Cryptonomicon

"But everyone's going to disagree with what the appraiser says, Nina, love," says Uncle Red. "Furthermore, the appraiser will totally miss out on the emotional dimension, which evidently looms very large here, or so it would seem, based on the, uh, let's say melodramaticcharacter of the, uh, discussion, if discussion isn't too dignified a term for what some might perceive as more of a, well, catfight, that you and your sisters were conducting all day yesterday."

Randy nods almost imperceptibly. He pulls up and parks next to the furniture that is again clustered around the Origin. At the edge of the parking lot, near where the Y axis (here denoting perceived emotional value) meets a retaining wall, the Shaftoes' hot rod sits, all steamed up on the inside.

"The question reduces," Uncle Red says, "to a mathematical one: how do you divide up an inhomogeneous set of nobjects among m people (or couples actually); i.e., how do you partition the set into msubsets (S [sub 1],S [sub 2], ... ,S [sub m]) such that the value of each subset is as close as possible to being equal?"

"It doesn't seem that hard," Aunt Nina begins weakly. She is a professor of Qwghlmian linguistics.

"It is actually shockingly difficult," Randy says. "It is closely akin to the Knapsack Problem, which is so difficult to solve that it has been used as the basis for cryptographic systems."

"And that's not even taking into account that each of the couples would appraise the value of each of the nobjects differently!" Uncle Red shouts. By this point, Randy has shut off the car, and the windows have begun to steam up. Uncle Red pulls off a mitten and begins to draw figures in the fog on the windshield, using it like a blackboard. "For each of the mpeople (or couples) there exists an n-element value vector, V, where V [sub 1]is the value that that particular couple would place on item number 1 (according to some arbitrary numeration system) and V [sub 2]is the value they would place on item number 2 and so on all the way up to item number n.These mvectors, taken together, form a value matrix. Now, we can impose the condition that each vector must total up to the same amount; i.e., we can just arbitrarily specify some notional value for the entire collection of furniture and other goods and impose the condition that

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where [tau] is a constant."

"But we might all have different opinions as to what the total value is, as well!" says Aunt Nina, gamely.

"That has no impact mathematically," Randy whispers.

"It is just an arbitrary scaling factor!" Uncle Red says witheringly. "This is why I ended up agreeing with your brother Tom, though I didn't at first, that we should take a cue from the way he and the other relativistic physicists do it, and just arbitrarily set [tau] =1. Which forces us to deal with fractional values, which I thought some of the ladies, present company excluded of course, might find confusing, but at least it emphasizes the arbitrary nature of the scaling factor and helps to eliminate thatsource of confusion." Uncle Tom tracks asteroids in Pasadena for the Jet Propulsion Laboratory.

"There's the Gomer Bolstrood console," Aunt Nina exclaims, rubbing a hole in the fog on her window, and then continuing to orbitally rub away with the sleeve of her coat as if she is going to abrade an escape route through the safety glass. "Just sitting out in the snow!"

"It's not actually precipitating," Uncle Red says, "this is just blowing snow. It is absolutely bone dry, and if you go out and look at the console or whatever you call it, you will find that the snow is not melting on it at all, because it has been sitting out in the U-Stor-It ever since your mother moved to the managed care facility and it has equilibrated to the ambient temperature which I think we can all testify is well below zero Celsius."

Randy crosses his arms over his abdomen, leans his head back, and closes his eyes. The tendons in his neck are as stiff as subzero Silly Putty and resist painfully.

"That console was in my bedroom from the time I was born until I left for college," Aunt Nina says. "By any decent standard of justice, that console is mine.