Face down, yet paradoxically with the wind in her face, Kallandra knew her night was about to be disturbed by another sphere dream. Determined to make her muscles work this time, she used all her willpower to lash out. More awake than asleep she raised herself on elbows to see that Derek had already sought sanctuary elsewhere.
Deciding a camomile tea would help dispel nightmares, she persuaded her petulant leg muscles to walk to the kitchen.
Instead of snoozing in the spare bedroom, she found Derek at the computer desk. The screen displayed a rotating Earth, with the spheres dotted. But even with a brassy-coloured image doing its best to please, Derek ignored it as he crafted in paper, scissors, and glue. Paper polyhedra hung from the ceiling by threads. A miniature solar system. Kallandra put up her hand to rotate an octahedron, an icosahedron, and batted a tetrahedron. Each represented approximations to the Earth with pencilled outlines of the continents. Each had six matchsticks glued at the points from where the spheres were departing.
“Is this playschool?” she said, giving the octahedron a playful tap so that it swung.
Derek laughed. With all the paraphernalia, he looked like a boy in a toyshop.
“That’s the one.”
“Right, let me guess,” she said in response to his enigmatic statement. “The Earth is really made of eight triangles, which in time have eroded to the present-day globe.”
“You must have noticed something odd about the geographical location of the spheres?”
“If you mean there’s only one per continent, we’ve all spotted that.”
Derek smirked and steepled his fingers. “Actually, there is a continent that is minus a sphere, but there’s more to their distribution than that. They are remarkably equidistant from each other. You’re not listening, are you?”
“Sorry, I was wondering what you’d stuck on the ends of the matchsticks. It’s not….” She thought earwax, but realised it was the amber glow reflection from the nearby screen onto the silver-painted match heads.
“Concentrate can’t you? Look, it’s too much of a coincidence for distribution to be equidistant. Especially, when we consider plate tectonics have shifted the crust such that all the present sphere locations were in vastly different places two billion years ago.
Whoever planted them had to calculate predicted crust drifting—”
“Not necessarily. We’ve seen how the spheres can slice through tough rock.
Suppose they’ve been stationary while the rocks flow through them since they were planted all that time ago.”
“Then, sweet Kallandra, we’d see tunnels going sideways like drift mines—oh, they would’ve melted and deformed since then, but it implies the spheres can withstand high temperatures.”
“That wouldn’t surprise me. I wonder what they’re for? They’re not big enough to be gathering minerals unless there’s a very rare one.”
“Perhaps they were adding something to the planet, not removing it. After all, Feubacher mentioned the origin of atmospheric free oxygen coincides with them arriving.”
“Yeah, Claude told me it coincides with the start of plate tectonics too. Was that a good thing: to bring us volcanoes and earthquakes?”
“Volcanoes added water to the planet’s surface, as well as gases. Anyway, I thought you had a completely different theory to the geological effects.” He picked up an octahedron ready as a visual aid for his next sentence.
“I do, but it’s simmering, not ready for consumption. Go on, where are the missing spheres?”
Derek looked disappointed. “What makes you think two are missing?”
“It’s an eight sided figure you have there, pretending to be the Earth. You have dots where the six spheres are, therefore—”
“I could have made a six-sided polyhedron.”
“Why can’t you say ‘cube’? But you wouldn’t because you’re fiddling the geometry statistics.” She laughed. “Go on, why not?”
He picked up a couple of paper cubes with continental outlines. “I couldn’t find a configuration for a cube where the spheres are near the centres of the faces. But for an eight-sided polyhedron the six spheres are more or less central. See?” He was excited at his discovery. “And the crucial point is that it shows where two more spheres might be found.” He turned the octahedron to show her a blank triangular face.
“South Pacific, and where else? Ah, Western Atlantic—hang on, no, nearer the Caribbean. You know what that area is known as?”
He nodded. “Bermuda Triangle. So you think a sphere down there has been sucking down ships and making planes vanish?”
“Derek, there are many theories attempting to explain the Bermuda Triangle.
We’ve just added one more. Interesting because the religious furore is partly because the spheres have desecrated ancient sites. We think the sites became sacred or special because of some influence of the buried spheres. That kinda fits with the Bermuda Triangle—special even if not religious. What South Pacific island has ancient religious significance?”
“Easter Island,” he said. “I haven’t checked the Web for one of the moai rising up into the sky sitting on top of a sphere. That would be a sight.”
“Ha! Floating giant stone heads. But if these two are coming out, why haven’t we seen them?”
“After two billion years they might have malfunctioned or couldn’t cope with particularly active earthquakes, or plate subduction zones.”
“Possibly. Derek, you have no sphere coming out of the Antarctic, ah, the sphere-less continent, or the north pole. Have you been fiddling the polyhedra to fit the facts, you naughty mathematician?”
“I’m a designer. OK, I do engineering mathematics, which means I look at the results and see how real life gives me those solutions. The only shape that fits the data well is an octahedron orientated with the known six spheres approximately in their face centres. I don’t know why they weren’t arranged so that none are flying out of the poles.
Do you?”
“I think I do. They are flying machines—assuming they are machines and not living entities. Without doing the mathematics, they probably need some spin of the Earth to take off. That’s why our spaceships don’t leave at the poles.”
“But their vertical speed is only eight metres a day. Surely the latitude isn’t going to make any difference.”
“Maybe not, but we’re travelling east at eleven hundred kilometres per hour while standing here playing with models. At the poles the speed reduces to nothing. But who knows, perhaps they don’t like the cold.”
Derek’s finger made it into his left ear before she could stop him. “Kal. we should alert NASA to scan the Caribbean and Easter Island areas. Perhaps the spheres are out of sight, under water.”
“You do that, Derek, I’m going back to bed before it’s time to rise. I’m off back to Yosemite to laugh as Claude, army engineers and UCLA Geophysics people pit their might against the sphere.”
Derek pulled a pained face. “I thought the Colonel said you were to go back to the training program?”
“Of course, though you could say off course. I am flying there.”
“Not in the prototype Apoidea? It’s not designed for prolonged Earth Atmosphere flight.”
“Cool it, Derek. The co-pilot, navigator and I are testing a modification to the flying suits. So you can knock another rivet in the Apoidea tomorrow. I’m off.”