“But could you construct it?”
“In itself, that wouldn’t be difficult. The stone can be used to produce many wonders, including a machine that moves perpetually without any external power, but the simplest discovery was described also by an Arab, Baylek al-Qabayaki. Take a vessel filled with water and set afloat in it a cork into which you have stuck an iron needle. Then pass the magnetic stone over the surface of the water, until the needle has acquired the same properties as the stone. And at this point the needle — though the stone would also have done it if it had had the capacity to move around a pivot — will turn and point north, and if you move it with the vessel, it will always turn in the direction of the north wind. Obviously, if you bear north in mind and also mark on the edge of the vessel the positions of east, south, and west, you will always know which way to turn in the library to reach the east tower.”
“What a marvel!” I exclaimed. “But why does the needle always point north? The stone attracts iron, I saw that, and I imagine that an immense quantity of iron attracts the stone. But then … then in the direction of the polestar, at the extreme confines of the globe, there exist great iron mines!”
“Someone, in fact, has suggested such is the case. Except that the needle doesn’t point precisely in the direction of the daystar, but toward the intersection of the celestial meridians. A sign that, as has been said, ‘hic lapis gerit in se similitudinem coeli,’ and the poles of the magnet receive their inclination from the poles of the sky, not from those of the earth. Which is a fine example of movement provoked at a distance, not by direct material causality: a problem that my friend John of Jandun is studying, when the Emperor does not ask him to make Avignon sink into the bowels of the earth…”
“Let’s go, then, and take Severinus’s stone, and a vessel, and some water, and a cork …” I said, excited.
“Wait a moment,” William said. “I do not know why, but I have never seen a machine that, however perfect in the philosophers’ description, is perfect in its mechanical functioning. Whereas a peasant’s billhook, which no philosopher has ever described, always functions as it should… I’m afraid that wandering around the labyrinth with a lamp in one hand, a vessel full of water in the other … Wait, though! I have another idea. The machine would point north even if we were outside the labyrinth, would it not?”
“Yes, but at that point it would be of no use to us, because we would have the sun and the stars …” I said.
“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 Averroes 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 m 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.”