Factoring Humanity

There was a water hole, thought Heather. There was a common ground between species. But it was nothing as simple as a set of radio frequencies. The common ground wasn’t related to ordinary physics, or the chemistry of atmospheres, or anything that mundane. And yet it was something that in many ways was even more basic, more fundamental, more a part of the very fabric of existence.

The water hole was dimensional. Specifically, it was the fourth dimension.

There are nine and sixty ways of constructing tribal lays

And every single one of them is right!

Except that one of them was more right than all the others.

Depending on sensory apparatus, scheme of consciousness, consensual agreement with others of its kind, and more, a life form could perceive the universe, perceive its reality, in one dimension, two dimensions, three dimensions, four dimensions, five dimensions, and on and on, ad infinitum.

But of all the possible dimensional frames, one is unique.

A four-dimensional interpretation of reality is special.

Heather didn’t understand it all — as a psychologist, she had an excellent grounding in statistics, but she wasn’t really up on higher mathematics. But it was clear from what she’d read that the fourth dimension did have unique properties.

Heather had found the Science News Website and read, astonished, an article from May 1989 by Ivars Peterson that began:

When mathematicians — normally cautious and meticulous individuals — apply adjectives like “bizarre,” “strange,” “weird” and “mysterious” to their results, something unusual is happening. Such expressions reflect the recent state of affairs in studies of four-dimensional space, a realm just a short step beyond our own familiar, three-dimensional world.

By combining ideas from theoretical physics with abstract notions from topology (the study of shape), mathematicians are discovering that four-dimensional space has mathematical properties quite unlike those characterizing space in any other dimension.

Heather didn’t pretend to understand all that Peterson went on to say, such as that only in four dimensions is it possible to have manifolds that are topologically but not smoothly equivalent.

But that didn’t matter — the point was that mathematically, a four-dimensional frame was unique. Regardless of how a race perceived reality, its mathematicians would be inexorably drawn to the problems and singular traits of a four-dimensional framework.

It was a water hole of a different sort — a gathering place for minds from all possible life forms.

Christ.

No — no, not just Christ.

Christus Hypercubus.

She could make three-dimensional cubes out of her pages. And with forty-eight pages, one could make a total of eight cubes.

Eight cubes, just like in the Dali painting on Kyle’s lab wall.

Just like an unfolded hypercube.

Of course, Cheetah had said there was more than one way to unfold a plain, ordinary cube; only one of eleven possible methods yielded the cross shape.

There were probably many ways to unfold a hypercube as well.

But the circular marks provided a guide!

There was probably only one way to align all eight cubes so that the imaginary hoops went through them at the right places to line up with the circular marks.

She’d tried arranging the pictures as cubes before, hoping that they’d line up in meaningful patterns. But now she tried mapping them on her computer screen onto the separate cubes of an unfolded tesseract.

U of T had site licenses for most software used in its various departments; Kyle had shown Heather how to access the CAD program that had been used to determine the way in which the individual tiles fit together.

It took her a while to make it work properly, although fortunately the software operated by voice input. Eventually she had the forty-eight messages arranged as eight cubes. She then told the computer she wanted it to arrange the eight cubes in any pattern that would make the circular registration marks line up properly.

Boxes danced on her screen for a time, and then the one correct solution emerged.

It was the hypercrucifix, just like in Dali’s painting: a vertical column of four cubes, with four more cubes projecting from the four exposed faces on the second cube from the top.

There was no doubt. The alien messages made an unfolded hypercube.

What, she wondered, would you get if you could actually fold the three-dimensional pattern kata or ana?

It was a typically hot, muggy, hazy August day. Heather found herself glistening with sweat just from walking over to the Computer-Assisted Manufacturing Lab; the lab was part of the Department of Mechanical Engineering. She didn’t really know anybody there and so just stood on the threshold, looking around politely at the various robots and machines clanking away.

“May I help you?” said a handsome, silver-haired man.