The composition or history of Nahalon is unknown. Any query would of necessity be directed to 20 Arietis, or whoever the ultimate originator of that expedition was within the Hyades hierarchy.
Achaiah was descended from cursorial hunting creatures whose practice of pack cooperation and endurance hunting made them, of all candidates available to the Principality of Ain, the most akin to your own in psychology and social organization. Unfortunately, as with most carnivorous races, their social strategies are of limited range and somewhat antisocial.
Mickey said aloud, “The star monsters were a vampire orchid, a trap-door spider, a bone worm, a mushroom, and a hyena, all sent to our world by their master, a colony of whelks and winkles. Even if, for a million years, their biological ancestors have all been ghosts, these machine beings would still continue to be insurmountably different from each other. I have a strange intuition that the agents Ain sent to Sol did report back but that Ain did not understand the reports.”
12. Finite Games and Infinite
Montrose said, “My whole life, all these years—the aliens never knew we had translated the Monument. They did not know there was one. Hyades is not the Monument Builders, nor Praesepe, nor M3. What does it mean?”
Torment said, “It means all our lives have been based on a falsehood.”
Montrose and Del Azarchel, each in a different way, and with different degrees of obscenity said, “I don’t understand.”
Mickey said, “I do. Nobilissimus, Meany, divine Torment, my conversation with Ain revealed that there was no reason to send Rania to M3. The Cold Equations allow for a second method to prove our ability to cooperate with a star-faring civilization—all we had to do was cooperate. The invasion of which we were warned was only a last resort, should we refuse to share the burden of the expense for any expeditions approaching our world. That we were obligated to greet them with gifts, as equals greet equals, was an expression missing from the notation, and therefore neither of you, nor the Swans, nor the Myrmidons made any such attempt.”
For once, Montrose did not swear. He wept, and the tears turned to ice on his cheeks.
For once, Del Azarchel had no notion of how he should appear before other men or before the eyes of history. His face was utterly blank, like the face of a man who suffered a lobotomy. Eventually, after what might have been a short time or a long, Montrose whispered, “It was all unnecessary? Every damned thing we did?”
Del Azarchel said, “We knew the Monument had been redacted, edited, and yet we did not know what was missing. The Cold Equations are based on mathematical models of the mind—there were no missing steps, no errors, and the equations balanced! An interstellar civilization must be ruthless and pitiless if it is to maintain itself across such an abyss, across such spans of time. What did the redactors leave out? What was missing?”
Torment said, “The time value was set artificially low.”
Del Azarchel said, “What?” It was a snarl.
Torment showed them several of the cliometric equations she had stolen from the newborn human Dominion, Triumvirate. Then, she ran a trial of the same equations, again and again, each time increasing the amount of time under consideration until it was infinite. With each trial, the Concubine Vector, the margin where a certain degree of exploitation and sharp dealing was allowed between unequal partners, slowly shrank and shrank.
Montrose said, “It’s the long run. In the long run, honesty is the best policy, eh? But mathematicians have known about that little curiosity for years, centuries, longer. The long-run conditions never obtain, because the cost for waiting for the long run get higher the longer the long run runs—”
Torment said, “A child could have seen it.”
Montrose said, “So how come we did not see it? How come all us genius thinkers missed it?”
Torment said, “We failed to question our assumptions, which is a mental knack that does not depend on intelligence for operation but on innocence of perception.”
“What assumptions?”
She said, “The Concubine Vector equations were written on the Monument as if they seemed to be a logical corollary, and the only logical corollary, the basic mathematical expressions of law, morality, semantics, and logic. But we were reading a Monument with a crucial bit of logic missing. The missing axiom is the difference between a finite and an infinite game.”
She showed them a simple game-theory equation, where the final move of any game, being anticipated by the players, would be taken into account in the penultimate move, and that move again be anticipated by the antepenultimate move, and so on for all the moves.
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.”