The most important advances, the qualitative leaps, are the least predictable. Not even the best scientists predicted the impact of nuclear physics, and everyday consumer items such as the iPhone would have seemed magic back in the 1950s.

There is an ever-widening gap between what science allows and what we should actually do. There are many doors science can open that should be kept closed, on prudential or ethical grounds.

The stupendous time spans of the evolutionary past are now part of common culture (though maybe not in the United States Bible Belt, nor in parts of the Islamic world). Most people are at ease with the idea that our present biosphere is the outcome of four billion years of Darwinian evolution.

We are 'nuclear waste' from the fuel that makes stars shine; indeed, each of us contains atoms whose provenance can be traced back to thousands of different stars spread through our Milky Way.

Some global hazards are insidious. They stem from pressure on energy supplies, food, water and other natural resources. And they will be aggravated as the population rises to a projected nine billion by mid-century, and by the effects of climate change. An 'ecological shock' could irreversibly degrade our environment.

Maybe the search for life shouldn't restrict attention to planets like Earth. Science fiction writers have other ideas: balloon-like creatures floating in the dense atmospheres of planets such as Jupiter, swarms of intelligent insects, nano-scale robots and more.

If you take 10,000 people at random, 9,999 have something in common: their interests in business lie on or near the Earth's surface. The odd one out is an astronomer, and I am one of that strange breed.

During the 20th century, we came to understand that the essence of all substances - their colour, texture, hardness and so forth - is set by their structure, on scales far smaller even than a microscope can see. Everything on Earth is made of atoms, which are, especially in living things, combined together in intricate molecular assemblages.

To most people in the U.K., indeed throughout Western Europe, space exploration is primarily perceived as 'what NASA does'. This perception is - in many respects - a valid one. Superpower rivalry during the Cold War ramped up U.S. and Soviet space efforts to a scale that Western Europe had no motive to match.

Science is the one culture that's truly global - protons, proteins and Pythagoras's Theorem are the same from China to Peru. It should transcend all barriers of nationality. It should straddle all faiths, too.

Manufacturing doesn't just mean building cars and metal-bashing; it includes making pharmaceuticals and hi-tech electronics. A crucial part of the process is the research and development that allows better and greener products to come to market. Britain has traditionally had a strong science and engineering base.

In our interconnected world, novel technology could empower just one fanatic, or some weirdo with a mindset of those who now design computer viruses, to trigger some kind of disaster. Indeed, catastrophe could arise simply from technical misadventure - error rather than terror.

The practical case for manned spacef light gets ever-weaker with each advance in robots and miniaturisation - indeed, as a scientist or practical man, I see little purpose in sending people into space at all. But as a human being, I'm an enthusiast for manned missions.

Advances in technology - hugely beneficial though they are - render us vulnerable in new ways. For instance, our interconnected world depends on elaborate networks: electric power grids, air traffic control, international finance, just-in-time delivery, and so forth.

Not even the most secular among us can fail to be uplifted by Christianity's architectural legacy - the great cathedrals. These immense and glorious buildings were erected in an era of constricted horizons, both in time and in space.

The scientific community should work as hard as possible to address major issues that affect our everyday lives such as climate change, infectious diseases and counterterrorism; in particular, 'clean energy' research deserves far higher priority. And science and technology are the prime routes to tackling these issues.

Ironically, it is only when disaster strikes that the shuttle makes the headlines. Its routine flights attracted less media interest than unmanned probes to the planets or the images from the Hubble Telescope. The fate of Columbia (like that of Challenger in 1986) reminded us that space is still a hazardous environment.

Darwin and his successors taught us how our biosphere evolved, and thereby transformed our conception of humanity's place in nature. In the twenty-first century, space scientists are setting Darwin in a grander cosmic context - probing the origins of Earth, stars, atoms and the universe itself.

The Blair government perhaps ranks as the best the U.K. has had for 50 years. It cannot match the scale of Attlee's reforms, but has a fine record of constitutional reform and economic competence. In my own areas - science and innovation - there have been well-judged and effective changes.

There's now, for the first time, a huge gulf between the artefacts of our everyday life and what even a single expert, let alone the average child, can comprehend. The gadgets that now pervade young people's lives, iPhones and suchlike, are baffling 'black boxes' - pure magic to most people.

A monkey is unaware that atoms exist. Likewise, our brainpower may not stretch to the deepest aspects of reality. The bedrock nature of space and time, and the structure of our entire universe, may remain 'open frontiers' beyond human grasp.

I hope that by 2050 the entire solar system will have been explored and mapped by flotillas of tiny robotic craft.

It is foolish to claim, as some do, that emigration into space offers a long-term escape from Earth's problems. Nowhere in our solar system offers an environment even as clement as the Antarctic or the top of Everest.

In future, children won't perceive the stars as mere twinkling points of light: they'll learn that each is a 'Sun', orbited by planets fully as interesting as those in our Solar system.

As regards my own 'philosophy,' I continue to be inspired by the music, liturgy and architectural tradition of the Anglican Church in which I was brought up. No one can fail to be uplifted by great cathedrals - such as that at Ely, near my home in Cambridge.

When scientists are asked what they are working on, their response is seldom 'Finding the origin of the universe' or 'Seeking to cure cancer.' Usually, they will claim to be tackling a very specific problem - a small piece of the jigsaw that builds up the big picture.

Some of the 'aha' insights that scientists strive for may have to await the emergence of post-human intellects.

Crucial to science education is hands-on involvement: showing, not just telling; real experiments and field trips and not just 'virtual reality.'

The scientific issues that engage people most are the truly fundamental ones: is the universe infinite? Is life just a sideshow in the cosmos? What happened before the Big Bang? Everyone is flummoxed by such questions, so there is, in a sense, no gulf between experts and the rest.

Everything, however complicated - breaking waves, migrating birds, and tropical forests - is made of atoms and obeys the equations of quantum physics. But even if those equations could be solved, they wouldn't offer the enlightenment that scientists seek. Each science has its own autonomous concepts and laws.

There are at least as many galaxies in our observable universe as there are stars in our galaxy.

The first arrival of earthly life on another celestial body ranks as an epochal event not only for our generation, but in the history of our planet. Neil Armstrong was at the cusp of the Apollo programme. This was a collective technological effort of epic scale, but his is the one name sure to be remembered centuries hence.

We know too little about how life began on Earth to lay confident odds. It may have involved a fluke so rare that it happened only once in the entire galaxy. On the other hand, it may have been almost inevitable, given the right environment.

Indeed, our everyday world presents intellectual challenges just as daunting as those of the cosmos and the quantum, and that is where 99 per cent of scientists focus their efforts. Even the smallest insect, with its intricate structure, is far more complex than either an atom or a star.

The Swedish engineer who invented the zip fastener made a greater intellectual leap than many scientists do in a lifetime.

Over most of history, threats have come from nature - disease, earthquakes, floods, and so forth. But the worst now come from us. We've entered a geological era called the anthropocene. This started, perhaps, with the invention of thermonuclear weapons.

If we ever established contact with intelligent life on another world, there would be barriers to communication. First, they would be many light years away, so signals would take many years to reach them: there would be no scope for quick repartee. There might be an IQ gap.

The extreme sophistication of modern technology - wonderful though its benefits are - is, ironically, an impediment to engaging young people with basics: with learning how things work.

Perhaps future space probes will be plastered in commercial logos, just as Formula One cars are now. Perhaps Robot Wars in space will be a lucrative spectator sport. If humans venture back to the moon, and even beyond, they may carry commercial insignia rather than national flags.

The scientists who attack mainstream religion, rather than striving for peaceful coexistence with it, damage science, and also weaken the fight against fundamentalism.

The atmospheric CO2 concentration is rising - mainly due to the burning of fossil fuels. It's agreed that this build-up will, in itself, induce a long-term warming trend, superimposed on all the other complicated effects that make climate fluctuate.

The Cern laboratory in Geneva was set up in 1955 to bring together European scientists who wished to pursue research into the nuclear and sub-nuclear world. Physicists then had greater clout than other scientists because the memory of their role in the Second World War was fresh in people's minds.

We do not fully understand the consequences of rising populations and increasing energy consumption on the interwoven fabric of atmosphere, water, land and life.

I have no religious belief myself, but I don't think we should fight about it. In particular, I think that we should not rubbish moderate religious leaders like the Archbishop of Canterbury because I think we all agree that extreme fundamentalism is a threat, and we need all the allies we can muster against it.

Ever since Darwin, we've been familiar with the stupendous timespans of the evolutionary past. But most people still somehow think we humans are necessarily the culmination of the evolutionary tree. No astronomer could believe this.

The lives of those such as Charles Darwin and Albert Einstein are plainly of interest in their own right, as well as for the light they shed on the way these great scientists worked. But are 'routine' scientists as fascinating as their science? Here I have my doubts.

Science isn't just for scientists - it's not just a training for careers.

If we do find ET, we will at least have something in common with them. They may live on planet Zog and have seven tentacles, but they will be made of the same kinds of atoms as us. If they have eyes, they will gaze out on the same cosmos as we do. They will, like us, trace their origins back to a 'Big Bang' 13.8 billion years ago.

The first voyagers to the stars will be creatures whose life cycle is matched to the voyage: the aeons involved in traversing the galaxy are not daunting to immortal beings. By the end of the third millennium, travel to other stars could be technically feasible. But would there be sufficient motive?

Given the scale of issues like global warming and epidemic disease, we shouldn't underestimate the importance of a can-do attitude to science rather than a can't-afford-it attitude.