This understandable desire for privacy made it easy for the network highwaymen to conduct their electronic holdups: even when they were caught, they were treated gently by legal systems which did not know how to handle such novel crimes – and, after all, they had not really hurt anyone, had they? Indeed, after they had served their brief sentences, many of the perpetrators were quietly hired by their victims, on the old principle that poachers make the best game-keepers.

These computer criminals were driven purely by greed, and certainly did not wish to destroy the organizations they preyed upon: no sensible parasite kills its host. But there were other, and much more dangerous, enemies of society at work...

Usually, they were maladjusted individuals – typically adolescent males – working entirely alone, and of course in complete secrecy. Their aim was to create programs which would simply create havoc and confusion, when they had been spread over the planet by the world-wide cable and radio networks, or on physical carriers such as diskettes and CD ROMS. Then they would enjoy the resulting chaos, basking in the sense of power it gave their pitiful psyches.

Sometimes, these perverted geniuses were discovered and adopted by national intelligence agencies for their own secretive purposes – usually, to break into the data banks of their rivals. This was a fairly harmless line of employment, as the organizations concerned did at least have some sense of civic responsibility.

Not so the apocalyptic sects, who were delighted to discover this new armoury, holding weapons far more effective, and more easily disseminated, than gas or germs. And much more difficult to counter, since they could be broadcast instantaneously to millions of offices and homes.

The collapse of the New York-Havana Bank in 2005, the launching of Indian nuclear missiles in 2007 (luckily with their warheads unactivated), the shutdown of Pan-European Air Traffic Control in 2008, the paralysis of the North American telephone network in that same year – all these were cult-inspired rehearsals for Doomsday. Thanks to brilliant feats of counterintelligence by normally uncooperative, and even warring, national agencies, this menace was slowly brought under control.

At least, so it was generally believed: there had been no serious attacks at the very foundations of society for several hundred years. One of the chief weapons of victory had been the Braincap – though there were some who believed that this achievement had been bought at too great a cost.

Though arguments over the freedom of the Individual versus the duties of the State were old when Plato and Aristotle attempted to codify them, and would probably continue until the end of time, some consensus had been reached in the Third Millennium. It was generally agreed that Communism was the most perfect form of government; unfortunately it had been demonstrated – at the cost of some hundreds of millions of lives – that it was only applicable to social insects, Robots Class II, and similar restricted categories. For imperfect human beings, the least-worst answer was Demosocracy, frequently defined as 'individual greed, moderated by an efficient but not too zealous government'.

Soon after the Braincap came into general use, some highly intelligent – and maximally zealous – bureaucrats realized that it had a unique potential as an early-warning system. During the setting-up process, when the new wearer was being mentally 'calibrated' it was possible to detect many forms of psychosis before they had a chance of becoming dangerous. Often this suggested the best therapy, but when no cure appeared possible the subject could be electronically tagged – or, in extreme cases, segregated from society. Of course, this mental monitoring could test only those who were fitted with a Braincap – but by the end of the Third Millennium this was as essential for everyday life as the personal telephone had been at its beginning. In fact, anyone who did not join the vast majority was automatically suspect, and checked as a potential deviant.

Needless to say, when 'mind-probing', as its critics called it, started coming into general use, there were cries of outrage from civil-rights organizations; one of their most effective slogans was 'Braincap or Braincop?' Slowly – even reluctantly – it was accepted that this form of monitoring was a necessary precaution against far worse evils; and it was no coincidence that with the general improvement in mental health, religious fanaticism also started its rapid decline-

When the long-drawn-out war against the cybernet criminals ended, the victors found themselves owning an embarrassing collection of spoils, all of them utterly incomprehensible to any past conqueror. There were, of course, hundreds of computer viruses, most of them very difficult to detect and kill. And there were some entities – for want of a better name – that were much more terrifying. They were brilliantly invented diseases for which there was no cure – in some cases not even the possibility of a cure

Many of them had been linked to great mathematicians who would have been horrified by this corruption of their discoveries. As it is a human characteristic to belittle a real danger by giving it an absurd name, the designations were often facetious: the Godel Gremlin, the Mandelbrot Maze, the Combinatorial Catastrophe, the Transfinite Trap, the Conway Conundrum, the Turing Torpedo, the Lorentz Labyrinth, the Boolean Bomb, the Shannon Snare, the Cantor Cataclysm...

If any generalization was possible, all these mathematical horrors operated on the same principle. They did not depend for their effectiveness on anything as naïve as memory-erasure or code corruption – on the contrary. Their approach was more subtle; they persuaded their host machine to initiate a program which could not be completed before the end of the universe, or which – the Mandelbrot Maze was the deadliest example – involved a literally infinite series of steps.

A trivial example would be the calculation of Pi, or any other irrational number. However, even the most stupid electro-optic computer would not fall into such a simple trap: the day had long since passed when mechanical morons would wear out their gears, grinding them to powder as they tried to divide by zero...

The challenge to the demon programmers was to convince their targets that the task set them had a definite conclusion that could be reached in a finite time. In the battle of wits between man (seldom woman, despite such role-models as Lady Ada Lovelace, Admiral Grace Hopper and Dr Susan Calvin) and machine, the machine almost invariably lost.

It would have been possible – though in some cases difficult and even risky – to destroy the captured obscenities by ERASE/OVERWRITE commands, but they represented an enormous investment in time and ingenuity which, however misguided, seemed a pity to waste. And, more important, perhaps they should be kept for study, in some secure location, as a safeguard against the time when some evil genius might reinvent and deploy them.

The solution was obvious. The digital demons should be sealed with their chemical and biological counterparts, it was hoped for ever, in the Pico Vault.