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Let me tell you a bit of @gregeganSF's story about a xenomathematician - a space explorer who studies the mathematics of different civilizations.
"It's a significant mathematical result," Rali informed her proudly when she reached them.
(1/n)
"It's a significant mathematical result," Rali informed her proudly when she reached them.
(1/n)
He'd pressure-washed the sandstone away from the near-indestructible ceramic of the tablet, and it was only a matter of holding the surface at the right angle to the light to see the etched writing stand out as crisply and starkly as it would have a million years before.
(2/n)
(2/n)
Rali was not a mathematician, and he was not offering his own opinion on the theorem the tablet stated; the Niah themselves had a clear set of typographical conventions which they used to distinguish between everything from minor lemmas to the most celebrated theorems.
(3/n)
(3/n)
The size and decorations of the symbols labelling the theorem attested to its value in the Niah's eyes.
Joan read the theorem carefully.
(4/n)
Joan read the theorem carefully.
(4/n)
The proof was not included on the same tablet, but the Niah had a way of expressing their results that made you believe them as soon as you read them;
(5/n)
(5/n)
in this case the definitions of the terms needed to state the theorem were so beautifully chosen that the result seemed almost inevitable.
(6/n)
(6/n)
The theorem itself was expressed as a commuting hypercube, one of the Niah's favorite forms.
(7/n)
(7/n)
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.
(8/n)
(8/n)
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.
(9/n)
(9/n)
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.
(10/n)
(10/n)
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.
(11/n)
(11/n)
That a theorem took this form didn't guarantee its importance; it was easy to cook up trivial examples of sets and maps that commuted. The Niah didn't carve trivia into their timeless ceramic, though, and this theorem was no exception.
(12/n)
(12/n)
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.
(13/n)
(13/n)
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.
(14/n)
(14/n)
She explained as much of this as she could to the three archaeologists; they couldn't take in all the details, but their faces became orange with fascination when she sketched what she thought the result would have meant to the Niah themselves.
(15/n)
(15/n)
"This isn't quite the Big Crunch," she joked, "but it must have made them think they were getting closer".
(16/n)
(16/n)
The Big Crunch 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.
(17/n)
(17/n)
To find such a thing would not have meant the end of mathematics — it would not have subsumed every last conceivable, interesting mathematical truth — but it would certainly have marked a point of closure for the Niah's own style of investigation.
(18/n)
(18/n)
The story is called "Glory" and you can read the whole thing online here:
http://outofthiseos.typepad.com/blog/files/GregEganGlory.pdf
You can see other stories by Egan on his website:
https://www.gregegan.net/BIBLIOGRAPHY/Online.html
(19/n)
http://outofthiseos.typepad.com/blog/files/GregEganGlory.pdf
You can see other stories by Egan on his website:
https://www.gregegan.net/BIBLIOGRAPHY/Online.html
(19/n)
He has a new book of short stories! I ordered it on paper because I still feel there's something exciting about reading books that way.
(20/n, n = 20) https://twitter.com/gregeganSF/status/1220638322600509441
(20/n, n = 20) https://twitter.com/gregeganSF/status/1220638322600509441
