Cryptonomicon

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.

'Well, that brings me to the breakthrough that Randy and Tom and Geoff and I finally came up with at about two A.M., namely that the perceived economic value of each item, as complicated as that is in and of itself, viz the Knapsack Problem, is only one dimension of the issues that have got us all on such a jagged emotional edge. The other dimension-and here I really do mean dimension in a Euclidean geometry sense-is the emotional value of each item. That is, in theory we could come up with a division of the set of all pieces of furniture that would give you, Nina, an equal share. But such a division might leave you, love, just deeply, deeply unsatisfied because you didn't get that console, which, though it's obviously not as valuable as say the grand piano, has much greater emotional value to you.

'I don't think it's out of the question that I would commit physical violence in order to defend my rightful ownership of that console,' Aunt Nina says, suddenly reverting to a kind of dead-voiced frigid calm.

'But that's not necessary, Nina, because we have created this whole setup here just so that you can give your feelings the full expression they deserve!'

'Okay. What do I do?' Aunt Nina says, bolting from the car. Randy and Uncle Red hastily gather up their gloves and mittens and hats and follow her out. She is now hovering over the console, watching the dust of ice swirl across the dark but limpid, virtually glowing surface of the console in the turbulent wake of her body, forming little Mandelbrotian epi-epi-epi-vortices.

'As Geoff and Anne did before us, and the others will do afterwards, we are going to move each of these items to a specific position, as in (x, y) coordinates, in the parking lots. The x axis runs this way,' Uncle Red says, facing the Waterhouse House and holding his arms out in a cruciform attitude, 'and the y axis this way.' He toddles around ninety degrees so that one of his hands is now pointing at the Shaftoes' Impala. 'Perceived financial value is measured by x. The farther in that direction it is, the more valuable you think it is. You might even assign something a negative x value if you think it has negative value-e.g., that over stuffed chair over there-which might cost more to re-upholster than it is actually worth. Likewise, the y axis measures perceived emotional value. Now, we have established that the console has extreme emotional value to you and so I think that we can just go right ahead and move it down the line over to where the Impala is located.'

'Can something have negative emotional value?' Aunt Nina says, sourly and probably rhetorically.

'If you hate it so much that just owning it would cancel out the emotional benefits of having something like the console, then yes, Uncle Red says.

Randy hoists the console onto his shoulder and begins to walk in a positive y direction. The Shaftoe boys are available to hump furniture at a moment's notice, but Randy needs to mark a bit of territory here, just to indicate that he is not without some masculine attributes himself and so he ends up carrying more furniture than he probably needs to. Back at the Origin, he can hear Red and Nina going at it. 'I have a problem with this,' Nina says. 'What's to prevent her from just putting every thing down at the extreme y axis-claiming that everything is terribly emotionally important to her?' Herin this case can only mean Aunt Rachel, the wife of Tom. Rachel is a multiethnic East Coast urbanite who is not blessed or afflicted with the obligatory Waterhousian diffidence and so has always been regarded as a sort of living incarnation of rapacity, a sucking maw of need. The worst-case scenario here is that Rachel somehow goes home with everything-thegrand piano, the silver, the china, the Gomer Bolstrood dining room set. Hence the need for elaborate rules and rituals, and a booty division system that is mathematically provable as fair.

'That's where [tau sub e] and [tau sub $] enter into it,' Uncle Red says soothingly.

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'All of our choices will be mathematically scaled so that they add up to the same total values on both the emotional and financial scales. So if someone clumped everything together in the extreme corner, then, after scaling, it'd be as if they never expressed any preferences at all.'

Randy nears the steamed-up Impala. One of the doors makes a crackling noise as superannuated weatherstripping peels away from steel. Robin Shaftoe emerges, breathes into his cupped hands, and takes a parade-rest position, signifying that he is available to discharge any responsibilities out here on the Cartesian coordinate plane. Randy looks up over the Impala and the retaining wall and the ice-clogged xeriscape above that and into the lobby of Waterhouse House, where Amy Shaftoe has her feet up on a coffee table and is looking through some of the extremely sad Cayuse-related literature that Randy bought for Avi. She looks down and smiles at him and just barely, he thinks, restrains the impulse to reach up and twirl one finger around her ear.

'That's good, Randy!' shouts Uncle Red from the Origin, 'now we need to give it some x!' Meaning that the console is not devoid of economic value either. Randy does a right-face and begins to walk into the (+x, +y) quadrant, counting the yellow lines. 'Give it about four parking spaces! That's good!' Randy plonks the console down, then pulls a pad of graph paper out of his coat, whips back the first sheet, which contains the (x,y) scatterplot of Uncle Geoff and Auntie Anne, and notes down the coordinates of the console. Sound carries in the Palouse, and from the Origin he can hear Aunt Nina saying to Uncle Red, 'How much of our [tau sub e] have we just spent on that console?'

'If we leave everything else down here at y equals zero, a hundred percent after scaling,' Uncle Red says. 'Otherwise it depends on how we distribute these things in the y dimension.' Which is of course the correct answer, albeit totally useless.

If these days in Whitman don't make Amy flee from Randy in terror, nothing will, and so he's glad in a sick way that she is seeing this. The subject of his family has not really come up until now. Randy is not given to talking about his family because he feels there is nothing to report: small town, good education, shame and self-esteem doled out in roughly equal quantities and usually where warranted. Nothing spectacular along the lines of grotesque psychopathologies, sexual abuse, massive, shocking trauma, or Satanic rallies in the backyard. So normally when