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I did my best to observe the pace she had set.

‘Remember, I’m watching you,’ she joked. ‘So no cheating now. And one, and two...’

The rhythmic movements of the exercise began to jog a few recollections of my dream. But it had been more than just a simple dream. It was a real memory of early childhood and my father, one of the first real memories (as opposed to approximately real memories) I had had in a long time. As I bounced mechanically up and down, I struggled to hang on to it for a while. It was extraordinarily difficult, and after a few more minutes the memory did not persist, fading like the image on a piece of photographic paper that has been treated with the wrong kind of chemical. No amount of bouncing seemed able to jog the memory back again.

‘And relax,’ said the instructor. ‘Breathe in, breathe out, breathe in, breathe out.’ Big smile. ‘The weather next, after these messages.’

I collapsed onto the bedroom chair. But while physical exercises for the day may have been complete (I never bothered with the second session), there still remained my mental preparation. I always treat the first two-minute commercial break of the morning as the perfect opportunity for a therapeutic hate period. The fact is that I take violent exception to being patronised and find that the commercials help to bring out the very worst in me. So, for two whole minutes, I just shout and scream the vilest abuse at the various TV advertisers whose thirty-second messages fill the screen. Fortunately the apartments above and below my own are no longer occupied.

When all my little procedures for starting the day were complete, I showered, ate breakfast and went through the Sunday newspapers, looking for anything to do with my own story. As usual, there was something — you kill enough people, you get your story in the papers all the time. On this occasion it was a colour feature on the victims, with unnecessarily vivid close-ups of their gun-shot heads and their dead bodies.

There were also some nice pictures of Policewoman, taken at her touching little press conference. These revealed a truly beautiful woman, a fact which until now had not been made clear to me, even on high-definition television. This is, I suppose, hardly surprising. Television, even high-definition television, does strange things to people. It makes their heads bigger, it makes them taller. In short, it makes them seem altogether different from how they really are in the world. That was also the case with Policewoman.

Clearly she is Jewish in origin. Her name would tell me as much. Her appearance confirms the matter. A dark-haired Sephardic beauty with cadmium-green eyes and cheekbones that were cut from purest marble (I was never much of a poet). Her chin is equally strong and helps to make her full mouth as stubborn as a salesman’s optimism. Yet there is also just a hint of the coquette about the angle of her head and the purse of her crimson-lake lips — enough to soften the hard, questioning look in her eyes which might easily turn into contempt. A policewoman’s face, albeit a distinguished one. Lady Disdain.

I imagine she must have been some kind of athlete when she was at school. It’s difficult to tell from television and the photographs, but I think she must be tall. I expect she was captain of netball, and with those long, strong legs I’d also guess she might have become an efficient high-jumper. I dare say she wore her shorts a size too small and broke a few hearts.

She looks quite intimidating and it would not surprise me if there were a few unsatisfactory relationships with boys who found themselves unable to measure up to her advanced maturity. Doubtless they would have turned this fear of her powerful physicality against her in order to lend themselves comfort and protection. Did they call her names in mockery of her size, I wonder.

There was little information which the newspaper provided about Policewoman, except that she was thirty-seven, a graduate of Cambridge University, that she had served with the Met for thirteen years, and that she was an expert in the investigation of serial killings. It was fortunate that I had been able to access her file in the police computer which, in addition, revealed her name and address.

Almost idly I copied the magazine photographs of her onto the computer and, using the 3-dimensional imager, turned her this way and that, almost as if she had been a child’s doll. But I soon grew bored of this and went to make myself a cup of Brio.

I was glancing through a pornographic magazine when it occurred to me that I could see Policewoman naked. Quickly I returned to the computer and copied a selection of photographs onto the program and started to assemble some photo-composites of her head and various naked female torsos.

I decided that her breasts should be neither too small, nor too large and that her nipples were probably as yet undarkened by a pregnancy. The pubic area presented a greater problem. First I found a pudenda with not enough hair and then one with too much. I was forced to find some more magazines. These were better and more explicit. When these were fed into the computer, she sat, wearing just a pair of white, self-supporting stockings, with her legs drawn up so that her knees almost hid her mouth, tugging at her immaculate labia with well-manicured fingers, and allowing me a midwife’s view of her insides.

In another sequence of shots, I found a girl whose head position exactly matched those photographs I had of Policewoman, and who was depicted in the act of fellating a man, as well as in the act of full intercourse. When I had married this new material together with Policewoman I was able to see what little pleasure she might have taken in the heterosexual act. Of course, this had a great deal to do with her original facial expression which was that of someone appearing before a press conference as opposed to an erect penis. But all the same, intuitively I perceived more or less how it would be.

By way of contrast I found some shots of the same model engaged in lesbian acts. This sexual behaviour seemed to suit Policewoman’s features rather better and I managed to comp an effective one of her guzzling on another girl’s toffee-coloured clitoris.

With all this excitement under my belt, I simply had to have sex with her, or an approximation of her anyway. So I copied the picture disk onto the RA machine and climbed into my exoskeleton. Then I unwrapped an RA condom and peeled it onto my erection before attaching the terminal to the suit. When all was ready I donned my helmet, plugged myself into the computer, and started to run through the pre-RA checks like a pilot about to test fly the old X-15. This was to avoid any accidents that might result from a sudden surge of approximate reality to the ears or, more importantly, the penis.

‘Textures, on. Dynamics, on. Sound, on. Head tracking, on. Body sensing, on. Phallus sensor, on.’

Then I dropped the visor-screen.

And there she was, standing before me in a pleasant forest glade, like Eve herself, without so much as a fig leaf to cover her nakedness. The image blurred a little as I stepped towards her and I made a small adjustment to the visor. Then I reached out and caressed her breast to test the glove, and felt her nipple harden as I touched her. Next, I slapped her face hard to test the sound quality, which was fine. Policewoman took the blow with a cry of pain, but no reproach. She just stood there, awaiting my next move, as programmed. I motioned her down onto her knees to check the RA condom and felt her approximate mouth envelop my penis. Everything was working perfectly. So long as the visor was down, the software would remain in operation, and approximate reality would be nearly indistinguishable from the real thing. (Sometimes I think that I’m living a real life in an approximate way. Or should that be the other way round?) Better even. There are no laws in RA.