Factoring Humanity

The clock was counting down. It was now two minutes to the scheduled time for the next message.

“Professor Davis,” said the black female reporter, who had a pleasant Jamaican accent, “what are you thinking? What are you feeling as we wait for another message from the stars?”

Heather had done five other TV appearances over the last thirty-one hours, but she’d yet to come up with an answer she was happy with. “I don’t really know,” she said, trying to follow the reporter’s instruction not to look directly into the camera. “I feel like I’ve lost a friend. I never did know what he was saying, but he was there, every day. I could count on him. I could trust him. And now that’s shattered.”

As she said that, she wondered if Kyle was watching.

“Twenty seconds,” said the reporter.

Heather turned to look at the computer monitor.

“Fifteen.”

She raised her left hand, fingers crossed.

“Ten.”

It couldn’t be finished.

“Nine.”

It couldn’t have come to an end.

“Eight.”

Not after all this time.

“Seven.”

Not after a decade.

“Six.”

Not without an answer.

“Five.”

Not without the key.

“Four.”

Not with it still remaining a mystery.

“Three.”

Her heart was pounding.

“Two.”

She closed her eyes and astonished herself to find that she was thinking a silent prayer.

“One.”

Heather opened her eyes, focused on the screen.

“Zero.”

Nothing. It was over.

11

Heather pushed the door buzzer outside Kyle’s lab. There was no response. She touched her thumb to the scanning plate, wondering for a moment whether he’d delisted her from the index. But the door slid aside, and she entered the lab.

“Is that you, Professor Davis?”

“Oh, hello, Cheetah.”

“It’s been some time since you’ve dropped by. It’s good to see you.”

“Thanks. Is Kyle around?”

“He had to go down to Professor Montgomery’s office; he said he would be back shortly.”

“Thanks. I’ll wait, if that’s — Good grief, what’s that?”

“What’s what?” asked Cheetah.

“That poster. It’s Dali, isn’t it?” The style was unmistakable, but it was a Dali she’d never seen before: a painting of Jesus nailed to a most unusual cross.

“That’s right,” said Cheetah. “Dr. Graves says it’s been exhibited under several names, but it’s best known as ‘Christus hypercubus.’ Christ on the hypercube.”

“What’s a hypercube?”

“That is,” said Cheetah. “Well, actually it’s not a real hypercube. Rather, it’s an unfolded one.” One of the monitors on Cheetah’s angled console lit up. “Here’s another picture of one.” The screen displayed this:

[Picture A]

“But what the heck is it?” asked Heather.

“A hypercube is a four-dimensional cube. It’s sometimes also called a tesseract.”

“What did you mean a moment ago when you said it was ‘unfolded’?”

Cheetah’s lenses whirred. “That’s an intriguing question, actually. Dr. Graves has told me about hypercubes. He uses them in his first-year computing class; he says it helps students learn to visualize problems in a new way.” Cheetah’s cameras swiveled as he looked around the room. “See that box on the shelf there?”

Heather followed Cheetah’s line of sight. She nodded.

“Pick it up.”

Heather shrugged a little, then did so.

“Now that’s a cube,” said Cheetah. “Use your fingernail to pull the tab out of the slot. See it?”

Heather nodded again. She did as Cheetah asked, and the box started to come apart. She continued to unfold it, then laid it out on the tabletop: six squares forming a cross — four in a row, plus two sticking off the sides of the third one.

“A cross,” said Heather.

Cheetah’s LEDs nodded. “Of course, it doesn’t have to be — there are eleven fundamentally different ways you can unfold a cube, including into…hape and an S shape. Well, not that cube — it’s cut and scored for unfolding in that particular way. Anyway, that’s an unfolded cube — a flat, two-dimensional plan that can be folded through the third dimension to make a cube.” Cheetah’s eyes swiveled back toward the Dali painting. “The cross in the painting consists of eight cubes — four making the vertical shaft, and four more making the two mutually perpendicular sets of arms. That’s an unfolded tesseract: a three-dimensional plan that could be folded through the fourth dimension to make a hypercube.”

“Folded how? In what direction?”

“As I said, through the fourth dimension, which is perpendicular to the other three, just as height, length, and width are perpendicular to each other. In fact, there are two ways to fold up a hypercube, just as you could fold that two-dimensional piece of cardboard either up or down — up resulting in the shiny, white side of the cardboard making up the outside, and down resulting in the dull, plain side making up the outside. All dimensions have two directions: length has left and right; depth has forward and backward; height has up and down. And the fourth dimension, it has ana and kata.”

“Why those terms?”

“Ana is Greek for up; kata is Greek for down.”

“So if you fold a group of eight cubes like those in the Dali painting in the kata direction, it makes a hypercube?”

“Yes. Or in the ana direction.”