If the demise of God will leave a gap, different people will fill it in different ways. My way includes a good dose of science, the honest and systematic endeavour to find out the truth about the real world. I see the human effort to understand the universe as a model-building enterprise. Each of us builds, inside our head, a model of the world in which we find ourselves. The minimal model of the world is the model our ancestors needed in order to survive in it. The simulation software was constructed and debugged by natural selection, and it is most adept in the world familiar to our ancestors on the African savannah: a three-dimensional world of medium-sized material objects, moving at medium speeds relative to one another. As an unexpected bonus, our brains turn out to be powerful enough to accommodate a much richer world model than the mediocre utilitarian one that our ancestors needed in order to survive. Art and science are runaway manifestations of this bonus. Let me paint one final picture, to convey the power of science to open the mind and satisfy the psyche.

One of the unhappiest spectacles to be seen on our streets today is the image of a woman swathed in shapeless black from head to toe, peering out at the world through a tiny slit. The burka is not just an instrument of oppression of women and claustral repression of their liberty and their beauty; not just a token of egregious male cruelty and tragically cowed female submission. I want to use the narrow slit in the veil as a symbol of something else.

Our eyes see the world through a narrow slit in the electromagnetic spectrum. Visible light is a chink of brightness in the vast dark spectrum, from radio waves at the long end to gamma rays at the short end. Quite how narrow is hard to appreciate and a challenge to convey. Imagine a gigantic black burka, with a vision slit of approximately the standard width, say about one inch. If the length of black cloth above the slit represents the short-wave end of the invisible spectrum, and if the length of black cloth below the slit represents the long-wave portion of the invisible spectrum, how long would the burka have to be in order to accommodate a one-inch slit to the same scale? It is hard to represent it sensibly without invoking logarithmic scales, so huge are the lengths we are dealing with. The last chapter of a book like this is no place to start tossing logarithms around, but you can take it from me that it would be the mother of all burkas. The one-inch window of visible light is derisorily tiny compared with the miles and miles of black cloth representing the invisible part of the spectrum, from radio waves at the hem of the skirt to gamma rays at the top of the head. What science does for us is widen the window. It opens up so wide that the imprisoning black garment drops away almost completely, exposing our senses to airy and exhilarating freedom.

Optical telescopes use glass lenses and mirrors to scan the heavens, and what they see is stars that happen to be radiating in the narrow band of wavelengths that we call visible light. But other telescopes 'see' in the X-ray or radio wavelengths, and present to us a cornucopia of alternative night skies. On a smaller scale, cameras with appropriate filters can 'see' in the ultraviolet and take photographs of flowers that show an alien range of stripes and spots that are visible to, and seemingly 'designed' for, insect eyes but which our unaided eyes can't see at all. Insect eyes have a spectral window of similar width to ours, but slightly shifted up the burka: they are blind to red and they see further into the ultraviolet than we do — into the 'ultraviolet garden'.*)

The metaphor of the narrow window of light, broadening out into a spectacularly wide spectrum, serves us in other areas of science. We live near the centre of a cavernous museum of magnitudes, viewing the world with sense organs and nervous systems that are equipped to perceive and understand only a small middle range of sizes, moving at a middle range of speeds. We are at home with objects ranging in size from a few kilometres (the view from a mountaintop) to about a tenth of a millimetre (the point of a pin). Outside this range even our imagination is handicapped, and we need the help of instruments and of mathematics — which, fortunately, we can learn to deploy. The range of sizes, distances or speeds with which our imaginations are comfortable is a tiny band, set in the midst of a gigantic range of the possible, from the scale of quantum strangeness at the smaller end to the scale of Einsteinian cosmology at the larger.

Our imaginations are forlornly under-equipped to cope with distances outside the narrow middle range of the ancestrally familiar. We try to visualize an electron as a tiny ball, in orbit around a larger cluster of balls representing protons and neutrons. That isn't what it is like at all. Electrons are not like little balls. They are not like anything we recognize. It isn't clear that 'like' even means anything when we try to fly too close to reality's further horizons. Our imaginations are not yet tooled-up to penetrate the neighbourhood of the quantum. Nothing at that scale behaves in the way matter — as we are evolved to think — ought to behave. Nor can we cope with the behaviour of objects that move at some appreciable fraction of the speed of light. Common sense lets us down, because common sense evolved in a world where nothing moves very fast, and nothing is very small or very large.

At the end of a famous essay on 'Possible Worlds', the great biologist J. B. S. Haldane wrote, 'Now, my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose… I suspect that there are more things in heaven and earth than are dreamed of, or can be dreamed of, in any philosophy.' By the way, I am intrigued by the suggestion that the famous Hamlet speech invoked by Haldane is conventionally misspoken. The normal stress is on 'your':

Indeed, the line is often plonkingly quoted with the implication that Horatio stands for shallow rationalists and sceptics everywhere. But some scholars place the stress on 'philosophy', with 'your' almost vanishing: '. than are dreamt of inyaphilosophy.' The difference doesn't really matter for present purposes, except that the second interpretation already takes care of Haldane's 'any' philosophy.

The dedicatee of this book made a living from the strangeness of science, pushing it to the point of comedy. The following is taken from the same extempore speech in Cambridge in 1998 from which I have already quoted: 'The fact that we live at the bottom of a deep gravity well, on the surface of a gas-covered planet going around a nuclear fireball ninety million miles away and think this to be normal is obviously some indication of how skewed our perspective tends to be.' Where other science-fiction writers played on the oddness of science to arouse our sense of the mysterious, Douglas Adams used it to make us laugh (those who have read The Hitchhiker's Guide to the Galaxy might think of the 'infinite improbability drive', for instance). Laughter is arguably the best response to some of the stranger paradoxes of modern physics. The alternative, I sometimes think, is to cry.

Quantum mechanics, that rarefied pinnacle of twentieth-century scientific achievement, makes brilliantly successful predictions about the real world. Richard Feynman compared its precision to predicting a distance as great as the width of North America to an accuracy of one human hair's breadth. This predictive success seems to mean that quantum theory has got to be true in some sense; as true as anything we know, even including the most down-to-earth common-sense facts. Yet the assumptions that quantum theory needs to make, in order to deliver those predictions, are so mysterious that even the great Feynman himself was moved to remark (there are various versions of this quotation, of which the following seems to me the neatest): 'If you think you understand quantum theory. you don't understand quantum theory.'*)