Into the New Millennium: Trailblazing Tales From Analog Science Fiction and Fact, 2000 - 2010 (13 page)

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.