The Confusion

“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 Bucherrad 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.”

Fatio said: “So you are not troubled by the plight of my hypothetical scholar, a-mazed in the penetralia of your Knowledge Engine. But Doctor Leibniz, how many persons, dropped into a library of books written in unknown languages, could do what you did?”

“The question is more than just rhetorical. The situation is not merely hypothetical,” Leibniz answered. “For every human being who is born into this universe is like a child who has been given a key to an infinite Library, written in cyphers that are more or less obscure, arranged by a scheme-of which we can at first know nothing, other than that there does appear to be some scheme-pervaded by a vapor, a spirit, a fragrance that reminds us that it was the work of our Father. Which does us no good whatever, other than to remind us, when we despair, that there is an underlying logic about it, that was understood once and can be understood again.”

“But what if it can only be understood by a mind as great as God’s? What if we can only find what we want by factoring twenty-digit numbers?”

“Let us understand what we may, and extend our reach, insofar as we can, by the making of engines, and content ourselves with that much,” Leibniz answered. “It will suffice to keep us busy for a while. We cannot perform all of the calculations needed without turning every atom in the Universe into a cog in an Arithmetickal Engine; and then it would be God-”

“I think you are coming close to words that could get you burnt at the stake, Doctor-meanwhile, I turn to ice. Is there a place where we could strike a balance between those two extremes?”