Mathematics in SciFi

6/23/12 The Algebraist, Iain M. Banks, 2004. Every nook and cranny of the galaxy is full of life, but this story deals mostly with a human scholar of Dwellers, the life forms that populate gas giants. His quest is to search for a possibly mythical text, The Algebraist, which is “all about mathematics, navigation as a metaphor, duty, love, longing, honour, long voyages home ... that sort of stuff.” Banks’ writing style is as dense and detailed as befits such a complex universe. His sentences extend to paragraphs, his lists can’t stop at two or three examples but invariably explode to ten or twelve descriptors. There is sex, there is violence, there is politics, there is humor, but don’t let the title fool you, there is no Algebra!
However, there are a few scatterings of mathematics; “by any algebra of justice under any sun”, “Lagrange point”, “an algorithm for elegance”, “fractally spiraled”, “and some algebra ciphered into the base code”.
“It looked like algebra.” What does algebra look like? Especially an alien algebra?
I liked a couple of lines that could get the reader to refresh his basics. “the number of genuine galaxy-spanning wars didn’t make it to double figures. In base eight!” And if they had, how many would there be? :-) “7.35 x 10^8 seconds ago” I almost started to calculate that, but then he said, “about twenty years earlier.” “I suspect good luck will be necessary, if not sufficient.”
The holy grail of the plot is “some extra set of coordinates, or even a single mathematical operation, a transform, which, when applied to any given set of coordinates in the original list, somehow magically derived the exact position”