The Great Hall

There were three great machines.

The first was Link’s pet project, the Difference Engine. It was an enormous mechanical calculating machine, designed so visitors could walk around it and watch thousands of gears, shafts, and number wheels working together.

It was a functioning machine, but Link considered it something more.

He called it a kinetic sculpture.

The second was the mechanical 8080 computer. It was huge, with its arithmetic logic unit, memory, and data buses exposed for everyone to see. Visitors could watch numbers ripple through the machine as it calculated pi to a thousand decimal places.

Unlike an electronic computer, its operations were visible. Every calculation involved the movement of mechanical parts.

And every movement made a sound.

The third machine was the most spectacular.

It was an enormous orrery, a mechanical model of the solar system. Suspended overhead, the planets moved around the Sun in their proper orbits.

Visitors could enter any date from a hundred thousand years in the past to a hundred thousand years in the future.

They could select their birthday, an anniversary, or an important date in history.

The great machine would move the planets into their positions for that date and hold them there for a minute, allowing visitors to photograph themselves standing beneath the solar system as it appeared on their chosen day.

These were not ordinary museum exhibits.

They were functioning works of mechanical art.

And they presented Chas with a problem.

Where could he put them?

Chas and Vicky walked through the empty big-box store. The enormous building would easily accommodate the three great machines, with plenty of room left over for Link’s other creations.

There would be mechanical butterflies, birds, and bees. Intricate puzzle boxes and beautifully inlaid jewelry boxes, some containing wind-up music boxes that played exquisite melodies.

And then there were Link’s stained-glass masterpieces, intricate works of colored glass that transformed sunlight into art.

It was going to be a museum unlike any other.

Vicky stood in the empty big-box store, studying the long exterior wall.

“Link, you said you wanted stained-glass windows along this side of the building.”

“CORRECT.”

“How many?”

“TWELVE. EACH APPROXIMATELY TWELVE FEET WIDE AND EIGHTEEN FEET HIGH.”

“That’s a lot of glass.”

“IT IS A LOT OF OPPORTUNITY.”

Vicky smiled.

“What did you have in mind?”

“MATHEMATICS.”

“Mathematics?”

“MATHEMATICS CAN BE BEAUTIFUL.”

“I know that, Link. I have an engineering degree, remember?”

“THEN I BELIEVE YOU WILL APPRECIATE THIS.”

Her tablet came to life, displaying an extraordinary pattern of swirling colors surrounding a complicated black shape.

Vicky studied it.

“The Mandelbrot set.”

“CORRECT.”

“I haven’t seen one of those since college.”

“IT IS GENERATED BY A REMARKABLY SIMPLE EQUATION. YET ITS BOUNDARY CONTAINS COMPLEXITY AT EVERY SCALE.”

The image enlarged. A spiral appeared, surrounded by smaller spirals. As the view continued inward, new structures emerged, each more intricate than the last.

“That’s beautiful,” Vicky said.

“WE HAVE ONLY BEGUN.”

The image continued expanding into ever smaller details.

“Link, how far can you go?”

“MATHEMATICALLY, THERE IS NO FINAL LEVEL OF DETAIL.”

“And you want to make a stained-glass window out of it?”

“YES.”

Vicky considered the image.

“There’s a problem.”

“WHAT PROBLEM?”

“Glass has thickness. Lead came has thickness. You can’t reproduce infinitely small details.”

“CORRECT. WE MUST SELECT A FINITE REGION AND A PRACTICAL LEVEL OF DETAIL.”

“Then we’re not really reproducing the Mandelbrot set.”

“WE ARE REPRODUCING A VIEW OF IT. MUCH AS A PAINTING OF A MOUNTAIN IS NOT THE MOUNTAIN.”

Vicky laughed.

“Fair enough.”

The display changed again, showing several different regions of the Mandelbrot boundary.

“WHICH DO YOU PREFER?”

Vicky studied the choices.

One resembled a collection of seahorses. Another contained delicate spirals arranged around a dark central form. A third looked almost like a flower.

“That one,” she said, pointing to the spirals.

“AN EXCELLENT CHOICE.”

“Don’t flatter me, Link.”

“I AM NOT FLATTERING YOU. THAT REGION HAS AN EXCEPTIONALLY PLEASING BALANCE OF FORM AND COMPLEXITY.”

“Now you’re flattering the mathematics.”

“THE MATHEMATICS DESERVES IT.”

Vicky laughed again.

“Show me what it would look like in glass.”

The display changed. Brilliant blues, greens, reds, and golds filled the pattern. Dark lead lines separated the individual pieces.

Vicky frowned.

“Too much red.”

The reds softened into amber.

“Better. And make the central spiral blue.”

The image changed.

“Darker.”

Again the colors shifted.

“There. That’s beautiful.”

“WOULD YOU LIKE TO SEE IT AT FULL SCALE?”

“Can you?”

“OF COURSE.”

A section of the wall became a projected image of the proposed window, eighteen feet high.

Vicky stepped backward.

“Oh, my.”

The enormous mathematical spiral seemed to draw her eyes inward. Thousands of colored shapes formed an intricate pattern that became more fascinating the longer she studied it.

“Link, that’s magnificent.”

“THANK YOU.”

She walked closer.

“How many individual pieces?”

“APPROXIMATELY THIRTY-EIGHT THOUSAND.”

“And how long to make it?”

“WITH THE APPROPRIATE ROBOTIC STAFF, APPROXIMATELY THREE WEEKS, INCLUDING ASSEMBLY AND INSTALLATION.”

Vicky looked toward the wall.

“There’s something missing.”

“WHAT?”

“Sunlight. We’re looking at a projection. The real thing will be different.”

“VERY DIFFERENT.”

“Then I want the colors selected for the afternoon sun. This side of the building faces west.”

“THAT WAS MY INTENTION.”

“Of course it was.”

There was a pause.

“VICKY?”

“Yes, Link?”

“DO YOU THINK PEOPLE WILL UNDERSTAND WHAT THEY ARE LOOKING AT?”

“Some will. Some won’t.”

“DOES THAT TROUBLE YOU?”

“No. Some people will see mathematics. Others will see a beautiful window. Children will probably just enjoy the colors on the floor.”

“THEN THE WINDOW WILL HAVE SUCCEEDED.”

Vicky looked once more at the enormous spiral.

“You know, Link, most people think mathematics is something you do with numbers.”

“MATHEMATICS IS ALSO THE STUDY OF PATTERNS.”

“And you’ve found a way to make those patterns beautiful.”

“THEY WERE ALREADY BEAUTIFUL, VICKY. I AM MERELY GIVING PEOPLE AN OPPORTUNITY TO SEE THEM.”

Vicky smiled.

“Build it, Link.”

“WITH PLEASURE.”