“the boundary of Zelrijk-Aalberg has been litigated over in documents that, were they all stored in one location, would more than occupy all of the available space in the country. Many of those made references to landmarks such as trees that had died centuries ago, creeks that had changed their courses over time, or buildings that had not existed since the days of Charlemagne. Lacking modern conveniences such as GPS, the locals had fallen into the habit of using available landmarks to define the boundary. Every so often the count of Zelrijk-Aalberg would walk that boundary and beat said landmarks with a stick as an aid to memory, just as Anne-Solenne says. On one such occasion, this count—who happened to be mathematically inclined—was making his way across a tavern that straddled the boundary. The tavern had a tile floor with a long crack running across it. It had become an accepted fact that the crack constituted part of the boundary. The tavern actually dates to the 1170s and the crack is mentioned in a legal document, handwritten on vellum in the Year of Our Lord 1219. So, the count was sidestepping along this crack, whacking it with his ceremonial stick while his lawyers and servants looked on, when he got to noticing that it rambled this way and that, as cracks are wont to do, and that if one bent down and stared at a small portion of it through one’s lorgnette, one could see smaller ramblings superimposed on the larger ones, and so on and so forth. As a sort of practical joke he instructed a surveyor to calculate the precise length of this part of the boundary, taking into account all of its turnings this way and that. In less time than it took for the count to drink a tankard of beer, the surveyor had produced an answer. The count disputed the figure, threatened to strike the surveyor with his boundary-beating stick, and commanded him to measure it again, this time on his hands and knees using a ruler. In the meanwhile the count consumed another beer. The surveyor turned in a revised figure that was somewhat larger. The count renewed his threat and ordered him to repeat it a third time using a magnifying glass and a set of fine calipers.”
“So, that’s fractals in a nutshell right there,” Julian said. “The point being that the length of the crack—”
“—and hence of Zelrijk-Aalberg’s border—” Enoch added.
“—doesn’t actually have any one fixed value that can be known. The result of the measurement will depend on the resolution of the measuring device used.”
“This particular ancestor of mine didn’t actually live in Z-A, or visit it that often. He had an estate in Germany that was a thousand times as large. After all of this happened he went back there and wrote a paper about it, which was forgotten until the 1960s, when it came to light in the course of a dispute about who had first invented certain concepts from fractal geometry.”
With that it seemed as though the four Princetonians had arrived at the collective determination that Enoch was cool. Much older than them, to be certain, and with little in common, but definitely one of the gang for the next day and a half.
Any number of further questions could, of course, be asked of this man: where he had come from, how he had spent his career, and so on. And indeed some such questions did get asked as the sun swung slowly round into the west, coming hard into the windshield, and took its sweet time skidding toward the flat horizon before unceremoniously plunging behind a line of black thunderheads. Enoch’s answers tended to be vague, brief, and self-deprecating. He had a knack for segueing into some other topic that was invariably more interesting than whatever had just been asked of him. Consequently you could ask him questions all day long. But at the end of that day, you’d have spent three minutes getting answers and many hours talking about other things—and you’d prefer it that way.
The car was perfectly capable of driving through the night as its occupants slumbered, but it was cramped, and so they pulled off the interstate into a little oasis and hustled into the lobby of a chain motel just as wild fat drops of rain were beginning to smack down, exploding like water balloons, driven on sage-scented winds. The place had been built to serve as a truck stop back when