P. Route 66 is a stringy, dispersed landscape of American detritus. Unlit neon signs advertise long-closed postwar establishments called, for example, the “Atomic Inn.” From I-40 east of Albuquerque, pull off at Tucumcari and drive northeast along the diagonal of highway 54, which used to run all the way to Chicago. The landscape before you gradually flattens. The plains increase. Shortly before the Texas line you will find Nara Visa, New Mexico.
On ghosttowns.com, Nara Visa is categorized most poetically as “semi-ghost.” It is surrounded by the sort of ranches that look vacant but probably aren’t. Though it’s properly in the Mountain Time Zone, Nara Visa observes Central Time. The name is not Spanish; it is a mondegreen of the town’s original name Narvaez, after a prominent local sheepherding family.
There are everywhere decaying signs of occupation. There are people, but they are hiding. There is evidently still an occasional Cowboy Gathering in Nara Visa--one was scheduled for September 2013. “Shows are not organized until everyone arrives on Friday night,” the website reads. “A schedule of events is announced, but not rigidly followed.” Among these events is a bubble gum spitting contest. An account is given of the 2010 event, ostensibly the most recent. “Sunday ended the very successful and fun filled weekend with a biscuit and gravy breakfast followed by a Cowboy church service.”
Various vintage cars and trucks rust away along the road, and buildings fall into disrepair. The old historic school is still being used as a community center--in fact, it is the host and primary beneficiary of the Cowboy Gathering. The post office, established in 1902, is still open.
P. Two or three deserts away, depending on how you count them, over the Colorado Plateau and over the high Sierras and the Coast Range and down to the ocean, there is a place called Petaluma, California. It has been known by such monikers as the “Egg Capital of the World” and “Chickaluma” for its prominent chicken processing industry. The egg incubator was invented there in 1879. Petaluma remains notable for its large quantity of historic buildings, including many that survived the great San Francisco earthquake of 1906.
In late 1962 a composer named Harry Partch moved into one of the city’s abandoned chick hatcheries.
Partch’s story is long and sinuous, and it’s awfully hard to decide where to begin and which beautiful details to omit. Born in 1901, he spent much of his childhood in a small wild-west town in Arizona, the son of missionaries who had lived in China and who taught him songs in Yaqui and Spanish. He rambled up and down the west coast, studying music formally and informally, exploring tuning theory and history, and beginning to build his own instruments. In 1930, dedicated to forging a new path outside the European classical tradition, he burned all his juvenile compositions in a potbelly stove in New Orleans. He traveled to New York in 1933 and found some support from the community of experimental composers that had thrived there in the 1920s. He won a grant that took him to England for study and research. He met William Butler Yeats and planned a collaboration.
Then the Great Depression caught up with Partch, and he spent chunks of the subsequent decade traveling as a hobo, riding the rails and working occasionally while continuing to compose music and develop theories of harmony and tuning.
His relationship to the musical establishment improved in the 1940s; he received a Guggenheim grant in 1943 and worked in residence at the University of Wisconsin from 1944-1947. For the rest of his life he went wherever he could find financial support and safe housing for his large collection of hand-built instruments.
Partch lived in Petaluma for less than two years, long enough to write And on the Seventh Day Petals Fell in Petaluma. It is his only mature, extended work that is not vocal or theatrical in nature; the 35-minute form is entirely instrumental and was meant in part as a didactic exercise to train a new ensemble of performers. Some of the music became part of his final theater work, Delusion of the Fury, which premiered in 1969.
It doesn’t sound like anything you’ve heard before, because you’ve never heard these instruments before, because Partch built them, tailored them to fit his unique tuning systems.
There are no voices, no dialogue and no story, but the music still feels narrative in the way it progresses continuously between states. Every minute or so the music stops and there is a change; like a strange picaresque on the southwestern plains, the form travels in episodes, gets itself in and out of trouble as it floats downriver.
I don’t remember why I put on this music as I drove up highway 54, but I know that it felt perfectly right in Nara Visa and beyond as I crossed the Texas panhandle into that strange country far from the interstate highways, outside our own time. I think now of young Partch and his parents in their little house in Arizona, singing Chinese songs and speaking with Yaqui holy men. The wild west isn’t a whole region, anymore, but it’s out there in pockets; it emerges when and where we aren’t paying attention. When I drove through Nara Visa, though I didn’t see anyone, I wouldn’t have been surprised to glance through the broken windows of one of those paint-stripped old houses to see a young man in ragged clothes perched over a potbelly stove, burning all his papers but a notebook with some drawings of zithers and viols in scales no one had ever used before.
P. Königsberg was a Prussian city along both sides of the Pregel River. Today it is known as Kaliningrad, Russia. The city center encompassed two islands in the Pregel, and there were seven bridges that crossed from the mainland to, from, and between the islands.
The problem is this: how does one walk through Königsberg, crossing each bridge once and only once? The walk can begin and end anywhere, but each bridge must be crossed completely, and there can be no retracing of steps.
It is actually impossible, and when Leonhard Euler proved this mathematically in 1735 he opened the way to new frontiers in graph and topological analysis--just by proving that the task could not be done.
The first thing Euler did was dispense with the map. It was clear to him that starting and ending points and intermediate paths didn’t matter; only the order of bridges was important. He could therefore formulate the puzzle in abstract terms, eliminating unnecessary features to focus on points and their connections. He made, in short, a graph.
The fundamental question is how many bridges touch each landmass--in abstract terms, how many paths diverge from each point. Even-numbered nodes, that is, landmasses with an even number of bridges, are crucial. Such points can be accessed and then departed from, a traveler will never get stuck there. Königsberg had too many odd-numbered nodes. One odd-numbered node on the map would be fine; a traveler could start there and simply not return. But Königsberg had four. There were too many places to get stuck.
Variations of the problem have been formulated for math students, often with fanciful decorations of the nodes--taverns, for example, and castles occupied by Red and Blue Princes--but as we see from Euler, these descriptive elements are only a distraction from the basic mathematical information. The graph is what matters.
Two of the historic bridges were destroyed when Königsberg was bombed during World War II. When the puzzle is rewritten to fit the current, five-bridge Königsberg, the Eulerian walk becomes possible.
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