Christmas Hiatus: Banach-Tarski

The blog is on hiatus for the Christmas season. New stories will return in January. Here’s one from the archives:

There was Dr. Copolla. She was approaching now, her strigine eyes had located him from the other side of the lobby.

“Ah, the reporter?” she asked.

“Yes, I’m Kevin Jacobs,” he replied, shaking her hand.

“Did you bring it with you?”

From his bag he brought out a teddy bear. Light brown fur worn thin in places, black eyes and a red bowtie. An ear had been chewed to the point of destruction.

“How cute!” she said, taking the bear. “Does he have a name?”

“Mr. Ted,” he said, blushing slightly. “I named him when I was three.”

“We’ll take good care of him,” she said, beckoning for Kevin to follow, and they walked through a set of thick metal doors into a laboratory.

“So it works like a photocopier?” he asked.

“It’s called a Banach-Tarski machine,” she said, gesturing to a large metal box festooned with cables. “It creates an exact copy of any physical object. We want to use it to create three types of things. Can you guess, Mr. Jacobs? What would you use it for?”

“Copying rare things,” said Kevin. “Like osmium or lutetium.”

She nodded. “What else?”

“Stuff that’s difficult to manufacture?”

“Yes!” she agreed. “Like positronic brains or Alcubierre drives. Finally, the third type of thing. Can you guess? Extremely valuable objects that cannot be duplicated?” With this she held up Mr. Ted. Kevin looked, and shrugged.

“High sentimental value, Mr. Jacobs.”

Kevin’s eyes went wide. “You’re going to copy my bear?”

“I am.”

“Why would you want to duplicate a teddy bear?” said Kevin. “Millions are made every year.”

“Those are of no relevance,” said Dr. Copolla, “until given to a child, who loves and plays with them and imprints them with their own personality. If I gave you a freshly manufactured bear of Mr. Ted’s line, would you accept it?”

“I guess not,” said Kevin. “Three-year-old me would bawl his eyes out.”

“Precisely,” said Dr. Copolla. “Now, the Banach-Tarski machine only copies perfectly spherical objects. So we must encase teddy in a silicon crystal.”

She tightly sealed the bear in a plastic covering and placed it in a glass cabinet. Kevin saw a shiny metal surface grow around the bear and thicken into a ball. Copolla carefully removed the ball from the cabinet, placed it into the Banach-Tarski machine and flicked a switch. A loud whine and crackling noises filled the room.

“Matter is made of molecules,” yelled Dr. Copolla over the noise. “Which are made of atoms, composed of quarks, made of preons, made of holons and so on down infinitely. We measure everything, and then perform a Smale eversion using the Banach-Tarski function discovered in 1924. The result is…”
The machine clicked off, and silence fell. Dr. Copolla extracted two metal spheres, which she cracked open like eggs to reveal two identical Mr. Teds.

“Amazing!” cried both Kevins in unison.

Nobody moved.

Two identical journalists gazed at each other in shock.

“Uh oh,” said Dr. Copolla.

“What’s going on?” said one of the Kevins. “Who on earth is this?”

“A completely unforeseen side-effect,” said the scientist, the sound of panic beginning to seep into her voice. “Clearly my theory about sentimental value was completely wrong.”

“What theory?” cried the other Kevin. “What are you talking about?”

“The whole point of a duplicating machine is to make more of things that are very difficult to find, or even unique,” said Dr. Copolla. “The attachment between a child and their treasured toy is the most unique connection in the universe. If the toy is lost, the connection cannot be repaired, only replaced. But… of course!”

She picked up the two teddy bears, identical down to the chewed ears and direction of fur. “The bear is just a bear. We didn’t duplicate the toy, we duplicated the connection between the bear and the child. This caused another child to come into existence. It’s a quantum inevitability…”

Then she screamed, and dropped the bears back onto the worktop. Whereupon, they stood up.

“Well done, doctor,” said one of the bears. “You’ve arrived at a level of understanding of the universe further than most intelligent species ever reach. However, you have caused a problem. Don’t worry, we’ll fix it. But we need to make sure this doesn’t happen again.” The bear waved his paw, and the Banach-Tarski machine imploded in a shower of sparks.

“Sorry,” he said. “We’ll teach you how to do it properly. Kevins… meet your new twin.”

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