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.

Anton Zeilinger:"What I believe but cannot prove is that quantum physics teaches us to abandon the distinction between information and reality. The fundamental reason why I believe in this is that it is impossible to make an operational distinction between reality and information. In other words, whenever we make any statement about the world, about any object, about any feature of any object, we always make statements about the information we have. And, whenever we make scientific predictions we make statements about information we possibly attain in the future."

Paul Steinhardt: "I believe that our universe is not accidental, but I cannot prove it. Historically, most physicists have shared this point-of-view. For centuries, most of us have believed that the universe is governed by a simple set of physical laws that are the same everywhere and that these laws derive from a simple unified theory."

Gregory Benford: "Why is there scientific law at all? We physicists explain the origin and structure of matter and energy, but not the laws that do this. Does the idea of causation apply to where the laws themselves came from? Even Alan Guth's "free lunch" gives us the universe after the laws start acting. We have narrowed down the range of field theories that can yield the big bang universe we live in, but why do the laws that govern it seem to be constant in time, and always at work? One can imagine a universe in which laws are not truly lawful. Talk of miracles does just this, when God is supposed to make things work. Physics aims to find The Laws and hopes that these will be uniquely constrained, as when Einstein wondered if God had any choice when He made the universe."

Alison Gopnik: "I believe, but cannot prove, that babies and young children are actually more conscious, more vividly aware of their external world and internal life, than adults are. I believe this because there is strong evidence for a functional trade-off with development. Young children are much better than adults at learning new things and flexibly changing what they think about the world. On the other hand, they are much worse at using their knowledge to act in a swift, efficient and automatic way. They can learn three languages at once but they can't tie their shoelaces."

Lynn Margulis: "That our ability to perceive signals in the environment evolved directly from our bacterial ancestors. That is, we, like all other mammals including our apish brothers detect odors, distinguish tastes, hear bird song and drum beats and we too feel the vibrations of the drums. With our eyes closed we detect the light of the rising sun. These abilities to sense our surroundings are a heritage that preceded the evolution of all primates, all vertebrate animals, indeed all animals. Such sensitivities to wafting plant scents, tasty salted mixtures, police cruiser sirens, loving touches and star light register because of our "sensory cells"."

Mihaly Csikzentmihalyi: "When I first read your question, I was sure it was a trick—after all, almost nothing I believe in I can prove. I believe the earth is round, but I cannot prove it, nor can I prove that the earth revolves around the sun or that the naked fig tree in the garden will have leaves in a few months. I can't prove quarks exist or that there was a Big Bang—all of these and millions of other beliefs are based on faith in a community of knowledge whose proofs I am willing to accept, hoping they will accept on faith the few measly claims to proof I might advance."

Randolphe Nesse: "I can't prove it, but I am pretty sure that people gain a selective advantage from believing in things they can't prove. I am dead serious about this. People who are sometimes consumed by false beliefs do better than those who insist on evidence before they believe and act. People who are sometimes swept away by emotions do better in life than those who calculate every move. These advantages have, I believe, shaped mental capacities for intense emotion and passionate beliefs because they give a selective advantage in certain situations."

Douglas Rushkoff: "I can't prove it more than anecdotally, but I believe evolution has purpose and direction. It appears obvious, yet absolutely unconfirmable, that matter is groping towards complexity."

Donald Hoffman: "I believe that consciousness and its contents are all that exists. Spacetime, matter and fields never were the fundamental denizens of the universe but have always been, from their beginning, among the humbler contents of consciousness, dependent on it for their very being.

The world of our daily experience—the world of tables, chairs, stars and people, with their attendant shapes, smells, feels and sounds—is a species-specific user interface to a realm far more complex, a realm whose essential character is conscious. It is unlikely that the contents of our interface in any way resemble that realm. Indeed the usefulness of an interface requires, in general, that they do not. For the point of an interface, such as the windows interface on a computer, is simplification and ease of use. We click icons because this is quicker and less prone to error than editing megabytes of software or toggling voltages in circuits. Evolutionary pressures dictate that our species-specific interface, this world of our daily experience, should itself be a radical simplification, selected not for the exhaustive depiction of truth but for the mutable pragmatics of survival.

If this is right, if consciousness is fundamental, then we should not be surprised that, despite centuries of effort by the most brilliant of minds, there is as yet no physicalist theory of consciousness, no theory that explains how mindless matter or energy or fields could be, or cause, conscious experience."