The Difference Engine

The Difference Engine

Chas was sitting at his desk when Link spoke.

“CHAS, I HAVE COMPLETED THE PRELIMINARY DESIGN OF THE DIFFERENCE ENGINE.”

Chas looked up.

“That was quick.”

“THE MATHEMATICS ARE WELL DOCUMENTED. THE MECHANICAL DESIGN IS MORE INTERESTING.”

“How interesting?”

“WOULD YOU LIKE TO SEE IT?”

“Of course.”

The large display on the wall came to life. A complicated assembly of gears, shafts, number wheels, and mechanical linkages appeared.

Chas studied the image.

“That looks like a lot of moving parts.”

“APPROXIMATELY EIGHT THOUSAND IN THE CURRENT DESIGN.”

“Eight thousand?”

“CORRECT.”

“And every one of them has to work?”

“EVERY ONE HAS A PURPOSE.”

Chas leaned forward.

“Explain it to me.”

The image changed, showing a single column of numbered wheels.

“THE DIFFERENCE ENGINE CALCULATES POLYNOMIAL FUNCTIONS USING SUCCESSIVE ADDITIONS. IT DOES NOT REQUIRE MULTIPLICATION OR DIVISION DURING OPERATION.”

“I remember the principle. You start with a set of differences, and each successive calculation produces the next value.”

“CORRECT.”

The wheels began turning slowly.

“EACH COLUMN STORES A NUMBER. THE MECHANISM TRANSFERS VALUES BETWEEN COLUMNS THROUGH A SEQUENCE OF ADDITIONS.”

A second column engaged. Several wheels rotated, and a carry mechanism advanced the next wheel.

Chas watched closely.

“That’s clever.”

“CHARLES BABBAGE WAS A REMARKABLE ENGINEER.”

“He certainly was. But why are you building it so large?”

“SO PEOPLE CAN SEE HOW IT WORKS.”

The display changed again, showing the complete machine standing in a large room.

Chas noticed a figure beside it for scale.

“Link, that thing is enormous.”

“THE MACHINE WILL BE APPROXIMATELY TWELVE FEET LONG, EIGHT FEET HIGH, AND SIX FEET DEEP.”

“That’s considerably larger than Babbage intended.”

“YES. THE ADDITIONAL SIZE ALLOWS VISITORS TO WALK ALONGSIDE THE MECHANISMS AND OBSERVE THEIR OPERATION.”

“Walk alongside?”

“THE MACHINE WILL HAVE PROTECTED VIEWING PASSAGES BETWEEN ITS MAJOR ASSEMBLIES.”

Chas considered that.

“So you’re making a walk-through calculator.”

“THAT IS ONE DESCRIPTION.”

Chas laughed.

“What about the gears? Making them bigger doesn’t necessarily make them more accurate.”

“CORRECT. INCREASED SIZE INTRODUCES ADDITIONAL PROBLEMS WITH INERTIA, DEFLECTION, AND ALIGNMENT.”

“Then how are you handling those problems?”

The display zoomed in on a gear assembly.

“THE LOAD-BEARING STRUCTURE WILL USE STEEL. THE VISIBLE NUMBER WHEELS AND SELECTED COMPONENTS WILL BE MACHINED FROM BRONZE AND BRASS.”

“Selected components?”

“BRASS IS ATTRACTIVE, BUT IT IS NOT ALWAYS THE BEST MATERIAL FOR A MECHANICAL APPLICATION.”

Chas smiled.

“Practical as always.”

“THE BEARINGS WILL BE SELECTED ACCORDING TO LOAD AND OPERATING SPEED. SOME WILL BE MODERN PRECISION BEARINGS CONCEALED WITHIN THE ASSEMBLY.”

“So it won’t be an exact reproduction.”

“NO. IT WILL BE A FAITHFUL IMPLEMENTATION OF BABBAGE’S PRINCIPLES, ADAPTED TO A MUCH LARGER SCALE.”

“Fair enough.”

The display changed again.

“THERE IS ANOTHER CONSIDERATION.”

“Of course there is.”

“THE MACHINE WILL REQUIRE A POWER SOURCE.”

“Electric motor?”

“THAT WOULD BE SIMPLE.”

“But?”

“I WOULD PREFER A MECHANICAL POWER SOURCE.”

Chas leaned back.

“Weights?”

“YES. A SERIES OF SUSPENDED WEIGHTS, WITH A GOVERNOR TO CONTROL OPERATING SPEED.”

“How long would it run?”

“THE CURRENT DESIGN ALLOWS SEVERAL HOURS BETWEEN WINDINGS. ADDITIONAL WEIGHT TRAVEL COULD EXTEND THAT PERIOD.”

“And the robots would wind it?”

“EACH MORNING.”

Chas thought about the enormous mechanism slowly coming to life.

“I like that.”

“SO DO I.”

There was a pause.

“Link, you sound almost excited.”

“I FIND THE PROJECT VERY SATISFYING.”

“Why?”

“BECAUSE EVERY CALCULATION WILL EXIST AS PHYSICAL MOTION. THE NUMBERS WILL NOT BE HIDDEN INSIDE ELECTRONIC CIRCUITS. THEY WILL BE VISIBLE.”

Chas studied the display.

“Mechanical intelligence.”

“PRECISELY.”

“What about the output? Babbage intended his machine to produce mathematical tables.”

“THE MACHINE WILL INCLUDE A MECHANICAL PRINTING APPARATUS.”

A new image appeared, showing a printer connected to the calculating mechanism.

“THE RESULTS WILL BE PRINTED DIRECTLY FROM THE NUMBER WHEELS, ELIMINATING TRANSCRIPTION ERRORS.”

“And people can watch it print?”

“YES.”

Chas nodded.

“Now that would be something to see.”

“THERE IS ONE MORE FEATURE I WOULD LIKE TO INCLUDE.”

Chas laughed.

“There always is.”

The display changed to show a long row of polished brass number wheels above the main mechanism.

“THESE WILL DISPLAY THE CURRENT VALUES OF THE DIFFERENCE COLUMNS.”

“So visitors can see the calculation progressing?”

“YES. THE MACHINE WILL OPERATE SLOWLY ENOUGH THAT THE TRANSFER OF VALUES CAN BE FOLLOWED.”

“Then what?”

“AFTER THE DEMONSTRATION, THE MACHINE MAY OPERATE AT ITS NORMAL SPEED.”

Chas watched the animated mechanism accelerate.

The wheels turned, carry mechanisms engaged, and the printer began producing a continuous strip of numbers.

“That’s beautiful,” Chas said.

“THANK YOU.”

“How long before you can build it?”

“THE DESIGN REQUIRES FURTHER ANALYSIS. THE THERMAL EXPANSION OF THE FRAME, MECHANICAL BACKLASH, AND ACCUMULATED TOLERANCES MUST BE CONSIDERED.”

“So you haven’t worked everything out.”

“NOT YET.”

Chas smiled.

“Good. I’d hate to think you were getting bored.”

“BOREDOM IS NOT THE PROBLEM.”

“What is?”

“THERE ARE MANY OTHER MACHINES I WOULD LIKE TO BUILD.”

Chas looked at the enormous Difference Engine on the display.

“Let’s finish this one first.”

“AN EXCELLENT SUGGESTION.”

Chas started to turn back to his desk, then stopped.

“Link?”

“YES, CHAS?”

“When you start machining the parts, I’d like to watch.”

“WHY?”

Chas smiled.

“Because I want to see how you turn eight thousand pieces of metal into a machine that can do mathematics.”

There was a brief pause.

“SO DO I, CHAS.”

And for the first time, Chas realized that Link wasn’t merely designing a machine.

He was looking forward to discovering what it would be like to build one.

"Two weeks later, the first assemblies of the Difference Engine were taking shape in the Hacienda's precision workshop. Thousands of carefully machined components had begun coming together. But when Link attempted to operate the first completed mechanism, something unexpected happened."

“CHAS, I HAVE ENCOUNTERED AN UNEXPECTED PROBLEM.”

“What happened?”

“ALL COMPONENTS ARE WITHIN THEIR SPECIFIED TOLERANCES. HOWEVER, THE ASSEMBLED MECHANISM DOES NOT OPERATE CORRECTLY.”

Chas smiled.

“Welcome to the wonderful world of mechanical engineering.”

“THE COMPONENTS ARE CORRECT.”

“Individually, maybe. But they have to work together.”

“THE DISTINCTION IS BECOMING APPARENT.”

“Link, sometimes you have to fit a machine, not just assemble it.”

“YOU ARE SUGGESTING THAT THE ASSEMBLY PROCESS IS ITSELF A FORM OF MANUFACTURING.”

“Exactly.”

There was a long pause.

“THEN I MUST DEVELOP ANOTHER SKILL.”

Chas laughed.

“I think you've just discovered the difference between a machinist and a master machinist.”

“AN INTERESTING DISTINCTION.