Jascha Hoffman

Prefuse 73
One Word Extinguisher
[Warp; 2003]
Rating: 9.1

Up to now, Scott Herren -- the shy, lanky Atlantan responsible for Prefuse 73's fabulous glitch-hop debut Vocal Studies + Uprock Narratives -- hasn't made his name as a purveyor of confessional music.
The closest he ever came was the laptop catharsis of Delarosa and Asora, which had no secrets to tell; rather, its intricacies of meter and texture gave your head something to do while your guts spilled out over it. Vocal Studies + Uprock Narratives was hard-edged and fast-cutting, immersed in early rap techniques and sensibilities; it didn't express feelings, it steamrolled them. But One Word Extinguisher shows a range of emotional grappling usually foreign to instrumental hip-hop. It's clear that Herren was coming back to the studio night after night not just for skills and thrills, but for a measure of solace.

"The never-ending battle" is what Herren calls the break-up that lasted for the year-plus during which this album was in production. "I locked myself in my room working, disconnected the phone, bummed out as fuck," he told me in March. "You can't talk to anybody, you feel like shit, and it's the only thing you have to express yourself." A year of unspeakable suffering channeled into sixty ripe minutes: in the hands of anyone else, this could be torture.

The sorrow sparks with a sweeping wail of queasy ahhh's that carry stunted hopes for a soon-to-be-doomed relationship. Vocal scraps and a blood-curdling scream announce the descent of the mask of hip-hop rage, as an eightfold synth-scribbling bomb drops right into "The End of Biters", the first of several sucker-punching cutfests in the illustrious tradition of the edit record. Next comes Diverse's self-absorbed "Plastic", a screed that rails with righteous indignation against "pop trends and predetermined top-tens." All this over-the-top rebuke is obviously an escape from something.

Things begin to come into focus as "Uprock and Invigorate" bounces in with its edges exposed. Warm, fretless bass, flitting Rhodes, drizzling sawtooth, and a brittle snare intent on stocking up and locking down with every passing bar: everything is absolutely on point. But beneath the surface lies a hint of tension between the percussive exoskeleton and its syrupy core, an orderly contest of soul-versus-machine that momentarily eclipses the sense of loss.

The rest of the album projects this kind of tension into a giant battle of the sexes. "The Color of Tempo" mangles its feminine samples with a virile beatbox pattern; "90% of My Mind Is with You" breaks up heavy panting with a deliberately difficult, meter-defying beat, and ends with a series of mournful, defeated R&B samples. There can be no more doubt when, on "Female Demands", a girlfriendish voice casually tells Herren to "fuck with the beat here" only to be throttled by digital effects; the rest of the track feels like a giant damaged gynorcism. Before we know it, we're desperately trying to forget her, bumping with another woman who croons "you... you... you..." on the offs.

Meanwhile, straight meters are often sprinkled with triplet ligaments, propelling the beat with an uncommonly light touch. But Prefuse's rhythmic sophistication isn't just about alternating threes and fours -- as the lesson goes, it takes two interlocked meters to make African music. While Herren rarely tries to stand up in two meters at once, he often relies on the juxtaposition of mildly divergent rhythmic feels within the same beat, proving his mastery of some of the subtler tensions available to the instrumentalist.

Many tracks seem like tricks to distract us from the ongoing devastation. Sooner or later, it sinks in that we're in the company of an emotional fugitive, sealed in a room with machines whose perfect control, he is convinced, will allow him to avoid the inevitable emotional reckoning. Through scorn and bombast, through distraction and self-parody, through the sheer weight of craft, this Prefuse tries to wear his sorrow down, to crush himself, to explode the emptiness. A thrilling listen, but how could such a mission succeed?

I'm not sure how he did it. There's a glimmer of hope in the open restraint of "Choking You", a sawtooth shuffle scattered with chirpy, chalky bits. Another late track calls a gender truce, as a skeletal crunch frames some lightly doctored female vocals, giving a cold, sweet impression, like melon rinds left out in the rain. And the last track -- in spite of its metric and sexual duplicity -- gives a baffling promise of balance. Unexpectedly, the music becomes its own consolation.

Here's a problem Lewis Carroll enjoyed posing to kids like Alice: how many colors do you need to fill in any map so that neighboring countries are always colored differently?

It sounds simple enough. But when a Victorian law student first posed the question, guessing that it could be done with a mere four colors, logician Augustus De Morgan was stumped. While no one could devise a map that required more, a proof that every map requires only four colors proved remarkably elusive. Mapmakers didn't care, but problem-solvers were obsessed for decades, including the Bishop of London, a Kentucky colonel, and a California traffic cop. The question's very intractability has inspired innovations in computing and network theory, but some say it still has no satisfying solution.

Oxford professor Robin Wilson's Four Colors Suffice: How the Map Problem was Solved (Princeton: 2003) presents the colorful history of this conjecture, with an unassuming lucidity that will appeal to the mathematical novice. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride: after telling his class that the problem had been wasted on third-rate minds, the great number-theorist Herman Minkowski took weeks at the blackboard trying to solve it, finally admitting, "Heaven is angered by my arrogance; my proof is also defective."

The first dead-end occurred shortly after the problem was first posed in 1852. De Morgan became obsessed with his initial insight that in any group of four regions, each bordering every other, one region must be completely enclosed by the others, and thus safe from forcing any colors outside the group. Though undeniably true, this was a false start: looking at single groups of four, one at a time, fails to take into account the myriad ways these groups might interact in ways that force the use of more colors.

The next failure, which convinced mathematicians worldwide for over a decade, actually took giant steps in the right direction. Cambridge mathematician Arthur Cayley revived the problem in 1878 and suggested a totally new approach: if you assume there exist some maps that need more than four colors, and of those you take only the ones that have as few regions in them as possible, then you'll have a manageable but complete set of counter-examples on your hands. (Wilson calls these the "minimal criminals.") If you can show that none of these counter-examples can possibly exist, then you've shown that four colors suffice. The only problem is, there are lots of them.

London barrister and amateur mathematician Alfred Bray Kempe ran with this approach, devising an elegant method that claimed to cleanly dispatch with all possible counter-examples. He put one region after another at the center of a counter-example-first a two-sided shape, then a triangle, square and pentagon-then ruled them out by listing all the possible chains of regions that could branch off from them. The proof was widely accepted, and Kempe was elected a Fellow of the Royal Society, and even knighted.

But in 1890, Percy Heawood, an Oxford eccentric known for his immense mustache and flowing cape, produced a map that showed that one of Kempe's chains didn't work. Even as he disgraced Kempe, however, Heawood demonstrated the lasting value of his contribution, giving a full Kempe-style proof that five colors suffice. (As a result of Heawood's later work, we now know that any map drawn on a doughnut requires no more than seven colors, not counting sprinkles. "There are, of course, additional reasons why one seldom encounters a map of the United States on one's doughnut," mused novelist Tom Robbins.)

The modern story picks up in 1948, when German geometer Heinrich Heesch realized that if he could find a master set of patterns that can't appear in a minimal criminal, he would rule out all possible counter-examples and have a proof. But finding these patterns was really hard, and there were thousands of them.

Enter the computer. In 1976, after 2000 machine-hours at the University of Illinois, Kenneth Appel and Wolfgang Haken found every single one, turning out the first famous computer-aided proof. Some claimed this was not a proof, since it cannot be verified in detail by a human being. By admitting computer proofs into the canon, writes Robin Wilson, math was "in danger of becoming an empirical science, as fallible as physics." Far from a feat of pure reasoning, the answer appeared to some as a monstrous coincidence.

There's an unwritten law as old as math itself: proof comes with understanding. But Appel and Hanken's proof, while almost certainly valid, doesn't clear anything up. Math is changing because of proofs like theirs: Computer jocks like Stephen Wolfram insist that math needs to get beyond its infatuation with axioms, while string theorists say their results just can't wait for rigorous proof. And strangely, mathematicians are even starting to teach machines to prove theorems on their own. So maybe some day computers will explain why four colors are enough, in terms we can understand.