‘You mean turn the trajectories into points?’
‘Yes. Can you do that?’
She slipped a hand under her gown and scratched her shoulder. ‘You’re 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. ‘That’s the lake looking straight down from a great height. And you can spin it so that it’s 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 cluster of dots appeared near the edge of the lake. In the next frame they had vanished, but a second cluster had appeared, near the far end of the lake. ‘And here’s the disk, you can copy it over.’
‘Svetlana, I’ll 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. Clusters of dots waltzed slowly around each other; but frame by frame, the number of dots in each cluster 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 clusters. And the thing which had been trying to crawl up out of his unconscious mind began to surface. A thing even crazier than Shtyrkov’s rantings.
He put it aside, didn’t dare to think of it.
He zoomed into the clusters. At higher magnification there were clusters within clusters: in each cluster in each frame, the particles were grouped. But one level of clustering 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 Svetlana’s 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:
What about zero? How would zero particles be recorded? Without worrying about that, Petrie put in zeros where they seemed to make sense:
He said, ‘Oh God!’ aloud.
Four-base arithmetic. A counting system. The one we’d have developed if we’d had only four fingers. Converted to the familiar ten-base, the same numbers read by a ten-fingered creature were:
He went back to the spirals. Here the signallers were counting up to three, no further. Here, if anywhere, he was going to crack the code — if there was a code.
He took a pulse at random, 7.34159 seconds into the particle blast. They had tracked across the lake in two counter-rotating spirals, a fact which he ignored. He counted the little clumps along one of the spirals, a frame at a time, converting them to four-base arithmetic: 210333223132212310 …
For the hell of it, he put A = 0, B = 1 and so on: CBADDDCCDBDCCBCDBA …
There were no E’s or F’s. It looked utterly random. All he could say was that they were using a four-letter alphabet.
A four-letter alphabet.
They.
Petrie had come across a four-letter alphabet before. His mouth was dry.
He went to the second spiral of particles, the one which had waltzed with the first one. The particles here too were bunched in little groups of up to four. He did the same letter substitution and asked the computer to line up the letters from each spiral, in two long columns.
A pattern.
The two columns were thousands of rows long, each one looked totally random, and yet no two rows had the same letter. In fact, A in column one was invariably matched by B in two. B in one was matched by A in two and so on. He wrote:
He glanced at the computer clock for the first time in hours. It was five past four. And now the excitement which had been growing inside him was at the point where he felt himself going faint.
He stacked the movie frames one on top of the other, starting at the beginning of the blizzard. The program took an hour to put together. He kept making elementary blunders and knew he could have done the job in a third of the time had he been fresh. Finally he had something cobbled together. The clock said 5.40 a.m.; it would soon be dawn. He was light-headed with exhaustion.
He stacked the frames into a solid, three-dimensional shape. He made the shape tumble slowly on the screen.
And he felt something like fear.
Now, at last, he took the time to sum up his night’s work.
There were the rotating spirals: the double helix, now slowly tumbling on his screen, joined by rungs.
There was the four-lettered alphabet which ran through the rungs of the spiral ladders.
There was the complementarity, each letter on one half of the rung being matched by a consistent, different letter on the other half.
ABCD, an arbitrary choice of letters. Replace by AGCT.
Adenine, guanine, cytosine, thymine.
The building blocks of DNA.
9
Genome
Gibson spotted Petrie a couple of hundred metres away. The mathematician was wandering down the long path outside the castle; his head was bowed and he seemed to be muttering. His hands were waving as if he was addressing an imaginary audience. The path went towards the village but Gibson suspected the young man didn’t know where he was going.
A light mist was clearing from the trees and the early morning sky was blue, but there was ice in the wind.
Gibson took a short cut over the snow and caught up with Petrie at the church. The mathematician’s eyes were bloodshot and he had an overnight stubble. His face was drawn, almost as if he was in pain. He looked at Gibson vaguely, as if he didn’t recognise the man.
‘For Christ’s sake, Tom, look at you. Get to bed.’
‘What about the others?’ Petrie asked. The words came out slurred.
‘They flaked out hours ago.’
‘What about Freya?’ Petrie didn’t know why he’d asked that; it just came out.
‘She’s up early, like me. She’s reading a ton of downloads in the computer room.’
‘Has she made progress?’
Gibson made a so-so facial gesture. He was now pacing alongside Petrie; they turned left along a quiet road. A middle-aged man was sitting humped forwards on a hay-cart pulled by a small horse, sacking over his head and shoulders to protect him from the cold. There was an exchange of ‘Dobryden’, and then the horse had clip-clopped past them. The smell of hay and horse lingered in the cold morning air.
‘What about you?’
Petrie gave Gibson a strange look. He said, ‘I have something to announce.’
Gibson stopped. ‘Well?’