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PEEMSTER

The Mean Value we’re after, A, can now be expressed integrally as the Area of some intermediate-type rectangle whose height is taller [sic] than r but shorter [sic] than R. From here on it’s just tit. We need a constant. You always need a constant. Inc’s nodding his head sarcastically like I think I’m saying something sage. Let d be any constant, for computational reasons the closer to 1 the better, so like let d be the size of Hal’s Unit.

Hal Incandenza’s Addendum: In meters.

Michael Pemulis’s Resumption: Very funny. So now, just looking at the wicked-illuminating PEEMSTER diagram above, you can see that this Area we want:

is going to be bigger than the area of the rectangle with height r and but also smaller than the area of the rectangle with height R. Pure mental reason [sic] compels, then, that [sic] somewhere in there between r and R there’s an exact height, f(x’), such that (I have to say that every demonstration of a stats theorem has Let and such that in them, mostly I think because they’re so wicked much fun to say) such that the rectangle of this height f(x’) over the whole interval [a, b] has exactly the Area we want, the Mean Value of all the historic [sic] expenditure-ratios; in other words in abstracted form:

where (b — a) is just the size of the interval. And so have a look at the revealing diagram labeled HALSADICK:

This fucking works. You don’t have to crunch out a whole new ratio each time for each Combatant to dole out the ordnance. You just skim the highest and lowest ratios off the Eschaton records the Beanie-man keeps on each time. This is wicked. This is fucking elegant. Note that (Note that’s another like compulsitory [sic] term) note that the Combatant’s Mean-Value megatonnage will change, slightly, from Eschaton to Eschaton, exactly the way a like hitter’s season average will alter just a bit from at-bat to at-bat, depending integrally on what he delivered on his last trip to the plate and whatnot. Note also that you can use this Mean-Value time-saver with anything that varies within a (definable) set of boundaries and whatnot — like any line, or a tennis court’s boundaries, or like maybe say a certain drug’s urine-level range between Clean and Royally Pinched. As a like exercise, if you’re interested, play three hours of high-level competitive jr. top-level [sic] tennis and then calculate the Mean Value of the ratios of first serves to appearances at net and appearances at net to points won; for a serve-and-volleyer, this is how to tell how serve-dependent his match-performance is. DeLint does this kind of exercise every morning sitting on the can. It’s going to be interesting to see if [sic] Hal, who thinks he’s just too sly trying to outline Eschaton in the 3rd-person tense [sic] like some jowly old

Eschatologist with leather patches on his elbows [sic], if Inc can transpose [sic?] the math here without help from his Mumster. Later. P.S. Allston Rules.

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