Yesterday I talked about the Bücherrad(-rad-rad &cetera) portion of the awesome scene (in Neal Stephenson’s *The Confusion* in Wolfenbütten (thanks to Dani and Emily for the coding!), wherein Leibniz and Fatio explore the library that Leibniz inherited from Duke August and is now cultivating with his new-fangled cataloging and classification plans. Yesterday was cataloging. Today: classification.

“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.”

Liebniz 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 taurpaulins. He peeled up the edge of one and flung it back to reveal that the rampart was a stack of books, thousands of them…

How hilarious would it be if that was what a library was, actually. A nice big pile of books covered in a tarp? Also, how funny is it to imagine that that is what digital information storage is like? A big pile of information covered by a tarp. Only here the tarp is that the stuff is invisible until you retrieve it? (Did I stretch that too far? Or JUST FAR ENOUGH?!)

Also, I love the shout-out to the arbitrariness of classification. Yes, it is organized in a fashion, but that organization, even if it is “intuitive,” i.e., sciency books together in Dewey in 500s, is arbitrary, because, of course, “500” doesn’t mean science anymore than “fhqwhgads” does, but also because where do we cut off science? Computer science is in the aughts. Medicine is in the 600s. We are cutting the whole damn thing into chunks, pretty much wherever we understand it. Which is why the whole thing is constantly in flux. When I left my last job, I left a list of reclassification projects, just as my predecessor had done; there wasn’t time in nine years to finish them all.

And, shout-out to Saussure, calling Adam’s naming of the animals arbitrary. I guess it would’ve been a bigger shout-out if he’d clarified that Adam also had to pioneer taxonomy at the same time by deciding which animals were different enough that they got their own names. (Incidentally, taxonomy isn’t just used to describe biological taxonomy but any kind of classification– ours included!)

Continuing:

“Now [the books] are in a heap, later they shall be on shelves– either way, how do you find what you want?” Leibniz asked…

“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 content.”

“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. [ed. note: this is a reference to the language I mentioned that the Royal Society was trying to develop in which it was impossible to speak Untruth.] For any conceivable subject, there would be a unique number. Write that number on the spine the book and shelve them in order. Then you can go directly to the right part of the library and find all the 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.”

Word. I think that it is pretty common for libraries to fudge the Dewey a bit to keep books by the same author together. Of course, not to the extent of putting geometry and physics together, but to the point of, say, simplifying a call number down to one or two decimal points beyond the whole number so they will fit. I had to do this all the time, and often it involved rearranging and reclassing things.

Also, the part about putting the books in numerical order of when they were cataloged or acquired reminded me of a story I heard about someone, in a library class, cataloging books by the color of their covers. (Actually, the books in my bedroom are arranged in color order. We haven’t cataloged them yet.)

And on–

Leibniz stepped over to an empty bookcase and drew his finger down the length of one shelf from left to right. “A shelf is akin to a Cartesian number-line. The position of a book on that shelf is associated with a number. But only *one* number! Like a number-line, it is one-dimensional. In analytic geometry we may cross two or three number-lines at right angles to create a multi-dimensional space. Not so with bookshelves. The problem of the librarian is that books are multi-dimensional with their subject matter but must be ordered on one-dimensional shelves.”

…[ed. note: this is still Leibniz]

“…Consider the following: Suppose we assign the number three to Aristotle, and four to turtles. Now we must decide where to shelve a book by Aristotle on the subject of turtles. We multiply three by four to obtain twelve, and then shelve the book in position twelve.”

“Excellent! By a simple multiplication you have combined several subject-numbers into one– collapsed the multi-dimensional space into a uni-dimensional number-line.”

“I am pleased that you favor my proposal thus far, Fatio, but now consider the following: suppose we assign the number two to Plato, and six to trees. And suppose we acquire a book by Plato on the subject of trees. Where does it belong?”

“The product of two and six is twelve– so it goes next to Aristotle’s book on turtles.”

“Indeed. And a scholar seeking the latter book may instead find himself with the former– clearly a failure of the cataloging system.”

“Then let me step once again into the rôle of Simplicio and ask whether you have solved *this* problem.”

“Suppose we use *this* codimg instead,” quoth the Doctor, reaching behind the bokcase and pulling out a slate on which the following table had been chalked– thereby as much as admitting that the conversation, to this point, had been a scripted *demo’*.

2 Plato

3 Aristotle

5 Trees

7 Turtles

2×5=10 Plato on Trees

3×7=21 Aristotle on Turtles

2×7=14 Plato on Turtles

3×5=15 Aristotle on Trees

[etc.]

“Two, three, five, and seven– all prime numbers,” remarked Fatio after giving it a brief study. “The shelf-numbers are composites, the products of prime factors. Excellent, Doctor! By making this small improvement– assigning prime numbers, instead of counting numbers, to the various subjects– you have eliminated the problem. The shelf position of any book may be found by multiplying the subject-numbers– and you may be assured it will be *unique*.”

Oh, man. This part is just incredibly rich. Firstly, I love prime numbers! In fact, one of my favorite things in the world is trying to determine in my head whether a number is prime or not! And I’m no savant; it takes work! Two, I love his classification scheme! It makes as much sense as any other, as far as I can tell, with the obvious problem that I will address below. Three, I think it is an interesting proposal to factor in the author at the same time as the subject, instead of, as both Dewey and Library of Congress do: subject first, author second. Fourth, people are still tackling the issue of multi-subjected books. And with the proliferation of subject headings (and their sub-headings), subjects are being broken down minutely (which I think is to the good of all involved), while the classification systems don’t have room to accommodate the growth (which I think is just the sad truth of it all. I can memorize a string of numbers up to ten digits pretty reliably, but that is mostly because of my cataloging work. I think most people do well with three to five digits, again, reliably. Also, where would you put a sixteen digit string on a book? Across the title?)

[ed note: Fatio: ]”I predict that you will find success, Doctor Leibniz, and that one day there will rise up, in Berlin, Vienna, or even Moscow, a Knowledge Engine on a titanic scale. The shelves will extend for countless leagues and will be crowded with books all arranged according to the rules of your system. But I fear that I could very easily become lost in the bowels of that place. Looking at a shelf I might see some number, eight or nine digits long. I would know this to be a composite number, the product of two or more primes. But to decompose such a number into its prime factors is a notoriously difficult and tedious problem. There is a curious *asymmetry* about this approach, in other words, lying in the fact that *to its creator* the structure and organization of the great library will be clear as glass– but to a solitary visitor it will seem a murky maze of impenetrable numbers.”

“I do not deny it,” Leibniz answered without hesitation, “but I find in this a sort of beauty, a reflection of the structure of the universe. The situation of the solitary visitor, as you have described it, is one with which I am familiar.”

Beautiful! Of course it is insane to imagine people walking around doing complicated factoring in their heads in order to figure out what the hell section of the library they are in. But! Is it somehow more intuitive for people to find themselves at the end of the 700s looking for books about sports? People may be less lost if they have spent a lot of time in libraries or if they are familiar with the process of looking up books in catalogs and then scanning the shelves for that particular call number. But, honestly, if one were a “solitary visitor” to a library (one that didn’t explain on the ends of the stacks what kinds of books are housed within), how easy would it be for one to find a book on the subject of one’s choice or even to determine what section one was in? What *would* intuitive classification look like? And how would we shift to it?

In closing, I just want to say how indebted I am to Neal Stephenson for entertaining me thus and for awakening parts of my brain that had been long un-exercised. And, of course, the materials I have been quoting are copyrighted to the teeth, and I hope I have been applying fair-use in my blogging. (A subject I have yet to explore, which I know I REALLY MUST!)