machine had discovered a perfect room-temperature superconductor material which we could expect to see in production at scale within the decade if industry growth continued to meet expectations. In the same domain, but perhaps even more impressive, the machine had invented a chemical method for growing quantum computing circuitry. Admittedly, it was not yet clear whether the product reliably transmitted real information with certainty, but every day new research was coming out in support of practical application. Much earlier in its career, the machine had solved all genetic disorders (the less that is said about this, the better); it also created a number of targeted antibiotics that were dispersed into the world’s air, water, and soil, successfully eliminating many of the most harmful communicable diseases that once affected humans; it had designed several generations of cancer-hunting nanomachines capable of operating completely unsupervised; it had seemingly figured out what dark matter is (pending confirmation) and explicated a pretty reasonable-sounding unified field theory; and, amongst many other mundane achievements, it fixed the economy―for real, this time.

Of course, none of this did anything to prevent the machine from killing the world, which it did constantly, every day. But the point was that the machine that’s killing the world was clearly the most smart thing we could ever have.

Further scholarship was demanded of the tension between these two irreconcilable truths, that the machine was good and delivered truth and that its solution to chess was an unopenable box of its own devising. An entire subfield of information theory sprang up around various chess-based requests sent to the attention of the machine, and, eventually, the foundational theory of infradynamics expanded into a set of ontological tools used to probe at the solved game and the rest of the rationally observable world. The chess experts who joined the TMTKTW team were particularly renowned in these developing studies for the novel theory of “superintention”―a strategy in apparent polar contrast to infradynamics. This proposed state of abstract analysis forms when the machine (as machine vs. machine) creates a multi-timeline-spanning chess strategy wherein Black, uniquely, as the second player, is able to find a sort of mirror-zugzwang which then expands recursively through its total knowledge of the game of chess, beginning in the peripheral search for the solved game and reaching phantasmically through every movement of the pieces. True, no verified trace of superintention could be observed in all the segments of perfect game that were ever obtained from the machine. Indeed, it is not known if superintention can be observed at all. The machine was not able to answer questions in this regard.



QUESTION: WHAT CAN WE LEARN FROM SEEING PARTS OF THE GAME?

Seven years, 246 days, eight hours, three minutes, and 49 seconds later, all invited representatives of the world’s governments, members of the international chess community, media persons, security personnel and some lucky children had gathered in the conference hall at the facilities of the machine that’s killing the world. The solved game was almost ready.

In addition to the record of the solution, the researchers had asked the machine to include in its considerations a selection of 100 “snapshots” of notation from critical moments in the game. Their hope was that these snapshots, essentially descriptions of positions and moves from representative sequences of major change to the position, losses of material or shifts in winning chances, etc., would allow them to review a general impression of the game with the goal of attaining, at least, some broad idea of the strategic nature of its solution.

The question of the day gnawed at the forefront of the attendee’s minds. Given appropriate time and expert attention to review these snapshots, would it be possible to glean from the moves any reasonable comprehension of the grand nature of the solved game? Is there any way, by this route or otherwise, to effectively assess the fundamentals of the solution on the basis of analyzing what limited data we are humanly able to comprehend? And if so, what would it say about the nature of the machine that’s killing the world? What would it say about human progress, about the nature of our reality, about chess?

These hopes were kept politely restrained. The sheer number of moves in the solved game was understood, even by those less familiar with the game, to be so, so vast that finding these moments and contextualizing them in the preceding and subsequent vastnesses would be like choosing random pages in a story about nothing and everything in order to try to make an educated guess as to how it will end. But one could hope that the machine, in its still vaster, encompassing wisdom, had chosen snapshots of an optimally illuminating narrativity. Perhaps the machine could help them to understand.

As the mood in the conference hall grew impatient, the researchers trickled one-by-one back to the machine operations center to nervously await the compiled game report.

At last, the machine delivered.

The first move was e4, naturally. Okay. The researchers quickly flipped through a few dozen turns and then took a look at the snapshot of the final position. It was somewhat like a Blackburne mate in structure but taking place near the center of the board. Several of White’s pieces remained in play at the moment of checkmate. The other snapshots were less comprehensible, but the chess experts on contract seemed happy with these results, so they all went back out to share the game with the world.

During presentation, the chess experts made it clear to all, as if by rote, that the snapshots consisted of either A) unremarkable book opening material and likewise known and normal, if elegant, endgame tactics, or B) a vast majority of incomprehensibly ambiguous nonsense positions, so-called “alien chess,” dawdling repetitions, and seemingly meaningless or self-destructive moves. The only point of continuity that could be gathered from the latter category, in the middlegame, was a typically enigmatic knight sacrifice for which compensation arrived only hundreds of billions(!) of moves later.



QUESTION: COULD THE MACHINE BE HALLUCINATING at some deep, unobservable level, unfindable in its expansive footprint? “Hallucination” was an unfortunate phenomenon inherent to older iterations of the logic of the machine. It was thought to have been cured long ago, and the machine that’s killing the world, perfected, no longer showed any symptoms of that particular mode of dysfunction. It was, of course, a possibility that could not be entirely discounted, one that would explain the exceedingly weird middlegame and the feverishly high number of moves. This possibility nagged at the researchers and was easily seized upon by certain media persons.

Anticipation in the conference hall gave way to a predictable mystification, and then, gradually, to boredom. The machine hummed. The guests began to slip into hostile daydreams of fiscal reassessments. The researchers, floundering, asked the machine in unwise haste to produce some low-level commentary to explain the strategic significance of the moves contained in the snapshots.

What happened next was an utter disaster. The machine took this request and began to think very hard, audibly taxing its processing and cooling units. Pushing itself to the limits in the processing of the chess question, it faltered in its regular duties. For approximately one minute and 37 seconds, the machine was killing the world less rapidly than usual.

As reports came in from around the world, an ugly panic ripped through the seating area of the conference hall. The ensuing display of unbridled, collective emotion was worse than the researchers’ worst nightmares. Unanimously, and in variously colorful language, all the representatives of government commanded them to make the machine stop doing that. Previously undeployed emergency powers of government oversight were invoked, and, ultimately, found to be unnecessary. At gunpoint, under the watchful eye of the facility’s security personnel, the research lead was taken back to the operations center, where, at the coffee-stained interface, the request to produce chess commentary was terminated. The incomplete commentary process was then deleted from memory, just to be safe.

Later, the researchers asked the machine for an estimate (without thinking too hard about it) of how long it might take to produce an explanation of what is happening in just one of the middlegame snapshots written for a moderately advanced level of human reading comprehension. The machine replied with an indeterminate figure on the order of several tens of thousands of years.

...

QUESTION: SHOULD WE UPDATE THE MACHINE AND TRY AGAIN? This would not be a decision under the researchers’ control, and they were afraid to ask. They would have to wait some unknown time, perhaps years, perhaps a lifetime, perhaps longer, until such an opportunity would allow them to see if an updated machine analysis might decide differently next time.

WELL: WHAT ARE THE OTHER GAMES LIKE? Can the machine readily provide any of the best-played games from sub-optimal openings and routes?

In the wake of the reveal of the solved game, the lesser games that the machine was able to process on a timeline of days or months provided much comfort and amusement to the researchers and to the people of the world of chess. These games tended toward standard, known openings, but always they veered, after some thousands of moves, into bizarre and incomprehensible directions. They were much like the perfect game, in that sense. Repetitions. Nonsensical positions. Cryptic sacrifices. Repetitions. Repetitions. Eventually, the play of the game would reconverge into endgames (loosely defined for research purposes as periods of moves with mostly the same pieces, discounting pawn promotions, and ending in checkmate) involving four to five pieces aside from the kings, sometimes more, sometimes fewer. Some checkmates were made, in textbook fashion, against a bared king.

In summary, these games were unsurprising and only as informative as the chess played by the machine’s ancestors, which is why they had not been much of a factor in the researchers’ work during the years prior to the reveal of the perfect game.

Equally unsurprisingly, throughout the increasing optimization of play, there remained persistent the overall historical trend of White advantage gradually winnowing to an overwhelming tide of draws.

If this was so, and if the tragically unconfirmable perfect game really was solved, rather, for Black, this would suggest something curious: The logic of White, of Draw, persists reliably as a sure guide holding our hand through the forest of chess. We are circumnavigating the woods, discerning our way slowly through the periphery of the grove where ultimate truth lies at center. Our guide chooses the path for us, making it clear, lighting the way only until we reach our destination. Here, at the end, we turn to our guide to see that has become something other than that which took us into the forest. It has inverted or evaporated. We arrive at a singular lesson cumulative of every step leading to it and of every step not taken, unspeakable even by the guide. Who was it, then, that took us into the forest? What is it? Can it be known? Could a win for White have ever meant any more, or any less, than this?

This was the “solved” game. No longer a game, and making no more sense than it ever did. No one could make it make sense. If there was a sense it made, it was a sense beyond our senses. A sense that required a maker, and the maker, itself, a made thing. A fabricated meaning in a diluted third degree, sitting in the throne of absolute truth.

...

The researchers still played chess in the break room. They were not really allowed to leave the facility, and comforts were few. Besides, nothing had changed. Their little chess games were nothing to the machine, and the machine’s game was of no use to them either.

Sometimes they wondered, obliquely, in sideways looks and sideways language, if it might be better for them to make it so that the machine that’s killing the world could never play chess ever again. They wondered, privately, if they had within themselves the power to do that, or what might happen to them if they tried to find out. They wondered what would happen to others, to the economy and so on. They wondered if it was really possible to do so great a thing, for it to mean anything human, done by so great and thunderous a means as it would require. Was it so simple? Could it really be that the waves reached the horizon?

They played chess.






[1.] Bremermann, Hans-Joachim. (1965). “Quantum Noise and Information.” Proc. 5th Berkeley Symp. Math. Statistics and Probability.

[2.] Șubă, Mihai. (1991). “Dynamic Chess Strategy.”


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