The Confusion

Fatio closed his eyes, which was the only way to pry his attention from the outlandish skeletons, and stepped back, then maneuvered over to join Leibniz.

“Behold, the Bucherrad!”* Leibniz said.

Viewed end-on, the Bucherrad was hexagonal, and nearly as tall as Fatio. When he worked his way round to the front, he saw that it consisted mostly of six massive shelves, each one a couple of fathoms long, bridging the interval between hexagonal end-caps that were mounted on axles so that the whole apparatus could be revolved. But each of the six shelves was free to revolve on an axis of its own. As the Bucherrad spun, each of those shelves counter-rotated in such a way that it maintained a fixed angle with respect to the floor, and did not spill its load of books.

Going round to the other end, Fatio was able to see how it worked: a system of planetary gears, carven from hard wood, spun about the central axle-tree like Ptolemaic epicycles.

Then Fatio turned his attention to the books themselves: curious folio volumes, hand-written, all in the same hand, all in Latin.

“These were written out personally by one Duke August, a forerunner of that lot you just met. He lived to a great age and died some twenty-five years ago. It was he who assembled most of this collection,” Leibniz explained.

Fatio bent slightly at the waist to read one of the pages. It consisted of a series of paragraphs each preceded by a title and a long Roman numeral. “It is a description of a book,” he concluded.

“The process of abstraction continues,” Leibniz said. “Duke August could not keep the contents of his library in his memory, so he wrote out catalogs. And when there were too many catalogs for him to use them conveniently, he had woodwrights make Bucherrads-engines to facilitate the use and maintenance of the catalogs.”

“It is very ingenious.”

“Yes-and it is threescore years old,” Leibniz returned. “If you do the arithmetick, as I have, you may easily demonstrate that to hold all the catalogs needed to list all the world’s books would require so many Bucherrads that we would need some Bucherradrads to spin them around, and a Bucherrad-rad-rad to hold all of them-”

“German is a convenient language that way,” Fatio said diplomatically.

“And so on with no end in sight! There are not enough woodwrights to carve all of the gears. New sorts of knowledge-engines will be demanded.”

“I confess you have lost me, Doctor.”

“Observe-each book is identified by a number. The numbers are arbitrary, meaningless-a kind of code, like the names Adam gave to the beasts. Duke August was of the old school, and used Roman numerals, which makes it that much more cryptickal.”

Leibniz led Fatio away from the center of the floor toward the rugged stone walls, which were mostly barricaded by high thick ramparts covered in canvas tarpaulins. He peeled up the edge of one and flung it back to reveal that the rampart was a stack of books, thousands of them. All of them had been bound in the same style, in pigskin (for like many noble bibliophiles Duke August had bought all his books as masses of loose signatures and had them bound in his own bindery, by his own servants). The newest ones (say, less than half a century old) were still white. More ancient ones had turned cream, beige, tan, brown, and tar-colored. Many bore scars of long-forgotten encounters between pigs and swineherds’ cudgels. The titles, and those long Roman numerals, had been inscribed on them in what Fatio now recognized as Duke August’s hand.

“Now they are in a heap, later they shall be on shelves-either way, how do you find what you want?” Leibniz asked.

“I believe you are now questioning me in a Socratic mode.”

“And you may answer in any mode you like, Monsieur Fatio, provided that you do answer.”

“I suppose one would go by the numbers. Supposing that they were shelved in numerical order.”

“Suppose they were. The numbers merely denote the order in which the Duke acquired, or at least cataloged, the volumes. They say nothing of the contents.”

“Re-number them, then.”

“According to what scheme? By name of author?”

“I believe it would be better to use something like Wilkins’s philosophical language. For any conceivable subject, there would be a unique number. Write that number on the spine of the book and shelve them in order. Then you can go directly to the right part of the library and find all books on a given subject together.”

“But suppose I am making a study of Aristotle. Aristotle is my subject. May I expect to find all Aristotle-books shelved together? Or would his works on geometry be shelved in one section, and his works on physics elsewhere?”

“If you look at it that way, the problem is most difficult.”