The Year's Best Science Fiction 10

Mr. Kagan will say no more about himself than that he is a graduate student of mathematics. I can add only that, in his first year of publication, two of his stories were selected for annual “Best” collections.

What follows is what I did persuade him to say something about. If your math, like mine, extends only to a vague familiarity with words like vector, tensor, set, and Riemann space, Mr. K’s glossary should help you determine where the mathematical facts leave off, and the fun-and-fantasy begins.

Metamathematics: Study of the underlying structure of math.

Nonosecond = one billioneth of a second.

Gogol: 10¹⁰⁰ (10 with a hundred zero’s.)

Googolplex: (10¹⁰⁰)¹⁰⁰

Degenerate: (in math) a trivial or simple case—a point is a degenerate circle.

Isomorph(ism): A correspondence between two math systems which preserves structure.

Hausdorf Space: A “mathematical space” where any two points can be separated (“housed-off”).

Communitivity: The mathematical condition: a x b = b x a

Set: A collection or bunch

Class: A set

Group: A mathematical structure: e.g., the integers with addition as the operation.

Ring: A group with multiplication defined as a second operation.

Field: A group under addition and under multiplication, too.

Composing: Doing in a row: e.g., doing one operation, then a second, then a third.

Transformation: mapping a math structure from one place to another.

Orthogonal Transform: A transform that preserves lengths.

Inner Product Transform: A transform that preserves “inner-product.”

Degenerate Transform: A transform that doesn’t preserve anything in particular.

Well-Ordering Principle: Any collection of sets of a set can be ordered (but in a sequence).

Axiom of Zemelo: Assuming the well ordering principle.

Bolzano Weirstrauss Points: “Limit Points” of sequences—the values certain sequences of numbers approach infinitely closely.