"Greg Egan - Glory" - читать интересную книгу автора (Egan Greg)

The theorem itself was expressed as a commuting hypercube, one of the NiahтАЩs favorite forms. You
could think of a square with four different sets of mathematical objects associated with each of its
corners, and a way of mapping one set into another associated with each edge of the square. If the maps
commuted, then going across the top of the square, then down, had exactly the same effect as going
down the left edge of the square, then across: either way, you mapped each element from the top-left set
into the same element of the bottom-right set. A similar kind of result might hold for sets and maps that
could naturally be placed at the corners and edges of a cube, or a hypercube of any dimension. It was
also possible for the square faces in these structures to stand for relationships that held between the maps
between sets, and for cubes to describe relationships between those relationships, and so on.

That a theorem took this form didnтАЩt guarantee its importance; it was easy to cook up trivial examples of
sets and maps that commuted. The Niah didnтАЩt carve trivia into their timeless ceramic, though, and this
theorem was no exception. The seven-dimensional commuting hypercube established a dazzlingly elegant
correspondence between seven distinct, major branches of Niah mathematics, intertwining their most
important concepts into a unified whole. It was a result Joan had never seen before: no mathematician
anywhere in the Amalgam, or in any ancestral culture she had studied, had reached the same insight.

She explained as much of this as she could to the three archaeologists; they couldnтАЩt take in all the details,
but their faces became orange with fas-cination when she sketched what she thought the result would
have meant to the Niah themselves.

тАЬThis isnтАЩt quite the Big Crunch,тАЭ she joked, тАЬbut it must have made them think they were getting closer.тАЭ

тАЬThe Big CrunchтАЭ was her nickname for the mythical result that the Niah had aspired to reach: a
unification of every field of mathematics that they considered significant. To find such a thing would not
have meant the end of mathematicsтАФit would not have subsumed every last conceivable, interesting
mathematical truthтАФbut it would certainly have marked a point of closure for the NiahтАЩs own style of
investigation.

тАЬIтАЩm sure they found it,тАЭ Surat insisted. тАЬThey reached the Big Crunch, then they had nothing more to live
for.тАЭ

Rali was scathing. тАЬSo the whole culture committed collective suicide?тАЭ

тАЬNot actively, no,тАЭ Surat replied. тАЬBut it was the search that had kept them going.тАЭ

тАЬEntire cultures donтАЩt lose the will to live,тАЭ Rali said. тАЬThey get wiped out by external forces: disease,
invasion, changes in climate.тАЭ

тАЬThe Niah survived for three million years,тАЭ Surat countered. тАЬThey had the means to weather all of those
forces. Unless they were wiped out by alien invaders with vastly superior technology.тАЭ She turned to
Joan. тАЬWhat do you think?тАЭ

тАЬAbout aliens destroying the Niah?тАЭ

тАЬI was joking about the aliens. But what about the mathematics? What if they found the Big Crunch?тАЭ

тАЬThereтАЩs more to life than mathematics,тАЭ Joan said. тАЬBut not much more.тАЭ

Sando said, тАЬAnd thereтАЩs more to this find than one tablet. If we get back to work, we might have the