William Gibson: The Difference Engine

As always, I searched that day for land, in all four directions, but could still find none. How melancholy it was! Then by chance, with the Captain's permission, I climbed up one of the masts. From the great height, with sails and smokestack far below me, I was amazed to make out the coast of Europe—a mere hair's-breadth of green, above the watery horizon. I shouted down to Matsumura: "Come up! Come up!" And up he came, very swiftly and bravely.

Together atop the mast, we gazed upon Europe. "Look!" I told him. "Here is our first proof that the world is really round! While we were standing down there on deck we could not see a thing; but up here, land is distinctly visible. This is proof that the surface of the sea is curved! And if the sea is curved, why, then, so is the whole earth!"

Matsumura exclaimed, "It's fantastic—it's just the way you say! The Earth indeed is round! Our first real proof!"

–MORI ARINORI, 1854.

It seemed that Her Ladyship had been ill-served by the Paris publicists, for the lecture-hall, modest as it was, was less than half-filled.

Dark folding-seats, in neat columnar rows, were precisely dotted by the shiny pates of balding mathematicians. Here and there among the savants sat shifty-eyed French clackers in middle-age, the summer linen of their too-elegant finery looking rather past the mode. The last three rows were filled by a Parisian women's club, fanning themselves in the summer heat and chattering quite audibly, for they had long since lost the thread of Her Ladyship's discourse.

Lady Ada Byron turned a page, touched a gloved finger to her bifocal pince-nez. For some minutes, a large green bottle-fly had been circling her podium. Now it broke the intricacy of its looping flight to alight on the bulging archipelago of Her Ladyship's padded, lace-trimmed shoulder. Lady Ada took no apparent notice of the attentions of this energetic vermin, but continued on gamely, in her accented French.

The Mother said:

"Our lives would be greatly clarified if human discourse could be interpreted as the exfoliation of a deeper formal system. One would no longer need ponder the grave ambiguities of human speech, but could judge the validity of any sentence by reference to a fixed and finitely describable set of rules and axioms. It was the dream of Leibniz to find such a system, the Characteristica Universalis…

"And yet the execution of the so-called Modus Program demonstrated that any formal system must be both incomplete and unable to establish its own consistency. There is no finite mathematical way to express the property of 'truth.' The transfinite nature of the Byron Conjectures were the ruination of the Grand Napoleon; the Modus Program initiated a series of nested loops, which, though difficult to establish, were yet more difficult to extinguish. The program ran, yet rendered its Engine useless! It was indeed a painful lesson in the halting abilities of even our finest ordinateurs.

"Yet I do believe, and must assert most strongly, that the Modus technique of self-referentiality will someday form the bedrock of a genuinely transcendent meta-system of calculatory mathematics. The Modus has proven my Conjectures, but their practical exfoliation awaits an Engine of vast capacity, one capable of iterations of untold sophistication and complexity.

"Is it not strange that we mere mortals can talk about a concept—truth—that is infinitely complicated? And yet—is not a closed system the essence of the mechanical, the unthinking? And is not an open system the very definition of the organic, of life and thought?

"If we envision the entire System of Mathematics as a great Engine for proving theorems, then we must say, through the agency of the Modus, that such an Engine lives, and could indeed prove its own life, should it develop the capacity to look upon itself. The Lens for such a self-examination is of a nature not yet known to us; yet we know that it exists, for we ourselves possess it.

"As thinking beings, we may envision the universe, though we have no finite way to sum it up. The term, 'universe,' is not in fact a rational concept, though it is something of such utter immediacy that no thinking creature can escape a pressing knowledge of it, and indeed, an urge to know its workings, and the nature of one's own origin within it.

"In his final years, the great Lord Babbage, impatient of the limits of steam-power, sought to harness the lightning in the cause of calculation. His elaborate system of 'resistors' and 'capacitors,' while demonstrative of the most brilliant genius, remains fragmentary, and is yet to be constructed. Indeed, it is often mocked by the undiscerning as an old man's hobby-horse. But history shall prove its judge, and then, I profoundly hope, my own Conjectures will transcend the limits of abstract concept and enter the living world."

Applause was thin and scattered. Ebenezer Fraser, watching from the shelter of the wings, in the shadow of ropes and sandbags, felt his heart sink. But at least it was over. She was leaving the podium to join him.

Fraser opened the nickeled catches of Her Ladyship's traveling-bag. Lady Ada dropped her manuscript within it, followed it with her kid gloves and her tiny ribboned hat.

"I think they understood me!" she said brightly. "It sounds quite elegant in French, Mr. Fraser, does it not? A very rational language, French."

"What next, milady? The hotel?"

"My dressing-room," she said. "This heat is rather fatiguing… Will you hail the gurney for me? I'll join you presently."

"Certainly, milady." Fraser, the bag in one hand, his sword-cane in another, led Lady Ada to the cramped little dressing-room, opened the door, bowed her within, set her bag at her neatly slippered feet, and closed the door firmly. Within the room, he knew. Her Ladyship would seek the consolation of the silvered brandy-flask she had hidden in the left-hand lower drawer of her dressing-table—wrapped, with pathetic duplicity, in a shroud of tissue-paper.

Fraser had taken the liberty of providing seltzer-water in a bucket of ice. He hoped she would water the liquor a bit.

He left the lecture-hall by a rear door, then circled the building warily, from old habit. His bad eye ached below the patch, and he made some use of the stag-handled sword-cane. As he had fully expected, he saw nothing resembling trouble.

There was also no sign of the chauffeur for Her Ladyship's hired gurney. Doubtless the frog rascal was nursing a bottle somewhere, or chatting-up a soubrette. Or he might, perhaps, have mistaken his instructions, for Fraser's French was none of the best. He rubbed his good eye, examining the traffic. He would give the fellow twenty minutes, then hail a cab.

He saw Her Ladyship standing, rather uncertainly, at the lecture-hall's rear door. She had put on a day-bonnet, it seemed—and forgotten her traveling-bag, which was very like her. He hurried, limping, to her side. "This way, milady—the gurney will meet us at the corner…"

He paused. It was not Lady Ada.

"I believe you mistake me, sir," the woman said in English, and lowered her eyes, and smiled. "I am not your Queen of Engines. I am merely an admirer."

"I beg your pardon, madame," Fraser said.

The woman glanced down shyly at the intricate Jacquard patterning of her white-on-white skirt of fine muslin. She wore a jutting French bustle, and a stiff high-shouldered walking-jacket, trimmed with lace. "Her Ladyship and I are dressed quite alike," she said, with a wry half-smile. "Her Ladyship must shop at Monsieur Worth's! That's quite a tribute to my own taste, sir, n'est-ce pas?"

Fraser said nothing. A light tingle of suspicion touched him. The woman—a trim little blonde, in her forties perhaps—wore the dress of respectability. Yet there were three gold-banded brilliants on her gloved fingers, and showy little stems of filigreed jade dangled at her delicate earlobes. There was a killing beauty-patch—or a black sticking-plaster—at the corner of her mouth, and her wide blue eyes, for all their look of seasoned innocence, held the gleam of the demi-mondaine—a look that somehow said, I know you, copper.