Illustration by William Warren
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-Khwarizmiand 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 thereeager, bustling, busyto 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 coversand 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: ingeniatorthe engineerand 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 Parisa 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 Aristotleand 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 millssixty-eight between Bar Street and the eastern tip of the Isle of Our Ladyand 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, disengageand the grindstone continues to roll for a time before coming to a stop.
Buridan has often seen such posterior motionor 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 themingeniator, miller, apprentice, shareholdersstare 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 himselfunfairly, 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 himhe is but three-and-twenty. Yet he is, after all, a Fellow of Merton College; and while Oxford is not Pariswhat 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 formactual contactis 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 contactan 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. Albansyou know the ‘Instrument Makers’? Abbot Richard has only just died, it grieves me to saybut 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 heator “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 hömois 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 blenumin a plenumthe 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 Physicsand 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 friendshe 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, andGood day to you also, m’lady! And such superb melons!”
Now he has his master’s attention. Buridan asks to seethe new spectacles; not the lady’s melonsand 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 himand 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 cluba 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 stoneand 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.’”
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