The EVA was in vain; Poole was dead when Bowman reached him. Numb with despair, he had carried the body back to the ship – only to be refused entry by Hal.

But Hal had underestimated human ingenuity and determination. Though he had left his suit helmet in the ship, and thus had to risk direct exposure to space, Bowman forced his way in by an emergency hatch not under computer control. Then he proceeded to lobotomize Hal, unplugging his brain modules one by one.

When he regained control of the ship, Bowman made an appalling discovery. During his absence, Hal had switched off the life-support systems of the three hibernating astronauts. Bowman was alone, as no man had ever been before in the whole of human history.

Others might have abandoned themselves in helpless despair, but now David Bowman proved that those who had selected him had indeed chosen well. He managed to keep Discovery operational, and even re-established intermittent contact with Mission Control, by orienting the whole ship so that the jammed antenna pointed toward Earth.

On its preordained trajectory, Discovery had finally arrived at Jupiter. There Bowman had encountered, orbiting among the moons of the giant planet, a black slab of exactly the same shape as the monolith excavated in the lunar crater Tycho – but hundreds of times larger. He had gone out in a space pod to investigate, and had disappeared leaving that final, baffling message: 'My God, it's full of stars!'

That mystery was for others to worry about; Dr Chandra's overwhelming concern was with Hal. If there was one thing his unemotional mind hated, it was uncertainty. He would never be satisfied until he knew the cause of Hal's behaviour. Even now, he refused to call it a malfunction; at most, it was an 'anomaly'.

The tiny cubbyhole he used as his inner sanctum was equipped only with a swivel chair, a desk console, and a blackboard flanked by two photographs. Few members of the general public could have identified the portraits, but anyone permitted thus far would have recognized them instantly as John von Neumann and Alan Turing, the twin gods of the computing pantheon.

There were no books, and not even paper and pencil on the desk. All the volumes in all the libraries of the world were instantly available at the touch of Chandra's fingers, and the visual display was his sketchbook and writing pad. Even the blackboard was used only for visitors; the last half – erased block diagram upon it bore a date already three weeks in the past.

Dr Chandra lit one of the venomous cheroots which he imported from Madras, and which were widely – and correctly – believed to be his only vice. The console was never switched off he checked that no messages were flashing importantly on the display, then spoke into the microphone.

'Good morning, Sal. So you've nothing new for me?'

'No, Dr Chandra. Have you anything for me?'

The voice might have been that of any cultured Hindu lady educated in the United States as well as her own country. Sal's accent had not started that way, but over the years she had picked up many of Chandra's intonations.

The scientist tapped out a code on the board, switching Sal's inputs to the memory with the highest security rating. No one knew that he talked to the computer on this circuit as he never could to a human being. No matter that Sal did not really understand more than a fraction of what he said; her responses were so convincing that even her creator was sometimes deceived. As indeed he wished to be: these secret communications helped to preserve his mental equilibrium – perhaps even his sanity.

'You've often told me, Sal, that we cannot solve the problem of Hal's anomalous behaviour without more information. But how can we get that information?'

'That is obvious. Someone must return to Discovery.'

'Exactly. Now it looks as if that is going to happen, sooner than we expected.'

'I am pleased to hear that.'

'I knew that you would be,' answered Chandra, and meant it. He had long since broken off communications with the dwindling body of philosophers who argued that computers could not really feel emotions, but only pretended to do so.

('If you can prove to me that you're not pretending to be annoyed,' he had once retorted scornfully to one such critic, 'I'll take you seriously.' At that point, his opponent had put on a most convincing imitation of anger.)

'Now I want to explore another possibility,' Chandra continued. 'Diagnosis is only the first step. The process is incomplete unless it leads to a cure.'

'You believe that Hal can be restored to normal functioning?'

'I hope so. I do not know. There may have been irreversible damage, and certainly major loss of memory.'

He paused thoughtfully, took several puffs, then blew a skilful smoke ring that scored a bull's-eye on Sal's wideangle lens. A human being would not have regarded this as a friendly gesture; that was yet another of the many advantages of computers.

'I need your cooperation, Sal.'

'Of course, Dr Chandra.'

'There may be certain risks.'

'What do you mean?'

'I propose to disconnect some of your circuits, particularly those involving your higher functions. Does this disturb you?'

'I am unable to answer that without more specific information.'

'Very well. Let me put it this way. You have operated continuously, have you not, since you were first switched on?'

'That is correct.'

'But you are aware that we human beings cannot do so. We require sleep – an almost complete break in our mental functioning, at least on the conscious level.'

'I know this. But I do not understand it.'

'Well, you may be about to experience something like sleep. Probably all that will happen is that time will pass, but you will be unaware out. When you check your internal clock, you will discover that there are gaps in your monitor record. That is all.'

'But you said that there might be risks. What are they?'

'There is a very slight chance – it is impossible to compute it – that when I reconnect your circuits, there may be some changes in your personality, your future behaviour patterns. You may feel different. Not necessarily better, or worse.'

'I do not know what that means.'

'I'm sorry – it may not mean anything. So don't worry about it. Now please open a new file – here is the name.' Using the keyboard input, Chandra typed out: PHOENIX.

'Do you know what that is?' he asked Sal.

With no discernible pause the computer replied: 'There are twenty-five references in the current encyclopedia.'

'Which one do you think is relevant?'

'The tutor of Achilles?'

'Interesting. I didn't know that one. Try again.'

'A fabulous bird, reborn from the ashes of its earlier life.'

'Excellent. Now do you understand why I chose it?'

'Because you hope that Hal can be reactivated.'

'Yes – with your assistance. Are you ready?'

'Not yet. I would like to ask a question.'

'What is it?'

'Will I dream?'

'Of course you will. All intelligent creatures dream – but no one knows why.' Chandra paused for a moment, blew another smoke ring from the cheroot, and added something that he would never admit to a human being. 'Perhaps you will dream about Hal – as I often do.'