«Odd,» agreed Reg. «I've certainly never come across any irreversible mathematics involving sofas. Could be a new field. Have you spoken to any spatial geometricians?»

«I did better than that. I called in a neighbour's kid who used to be able to solve Rubik's cube in seventeen seconds. He sat on a step and stared at it for over an hour before pronouncing it irrevocably stuck. Admittedly he's a few years older now and has found out about girls, but it's got me puzzled.»

«Carry on talking, my dear fellow, I'm most interested, but let me know first if there's anything I can get you. Port perhaps? Or brandy?

The port I think is the better bet, laid down by the college in 1934, one of the finest vintages I think you'll find, and on the other hand I don't actually have any brandy. Or coffee? Some more wine perhaps?

There's an excellent Margaux I've been looking for an excuse to open, though it should of course be allowed to stand open for an hour or two, which is not to say that I couldn't… no,» he said hurriedly, «probably best not to go for the Margaux tonight.»

«Tea is what I would really like,» said Richard, «if you have some.»

Reg raised his eyebrows. «Are you sure?»

«I have to drive home.»

«Indeed. Then I shall be a moment or two in the kitchen. Please carry on, I shall still be able to hear you. Continue to tell me of your sofa, and do feel free in the meantime to sit on mine. Has it been stuck there for long?»

«Oh, only about three weeks,» said Richard, sitting down. «I could just saw it up and throw it away, but I can't believe that there isn't a logical answer. And it also made me think — it would be really useful to know before you buy a piece of furniture whether it's actually going to fit up the stairs or around the corner. So I've modelled the problem in three dimensions on my computer — and so far it just says no way.»

«It says what?» called Reg, over the noise of filling the kettle.

«That it can't be done. I told it to compute the moves necessary to get the sofa out, and it said there aren't any. I said „What?“ and it said there aren't any. I then asked it, and this is the really mysterious thing, to compute the moves necessary to get the sofa into its present position in the first place, and it said that it couldn't have got there. Not without fundamental restructuring of the walls. So, either there's something wrong with the fundamental structure of the matter in my walls or,» he added with a sigh, «there's something wrong with the program. Which would you guess?»

«And are you married?» called Reg.

«What? Oh, I see what you mean. A sofa stuck on the stairs for a month. Well, no, not married as such, but yes, there is a specific girl that I'm not married to.»

«What's she like? What does she do?»

«She's a professional cellist. I have to admit that the sofa has been a bit of a talking point. In fact she's moved back to her own flat until I get it sorted out. She, well…»

He was suddenly sad, and he stood up and wandered around the room in a desultory sort of way and ended up in front of the dying fire. He gave it a bit of a poke and threw on a couple of extra logs to try and ward off the chill of the room.

«She's Gordon's sister, in fact,» he added at last. «But they are very different. I'm not sure she really approves of computers very much. And she doesn't much like his attitude to money. I don't think I entirely blame her, actually, and she doesn't know the half of it.»

«Which is the half she doesn't know?»

Richard sighed.

«Well,» he said, «it's to do with the project which first made the software incarnation of the company profitable. It was called Reason, and in its own way it was sensational.»

«What was it?»

«Well, it was a kind of back-to-front program. It's funny how many of the best ideas are just an old idea back-to-front. You see there have already been several programs written that help you to arrive at decisions by properly ordering and analysing all the relevant facts so that they then point naturally towards the right decision. The drawback with these is that the decision which all the properly ordered and analysed facts point to is not necessarily the one you want.»

«Yeeeess…» said Reg's voice from the kitchen.

«Well, Gordon's great insight was to design a program which allowed you to specify in advance what decision you wished it to reach, and only then to give it all the facts. The program's task, which it was able to accomplish with consummate ease, was simply to construct a plausible series of logical-sounding steps to connect the premises with the conclusion.

And I have to say that it worked brilliantly. Gordon was able to buy himself a Porsche almost immediately despite being completely broke and a hopeless driver. Even his bank manager was unable to find fault with his reasoning. Even when Gordon wrote it off three weeks later.»

«Heavens. And did the program sell very well?»

«No. We never sold a single copy.»

«You astonish me. It sounds like a real winner to me.»

«It was,» said Richard hesitantly. «The entire project was bought up, lock, stock and barrel, by the Pentagon. The deal put WayForward on a very sound financial foundation. Its moral foundation, on the other hand, is not something I would want to trust my weight to. I've recently been analysing a lot of the arguments put forward in favour of the Star Wars project, and if you know what you're looking for, the pattern of the algorithms is very clear.

So much so, in fact, that looking at Pentagon policies over the last couple of years I think I can be fairly sure that the US Navy is using version 2.00 of the program, while the Air Force for some reason only has the beta-test version of 1.5. Odd, that.»

«Do you have a copy?»

«Certainly not,» said Richard, «I wouldn't have anything to do with it. Anyway, when the Pentagon bought everything, they bought everything. Every scrap of code, every disk, every notebook. I was glad to see the back of it. If indeed we have. I just busy myself with my own projects.»

He poked at the fire again and wondered what he was doing here when he had so much work on. Gordon was on at him continually about getting the new, super version of Anthem ready for taking advantage of the Macintosh II, and he was well behind with it. And as for the proposed module for converting incoming Dow Jones stock-market information into MIDI data in real time, he'd only meant that as a joke, but Gordon, of course, had flipped over the idea and insisted on its being implemented. That too was meant to be ready but wasn't. He suddenly knew exactly why it was he was here.

Well, it had been a pleasant evening, even if he couldn't see why Reg had been quite so keen to see him. He picked up a couple of books from the table. The table obviously doubled as a dining table, because although the piles looked as if they had been there for weeks, the absence of dust immediately around them showed that they had been moved recently.

Maybe, he thought, the need for amiable chit-chat with someone different can become as urgent as any other need when you live in a community as enclosed as a Cambridge college was, even nowadays. He was a likeable old fellow, but it was clear from dinner that many of his colleagues found his eccentricities formed rather a rich sustained diet — particularly when they had so many of their own to contend with. A thought about Susan nagged him, but he was used to that. He flipped through the two books he'd picked up.

One of them, an elderly one, was an account of the hauntings of Borley Rectory, the most haunted house in England. Its spine was getting raggedy, and the photographic plates were so grey and blurry as to be virtually indistinguishable. A picture he thought must be a very lucky (or faked) shot of a ghostly apparition turned out, when he examined the caption, to be a portrait of the author.