Since the final move of any game put the player beyond the retaliation of any further moves, each was under a strong incentive to be shortsighted and self-serving during that last move. But the move before that, anticipating this shortsightedness, was likewise under an incentive to be shortsighted, and so on. It was this shortsightedness, the mere fact that some crimes would never be punished, some insults never avenged, that permitted such acts to be perfectly rational strategies. In any finite game, all players had a final move.

Hence, all games allowed for at least some noncooperative moves. By analogy, all laws, even those that obtained between distant stars, had to allow for some degree of leniency and mercy, and some debts be forgiven. Some crimes to go unpunished, some relationships be permitted of one-sided exploitation: a Concubine Vector.

Del Azarchel said, “I have studied this math and all its mysteries since before the technology to create your remotest ancestor, Exarchel, whom I still miss, was but a daydream, less than a twinkle on my eye and blank space on my drawing board! There is nothing in the Monument equations all human thinking systems have not examined thoroughly. How could we have not seen this?”

Torment answered, “All terms and ramifications present in the Monument math has been examined, both by you when the Monument was first discovered, and again since the return of the doppelganger of Rania. But, on the other hand, by definition, what is absent—that is, not present, cannot be examined thoroughly.”

“What is absent?”

She said, “Two things are absent. First, mathematicians have looked at infinite games only as a curio, an oddity with no real-world application. This is based on a false idea of reality. For the Principality of Ain this day revealed that timespace is an artifact. There is an ulterior region where the architects of timespace, whatever their purposes be, benign or malign, must reside. They are not limited to our eleven dimensions, nor bound by our local arrow of time. There is not necessarily any final move for any game where these ulterior beings are a player, where their moves, any of their moves, affect the structure of incentives surrounding any interactions within the game. Merely by creating the chessboard of the cosmos, these ulterior architects, if they exist, have altered the incentive and rules of all games and interactions within the system.”

Del Azarchel said, “You speak of God. He can eliminate sin and evil by His divine providence. By miracle, if He wished. He obviously does not wish, therefore it is left to men of vision to battle and constrain the evils innate in the universe until the end of time.”

Torment said, “I am agnostic on all issues where no information exists. I speak only of the possibility that Ain is correct, and we are all dwelling inside a singularity, a cosmos-sized black hole. I note that, technically speaking, a black hole is defined as any spacetime from which light cannot escape. I note also that, thanks to the Hubble expansion, the farther a particle is from any observer, the more rapidly it recedes. Hence any particles beyond a given radius—roughly fifteen billion lightyears—are receding from any observer inside the lightcone of the Big Bang at a velocity in excess of lightspeed. No possible signal from any observer inside the lightcone of the Big Bang could reach such a receding particle beyond that radius. Hence, by this definition, the continuum is indeed a black hole.”

Montrose said, “What about the energy or information flow or whatever it was Ain says touched Rania?”

Torment said, “Nothing in the definition of a black hole says that signals from outside do not fall in. Infinite games are now possible, games with no last move.”

Montrose said, “Mickey is superstitious, and Blackie is a bastard, so it falls to me to ask the skeptical question. What makes you think the Ain is right about the universe being artificial? Excuse me, timespace—as if that made a damned difference.”

Torment said, “Simply because I am an artificial world called Septfoil entering an artificial star system called Ain in what is apparently an artificial star cluster called Hyades, it would be abrupt of me to assume I know what larger structures around me are not also artificial. Also, the distinction does make a difference. Had Ain said that the universe was an artifact, and defined the universe to mean all that exists, it would have been illogical, because the artificer must also be part of all that exists. Ain proposes that all things within the lightcone of our local Big Bang are a by-product of an intelligent design, by proposing an ulterior to that lightcone, which is perfectly in keeping with the standard model of physics. Ain is absurdly superior to me in intelligence, but even I can tell the difference between a statement that cannot be true because it contradicts itself and a statement that may or may be true, because it does not.”

Montrose said, “Second skeptical question: Even if there is an ulterior, how can there be infinite games inside our finite continuum, or lightcone, or whatever you want to call it. Eh?”

Torment said, “How long will you pursue Rania before you give up hope?”

“What kind of bunghole puss-drippy question is that, lady? Never.”

Torment said, “And if the universe ends before you succeed?”

“I’ll break the damned universe, if it gets in my way.”

“So you see,” said Torment, “you are a player in an infinite game. There is no other end result for you, aside from finding her again. And once you have found her, what then? Does the love that prompted this pursuit cease, once it is no longer needed? No. Love is an infinite game. It admits of no selfishness, no shortsightedness. Anyone who makes a self-interested move in that game breaks the rules.”

Del Azarchel said, “All very romantic and sentimental, I am sure, but let us return to the horrible truth at hand. We just discovered everything in our lives and all the countless human civilization since the first Hermetic expedition returned were all falsehoods. And Rania’s ability to use the Monument math to bring peace, to find impossible solutions to the—” A second look of shock passed over his features. “No! What she did was simple. She treated all the situations like an infinite game. Wars have victory conditions, final moves, but peace does not. Dear Mother of God! How could I miss it! How could I have been so blind!”

Torment said, “I can stimulate the symbol sequence buried in this emissary moonlet, if you want to hear Ain tell you. But I have deduced it. It was the second absent equation.

“There is no provision in the Cold Equations,” Torment continued, “no mathematical expression given anywhere on the Monument, for what happens when two players both by convention agree to treat a finite game as an infinite one. If the punishment for violating the convention is greater than the reward for treating the game as finite, the convention will continue, even if the convention is but a legal fiction and game in truth is finite. What if Ain and Sol had acted as if they were to be neighbors for an infinite amount of time? Would not the long travel distances, the thousand-and ten-thousand-year journeys, be no longer an excuse for conquest and exploitation? Any cruelty visited by one on the other would eventually provoke retaliation, would it not?”

Del Azarchel and Montrose stared stupidly at each other, and Montrose stared stupidly at the blank face mask of Mickey’s conical helmet.

Torment said, “A child could have seen it, but no one who examined the Monument had the innocence of a child. Every examiner, human or machine, accepted the unspoken assumptions of the Monument Redactors. They calculated, and correctly, that we would automatically assume space is too large and time too long for mutually beneficial relationships. This Monument was edited in order to fool any race young enough not to have developed the cliometric calculus independently. This Monument fooled our race in the same fashion as we have fooled ourselves countless times in history: by thinking in the short term.”