Fifty years ago, the American physicist Theodore Maiman created the first laser. At first, it seemed a curiosity; not even its inventors could predict the range of its uses, from eye surgery to DVD players. Likewise, some of this year's scientific advances may be transformative 50 years from now - even though we have no inkling of it today. Many concepts that seem impossible now might be realised in coming decades. But, in a still longer perspective, it is interesting to speculate whether we will reach a limit - if there are some scientific mysteries that will forever baffle us, phenomena that transcend human understanding.
Einstein said that "the most incomprehensible thing about the world is that it is comprehensible". Our brains have not changed significantly since our ancestors roamed the African savannah, so it is remarkable that we have had any success in grasping facets of the cosmos and the quantum - both so remote from the everyday experience. Einstein would have been particularly gratified at how our cosmic horizons have expanded. We now know that our sun is one of several hundred billion stars in our galaxy, which is itself one of many billion galaxies in the range of our telescopes. And this complex panorama emerged from a hot, amorphous "beginning" nearly 14 billion years ago.
In my own subject of astronomy, the controversies of my student days (such as Big Bang versus steady state theory) have now been settled. Some inferences about the early universe are now as firmly evidence-based as anything a geologist could say about the history of the earth - we know what the conditions were a second after the Big Bang. But, as always in science, each advance brings into focus questions that couldn't have been posed before.
The "beginning" itself (if there was one) is still a mystery. In the first fraction of a second, conditions would have been far hotter and denser than we can simulate in the lab. Einstein's theory of general relativity is not enough to understand what banged and why, because it treats space and time as smooth and continuous. We know that no material can be chopped into arbitrarily small pieces; eventually you get down to discrete atoms. Likewise, space may manifest a complicated grainy structure - but this is thought to be on scales a trillion trillion times smaller than atoms.
Yet there may be mysteries, too, at the largest conceivable scales. There could be far more beyond our horizon, as it were, than the vast expanse that our telescopes can observe. There could have been many "Big Bangs" - not just the one in whose aftermath we exist.
Some have speculated that other universes could exist in tandem with ours. Imagine ants crawling around on a large sheet of paper (their two-dimensional universe). They would be unaware of a similar sheet that is parallel to it. Likewise, there could be another entire universe (with three-dimensional space, like ours) less than a millimetre away from us, but we would be oblivious to it if that millimetre were measured in a fourth spatial dimension, while we are imprisoned in just three.
The microstructure of space, and the true extent of physical reality, are among the "open frontiers" of science: intellectual domains where we are still searching for the truth. They are in effect the very large (the cosmos) and the very small (the quantum). But only a tiny proportion of researchers are cosmologists or particle physicists. There is a third frontier, too: the very complex.
Our everyday world presents intellectual challenges just as daunting as those of the cosmos and the quantum, and that is where the vast majority of scientists focus their efforts. It may seem incongruous that scientists can make confident statements about galaxies billions of light years away, while being baffled about matters close at hand that we all care about - common diseases, for instance. But this is because living things, with intricate levels of structure, are far more complex than atoms and stars.
That said, everything, however complicated - breaking waves, migrating birds and tropical forests - is made of atoms and obeys the equations of quantum physics. But the uncertainties of subatomic physics are irrelevant to biologists; even if those equations could be solved, they would not offer the enlightenment that scientists seek.
Each science has its own autonomous concepts and laws. Problems in biology remain unsolved because it is hard to elucidate their complexities, not because we scientists do not understand subatomic physics well enough. This thought takes me back to my initial question: are there intrinsic limits to our understanding, or to our technical capability? Could some branches of science come to a halt simply because we bump up against limits to what the human brain can understand?
Physicists may never understand the bedrock nature of space and time because the mathematics is just too hard; but I think our efforts
to understand very complex systems - above all, our own brains - will be the first to hit such limits.
Perhaps complex aggregates of atoms, whether brains or machines, can never understand everything about themselves. Some aspects of reality might elude us because they are beyond human brains, just as surely as Einstein's ideas would baffle a chimpanzee.
Computers will help: future discoveries may be made by "brute force" rather than by insight. Even back in the 1990s, the higher processing speed of IBM's Deep Blue allowed it to outperform the chess player Garry Kasparov. Astrophysicists can already create a "virtual universe" in a computer and do "experiments" calculating how stars and galaxies evolve, and how our moon formed in a crash between the young earth and another planet.
Despite our limitations, many envisage human beings as the culmination of the evolutionary process. This doesn't seem credible to any astronomer, aware as they have been, ever since the work of Charles Darwin, not only of the stupendous time spans of the evolutionary past that led to our emergence, but also of the huge time-horizons extending into the future. Our sun formed 4.5 billion years ago, but it's got six billion more before the fuel runs out.
And the expanding universe will continue, perhaps for ever, becoming (according to the best current long-range forecast) ever colder, ever emptier. So, even if life were now unique to earth, there would be scope for post-human evolution - whether organic or silicon-based - on the earth or far beyond it.
It won't be human beings who witness the sun's demise: it will be entities as different from us as we are from an insect. For them, string theory and brain science might be a doddle, but they will probably be flummoxed by mysteries we cannot even imagine. l
Martin Rees is the Astronomer Royal, Master of Trinity College, Cambridge, and a former president of the Royal Society