Now there as a minuscule tickle on her right hand. Another snowflake had landed near the first. Then a chain of three snowflakes fluttered past her eyes. Startled, she stepped back, lifting the hand that held the snowflakes.
Two more snowflakes landed on her left hand, making three on that hand and two on the right. A chain of five circled her. She shook her head, astonished.
“Wherever we are, it’s an improvement.” It was Asimov, returning to the deck. “What are all these flying whatchamacallums?”
“They’re insects of some kind.” She laughed. “I think they are trying to teach me arithmetic.”
The snowflakes regrouped and tried something different. Two went by, then two more, followed by four. Three and two were followed by six, four and two by eight. “Multiplication,” she acknowledged. She flashed five fingers two times.
They regrouped again. Four came by, followed by two groups of two. Nine, followed by two groups of three. Sixteen, followed by two groups of four. “Square roots!” she said. She flashed five fingers five times with her left hand, then flashed five fingers twice with her right.
A third regrouping. Grace was expecting cube roots. Instead, the snowflakes glided by slowly in a long line: a flake, a space, a flake, a space, two flakes, a space, three flakes, a space, five flakes, a space, eight flakes, a space, thirteen flakes, a space….
“The Fibonacci sequence!” Asimov couldn’t keep his mouth shut.
“They’re talking to me,” Grace complained jokingly, and flashed twenty-one fingers.
Asimov held out his hands. A snowflake landed on each, starting him out simply with one plus one.
“No short cuts,” said Grace.
“Perhaps they form some kind of collective intelligence,” Asimov mused. “The whole is more than the sum of the parts. That’s the theory behind computers, after all. Each relay is a binary decision point. But put them all together and….” He waved his hands. The snowflakes were up to three plus two: three on his left hand; two on his right.
Asimov was being patronizing again. But watching the snowflakes had mellowed Grace’s mood. “I know all that already. If we make it home,” she said, then corrected herself: “When we make it home, I’ll be working with the Mark I.” The Mark I was the world’s first large-scale automatically sequenced digital computer.
“Oh,” Asimov said humbly. “I should have figured. I’m always attracted to beautiful older women who are smarter than I am.”
“Isaac, if you were a military man, that would be insubordination. But I’ll overlook it in a civilian,” Grace said absently. She addressed the snowflakes politely. “What I need to know is how to find our way home. Simple arithmetic won’t help me there. It’s more of a geometry problem.”
All the snowflakes formed a whirling ball in the air. Individual flakes flew out, one, one, two, three, five, eight…, the smaller groups converging loosely in a dome over Grace and Isaac, who for once stood speechless. The dome grew quickly until it contained hundreds of the insects, arranged in helical spirals like the seeds on a sunflower. Responding to invisible cues, they whirled in place, first to emphasize their arrangement in left-twisting spirals, then to emphasize their right-twisting spirals.
“I have no idea how to respond,” Grace said to Isaac. “I don’t know what answer they want from me on this one.”
As they watched, six snowflakes, along a single helix winding down from the top, started whirling madly, then curved in on one another in a small loop back to the top.
There was a message there for her, she was sure, but she couldn’t figure it out.
Grace felt something in the air — a crackle of static electricity. “Wait!” she cried, but the ship’s vibration drowned out her voice. St. Elmo’s fire crackled among the guy cables and railings. They were jumping again.
She closed her eyes, striving to retain the image of the snowflake sphere, with its helices and loop. Suddenly the air on her face was cold. The breeze carried a chemical taint that reminded Grace of drying paint and diesel exhaust. Her breath burned in her throat.
She opened her eyes. The snowflakes were gone. The moon was gone. The sun was low on the western horizon, setting cold and red over dark, still waters.
In her heart, she mourned the loss of all the snowflakes were about to teach her. Now she knew how it must have felt to an Alexandrian scholar to stand watching as the Great Library burned.
The vibrations shuddered to a stop. Duty called. Putting away all thought of the snowflakes, she asked, “Where are we?”
“At the end of the world,” Asimov murmured, his face bleak.
They found Heinlein on the main deck pushing through a crowd of sailors roused from sleep by the jump. The sailors clustered at the rail, staring at the dim sun that hung motionless over the black water. There was no life in that water; Grace knew that. And somehow, that absence of life was more threatening than any number of krakens and plesiosaurs.
Heinlein wore an expression that combined mortification and despair. Grace knew in a glance that he had been responsible for their last jump. “You pulled the switch,” she said. “Where was it?”
“I didn’t have a choi— ” He caught himself. “In the torpedo room.”
“You acted without consulting your commanding officer? You simply acted on whatever thought came into your head?” He had ruined their best chance of getting back now. “No wonder you were refused a commission, Mr. Heinlein. You are not cut out to be part of a military force.”
He looked as if she had spit in his face. “It seemed important to act, Ensign Hopper. There are…forces conspiring to keep us from getting home. So I set the controls for full reverse.”
“It was an honest mistake.” He was, she suspected, cracking under the stress — and how long before that happened to all of them? She had to help Heinlein keep his courage up. Blaming him at this juncture would not help. “But you were acting on the misconception that we were operating in a linear system — switch it one way, we go forward; switch it the other, we go back. Clearly, it’s not that simple.” Asimov stood at the rail, as if mesmerized by the setting sun. She turned away from Heinlein to give him time to collect himself. “Talk to me, Mr. Asimov.”
He blinked, as if waking from a dream. “Eh?”
“We need to approach this problem from a new angle. The snowflakes were trying to show me something, but…I’m not quite there. Just talk about it. Talk about what we know so far. Explain it to me.”
“What we know? We don’t really know anything, but we think that resonant frequencies have something to do with it.” He started slowly, then gathered speed as he warmed to his topic. “We think that we’re rotating through dimensions beyond the four that we normally sense. We’re rotating and we need to rotate back into alignment with the dimensions where we live.”
“Rotating…,” Grace muttered. “And we need to rotate back. If we were rotating in three dimensions, I’d approach this with spherical trigonometry. But we’re rotating through a multidimensional sphere. Perhaps that’s what the snowflakes were driving at. To calculate the length of a jump, we need to consider a projection of that multidimensional sphere into three dimensional space. What are our known variables?”
Heinlein frowned, struggling to answer. “We jumped in space — from four hours south of Philadelphia to Bermuda. Then to the Sargasso Sea. But who knows after that?”