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Quaestiones Super Caelo
Et Mundo
Michael F. Flynn

When big events happen can depend on little things …

 What happened before.

If you stand on the mountain peak of any great age and gaze toward the past, you may spy in the purpled west the jagged range of another great age. And make no mistake: those distant peaks mark as great an age as any, and there were giants on the earth, men whose names ought never be forgotten:

Peter Abelard and Bernard of Clairvaux; Blanche of Castile and Good King Louis; Hildegarde of Bingen, “the Sybil of the Rhine.” Robert of Chester, Adelard of Bath, Peter of Cluny. They are all “of” somewhere, but they go everywhere. Abelard has returned to teaching and at his aged feet sit Arnold of Brescia and John of Salisbury. Young Eleanor of Aquitaine is the Queen of France and patroness of the troubadours. Oh, those were names to conjure with!

Something is happening. Something is in the very air. Adelard of Bath has inhaled the Elements of Euclid in Arabic and exhaled them in Latin. Robert of Chester has translated the Al jabr of al-Khwarizmi—and Peter of Cluny desires he do the Qur’an while he’s at it. And what about this Aristotle person?

In the center of the maelstrom: Toledo, glorious Toledo. They are all there, or they come there—eager, bustling, busy—to Archbishop Raymundo and his translation school. Gundisalvo is there. Robert of Chester has come, and Hermann of Carinthia. John of Seville and Plato of Tivoli. The names alone tell the tale: Spaniard, Englishman, German, Frenchman, Italian, all of Europe has gone mad for reading. They rub shoulders with al-Battani and ibn Sina, with Jacob ben Mahir and Moses ibn Tibbon. There has been nothing like it in all the world since the storied House of Wisdom in old Baghdad, before what once there flowered died.

These are no stolid peasants, gawping at wonders collected by their betters. They’ve been schooled for generations by the encyclopediasts of decaying Rome, by Macrobius and Pliny, by the Old Logic of Boethius. They know their Plato, and those tantalizing fragments of Aristotle that had drifted West before the old imperium fell. Thin soup, maybe, but they have a taste for soup!

Gerard of Cremona has dipped his pen, and when he is done, Europe will be drunk with Pierian spring-water. He has come to Toledo in search of Ptolemy’s Almagest, and there, as his students would one day write of him, “seeing the abundance of books in Arabic on every subject, and regretting the poverty of the Latins in these things, he learned the Arabic language, in order to translate. To the end of his life, he continued to transmit to the Latin world, as if to his own beloved heir, whatever books he thought finest, in many subjects, as accurately and as plainly as he could.”

No finer epitaph was ever written.

He was the education of Europe. Ptolemy’s Almagest. The Physics of Aristotle and his Meteorology, On the Heavens and the Earth, On Generation and Corruption, the Posterior Analytics, Euclid’s Elements, The Geometry of the Three Brothers, Galen’s Medical Art, ibn Sina’s Canon of Medicine, al-Razi’s Book of Divisions. A dozen astronomical texts, seventeen on mathematics and optics, fourteen on logic and natural philosophy, twenty-four on medicine. Did that man never sleep?

Hardly ever; but the sun does grow long and a man’s eyes are not what they once were. Reading glasses are a hundred years yet to come, and the toll is telling in squints and headaches, and one day Gerard rubs the bridge of his nose and considers his bed.

The candle gutters. The sun has touched the rim of the Toledo hills. Hermann has gone, and John. He is alone in the scriptorium. Books whisper from pigeonholes racked upon the walls. The toll of the Angelus drifts through the windows with the breeze. Gerard reaches out, fingers poised to pinch the candle flames.

But, no. Perhaps one more, something to read before sleep. He scans the shadow-gathered room, spies a dusty bin in an ill-lit corner. He goes to it and finds there a folio written on brittle papyrus. But the writing is Greek, not Arabic, and he sighs because Greek is not his strength. He closes the cover, almost puts it back. Yet . . . Greek can be translated using verbum de verbo, its word order being much like Latin. So, why not?

He carries the volume back to his desk. On such whims, turn worlds.

His lips move as he reads the title. Commentary on the Physics of Aristotle, by John Philoponus, and he laughs. John “the Work-lover”? He thinks he might have enjoyed this man’s company.

Gerard has already teased the text of the Physics from amidst ibn Rushd’s Arabic commentary, but copyist errors multiply like loaves and fishes, and the Arabic had come from the Syriac, which had come from the Greek. How many stumbles of the pen on that journey? Now here is a Greek commentary on the same text. He can check the Philoponus against the ibn Rushd and thereby synthesize a more accurate version of the Aristotle. He reads further and sees that Philoponus has dedicated his work to . . .

Justinian, emperor of the Romans.

A cold hand seizes Gerard’s belly when he reads that. Age wafts from the text as the breeze off an Alpine glacier. The Goths had ruled Italy when these words were written. The Hagia Sophia was new, and Mohammed not yet born. Yet, Aristotle was as distant to Philoponus as Philoponus is to him. Gerard feels suddenly the gaping depth of time; and hears the echo of a long, slow dialogue whispered across the ages.

He impales a fresh candle on the sconce and begins to read. This first pass will be to grasp the gist of the book (and he will note difficult passages as he reads) but it is also for pleasure. A few chapters, then to bed.


But the candle stub finds him hunched over his copy desk, brow furrowed, a knuckle caught in his teeth. Philoponus’ thesis is clear.

Aristotle is full of crap.

Gerard suddenly imagines a new volume. A disputatio. He will couple this work with Aristotle’s recovered text into a gigantic sort of Sic et non. Let the two old Greeks wrestle between the covers—and the Latins would judge the winner. He scrapes a sheet of palimpsest clean with his razor, dips his quill into the ink, and joins the dialogue.


The sun is up and dozens of candles have lived and died and still Gerard writes, stopping now and then only for quick meals or fitful naps. By summer’s fevered end, he will have finished and the manuscript will go to the copyists.

Afterward, matters great and small progress pretty much as before.

But, not quite.


What happened after.

Two hundred years have fled and Gerard is dust forgotten. The New Age is seized with enthusiasm for power. Water has been tamed, and the wind harnessed; and some dream of controlling the very gravity of the earth. Camshafts and overhead springs and newfangled cranks. Clocks have begun to toll the hours in the public squares of Europe. A new word has appeared: ingeniator—the engineer—and for the first time in history, a civilization does not cinch its saddle upon the sweating backs of slaves.

It is Paris, it is the center of the world, and Jean Buridan de Bethune makes his way through the raucous stalls in the cathedral market place. Fishmongers cry, greengrocers hawk their produce, butchers whack great carcasses hung from hooks. A jongleur sings over his lute while his apprentice taps a small tambour. Pilgrims throng the square, pointing and chattering. The tower bell above the Church of Our Lady of Paris announces tierce, and Buridan, peering past the scaffolding that still adorns the cathedral’s upper reaches, gauges the sun’s position. He plunks some copper pennies on the bench and departs the poulterer’s stall one goose the wealthier.

Buridan himself is goose-plump, but he is a chimera: his nose evokes a horse, his lips a frog. He is an important man, Rector of the University of Paris—a great, sprawling guild of masters brooding like doves on that very left bank of the Seine where Abelard once taught. He has mastered every science known to man. He can recite the Physics of Aristotle—and explain where the Stagerite went wrong. Students flock to him with their fees, so that he has become that singular anomaly: a scholar with a full purse. He is the sort to whom legends cling like filings to a lodestone. Some say he once struck the Pope on the head with a shoe in a quarrel over a woman. Perhaps the story is even true; Buridan never denies it. The two had been students together at this very university; but he is past forty now, and gray flecks his temples. He no longer fights over women and counts himself fortunate even to find his shoe.

At the Grand Bridge, he encounters Marcel Etienne, the clothier. A young man with smoldering eyes, suddenly heir to his grandfather’s commercial empire, Etienne aspires to the office of Provost of the Grand Fraternity of Our Lady, and spends his time “beating the kettledrum” for votes among the merchants that sell there. Buridan finds himself trapped by the geometry of bridges.

“Bad news from Flanders, Rector,” the merchant declares in lieu of greeting. “Van Artevelt and the cloth makers have risen up and the price of your new cloak will rise up with them.”

Buridan lifts the goose’s head from its leather bag. “Do you hear, my old? Master Etienne demands more for my cloak because some weavers in Flanders have gone out.”

The goose remains noncommittal; the clothier does not. What do Arts Masters know of money and trade! Etienne waves a hand, encompassing all of commerce and politics. “For three years now,” he explains, “Edward has cut them off from the English wool, which as all men know is the best wool to be had. Now the weavers have gone to the streets to declare him the rightful king of France.” Etienne wags a finger with the assurance of youth. “Mark me, Master Buridan. This will be Edward’s casus belli. Soon, English ships appear off Sluis and seize Flanders. What then, the price of your cloak?”

There is more. Etienne’s verbal carnivale runs from the “Matins of Bruges,” through the Battle of the Golden Spurs, to the white heron served to the king. He recounts how, following the Revolution, the Flemings had traded exigent guild masters for Count Guy, then Count Guy for King Philip. Now, languishing under the oppressions and taxes of the French crown, they seek the English to rid them of the French.

Buridan thinks the Flemings slow learners. He pleads another appointment and escapes Etienne’s lecture. Everyone, it seems, would be king of France: Valois, Navarre, Burgundy, now Plantagenet. He thinks that if there is a war, Valois will call on his vassal, the Duke of Aquitaine, to fight his enemy, the King of England, and he laughs because Edward Plantagenet holds both titles.

The waters of the Seine are choked with floating mills—sixty-eight between Bar Street and the eastern tip of the Isle of Our Lady—and Buridan pauses at the parapet of the Grand Bridge to watch the wheels splash and turn and the water sparkle in the sun. The prospect is at once restful and invigorating. The mills are moored under the arches, where the current is stronger. Thirteen churn under the Grand Bridge alone. Beneath his feet mill stones rumble, saws rasp, fulling hammers thud.

A stocky man in a dusty cloak brushes past him with two apprentices in his wake. The apprentices carry a large wooden cam slung on a pole across their shoulders. They clamber down the broad stone stairs that lead from the bridge to the riverside, where a miller steps forth from one of the floating mills to welcome them. Consumed by a sudden curiosity, Buridan follows.

Nor is he alone. The ingeniator has attracted a small crowd, as men find ever in the labor of others a reason to desist from their own. However, the miller expels all bystanders from the mill, save only “my sir, the Rector” and a man and woman of bourgeois mien. These two, as polite introductions reveal, are members of the Anonymous Civil Society of the Mills of the Seine, and between them they hold seven of the eight “shares” of this particular mill. The miller himself is but their hireling.

That worthy stands by, bouncing a little on the balls of his feet. “What we really need is an overshot,” he tells Buridan, as if in confidence. “An overshot wheel delivers more of the power of the current, but tell the Town Council that! It would not close the channel of the navigation, no, my sir. It wants a small dam only, but—” But the ingeniator calls on him to stop the grindstone, if he would please, so that work might proceed on his by-Our-Lady improvements. So the miller and his apprentice heave on a mighty wooden lever to disengage the crown gear. Gears shift, disengage—and the grindstone continues to roll for a time before coming to a stop.

Buridan has often seen such posterior motion—or momentum, to use the Latin. Aristotle thought it a great mystery how a thing might move after parting contact with the mover; but modern science has found the answer in the impetus. Yet he considers that circular motion is not natural to the sublunar region, belonging rather to the celestial realm, where the planetary stars . . .

“Holy Blue!” he cries. “And yet they still move!”

All of them—ingeniator, miller, apprentice, shareholders—stare in amazement as Rector and goose fly from the mill to his lodgings on the Left Bank.


At sept, Albrecht of Saxony finds Buridan in his quarters, scribbling fiercely. He does not interrupt his teacher, but proceeds to the fireplace, where the wood is green and not burning well. He finds a bellows to blast the fire, but it is flat and, pull as he might on the handles, he cannot extend it. Albrecht is a young man of twenty, a most promising student, with fine features and hair like tow. His fingers taper delicately and his nose is long and thin.

Albrecht throws the instrument down. “There is something wrong with your bellows,” he tells Buridan, but the master continues to scribble, pausing only to wave the quill over his head to show that he has heard. Albrecht shrugs, finds a sufflator, and takes it outside and down the stairs to fill it with water. The sufflator is cast of brass in the form of a human head with its lips pursed and cheeks blown out, like the boreal figures that represent the winds. By the rain barrel, he checks that the mouth-plug still dangles from the end of its chain. “You, at least, will answer,” he tells the head.

“In his own good time,” says Nicole Oresme, who has just arrived and has paused before climbing the stairs to Buridan’s quarters, “much like our Master.” Nicole is the complement to the Saxon. A Norman blockhead, he sometimes calls himself—unfairly, because his head is more sphere than block, the perfection of its curves spoilt only by the undershot chin. “Why did you fetch only the one head? Two heads are better than one. Wait, I’ll get the other.”

Albrecht watches him scamper up the stairs two at a time. Nicole is obnoxiously precocious. At fourteen, he has only this year achieved adulthood, yet he shines already a star in the academic heavens. Worse, he knows it.

The Saxon turns to the rain barrel and puts the funnel between the sufflator’s pursed lips.

“You know what that looks like, don’t you?” Nicole is on the landing above him, a second sufflator in his hand.

Albrecht does not look up. “I think you’ve told me once or twice.”

“Like it’s performing fellatio.”

“Or thrice. Don’t you plan to become a priest or something?”

“Not yet. Has the Englishman come?”

Albrecht jams the stopper into the sufflator’s mouth, giving it an extra rap to make sure it is tight. “Not yet. The Mastah went himself this morning out, and fo’ the dinnah bought a goose. Cook has it now.” Being a Saxon, Albrecht sometimes drops his final –er and twists his long o’s and u’s into peculiar diphthongs. This gives his Latin a whimsical inflection, whence the passive voice of his verbs masquerades oft as the dative of their participles.

Oresme makes a show of sniffing the air. “Will it be ready in time? Will one goose feed four?”

“If not, you may fast as a penance for your vulgarity.”

In answer, Nicole puffs his cheeks out and blows hard on the finger he has stuck in his mouth. Albrecht cries, “Catch!” And he throws the sufflator, now full of water, like a Scotsman hurling a stone, taking the younger man off his guard.

Nicole is near-sighted. He fumbles for the head one-handedly and in so doing loses his grip on the other, and both sufflators seek their natural place, landing at the Saxon’s feet.

The young Norman scampers down the stairs. “Look what you made me do!” he complains. “If you’ve busted the master’s brass balls . . .”

But both are whole. A relief! Albrecht fills them and, this time places the one in Nicole’s arms as gently as a nurse returning a mother’s newborn. The other, he carries himself. On his way up the stairs, he glances down at the place where the brass heads had struck, and purses his own lips in unconscious imitation.


If the world does turn on itself with a diurnal motion, as Buridan and others suspect it may, it makes precious little noise in doing so. The hinges of the world must be well greased, for it turns over always in quiet moments. It turned over once when Gerard of Cremona picked up his pen. It turns over again when Jean Buridan de Bethune puts his down; and maybe there is just the slightest creak when he does. If there has ever been such a creak, it is then, it is there, in that room.

Possem enit dici, he has written, quod quando deus creavit sphaeras coelestes, ipse incepit movere unamquamque earum sicut voluit; et tunc ab impetus quam dedit eis, moventur adhuc, quia ille impetus non corrumpitur nec diminuitur, cum non habent resistentiam.

Or to put the matter more plainly: A body set in motion will continue in that motion if it meets no resistance.

There. In a few strokes of the pen he has disenchanted the heavens. There is no need to suppose the celestial spheres filled with Aristotle’s “fifth element,” the quint essence, whose natural motion is circular. No need to distinguish celestial from sublunar physics. Since God created the heavens and the earth, the same forms that account for earthly motions may also account for those of the heavens. Uniform motion above, where there is no resistance, difform motion below, where there is.

“After leaving the arm of the thrower,” he tells his students, “the projectile is moved by an impetus proportional to the body’s weight and speed. The body will continue to be moved so long as this impetus remains stronger than the resistance, and, the impetus being permanent, motion will be of infinite duration if it be not corrupted nor diminished by a contrary force resisting it, or by one inclining it to a contrary motion.”

Nicole bounces with excitement. “Then you don’t need the Stagerite’s Intelligences to keep the spheres turning!”

Buridan shrugs eloquently. Aristotle is full of crap, his shoulders say. If the Stagerite was wrong on matters of theology, as a Bishop of Paris once decreed, then might he not also be wrong on matters of the physics? “As my own master was fond of saying,” he tells his students, “we ought not call upon entities we do not need. One might assume that there are many more separate substances than there are even celestial spheres and celestial motions, and invoke whole legions of angels to move them . . .” He waves his arms grandly at this. “. . . but this cannot be demonstrated by arguments originating from the senses, and the philosophy of nature demands always that our arguments be sensible.”

Albrecht glances toward the stairway with a contemplative look and his lips part, as if to speak, but the young Norman pipes up. “The world is a gigantic clock that God set in motion at the Creation and runs now by itself!”

“The machina mundi,” Buridan repeats the common phrase, “runs by the laws of nature set by nature’s God.”

Albrecht smiles. “A clockwork world? Ach, that has right. The Lord has better things to do than spinning planetary spheres. Saving Nickl’s soul wants his full attention.”

Oresme tries to knock Albrecht’s cap off, but is defeated by the Saxon’s height. He settles for making a fig with his left hand. “But master,” the young man says, “according to the Stagerite, velocity is the ratio of the motive force to the resisting force. So without resistance, speed must be instantaneous, and a body would be in two places in the same instant, which is impossible.”

“Which alone tells us that Aristotle was mistaken,” Buridan comments. “Albrecht, would you explain for our bachelor?”

Internal resistance, yngling,” the Saxon replies with a swat, easily ducked, toward the Norman’s head. “All material bodies are compösed of elements in various proportions; so that in part they fall and in other parts, rise. Thus, a falling body will from its own airy or fiery parts resistance encountah, even in . . .” His voice trails off at the end. “. . . a void.”

“Should a void exist,” Buridan adds the usual disclaimer. “This ‘intrinsic resistance’ makes it difficult to start a heavy body into violent motion.” He waves his hand. “The external resistance from the air, pfft! For a heavy body, it is nothing. No, lad, a body resting wants to remain so, by an inner nature which we call ‘inertia.’ Or ‘ideleness.’”

“Like Albert? It’s hard to get ‘Farm-boy’ moving, too!”

Buridan smiles. “Albertus!” he says, because the lean Saxon has not responded to the jape. “You are not listening! What engages that subtle mind of yours?”

The Saxon suspects gentle mockery, for the Franks do love to chatter, and thus confuse Germanic silence with having naught to say. “When Nickl the two heads dropped . . .” he stammers, falling into the rhythms of his milk-tongue. But what notion the plummeting sufflators has suggested goes once more unsaid when Nicole waves the bellows.

“Shit! Someone’s plugged the damned thing!”

Buridan snatches it from him before he can remove the plug. “A small gift for Heytesbury when he comes.”

“A plugged bellows? Oh, the Picard humor, she is more subtle than even the Saxon.”

“Mock not the Ch’ti!” Buridan says gravely. “This jape,” he says aside to Albrecht, “from a man who drinks from a ‘mug’ instead of a ‘tasse,’ and whose land boasts ‘castels’ rather than ‘kateaus.’”

Albrecht scratches his head. “Don’t the French say, ‘chateau’?”

Buridan waves dismissal. “The French speak with porridge in their mouths. When I eat with the French Nation, the servants affect not to understand Picard.”

The Saxon shrugs. “Norman, Picard, French . . . It is to me all the same.”

“Well said!” booms a new voice from the doorway, and they turn, and there framed they spy a tall man, all bones and angles, with a nose like a halberd and long, wild hair that suggests motion even while standing still. “Yet they lump your savage folk with mine,” he cries, “into a single nation!”

Buridan grins. “Anglo, Saxon, it all sounds the same to me. That’s why civilized men use Latin.” He rises from his stool and welcomes his guest. “William, how delightful!” The newcomer’s youth surprises him—he is but three-and-twenty. Yet he is, after all, a Fellow of Merton College; and while Oxford is not Paris—what town is?—she produces scholars of no mean merit.

The Englishman returns the embrace, though not the kisses on the cheek. “Greetings,” he says, “from ‘the Calculators of Merton.’ And are these your two prizes? Not very likely specimens, what?” He exchanges a hearty grip with Albrecht and claps young Nicole on the shoulder.

Buridan shrugs. “One manages. I thought we would eat here in my quarters, rather than in the Nations. After all,” he indicates the four of them, “in which would we dine, Norman, Picard, or Anglo-German?”

“Your ‘Nations’ are like our ‘Colleges,’ what? Endowments that provide scholars with room and board? Yes, I rather thought so; though ours are not based on the language the scholars speak. Still, I suppose that if students must board together, they ought to be able to talk together at table. Where shall I be quartered? Here? Excellent! Excellent! Just a moment.” And the whirlwind spins and shouts, “Oswy! Oswy!”

The short, burly servant is standing right behind him with a coffer on his shoulder and resignation on his face. “Oswy!” William tells him, “We are to have the room two doors on the right. This side, the right. Yes. Two doors.”

Oswy turns just as the kitchen maid enters with the goose on a great tray. There is a confusion of coffer and goose, and an evolution much like an estampe; then the wench is dancing into the room, the platter precarious, the goose in deadly peril!

Saved by the Norman! A steady hand to the platter, a steadier one to the waist, and all that is lost is a little grease splashed upon the hearthstones, and a few years in Purgatory for the thoughts that rush through the young man’s mind. A whisper, a giggle, a nod, then she is at work at the hearth, casting sheep-eyes at Nicole while she impales the goose on the roasting spit. After engaging the spit’s chain to the blades, she wrestles the two sufflators to the fire’s edge. “This’ll do ye up fine, m’sir Rector,” she says. “Cook says she’s done, but ye should let ’er roast a bit ‘till the skin gets crispy-like afore ye eat ’er.”

“Very good, Lizette. You may set the table . . .” Buridan looks around the room, and each table is encumbered with books. “. . . that one. Boys, put the books in their cases, so they don’t get soiled. Here, William, this is for you.” And he hands his guest the bellows.

Wench, grease, spit, table . . . bellows? The Englishman turns his attention to the device now pressed into his hand. He hesitates, pulls tentatively on the handles, scowls a bit, discovers the plugged nozzle, and falls into a study. Finally, he bursts into laughter. “Nature abhors a vacuum!” he cries.

Stacking the books at the table, Albrecht and Nicole glance at each other, then at the Englishman. “All right . . .” says the Saxon.

“The principle of first and last moments,” Heytesbury exclaims. “Surely, your master has . . . He hasn’t! Why, what a sorry deficiency!” He waves his hands as he talks, a human windmill. He may fly off like a bird at any moment! “‘Sooth, it is simplicity itself, and illuminates natural philosophy with mathematics.”

“‘Sooth’?” says Nicole.

“The Merton Calculators,” Buridan comments aside to his students, “believe that ratios and geometries can reveal the secrets of nature.”

“While the Parisians place their faith in reason,” the Englishman parries off-handedly. “Bradwardine says that anyone who studies the Physics without mastering mathematics will ‘never enter the portals of knowledge.’ The plug will not allow the air to rush in to fill the vacuum, so nature prevents the two plates of the bellows from separating. To see why this is so, consider the separation of two parallel plates in general. Remember, God may do anything short of a logical contradiction, so He may permit a vacuum if He so chooses. But has He ever done so in fact?”

He spreads his hands, as if in appeal, to the two students, who remain mute.

“Come now,” the Englishman insists. “If two plates are in perfect mathematical contact, with no material between them, and they are separated in such a fashion as to remain parallel, it would seem that a momentary vacuum must be produced. Why?” He stabs a finger at the Norman.

Oresme sees no escape. He twists his hand palm up, as if to say it is obvious. “Because at the moment of the separation the air will rush in from the perimeter, but some brief time must elapse before it reaches the center.”

“Excellent! Yet, how can this be?” Heytesbury continues, “Consider first the two plates approaching.” His hands are plates. They approach. “The air between them becomes progressively more rarefied; yet at no time does the air actually part to form a vacuum in the center because there is no last moment at which rarefaction ceases prior to the contact of the plates. Thus, there is no last instant in which the plates are separated. But there is a first instant in which they are in contact. Rarefaction approaches a vacuum, but never attains it because the limiting form—actual contact—is extrinsic to the intension of the rarefaction itself.”

Albrecht nods. “And separation likewise? There is no first instant of separation?”

Nicole pokes him. “Of course not, Farm-boy. Suppose there is a first moment of separation. But, if they are separated, there must be a small distance between them—”

“And so,” the Saxon’ voice overrides him, “however small, a smaller distance must have preceded it. Thus, we haff a last moment of contact—an intrinsic limit to contact, doch?—but no first moment of separation.” He shakes his head slowly, grappling with the idea of open and closed sets.

Heytesbury waves his hand dismissively while he paces about the room. “We Mertonians have not determined all the questions the continuum raises, but we do know that Aristotle was wrong about forms. They are not ‘either/or.’ They are ‘more or less.’ A form like rarefaction can be intensified or diminished. If we could but measure that . . .” This last he says wistfully, gazing upward, as if entreating God for an instrument, any instrument, that could measure density or heat or color or charity.

Dropping his eyes, he notices that the goose turns on the spit with no hand moving it. A problem of impetus! Another of Buridan’s pranks? He studies the spit from various angles; spies a chain wrapped around a toothed wheel; crouches and looks up the flue.

“Attend!” the Rector cries. “Your hair!”

But the ends are singed only a little. “There is a wheel with blades in the chimney,” the Englishman says as he straightens, snuffing the sparks in his hair, “and the hot air rising to its natural place turns the wheel, which turns the spit.”

Buridan nods. “But yes! We call it a turbinus, after the spinning top the Romans used as a toy. They are become quite popular of late. It is mere engineering; yet it illustrates the matters philosophical. It is in principle as the water wheel, no? But instead of the water rushing down, it is the air, as is proper, rushing up.”

“Exquisite! Both air and water take on the nature of a fluid, what? Oh!” He takes a sharp turn into another topic. “The monks at St. Albans—you know the ‘Instrument Makers’? Abbot Richard has only just died, it grieves me to say—but he crafted a most exquisite instrument . . . You know how the ingeniators are trying to build a portable clock? A peripatetic timepiece for the Aristotelians, hah! ‘Sooth, ’tis not enough to erect one in every town square; now there must be one in every house. Soon, they will dangle on lanyards from our very necks, hah-hah! But the ingeniators envision that which they wish to achieve, then they essay divers arrangements of gears and balances to find their way to this vision. I hear they are trying springs; but springs lose potency as they unwind and they’ve not yet come up with a device to compensate for that. So Abbot Richard, knowing how young men like your Nicole, cannot see far off but only close at hand, envisioned a lens—”

At this juncture, the first sufflator blows. The fire, transferring its quality of heat to the water, has brought the latter to a boil. The stopper pops out of the figure’s pursed lips, and the head of steam vents into the hearth with a long, high whistle. Steam is air and water, and water is contrary to fire; but the element of air dominates and so blasts the fire into more lively flames.

“It does sound like whispering,” Heytesbury observes in an aside. “Pope Sylvester had one of these in the old days, and simple folk thought that the head whispered secrets to him. Look how fast your turbine spins with the jet upon it! Hah! Delightful!”

The second head of steam sits upon the pool of grease that had earlier been spilled by the serving wench. When it erupts, the head slides backward through the grease, away from the fire until it reaches drier wood and resistance halts it.

“Holy Blue!” cries Buridan in amazement. Heytesbury cups his chin, laying a finger by his nose, and stares at the sufflator, whose jet now spews steam uselessly into the room. The two students look at each other.

“It moved,” Nicole tells the senior.

“So there must have been a mover,” Albrecht agrees. “The steam?”

“No, the steam went that way, but the head slid this way.” A new species of motion? But motion is not an entity, only a term used to describe a body’s successive acquisition of the form of location. But what had just pushed it? The steam is implicated in some manner. As more and more heat is placed into the water, the intensity of the heat—or “temperature”—increases because the volume of the water remains the same. So it is clear why the excess heat seeks to escape in violent motion. Yet, why should the sufflator take on a contrary motion?

Miracles are, of course, possible; but Aquinas had warned that an action may seem miraculous only because its form is occult, which is to say, “hidden.” Yet what is occult to one man may be manifest to another, or to the same man at a different time. Nicole considers how he might become that man. He ought first establish, by repeating the experience, that a common course of nature obtains, for no certain knowledge may be had of chance events. The others bustle about him almost unperceived while he ponders the question.


Dinner passes less dramatically and the only “talking heads” are those of which one normally expects vapors. Servants take their accustomed places behind the chairs, to fetch fowl or ale as the diners’ appetites move them. Heytesbury’s man, of course, attends his master, but Buridan’s kitchen wench jostles the other servants to stand behind Oresme. The young Norman grins at nothing in particular.

Heytesbury hints at a marvel he has brought with him, gesturing with his fork so wildly that, sitting beside him, Albrecht fears impalement. “The very one Abbot Richard fashioned.” Heytesbury does not amplify, and Nicole suspects that he enjoys drawing out the suspense. It had best be a damned good marvel, he thinks.

“Abertus,” Buridan comments over a leg of goose and black currant sauce, “you have been more absent-minded than usual this afternoon.”

“Well . . .” Albrecht rubs his long, thin fingers down his chin. “I can see how homogenous mixed bodies must move at the same speed in a vacuum, regardless of their weights; but their motion in a plenum still puzzles me.”

Oresme laughs. “That was clear, cabbage-head.”

The Saxon turns on him like an act of nature. “One day, ‘Lefty,’ you will toss one jape too many. I may have grown up on a farm, but we farm-boys know something you city-folk do not.”

“Really! And what is that?”

“We know shit when we see it.”

Buridan and Heytesbury burst into laughter, and Nicole mutters a word that is no more Latin than “‘sooth,” but which is commonly heard in low places about Normandy.

Albrecht explains his reasoning to Buridan: “If a body is hömo—is homogeneous, every part of its material contains the same proportions of elements and so each portion of material must at the same speed fall. So, imagine such a body divided now into one-third part and two-thirds parts. Since each body possesses the same ratio of gravity to levity, each must fall at the same speed. In a blenum—in a plenum—the external resistance would be greatah on the largah body, but . . .”

“But?” his master prompts him. Heytesbury, listening bright-eyed, grins to bursting with a secret. “Oswy!” he bellows. The servant standing behind him tugs his forelock. “Oswy, bring me my satchel! There’s a good fellow.”

“But I saw dhem fall,” Albrecht says, his enthusiasm resurrecting his Saxon accent. “Nickl dropped böth sufflatahs, and you haff dtold us how seeing d’ millstone caused you to reconsidah heavenly mötions, ond you haff always said dhat natural philosöphy begins vit d’ senses, ond Albertus Magnus wröte dhat ‘Experience is d’ önly guide,’ ond . . .”

Ond his Master and fellow student stare with amazement. They have never before heard so many words jostling and stumbling out of the Saxon’s mouth at one time.

Ond,” Albrecht concludes, “I saw böth heads strike d’ ground at d’ same möment, even dö one was vit water and one vit air filled. But vatter falls ond air rises, so d’ second head ought haff less guickly g’fallen.” Oh, the mush-mouth drawl of the Saxon hills can baffle a Bavarian, let alone a Picard, a Norman, and an Englishman. It is difficult enough to follow his accent, let alone his reasoning.

“Perhaps it did,” Buridan suggests when he has “buzzled öut” his student’s idea. “It is a question of summing up the parts of each element. If the sums are of similar magnitude, even if one be slightly the greater, no sensible difference may result. Nicole, did you see it happen?”

But the Norman shakes his head. “I wasn’t watching. It wasn’t my fault they fell . . .”

Buridan waves a hand in dismissal. “Perhaps the difference in gravity was too slight to be sensible. What if you were to drop a sufflator and . . . the Moon!”

Heytesbury barks laughter. He had not looked for that example. His eyes dance, resting on the Saxon, eager for his response. He knows the game of obligations. As interlocutor, Buridan will try to trap his student into holding a contradiction. At this juncture, his man, Oswy returns and places a leather satchel in his hands, and this he lays on the table before him.

“What foolishness!” Albrecht cries in despair. “The Moon cannot fall!”

“But God could cause the Moon to fall if he desired,” his Master insists, “so consider, secundum imaginationem . . .”

Heytesbury interrupts the “thought experiment” before it can progress further. “Albert, have you ever read Philoponus?”

The Saxon frowns. “No. His books are heretical. He said the Trinity was three different gods.”

“He wrote other books,” Heytesbury says quietly.

Buridan’s eyes drop to the satchel with sudden interest. “He wrote a commentary on Aristotle,” he says, “that refuted much of the Physics—and justly so, in my opinion. Gerard of Cremona was supposed to have translated him, but . . .”

“But who wants to read a heretic’s book?” says Nicole.

Buridan turns to him. “The same who would read a pagan’s book, or a Saracen’s.” He nods toward his own shelves, where Aristotle and Plato rub shoulders with Avicenna and Averröes. “A man may fall into error in his faith, and yet see nature clearly. Recall Augustine On Christian doctrine, or Aquinas, or Albertus Magnus.” He returns to Heytesbury. “But Cremona’s ‘Philoponus’ has been lost. Abelard knew it in the old days, and thought ill of its ‘base mechanic doctrines,’ but the manuscript itself . . .”

“. . . came into the hands of Brother Roger Bacon,” Heytesbury tells him. “The ‘Wonderful Doctor’ was trained by Grosseteste himself, and also here in Paris by ‘Pilgrim Pierre,’ and so had a high regard for the evidence of the senses. I think he came by Abelard’s copy when he was here. You’ve read the treatises Bacon wrote for the Pope, of course.”

Buridan nods. He has not taken his eyes off the satchel. He knows what must be in there. It is all he can do to refrain from elbowing the Englishman aside and tearing the contents from its canvas wrapper. “I have always thought it a scandal,” he said, “that your Order burdened him with so many other labors that he was unable to write more than he did.”

Heytesbury waves a hand. “A general prohibition. An Italian brother had written theological treatises containing heretical ideas, so our General required all writings be reviewed by peers within the Order before being sent out. Brother Roger expressed himself carelessly in his theology, and had insulted many potential friends—he really could be quite the ass, the older brothers tell me. But, as it may, his copy of the ‘Lost Cremona’ has lain buried in our library these past thirty years since his death. Bradwardine has only just discovered it.”

“And. . . ?” Buridan’s voice is heavy with lust. He is a sailor in sight of port, and Heytesbury realizes that he can suspend the matter no further. He opens the satchel and removes two bundles. One is a ream of parchment, quarto, tied between two stiff boards, which he hands to the Paris Master. The other is a smaller bundle tied in a rag. This, he passes to Oresme. Albrecht grumbles. What, no gift for him?

“Do not fret, my Saxon giant,” the Englishman assures him with a clap to the shoulder. “There is a passage in the Philoponus that will interest you greatly. You recall how Brother Roger wrote, ‘Without experience nothing can be known sufficiently’?”

“As did Albertus Magnus,” the Saxon replies, defending his namesake. “Remember how he always added to his statements, Fui et vidi experiri. ‘I was there and saw it for myself.’”

Heytesbury brushes imaginary flies. “Yes, yes. And ‘Pilgrim Pierre,’ and Aquinas, and all the others said alike. But Brother Roger wrote of degrees of experience, and one, which he called the ‘best experience,’ is one in which all the forms affecting the experience have been accounted for by deliberate arrangement.”

By deliberate arrangement? Albrecht purses his lips. “Would not artificial conditions affect the body’s natural behavior? It is the natural behavior we wish to understand.”

“Shit!” says Oresme, who is frowning over the pair of spectacles he has found in the bundle. “I’m no old man to need reading glasses.”

Heytesbury turns to him, “Put them on! Put them on!” Then, without sensible pause, turns back to Albrecht and says, “Philoponus thought contrived experiences useful. So did Bacon, who wrote that we learn more through artful vexation of nature than we do through patient observation.”

Albrecht glances at Nicole, who is gawking with wonder out the window of the apartment. “And what does Philoponus say about these ‘best experiences’?” he asks.

“Yes, what does he say?” asks Buridan, who has been eagerly skimming the pages. He is already making plans to have a bookbinder set them between covers, and to have the university stationers produce several additional copies. His purse can afford the labor. Whether his patience can afford the wait is another matter. Yet the laborious process of copying a single book is one reason why so many become lost to mice and mildew and fire. If only there were some way in which a book could be written once, yet read many times.

Heytesbury is smug. “Why only that Philoponus, using a contrived experience, determined as your Saxon giant, that, against Aristotle, bodies fall at the same speed, regardless of their weight, and that their speed increases in . . .”

“In uniformly difform motion,” says the Saxon. Then, to the startled looks he receives, adds, “It stands obvious, no?”

“I can see!” Nicole exclaims. But he does not mean that he understands Philoponus, or Heytesbury, or even Albrecht. He has discovered the world beyond his nose-tip. “There is a drover at the corner—” He stands at the window, pointing. “He holds a crook and drives one, three, eight pigs toward the pens. And that lady wears a kirtle in orofrise done up with scenes of hunting, and—Good day to you also, m’lady! And such superb melons!”

Now he has his master’s attention. Buridan asks to see—the new spectacles; not the lady’s melons—and Heytesbury explains how Abbot Richard had reasoned that if ‘lentil-shaped’ glasses help a man see close at hand, a concave shape must help him see farther away. “And there are the laws of perspectiva,” he adds, “which Grosseteste used in De iride. Father Abbot drew diagrams of the paths of the rays, after Witelo’s methods, as they enter and leave the faces of the lens. The most difficult task was the artisan’s. Grinding a concave glass is not as simple as your convex reading lenses.”

There is no help for it. Each must try Nicole’s new spectacles, although none else can see more than a blur with them. Albrecht is nettled that Nicole has made himself once more the center of attention.


It is a rowdy era, as are all those eras when everything flips over. There are brawls high and low. Rhineland barons squabble. Kaiser Ludwig strong-arms Margaret Pocket-Mouth, the Ugly Duchess of Tyrol. The theologians of Paris have declared Pope John a heretic, again; and William of Ockham, safe at the Kaiser’s court, wastes his pen on political screeds against him. The French fleet sails into Southampton and fires the town. In the Mediterranean, Genoa and Venice stumble through the final years of their long, drawn-out mutual suicide pact.

And in Paris, it is morning and a gang of young townies have spotted Nicole Oresme returning to Buridan’s quarters in the University. Town has hated gown ever since the Pope freed the universities of local laws and exactions, and this bird is too easy a prey to pass up. Nicole might have seen them sooner, save that he is gawking everywhere in fascination of his new spectacles.

And what a spectacle he makes of it! Stopping, peering, laughing in delight. The laughter strikes the laborers as being at their expense. Another sneer from the haughty scholars at the common workman. Once again, the young Norman has made himself the center of attention, though he awakens only slowly to the honor.

Nicole finally notices the train of journeymen and apprentices he has acquired, sees their roughened, horny hands, hears their sniggering laughter. Perhaps there is no more harm in them than mere mockery, but the young scholar suddenly feels very small and very alone, and so he bolts suddenly toward the safety of the university.

It is the very worst thing he could have done. He is a flushed bird in flight! His gown flaps like wings. Even his cries for help sound remarkably avian. His pursuers are falcons launched.

Norman sandals slap cobblestones down narrow lanes. He overturns laundry baskets, thrusts aside screeching harpies. A stone hurtles past him—and he thinks, madly, of the prior day’s discussion of bodies in motion. A second stone resets his academic priorities. Six-to-one is not fair odds, but he doubts his pursuers would care. He turns another corner . . .

. . . and Albrecht of Saxony is suddenly there, with his long, grave Saxon face and clumsy demeanor. This fails to dampen the townies’ humor. Two scholars? It is still three-to-one!

Save that one is a farm boy and has grown up wrestling with calves and other livestock. He may be long and thin, but every thumb-length is tough as rope. Besides, he has a club—a billet snatched up from the construction site, and he knows its use. Rural Saxony has not schooled him in meekness. A swing breaks a pursuer’s forearm, drawing a howl; a stab blows the wind from the brisket of another. The townies grumble and draw back. But others have come in response to their shouts.

Albrecht directs a fighting retreat, but the university is too far and the crowd now too many. Stones begin to fly again and what had begun as a near-amiable thrashing may soon end in riot and murder. Albrecht and Nicole back up a narrow alley, instinctively warding their flanks.

Then the militia are about them: a dozen halberdiers in the livery of the university corporation.

An unworldly scholar or two is one thing; grim-faced men who know how to kill is quite another. The mob breaks up sullenly. One reckless youth hurls a final stone—and is felled by the butt end of a poleaxe. That is the end of it. A few shouted imprecations follow—“staircase wit”—but words are nothing compared to sticks or stones. Albrecht throws his billet-club to the ground. His fingers tremble, but he does not permit Nicole to notice.

The two scholars take stock while the militia escorts them into the university precincts, where university law prevails. A few bruises. A cut on Albrecht’s cheek. And Nicole’s proud new eyeglasses broken.


“But the glass is intact,” Buridan comforts him when he inspects the wreckage later. He seems more concerned for the marvelous invention than for his two students. He had given them but a glance of amusement, and cautioned them against brawling, “unless the numbers be more in your favor.” He is more concerned that the militia left the grounds to effect the rescue, something he will now need to square with the Provost of the City. Heytesbury arrives from his rooms, attracted by the commotion and, informed of the circumstances, recounts tales of mighty combats in Oxford town. Hundreds of scholars massed against a like number of townies and armed with tight-packed balls of snow and ice.

“The ice is the worst,” he gravely assures them.

Nicole thinks stones worse than ice, and knows a little pride that he has endured such combat. When he tells the kitchen wench later, the size of the mob has swollen and the billet-club is in his own hands. Three downed at a blow! She pretends to believe him.


“You were correct,” Buridan tells his senior student after Nicole has parted to rest from his ordeal. “It is obvious.”

Albrecht blinks. “Obvious that. . . ?” he says, creating an expectant silence for his master to fill.

“That falling bodies exhibit uniformly difform motion. The velocity increases with each increment of distance fallen.”

Heytesbury purses his lips. “Obvious to you, perhaps, John. . . .” He also wonders why it has taken the Paris Master a full day to determine the obvious.

“But it is clear from the theory of the impetus,” Buridan declares. “What causes a body to fall? Some say that a body’s substantial form causes it to fall; but that begs the question. I say it is the body’s gravity, its weight. But consider now that a body’s weight is constant . . .”

“And yet it clearly moves faster and faster as it falls,” Albrecht adds. “So gravitas cannot be the cause of the difform motion, since an unchanging thing cannot cause a changing thing.”

Heytesbury scratches his head. “Proximity to its natural place? The longer the body falls, the closer it is to its place; and so, as a lover rushes as he nears his beloved, it moves faster.”

“Unconvincing,” said Buridan, dryly. “What else might it be?”

Albrecht tugs on his chin. “Rarefaction?” he suggests. “A body moving through air becomes warm through friction, and warmer air is more rarified and so presents less resistance to the falling body.”

Buridan shakes his head. “But no. I will tell you. In the beginning, gravitas alone moves the body and it moves slowly. But in moving, the body acquires an impetus. This impetus together with its original gravitas now moves it. We may call this ‘accidental heaviness,’ to distinguish it from the body’s ‘substantial heaviness.’ The motion thereby becomes faster; and by the amount it is faster, so the impetus becomes more intense, adding still more accidental heaviness.”

Heytesbury is rendered momentarily mute. Then he hollers, “Oswy!” and before he can articulate his desire, his long-suffering servant has appeared and placed a palimpsest on the table before him, proffering a quill. “Ink!” cries the Englishman, a request fulfilled by Albrecht, who, standing by the window, is closest to Buridan’s desk. “This parchment is already marked up,” Heytesbury complains. “Lend me your razor, John. I need to scrape it off.”

Buridan hands him the razor, remarking that it had once belonged to his teacher, before he went off to the Kaiser’s court. “A countryman of yours.”

Heytesbury blinks, studies the instrument, purses his lips. “Ockham’s razor? He certainly knew how to clear a page. Hah!” For the next few moments, Heytesbury makes notations on the sheet. “I must see if there be a way to express your theory in the arithmetic of fractions. Bradwardine has a pleasing notion which he styles ‘instantaneous velocity.’”


Buridan had sent Oresme to rest from his ordeal, but he is not in the master’s bedchamber when Albrecht comes to fetch him. The Saxon sits upon a stool and considers the possibilities then, shaking his head, he departs for the servants’ quarters, where he finds the younger man swyving the serving wench, Lizette. “The master desires to see us,” he announces while the two scramble for their clothing. Nicole gives him a dark look and Albrecht shrugs. “He told you to lie down.”

“He didn’t say ‘alone.’”

Albrecht grunts and glances at the young woman, who clutches her cover-slut to her. He smiles politely while Nicole pulls up his hose.

“What is it?” Nicole asks as he hops down the hall in the Saxon’s wake, tugging on his shoe.

“The Master desires us to contrive an experience.”


“I have paid the stationer to copy that section of the Philoponus which deals with contrived experiences,” Buridan explains when they have forgathered in the instruction room. “He should have rough copies for you tomorrow. I desire you master that section and contrive an experience, in imitation of Philoponus, to proof whether our Albrecht has correctly described falling bodies.”

Heytesbury, sitting to the side at a writing desk, scribbling on parchment with quill and straightedge, speaks without looking up, “Meanwhile, I will employ the compounding of fractions to express all this in mathematical form.”

Albrecht says, “I see no reason why the world should be reducible to mere mathematics. In the sensible world, there are no infinite lines, no dimensionless points, no perfect spheres tangent to perfect planes.”

Heytesbury turns and lifts his reading spectacles from his nose. “My dear     boy . . .” He is but three years Albrecht’s senior, but he has determined and incepted and is a Fellow of Oxford. “My dear boy,” he says, “Light is the first form that came to primary matter at creation. The entire world thus results from the propagation of luminous species; and, as light propagates rectilinearly as a succession of waves, we can describe it using rays and reflections according to geometrical laws. Hence, to understand the geometry of space and time is to understand space and time, what!”

Albrecht is stubborn. “You cannot mean that even the bricks of this building are a form of light!”

Buridan intervenes. “Grosseteste’s metaphysics need not concern us. That the world is a consequence of geometry strikes us here at Paris as unduly Pythagorean. Abstractions like rays and numbers are constructs of the human mind and cannot be the efficient causes of sensible facts. No, Master William, it is experience of the senses, not mathematics, that will proof the proposition.”

Nicole, listening in unwonted silence, wonders whether the Oxonian and Parisian schools might be united to the benefit of both and the glory of God.


Several days pass while each engages his particular task.

Albrecht and Nicole wrangle with the text. Buridan tries to describe the propter quid of freely falling heavy bodies. Heytesbury wrestles with compounded fractions, trying to capture the insights of the physicists in a net of numbers.


If the impetus continually adds increments of gravitas to a falling body, the Englishman reasons, then the body’s weight while descending is greater than its weight at rest. Jordanus of Nemours had distinguished between gravitas secundum situm, or “positional gravity,” and gravitas in descendendo, or “free-falling gravity.” But that bodies in motion become weightier the faster they move is contrary to experience. Or is it? Who can weigh a body while in motion? To rest on the balance beam, its motion must be arrested, so that if one learns its weight, its speed remains unknown. Whereas, to observe the speed, the body cannot be weighed. . . .

Further, if resting weight and falling weight are distinct, as Jordanus wrote, there must be some as-yet occult form underlying a body’s manifest weight, whether falling or no. Something that informed weight without being weight . . . Interesting. He scribbles a marginal gloss on the page.

Now, motion is the successive accumulation of the form of distance, and difform motion is the successive accumulation of the form of velocity. But uniformly difform motion means that equal increments of velocity are obtained at each interval, so the incremental impetus must be proportional to the same quantity at each interval. But impetus is proportional to the weight and speed of the body. So, if moving weight is continually increasing, it must be the rest weight that increases the velocity.

But how short is the duration of each interval in which velocity is acquired? Time is a continuum, not a succession of discrete moments, so there is no natural and necessary duration to an interval. Then let the intervals become of shorter and shorter duration. But then in no time, no distance would be covered, and so no velocity would result! Hah!

Perhaps if he considers the shortening of intervals as he had the rarefaction of air between approaching planes . . . He can then define Bradwardine’s “instantaneous velocity” as an extrinsic limit. . . . The intervals become shorter ad infinitum, but there is no “last” duration . . . Hah! A very pretty problem.

A pretty problem which at times causes him to throw his quill across the room in frustration and to apply his razor to the sheet of palimpsest. If he works the problem much longer, that sheet will be scraped to translucency.


And meanwhile, Albrecht and Nicole pore over two scratch copies of the Philoponus chapter that they have dubbed On the vexation of nature and which they have obtained from the stationer. They compare the two copies word for word, correct the spellings and disagreements, rush back to the stationer to consult the original (which the clerks are now rendering in full), identify some likely errors that Cremona himself seems to have made, debate whether a ratio has been carelessly inverted, and generally wrangle over the text. No conclusion should be drawn from a text unless it is faithful to the master’s copy.


And meanwhile, Buridan drafts his ideas on uniformly difform motion, incorporating Albrecht’s thesis and Heytesbury’s sometimes-peculiar suggestions. Let moments approach intervals of no duration? Absurd! Velocity is the ratio of the distance traversed to the time spent, and a ratio over zero is infinite, which would imply that finite motion is infinitely fast at each moment, a foolishness. Heytesbury replies that a duration of zero is extrinsic and, as the distance covered also decreases, the ratio remains always finite. After this, he trails off into confusion, or Buridan fails to follow the trail, or both.


One evening, Buridan notices Oresme’s broken eyeglasses still lying on the corner of his desk and chides himself for having forgotten their repair. Idly, he holds the new-fangled glass at arm’s length to inspect the damage; and, inasmuch as he is wearing his reading spectacles at the time, he is astonished to see a blurred image with the seeming of great distance. Yes, a tiny ymago of the building across the street. On a whim, he reverses the two, holding his own lens at arm’s length and peering through Nicole’s strange new concave glass.

And nearly drops them both. The image now appears large and close, as if the building has toppled in through his very window! Startled, he checks with his own eyes and is gratified to see the structure still in its proper place. The image, then, is mere illusion. He sets the glasses aside and reminds himself to take them to the optician for repair.


Albrecht and Nicole desire to measure the time taken by a falling body to traverse successive distances and, having no notion how this might be accomplished, have decided to consult one who works with time for a living. “A mere artisan,” grumbles Nicole as they search out the street of the clockmakers.

“And we have need of his art,” Albrecht answers cheerfully. He asks of a man passing in the other direction the name of the most skilled horologist and receives in return the name of Fernand of Quoeux, “the third shop on the right.”

Albrecht thanks him, and he and Nicole resume a previous argument.

“If the body rolls down a ramp, as Philoponus used,” Albrecht says, “then the motion is constrained and not natural. It does not fall free, hence no gravitas in decendendo. Why can’t we just drop two balls of different weight from the balcony?”

“Because,” Nicole tells him again, “the Englishman desires to measure the distance fallen and the time taken, and we cannot do that with free fall. It passes too quickly. We must retard the bodies’ motions by rolling them down inclines. The Master is confident that the relationship will remain apparent even if the actual velocities are less. Have you never read On the theory of weights? Jordanus wrote it when he was old, and corrected all the mistakes in his earlier book. He solved the problem of motion on a ramp, something which the ancients never did. We need only eliminate resistance from the material of the ramp. Grease, perhaps.”

Grease . . . He is still wondering why that sufflator moved backward. It seems to him a more interesting puzzle than Albrecht’s. Could the method of contrived experience determine that question? First, he must repeat the experience to learn whether a common course of nature obtains. Then . . . Then, what?

Albrecht is puzzled by his companion’s unwonted silence; but, grateful for the respite, he does not interrupt the young man’s thoughts until they have arrived at the clockmaker’s shop.

Fernand of Quoeux owns a broad face with thick, pendulous lips and a basset hound’s liquid eyes. His hair is white and sparse, save on his lip, where it flourishes. He is engaged in close discussion with Georges the carpenter, who owns a shop on the next street. Nicole is delighted to discover in them two fellow Normans, and they fall into a discussion in which “pockets” replace “sacks” and “hardelles” replace “filles” and they agree that the weather is “muggy” and not, as the French would say, “humid.” Albrecht finally interrupts the reunion and explains to the clockmaker what they want and why.

The carpenter has stayed to listen. “Time and distance of a falling body?” he laughs. “Of what use is that to know?”

Nicole and Albrecht are struck dumb. They had never thought of using it for anything. Finally, Nicole says, “So you know how much time you have to get out from under.” He does not add “fool” as an address, but the carpenter hears it anyway. He swells like a banty cock, but the clockmaker places a hand on his shoulder to quiet him. Should an argument breaks out, he might lose the work!

“If you would build this inclined plane they want, Georges,” he tells his friend, “the payment would be a practical result.”

“Pfui! A simple task, mere apprentice work. Not worth my time. How big would you want it?”

Nicole has been thinking about this very matter. “Fifteen or twenty shoes tall. And both the slope and the height of the incline must be adjustable.” Albrecht lifts an eyebrow, but says nothing.

Carpenter and clockmaker look at each other, adding pounds and pennies with an arithmetic skill that would shame the Calculators of Merton. Finally, Fernand asks, with a skeptical study of their robes—for he has been cozened by scholars before—how they would pay for the labor. When they tell them that my sir the Rector will pay for all, their eyes light up and the price is adjusted upward by a compounding of fractions.


Days pass while Buridan awaits the clock, and the ramp grows in the courtyard behind his office. The carpenter and his boys hammer away before an ever-shifting audience of curious scholars, who propose an ever shifting cloud of speculation over its intended use.

One day, while Heytesbury, Albrecht, and Nicole wait in the Rector’s office for Buridan’s appearance, the Englishman explains Grosseteste’s view of uniformly difform motion. He paces as is his wont—a peripatetic scholar, indeed!—and waves his arms the while. Nicole whispers to Albrecht that the best way to silence the Englishman would be to hold his arms to his sides; and he is prepared to compare the arm motions to those of a bellows, which also forces air out of an orifice, when Heytesbury mentions the Mean Speed Theorem: “Whether a latitude of velocity commences from some finite degree,” he explains, “every latitude, so long as it terminates at some finite degree, and so long as latitudes are gained or lost uniformly during some assigned period of time, will traverse a distance exactly equal to what it would traverse in an equal period of time if it were moved uniformly at its mean degree of velocity.”

Albrecht is rendered mute as he tries to pierce through the manifest grammar to the occulted mathematics. “So, a body in uniformly difform motion,” he ventures, “would the same distance cover as it would have covered had it possessed simple uniform motion at the mean speed.” Heytesbury nods happily, and Albrecht wonders why this Grosseteste could not have stated it in that manner.

Nicole has been sketching on a scrap of paper. He represents the passage of time with longitude, drawing a line from left to right. The successive latitudes of velocity acquired, he represents by perpendicular lines drawn upward. If increments of velocity are attained uniformly, each line’s extension is successively longer by the same amount. He sees that the lines approximate a right triangle. But if the passage of time is a continuum, as even the ancients recognized, he may replace his procession of sticks with the simple triangular figure. The height of the triangle signifies the final form of velocity attained.

He draws a horizontal line whose latitude is half the height of the triangle.

And gasps.






The Englishman is correct in every detail! A few theorems of Euclid and the conclusion follows!

The others come to his side and study what he has drawn. Nicole stammers something about “equal triangles” and “similar sides” but the gist of it is that the area of the triangle ABC produced by uniformly difform motion has precisely the same area as the rectangle ABGF produced by simple uniform motion.

“Then the area enclosed by the figure somehow signifies the distance traversed,” Heytesbury cries. He stands suddenly erect and turns his head to look off into the distance. “If distance is to time as area is to length . . . Hah! Area is the doubling of length, so distance must be proportional to the double of time! No, by His wounds!” he swears and flies to Buridan’s desk, where he seizes the quill and scratches away on palimpsest. “The area of the triangle is half the length of the base doubled by the height, so distance must be proportional to half the doubling of time!” He turns in the chair and stares wide-eyed at the two students. “It remains only to discover the constant of proportionality!”

Nicole’s mouth drops open. He is mesmerized by an image of geometry and arithmetic blending into a harmonious whole. A unified mathematics! “We could say ‘square’ the ratio instead of ‘double’ it,” he ventures, applying geometric language to arithmetic.

“Indeed we could,” Heytesbury agrees. “But what would we say if we were to compound the ratio in quarto? Or reduce it by three-fourths? But . . .”

But whatever thoughts engage his mind are forgotten when Buridan storms into the room. Under his arm, he bears a new copy of the Philoponus; while under his considerable nose, he wears drooping, down-turned lips. As the lips, too, are considerable, the overall effect is one of grave displeasure. “What is it, John?” Heytesbury asks in concern.

The Philoponus thuds to the desk; the Rector, to his seat. “That little Greek catamite,” he exclaims, “discovered the impetus! He stole my idea!”

“He’s dead, John,” Heytesbury informs him. “Long ago.”

“I know,” The Rector sighs, “but it was a humbling experience, once I realized what Philoponus meant by the ‘carrier.’ You could have told me!”

Heytesbury spreads his hands. “I didn’t realize. I’m a logician, not a physicist.”

“He wrote that his ‘carrier’ was proportional to the weight of the body, so that a bullet, a cork, and a feather, thrown with the same force, will travel different distances. Once I read that . . . Holy blue! Do you know what most disturbs me?”


Buridan raps the book with his knuckles. “That the book was so long lost! Think, William! How far might the philosophy of nature have come had we known of the impetus since Cremona’s day?” He shrugs from his elbows in a gesture so Gallic that Albrecht nearly laughs aloud.

“But Master,” says Nicole, “surely the Philoponus might have been read by many, but never understood until a mind sufficiently supple considered it!”

Buridan’s laugh is froglike. “Well, William, you see that my students learn the most important lesson of all!”


“Permit me to inspect your lips,” Albrecht tells Nicole later as they walk the streets to their quarters.

“What? Why? Are they soiled?” The Norman wipes them with a kerchief.

“No,” says Albrecht. “I thought they might have turned brown from kissing our Master’s arse.”

Nicole shoves the laughing Saxon, with no more effect than if he had shoved a tree. Rather it is the Norman who staggers backward a few steps.

“What make you of the Englishman’s notion?” asks Albrecht. “That the traversed distance is proportional to half the weight of the body and the doubling—I mean, the ‘squaring’—of the elapsed time.” He cocks his head, his gaze on some unseen world. “If the body be uniform and the space a void. But would it be true in a plenum and for a heterogeneous body? Suppose we drop two bodies in water? One may fall more slowly than the other depending on its weight . . . A stone and a cork . . .”

Stone and cork? Nicole grabs him suddenly by the sleeve. “Wait!” And the two come to a halt in the crowded street, earning curses from carters and housewives who find their way suddenly blocked. “No, not the weight . . . Think latitude of forms! A uniformly difform distribution of forms must result from a single agent. Apply heat to one end of a rod, and the heat in the rod will be difform—the near end hotter, the far end cooler, just as light dims difformly from its source!”

“And . . .” asks the senior, who has grown conscious of the milling stream of humanity parting angrily around them. He gently presses his companion to the side of the street.

“And . . .” Nicole stammers, “and . . . We distinguish the total amount of heat in a body from the intensity of the heat, no? If two bodies of different size contain the same amount of heat, we say the intensity of the heat, the ‘temperature,’ is greater in the smaller body. So if two bodies of different size contain the same quantity of gravity, gravitas secundum numerositatem, then there must be an intensity of latitude, gravitas secundum speciem, a specific gravity, that differs between them. What if motion is due to the difference in the gravitas speciem between the body and the medium? Your cork . . . A body that falls through air may float on water.”

Albrecht grunts. “No, I think the Englishman has right. The answer lies in the difference between rest weight and moving weight. Master Buridan says that, once impressed upon it, a body’s impetus is permanent until dissipated by resistance. What if the impetus is naturally in a body, at least in potency, and is only actualized by the moving agent? Then weight itself is but the result of a quantity of prime matter and its natural impetus to motion.”

“How can a body resting on the ground have motion?” Nicole asks skeptically. So saying, he imparts an impetus to a stone on the dusty lane and it skitters off to strike a mule on the hoof. The mule balks and the muleteer curses them.

Potential motion,” Albrecht tells him as they run off. “It would have a velocity, toward the center of the world, if the ground weren’t holding it back.”

The idea is so absurd that Nicole cannot stop laughing until they reach the corner where they go their separate ways. It is only after they have parted, that the Norman recalls his master’s answers to Aristotle’s objections to the motion of the earth. Suppose, secundum imaginationem, that the earth turns with a diurnal motion from west to east. Why do we not feel a consistent easterly wind, versus a northerly wind? Why do people not continually stumble as they try to keep their footing on a ground in motion? Why does a stone thrown upward not fall a league to the west if the earth moves eastwardly below it?

Buridan’s answer had been that if the air and the people are also moving, the appearances would be saved. The stone, of course, would be pushed to the east by the moving air. Only the Objection of the Arrow had stumped him. An arrow loosed upward cuts through the air and is not borne by it.

But now Nicole sees that Buridan has not pressed his argument far enough! Consider the arrow at rest. If the earth turns, the arrow is already moving toward the east! It has a horizontal impetus imparted by the earth, as well as its own natural downward motion. He stares at a loose stone resting in the dusty lane. It could be moving, he thinks, toward the east at many leagues every hour. Like the air, like the people, like the great Ocean Sea. Like me. It is a heady thought, and it nearly makes him as dizzy as Aristotle once supposed a turning earth ought, until he realizes that he has assumed the earth’s diurnal motion, not demonstrated it. He has merely completed his master’s demonstration that the appearances would be saved whether the earth turned or the heavens.

He stoops to pluck a stone from the lane and, hefting it, tries to feel its eastward motion. But he cannot, any more than a man on a ship can feel the vessel’s forward motion by placing his hand to the deck. He and the stone are both moving with the same speed and in the same direction. He sighs, deciding that there is no way to demonstrate the proposition by the senses alone. If he were affixed to the orb of the stars and looked down upon the earth, the earth would appear to turn; even as he, affixed to the earth and looking up, sees the heavens turn.

Perhaps he could make an experience by “artful vexation of nature.” An experientia facta est, to coin a phrase. A “fact.”

Suddenly exuberant, Nicole hurls the stone high in the air. It comes down, not many leagues westward, but atop the awning of Schmuel the silversmith directly beside him. Schmuel rises from his bench cursing in his outlandish tongue and Nicole laughs and scampers off.


Fernand delivers the water clock to the university precincts the next day. The apprentices wrestle it from the cart to the courtyard that the Rector has chosen for the contrived experience. The carpenters’ hammers compete with clockmakers’ shouts as they position the device beside the ramp. Curious scholars have formed a circle around the group, laughing and pointing, until the Rector wonders aloud whether the regent masters are waiting to start the lectiones ordinaria. Half the regents are themselves in the gawking crowd, but scholars and masters quickly disperse.

Heytesbury arrives and views the large basin with awe. “Why, ’tis a tunne-dish, i’sooth!” he cries in his own outlandish tongue. “It must hold four hogs’ heads!”

No one knows what he means and, when it is translated, one of the workmen bristles. “This ain’t no slaughter-bucket, begging your pardon, sir! Hogs ain’t in it.” But the Englishman explains that a hog’s head is a measure of volume used in his country and this both placates the men and amuses them with the queer notions of foreigners.

“Explain it to me again,” Buridan asks his guest. As a physicist, he is unaccustomed to instruments and making measurements. “The weight of the water is a surrogate for the passage of time?”

“Yes, yes!” Heytesbury exclaims. “That is why master Fernand made the basin so great. Is that not right, my good man?” he cries to the horologist, who has learned to ignore the whirlwind. “As the water in a basin diminishes,” he continues to his host, “so too does the weight pushing the water through the orifice; but with so large a reservoir of the water, the press does not sensibly diminish before it can be replenished. Hence, the water will issue forth with a uniform motion, and in equal increments of time we will obtain equal increments of water. As the rolling balls attain each of the distances marked on the inclined plane, we will accumulate the water in a flask, determine its weight, and so approximate the time. Hah! It is really quite pretty!”

Buridan nods. “But yes, I follow your reasoning, but it seems . . . distanced from the direct experience.”

“No more than a rule distances the carpenter from the length of his wood.”

Fernand shows them the five faucettes he has fixed to the basin and instructs them in their use. “First, turn the master faucet,” he tells them. “That will start the flow of water down all five channels and begin filling all five flasks. When your ball reaches the first mark, close the first faucet; at the second mark, the second faucet; and so on.” He instructs them soberly. Privately, he thinks them mad.

The Englishman tilts his head back. “And what are those contrivances perched atop your basin? Metal birds, what?”

Fernand stands taller. “But I am a master clockmaker, my sir, not a base metalworker. There must be bells and whistles to mark the times! It would shame me to give any less. As the water drains from the basin, the water in—you see that tall thin column? Yes. The water in that column will drop more rapidly, and a float dropping with it will, at the most minute intervals, cause the chirping of the bird.” He doubts that anyone other than scholars would ever need such minute times, but the challenge has given him a curious satisfaction. And, who knows? Were he to offer such a feature on his clocks . . .

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 banks 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.”

Later still would come deChaulliac’s small-seer and the incredible discoveries he made during the Great Death; Marsilius of Inghen’s infinitesimal algebra; Cardinal Nicholas of Cusa’s quicksilver thermometer and his creation of the first authentic vacuum; Da Vinci’s discovery of Uranus and his investigations into electricity with batteries and twitching frogs; Francis Bacon’s telephone; and the amazing plethora of inventions—from light bulbs to moving pictures—that spilled from the workshops of the acerbic Galileo Galilei. And not least of all, in 1682, the successful landing on the Moon of the rocket ship Buridan, flown by Captain Sir Isaac Newton, and propelled thither by the self-same forces first described by Oresme in his Experientia cum sufflatores.


What happens next.

If you stand on the mountain peak of any great age and gaze toward the past, you may spy in the purpled west the jagged range of another great age.

But what if you look to the east?