“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.”
“It is a pleasure to explain it to one who grasps the principle so readily,” Leibniz said. “Huygens and the Bernoullis have both spoken highly of you, Fatio, and I can see that they were by no means insincere.”
“I am humbled to hear my name mentioned in the same sentence with theirs,” Fatio returned, “but since you have been kind enough to so favor me, perhaps you will indulge me in a question?”
“It would be my privilege.”
“Your scheme is a fine way to build a library. For the correct position of any book may be found by taking the product of the several primes that correspond to its subjects. Even when those numbers grow to several digits, that presents no great difficulty; and in any event it is well known that you have invented a machine capable of multiplying numbers with great facility, which I now perceive is just one element of the immense knowledge engine you have proposed to build.”
“Indeed, all of these are of a piece, and may be considered aspects of my Ars Combinatorica. Did you have a question?”
“I fear that your library, once built, will be difficult to understand. You are seeking the help of the Emperor in Vienna, are you not?”
“It cannot be accomplished without the resources of a great kingdom,” Leibniz said vaguely.
“Very well, perhaps you are in communication with some other great prince. At any rate, it would seem, then, that you wish to make your Knowledge Engine on a colossal scale.”
“Marshalling resources is a continuing problem,” the Doctor said, still treading gingerly.
“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.”
“That is odd, for I conceive of you as the creator who stands with his hand on the Bücherrad and comprehends all.”
“You should know this about me. My father was a learned man who owned one of the finest libraries in Leipzig. He died when I was very small. Consequently I knew him only as a jumble of childish perceptions—between us there were feelings but never any rational connection, perhaps somewhat like the relationship that you or I have with God.”
And he related a story about how he had, for a time, been locked out of his father’s library, but later re-admitted.
“So I ventured into that library which had been closed up since the death of my father and still smelled like him. It might seem funny for me to speak of the smell, but that was the only connection I could draw at the time. For the books were all written in Latin or Greek, languages I did not know, and they treated of subjects with which I was completely unfamiliar, and they were arranged upon the shelves according to some scheme that must have been clear to my father, but to me was unknown, and would have been beyond my ken even if someone had been there to explain it to me.
“Now in the end, Monsieur Fatio, I mastered that library, but in order to do it I first had to learn Greek and Latin, and then read the books. Only when I had done these things was I finally able to do the most difficult thing of all, namely to understand the organizing principle by which my father had arranged the books on the shelves.”