Analog SFF, July-August 2007

by Dell Magazine Authors

  Heytesbury laughs in delight. “Well done, master clocksman!"

  The man shakes his head. “But, my sir, if only you saw the true clocks I have made!” He tugs his forelock and turns again to admonishing the clumsiness of his apprentices.

  Nicole and Albrecht arrive, the Saxon flourishing a metal rule—a mason's rod that he has “borrowed” from the nearby construction site. It is a “rule of thumb,” with tics in the metal at intervals of one thumb's-length, or uncias. “Nicole and I thought to mark the ramp at equal intervals of one shoe—how do you say it?"

  “Pied,” says Buridan.

  “Foot,” says Heytesbury. “But be certain to make an especially heavy mark,” the Englishman continues, “at the doubling points: one, two, four, eight, sixteen, and so forth. If the mathematics is true, our sphere will reach each of those marks at equal intervals. Oh, had Abbot Richard but lived to see this!” And he hurries off to give unsolicited advice to the workmen.

  Will the ramp and basin never be done? The carpenters work their levels and hang their plumbs and hammer wedges into the ramp to ensure its evenness. Water is hauled in buckets from the well and poured into the basin. Some tent canvas is produced to shield the basin from debris that might clog the channels. There is always one more task wanting. Buridan feels at times like Achilles chasing his tortoise: coming incrementally ever nearer without ever quite attaining the end.

  So, perhaps there is no last moment of activity; but there is a first moment at which all stands finished.

  Georges the carpenter has added a touch of his own. The lever that releases the ball to roll down the rails will also turn the master faucet. Watered by silver, his earlier skepticism has flowered into delighted cynicism. He has suggested a number of improvements to the device, each at an additional cost.

  Fernand insists on proving the water flow. “I know she's not a clock, rightly speaking,” the man says, “but ‘tis what we always do before I place my hallmark. A good clock, the water must flow equally at all times; so we will let the water flow through all five faucets for the same duration. Then you may weigh the flasks to ensure that the same weight of water has issued from each. If not, I have shims to adjust any that are off."

  The “calibration” proof is performed and Fernand adjusts nozzles two and five and soon all is in balance. The clockmaker surveys his handiwork, much as God is said to have done after His six days’ labor. “This has surely been the most peculiar instrument I have ever made!” Then from his workman's pouch he extracts a metal die and a sledgehammer and with these instruments strikes the mark of his guildhall into the basin.

  Buridan has seen such marks in passing his whole life. Perhaps he has even seen them being struck. But he has never seen it done after reading Philoponus, and it is as if he has never seen it before in his life. He grabs the clockmaker's wrist and pries the die from the man's astonished grasp.

  “The die is reverso,” he says, studying its face.

  “Surely!” Fernand snatches his precious hallmark from the Rector and returns it to his pouch. “Otherwise, the hallmark would be backward. We can't have that!"

  “What if..."

  What if ... Scholars have been accustomed to reasoning secundo imaginationem ever since the condemnation of certain propositions of Aristotle more than fifty years before. “What if you made one of these for each letter of the alphabet? Then you could strike any name or word you wish; and if you applied ink to the face, you could press it upon a page and write the same thing over and over, always the same!"

  Buridan is a philosopher, not a mechanic, but he realizes that there would be practical difficulties—in casting dies, holding them aligned, and so on; but ingeniators delight in overcoming such difficulties. Bacon's explosive powder, perfected by a Freiburg ingeniator, Berthold “the Blackened,” has recently been used in the Italian wars. Surely, printing with archetypes can be no more difficult!

  * * * *

  When the day comes for their contrived experience, Buridan and his helpers discover that the young scholars of the university have devised a new amusement, in which they themselves slide down the rails. This has produced some splinters in a few arses, which amuses the Rector, and has warped the rails out of true, which does not. He postpones matters, summons Georges and his apprentices to repair the damage, and sets the corporation militia to stand watch over the device.

  Having the day at leisure, he goes to fetch Nicole's newly repaired spectacles from Louis the optician, a gray-haired man with bulging eyes. They have been re-polished and affixed into a new frame of steel wire. Buridan asks the fee and the man waves him off.

  “That notion of yours has already more than paid the fee,” he says, presenting him with a pair of tubes, one sliding inside the other, the whole being nearly an arm's length. Buridan has quite forgotten, and the lensman reminds him. “You told me that looking through this new-fangled glass at a normal lens makes everything seem larger. So I ground me some new lenses and tried for myself. Took some while to get ‘em right—they must be planar on one side, y'see. The lens glass being at the far end and the concave glass at the nearer...” And he goes on regarding focal lengths and apertures. “But it works just like ye said. Here, you look through the small end, what I call the ‘ocular.’ That's right, my sir. Then you slide the tubes until everything is sharp."

  Buridan laughs with delight when, peering through the window, he sees the goldsmith in the shop across the street polishing a ring that he has crafted.

  “I call it a ‘look-glass,” the gray lensman says. “I let people peek for a denier each. You can see the bells in the cathedral tower. There, in the distance between the goldsmith and the apothecary.” The scene leaps into Buridan's eye, and he nearly jumps back in alarm.

  “It's become popular,” the lensman continues. “Four or five people come by each day to see, and some stay to purchase reading lentils, or they bring me their lenses to repair. Some of them tarry too long over the look-glass, though. There's a bawdy house down the street, and I think they hope for a glimpse through its windows. I need a sand-glass to call time on them."

  Buridan verifies the presence of the bawdy house, but the windows are shuttered. He tells the optician that Fernand the clockmaker can devise a water clock that raises an alarum at remarkably short intervals and Louis resolves to acquire one. “Then it's the ‘alarum-clock’ telling them their time is expired, and not me."

  Buridan, fearing his own time is expired, returns the tube, but the optician will not have it. “But no, my sir. It is that you must have one, since it was of your suggestion."

  The Rector thanks him and leaves the shop, but not before the optician calls him back for Nicole's glasses that he has left behind. On his way home, Buridan pauses at every street and aims the—the spectum latique? The tele skopos?—at every distant sight. Soon, he has acquired a train of citizens, both curious and amused at the Rector's strange activities.

  One of the curious is Marcel Etienne, newly elected provost of the cathedral market. He thinks all scholars unworldly, but also knows the Rector a shrewd magistrate. He prays a glimpse through the tube and Buridan points him toward the church of Our Lady.

  “I see nothing but a blur,” the clothier complains and Buridan explains about perspectiva and focus. The complaint shifts. “But the image, she is greenish. Pfui! She cannot be real."

  “That is but a consequence of metals in the glass.” Or so Louis had told him. Buridan resolves to write a tractatus on the optics of dual lenses.

  “Zut!” cries the provost. “Ernst the butcher places his thumb on the balance beam! That is an offence against the rules of the marketplace!” He takes his eye from the tube, looks at it, looks at Buridan. “How much do you want for it?"

  “It is a gift to me,” the Rector replies. “But Louis the optician can make another for you."

  “But this is wonderful! I can police the market without showing myself.” He turns to go, stops suddenly and looks about. Then he steps to the ban
ks of the Seine and aims the device downstream, past the Grand Bridge and the floating mills, into the far distance. For a time he studies the horizon and the crowd that has followed him to the riverside strains to see what transfixes his attention.

  Etienne closes the far-seer and slaps the tube absently against his palm. “I shall need two,” he says to Buridan. “One for my own use; but yes, one also for the Constable of France. Think, my sir the Rector! With such a ‘look-glass,’ the watchmen can mark the English fleet at many leagues distance, allowing the Constable to dispose his forces to best advantage. My thanks to you, Rector!” And with that, he presses the look-glass into Buridan's hands and dashes off for the glassmakers’ district.

  * * * *

  In his quarters once more, Buridan finds his houseguest bent over parchment, explaining some point of mathematics to Nicole Oresme. Buridan gives the bachelor his repaired glasses and shows the look-glass to Heytesbury.

  “A marvelous device,” the Englishman says after he has gazed in amazement out the window. “Bacon described just such an ‘optical tube’ in his Great Work: ‘And when we wish, things far off can be seen as near, and vice versa, so that at an incredible distance we might see grains of sand.' He learned of it from his master, Bishop Grosseteste, who wrote in De iride: ‘This part of perspectiva, when well understood, shows us how we may make things a very long distance off appear as if placed very close, and large near things appear very small, and how we may make small things placed at a distance appear any size we want, so that it may be possible for us to read the smallest letters at incredible distances, or to count sand, or seed, or any sort or minute objects.’ He even wrote that the Milky Way is composed of innumerable minute points of light, like grains of sand, if you can believe such a thing. Hah!.” Heytesbury passes the tube on to Oresme. “But of what use is it? Seeing grains of sand from a great distance? Really!"

  Buridan tells him how the market provost had seen the cheating of the butcher. “And a sailor, high upon a mast, may spy landfall—or another ship—from a greater distance. So also, a captain approaching battle. Perhaps herbalists may study a woodland to see if the herbs they desire be there or no, and so save themselves the trouble of a fruitless walk."

  “But I meant what use it may serve in science."

  “Why ... none I can think of. But you must tell them of this in Oxford."

  “Surely! It presents a pretty problem in perspectiva!"

  “No, Will. I mean, England himself must know of it. If the battle-captains of England and France can each spy the other's movements well before the contest is joined, there can be no more surprise on the field; and since success in war depends much on surprise, this device will make war that much less likely."

  Heytesbury agrees. Although it is of no matter to him whether Plantagenet and Valois make war on each other, it sometimes happens that the common folk come to harm, the Peace of God notwithstanding.

  Later, Nicole tells Albrecht and the Saxon shrugs. “It makes naught,” he says. “If a captain cannot find victory through surprise, he will do so through numbers. When all own a blickglas, armies will but grow greatah."

  * * * *

  The day comes at last.

  Albrecht has suggested that they test both the same quantity of gravity and the same intensity of gravity. So they have made three balls: a steel sphere, a second possessing twice the weight, and a larger fashioned of wood but of the same weight as the first.

  Heytesbury sends Oswy off to fetch a balance beam while Albrecht and Nicole arrange a table with pen, ink, “scrape-paper” that can be razored for re-use, and crack-pots to hold the paper down in the breeze.

  The Paris Master, for his part, watches with growing excitement. This is it. This is the thing. This is what all of them—The Wonderful Doctor, The Angelic Doctor, The Universal Doctor, Pilgrim Pierre—had been striving toward. Not merely experience carefully noted, but experience artfully arranged. Bacon's experientia optima.

  He stands like a man afflicted by a basilisk while about him his students direct the servants filling and carrying the flasks to where Heytesbury has set his balance beams. When the first ball—the smaller steel ball—rolls down the ramp, Buridan tells off the time using his own pulse, well aware that it races from the drama of the moment. The ball attains each mark at equal heartbeats. He studies Albrecht. The long, lean Saxon pretends to stoicism, but Buridan sees his hands clench and unclench as he waits for the results. Heytesbury writes some numbers on scraped paper and hands the flasks to Oswy to empty back into the basin.

  The next ball is the wooden one—larger than the first, but of the same weight so that its gravitas speciens is less. Heytesbury has expressed gravitas speciens as the ratio of the total gravity of the body to its volume. If velocity is proportional to the difference in specific gravity between the body and the resisting air, this ball ought to roll slower.

  Heytesbury announces the result, to the surprise of the students and masters and the indifference of the servants. (Rolling balls? Weighing water? It is all one to them with the madness of scholars.)

  Two balls with equal quantities but differing intensities of gravity have fallen in the same time. Now it is the turn of the larger steel ball. This one possesses twice the gravity of the first. Nicole hands it up to the servant sitting atop the ladder. He and Albrecht ensure that the master faucet is closed before they open the others. They lay the cam lever in place so that when the ball is released, the master faucet will open. If Aristotle is correct, this ball will fall in half the time as the first. If not, then Philoponus is correct.

  The others watch with their breath caught, but Buridan already knows what the result will be. Albrecht's intuition is correct. If anything, the young Saxon had not gone far enough. All heavy bodies must fall at the same speed, regardless of the longitude or the latitude of their gravity.

  But if the principle governing their fall is constant, it cannot inhere in the spheres, which are varied, for a variable thing cannot cause a constant result. But if not gravity, then what?

  The ball rolls; the water runs into the flasks.

  “Fui,” Buridan whispers, “et vidi experiri."

  * * * *

  That night, the Paris Master cannot sleep. Restless, he rises and paces his room. From down the hall, the sound of Heytesbury's snores. Through the window, the more silent sounds of night. A dog barks somewhere. An owl swoops in a hush of feathers on some incautious mouse.

  Earths and waters fall; airs and fires rise. That much is certain. Put dirt and water in a jar and shake it until everything is mixed. Then set it aside. Soon, the air will layer on the water, and the water on the earth. So has Aristotle's hypothesis of natural place been demonstrated by contrived experience.

  It is not reasonable that all bodies, of whatever weight, seek their natural place at the same speeds. Yet, he has seen for himself that it is so. And now that he has seen the matter, as it were from a different perspective, he wonders why so many people had thought otherwise for so long. Take two identical bodies and drop them side by side. They will fall with the same speed. Now let them fall closer to one another, and the same result would obtain. Now let only the most minute gap separate them, and still they fall at the same speed. What nonsense to suppose that if they were now joined the joined body would suddenly fall twice as fast!

  He picks up the optical tube and smacks his palm with it as he paces. I will become as bad as William for pacing, he thinks.

  “Suppose, secundum imaginationem," he wonders aloud, “that God has annihilated all material in the sublunar region.... “He checks himself, recalling his own reasoning that motion in the perfect and unchanging celestial realm is due to the same impetus as violent local motion. “Suppose God created a void space,” he amends his thought experiment. “And suppose there is a single part of earth introduced into it.” The particle of earth should move to the center of the world—but where would that center lie? Wherever the particle is. So it would not move, unless it
already had a motion, in which case it would continue to move indefinitely. So let it be at rest. Now let God introduce a second part of earth at rest elsewhere in the world. What manner of motion would result?

  Would the second particle of earth rush to the first; or the first to the second? But Nicole has told him of the relativity of motion—an inspired insight! There is no privileged place, so ... Would each particle rush toward the other, as Aristotle taught different Worlds would do?

  Buridan pauses by the window. The night air is cool. A full moon casts everything below into a faerie light of soft, gray shadows. He extends the optical tube and spies on the night. He sees a ghostly dog—perhaps the one he had heard barking earlier—and follows it until it disappears around a corner. On the next street, the night watch patrols. Buridan follows them with the look-glass as they appear through one alleyway after another. Their helmets glow creamy-white in the moonlight. He comes to a lighted window, and sees within a young man and a woman in apparent discord.

  Time for bed, he thinks and turns away.

  But, no. Perhaps one more, something to gaze on before sleep. He scans the shadow-gathered night and spies topping the church of Our Lady of Paris, the smooth, perfect face of the Moon upon the lunar sphere.

  He turns the optical tube to spy it.

  * * * *

  So began the Anno Mirabile, pregnant with all the years that followed:

  Albrecht's observation of the phases of Venus, Oresme's experiences with steam jets, and his blending of impetus and inertia into three natural laws of motion. Buridan's debates with Blasius of Parma and Nicolas of Autrecourt. The printing machine of Georges of Paris. The publication of Oresme's heliocentric system of the world on the very day he was consecrated Bishop of Lisieux. Buridan's famous visit to Avignon and his demonstrations to his old friend, now Pope Clement VI, and to Guy de Chaulliac, the pope's physician, during which he confounded his Aristotelian opponents in those public obligatios later titled “Dialectic Concerning Two World Systems."