“I know, I know. But if the machine functions both indoors and outdoors, why should it not be the same with our heads?”
“Our heads? Of course, they also function outside, and in fact, on the outside we know quite well the layout of the Aedificium! But it is when we are inside that we become disoriented!”
“Precisely. But forget the machine for now. Thinking about the machine has led me to think about natural laws and the laws of thought. Here is the point: we must find, from the outside, a way of describing the Aedificium as it is inside. . . .”
“But how?”
“We will use the mathematical sciences. Only in the mathematical sciences, as Averroës says, are things known to us identified with those known absolutely.”
“Then you do admit universal notions, you see.”
“Mathematical notions are propositions constructed by our intellect in such a way that they function always as truths, either because they are innate or because mathematics was invented before the other sciences. And the library was built by a human mind that thought in a mathematical fashion, because without mathematics you cannot build labyrinths. And therefore we must compare our mathematical propositions with the propositions of the builder, and from this comparison science can be produced, because it is a science of terms upon terms. And, in any case, stop dragging me into discussions of metaphysics. What the Devil has got into you today? Instead, you who have good eyes take a parchment, a tablet, something you can make signs on, and a stylus. . . . Good, you have it? Good for you, Adso. Let’s go and take a turn around the Aedificium, while we still have a bit of light.”
So we took a long turn around the Aedificium. That is, from the distance we examined the east, south, and west towers, with the walls connecting them. The rest rose over the cliff, though for reasons of symmetry it could not be very different from what we were seeing.
And what we saw, William observed as he made me take precise notes on my tablet, was that each wall had two windows, and each tower five.
“Now, think,” my master said to me. “Each room we saw had a window. . . .”
“Except those with seven sides,” I said.
“And, naturally, they are the ones in the center of each tower.”
“And except some others that we found without windows but that were not heptagonal.”
“Forget them. First let us find the rule, then we will try to explain the exceptions. So: we will have on the outside five rooms for each tower and two rooms for each straight wall, each room with a window. But if from a room with a window we proceed toward the interior of the Aedificium, we meet another room with a window. A sign that there are internal windows. Now, what shape is the internal well, as seen from the kitchen and from the scriptorium?”
“Octagonal,” I said.
“Excellent. And on each side of the octagon there could easily be two windows. Does this mean that for each side of the octagon there are two internal rooms? Am I right?”
“Yes, but what about the windowless rooms?”
“There are eight in all. In fact, the internal room of every tower, with seven sides, has five walls that open each into one of the five rooms of the tower. What do the other two walls confine with? Not with rooms set along the outside walls, or there would be windows, and not with rooms along the octagon, for the same reason and because they would then be excessively long rooms. Try to draw a plan of how the library might look from above. You see that in each tower there must be two rooms that confine with the heptagonal room and open into two rooms that confine with the internal octagonal well.”
I tried drawing the plan that my master suggested, and I let out a cry of triumph. “But now we know everything! Let me count. . . . The library has fifty-six rooms, four of them heptagonal and fifty-two more or less square, and of these, there are eight without windows, while twenty-eight look to the outside and sixteen to the interior!”
“And the four towers each have five rooms with four walls and one with seven. . . . The library is constructed according to a celestial harmony to which various and wonderful meanings can be attributed. . . .”
“A splendid discovery,” I said, “but why is it so difficult to get our bearings?”
“Because what does not correspond to any mathematical law is the arrangement of the openings. Some rooms allow you to pass into several others, some into only one, and we must ask ourselves whether there are not rooms that do not allow you to go anywhere else. If you consider this aspect, plus the lack of light or of any clue that might be supplied by the position of the sun (and if you add the visions and the mirrors), you understand how the labyrinth can confuse anyone who goes through it, especially when he is already troubled by a sense of guilt. Remember, too, how desperate we were last night when we could no longer find our way. The maximum of confusion achieved with the maximum of order: it seems a sublime calculation. The builders of the library were great masters.”
“How will we orient ourselves, then?”
“At this point it isn’t difficult. With the map you’ve drawn, which should more or less correspond to the plan of the library, as soon as we are in the first heptagonal room we will move immediately to reach one of the blind rooms. Then, always turning right, after two or three rooms we should again be in a tower, which can only be the north tower, until we come to another blind room, on the left, which will confine with the heptagonal room, and on the right will allow us to rediscover a route similar to what I have just described, until we arrive at the west tower.”
“Yes, if all the rooms opened into all the other rooms . . .”
“In fact. And for this reason we’ll need your map, to mark the blank walls on it, so we’ll know what detours we’re making. But it won’t be difficult.”
“But are we sure it will work?” I asked, puzzled; it all seemed too simple to me.
“It will work,” William replied. “But unfortunately we don’t know everything yet. We have learned how to avoid being lost. Now we must know whether there is a rule governing the distribution of the books among the rooms. And the verses from the Apocalypse tell us very little, not least because many are repeated identically in different rooms. . . .”
“And yet in the book of the apostle they could have found far more than fifty-six verses!”
“Undoubtedly. Therefore only certain verses are good. Strange. As if they had had fewer than fifty: thirty or twenty . . . Oh, by the beard of Merlin!”
“Of whom?”
“Pay no attention. A magician of my country . . . They used as many verses as there are letters in the alphabet! Of course, that’s it! The text of the verse doesn’t count, it’s the initial letters that count. Each room is marked by a letter of the alphabet, and all together they make up some text that we must discover!”
“Like a figured poem, in the form of a cross or a fish!”
“More or less, and probably in the period when the library was built, that kind of poem was much in vogue.”
“But where does the text begin?”
“With a scroll larger than the others, in the heptagonal room of the entrance tower . . . or else . . . Why, of course, with the sentences in red!”
“But there are so many of them!”
“And therefore there must be many texts, or many words. Now make a better and larger copy of your map; while we visit the library, you will mark down with your stylus the rooms we pass through, the positions of the doors and walls (as well as the windows), and also the first letters of the verses that appear there. And like a good illuminator, you will make the letters in red larger.”
“But how does it happen,” I said with admiration, “that you were able to solve the mystery of the library looking at it from the outside, and you were unable to solve it when you were inside?”
“Thus God knows the world, because He conceived it in His mind, as if from the outside, before it was created, and we do not know its rule, because we live inside it, having found it already made.”
“So one can know things by looking at them from the outside!”
“The creations of art, because we retrace in our minds the operations of the artificer. Not the creations of nature, because they are not the work of our minds.”
“But for the library this suffices, doesn’t it?”
“Yes,” William said. “But only for the library. Now let’s go and rest. I can do nothing until tomorrow morning, when I will have, I hope, my lenses. We might as well sleep, and rise early. I will try to reflect.”
“And supper?”
“Ah, of course, supper. The hour has passed by now. The monks are already at compline. But perhaps the kitchen is still
