A light switched on. Svetlana appeared, wearing an ankle-length yellow gown, curiosity and tiredness on her face.
"I need help.
"Whats the time?
"Ive no idea.
She disappeared and reappeared in a moment, wearing sandals and putting her arms into the sleeves of a long, red cotton dressing gown. "Its nearly two oclock.
He explained as they went. "The flow of particles. I need to see them face-on.
"You mean turn the trajectories into points?
"Yes. Can you do that?
She slipped a hand under her gown and scratched her shoulder. "Youre in luck, Tom. I can swivel the lake around.
She took the stairs two at a time, leaving a faint trail of perfume. Or was it hair shampoo? In the computer room she fired up, typed, and over her shoulder Petrie saw an erratic, roughly oval blue shape appear on her screen. She flicked her hair back and traced the shape out on the computer terminal with a red-painted fingernail. "Thats the lake looking straight down from a great height. And you can spin it so that its face-on to the particle flow. Look.
A single frame appeared on the screen, the lake penetrated by thousands of straight lines. She clicked on a little icon and the picture tumbled and the lines shrank until Petrie found himself looking, not at a confusing jumble of lines, but at a pattern of dots.
Svetlana scribbled a few lines in a spiral notebook and tore the sheet out. "Here are the instructions. You can take it a frame at a time, freeze it, run it forwards or backwards at any speed and so on, just like a video recorder. She pressed the return key and a little cl.u.s.ter of dots appeared near the edge of the lake. In the next frame they had vanished, but a second cl.u.s.ter had appeared, near the far end of the lake. "And heres the disk, you can copy it over.
"Svetlana, Ill buy you summer roses.
She screwed up her nose.
In the library, Petrie started again, but this time with dots rather than lines; and this time the patterns showed up with great clarity. He ran the frames like a slow-motion movie. Cl.u.s.ters of dots waltzed slowly around each other; but frame by frame, the number of dots in each cl.u.s.ter changed.
Then nothing the particle flow had stopped and then another sequence of changing patterns, looking completely different from the last.
He went back to the previous batch, the one with the waltzing cl.u.s.ters. And the thing which had been trying to crawl up out of his unconscious mind began to surface. A thing even crazier than Shtyrkovs rantings.
He put it aside, didnt dare to think of it.
He zoomed into the cl.u.s.ters. At higher magnification there were cl.u.s.ters within cl.u.s.ters: in each cl.u.s.ter in each frame, the particles were grouped. But one level of cl.u.s.tering was different; at this level, there were never more than four dots together. Sometimes a particle was solitary, sometimes it had a single companion or two or three, sometimes there were two pairs. But never more than four.
He wrote down the pattern on Svetlanas spiral notebook, and saw for the first time that his hand was trembling. He put them in order: 1, 2, 3, 1, 1-1, 1-2, 1-3, 2, 2-1, 2-2, 2-3, 3, 3-1, 3-2 ...
Drop the dashes. Put them into an array:
1.
2.
3.
1.
11.
12.
13.
2.
21.
22.
23.
3.
31.
32.
33.
What about zero? How would zero particles be recorded? Without worrying about that, Petrie put in zeros where they seemed to make sense: 00.
01.
02.
03.
10.