DEEP in the basement of a dusty university library in Edinburgh lies a small black box, roughly the size of two cigarette packets side by side, that churns out random numbers in an endless stream.

At first glance it is an unremarkable piece of equipment. Encased in metal, it contains at its heart a microchip no more complex than the ones found in modern pocket calculators.

But, according to a growing band of top scientists, this box has quite extraordinary powers. It is, they claim, the 'eye' of a machine that appears capable of peering into the future and predicting major world events.

The machine apparently sensed the September 11 attacks on the World Trade Centre four hours before they happened - but in the fevered mood of conspiracy theories of the time, the claims were swiftly knocked back by sceptics. But last December, it also appeared to forewarn of the Asian tsunami just before the deep sea earthquake that precipitated the epic tragedy.

Now, even the doubters are acknowledging that here is a small box with apparently inexplicable powers.

'It's Earth-shattering stuff,' says Dr Roger Nelson, emeritus researcher at Princeton University in the United States, who is heading the research project behind the 'black box' phenomenon.

'We're very early on in the process of trying to figure out what's going on here. At the moment we're stabbing in the dark.' Dr Nelson's investigations, called the Global Consciousness Project, were originally hosted by Princeton University and are centred on one of the most extraordinary experiments of all time. Its aim is to detect whether all of humanity shares a single subconscious mind that we can all tap into without realising.

Daniel Tammet is an autistic savant. He can perform mind-boggling mathematical calculations at breakneck speeds. But unlike other savants, who can perform similar feats, Tammet can describe how he does it. He speaks seven languages and is even devising his own language. Now scientists are asking whether his exceptional abilities are the key to unlock the secrets of autism....

Tammet is calculating 377 multiplied by 795. Actually, he isn't "calculating": there is nothing conscious about what he is doing. He arrives at the answer instantly. Since his epileptic fit, he has been able to see numbers as shapes, colours and textures. The number two, for instance, is a motion, and five is a clap of thunder. "When I multiply numbers together, I see two shapes. The image starts to change and evolve, and a third shape emerges. That's the answer. It's mental imagery. It's like maths without having to think."...

Last year Tammet broke the European record for recalling pi, the mathematical constant, to the furthest decimal point. He found it easy, he says, because he didn't even have to "think". To him, pi isn't an abstract set of digits; it's a visual story, a film projected in front of his eyes. He learnt the number forwards and backwards and, last year, spent five hours recalling it in front of an adjudicator. He wanted to prove a point. "I memorised pi to 22,514 decimal places, and I am technically disabled. I just wanted to show people that disability needn't get in the way."