It has often been noted that the major catalysts for the progression of knowledge, historically speaking, are not only discoveries of new truths, but also realisations that in fact, we know less than we thought. The progress of knowledge can therefore be charted by the way our ignorance increases to encompass more and more as time goes by. Perhaps the best example of this is in physics, to some the bedrock of our scientific understanding of the universe, and to most an industry selflessly devoted to keeping large numbers of people with strange hair, wearing leather elbow patches and sandals with socks, off the streets.

Newton's Laws

In not quite the beginning, there was Newton, and he discovered Newton's laws. The good thing about Newtonian mechanics is that in theory, given knowledge of where everything is and how fast it's moving, you can calculate where it's going to be in the future. This is very nice and ordered, and as anyone who has ever tried to keep track of a teenager knows, pointlessly naive. In particular, if you look at systems with more than two objects in, it's very hard to find out what the system's going to do. And since a butterfly somewhere flapped its wings and, as a side effect, created chaos theory, we have learned that even some systems previously thought to be fairly well behaved, fail to be predictable after a distressingly short time. So a great step towards ignorance was made.

Einstein's Theory of Relativity

After a long time when things were deterministic¹, along came Einstein. He was very clever, with particularly strange hair, and was definitely a sandal-wearer, replete with socks, towards the end of his life. He said that actually, things don't just move about in space, they bend space as they do so. This seemingly bizarre idea led to the general theory of relativity, described by many as the most stunningly beautiful and neat piece of work ever done (albeit only by those who should get out more, and stop wearing sandals). Einstein's equations are harder to write than Newton's. Apart from a few witty little catchphrases like 'E=mc²', they tend to have Greek letters everywhere. What they do achieve, however, is a huge step forward in ignorance as they show us that, if you take into account the fact that objects bend space, we can't really be sure about two-body systems any more. They generally turn out to be unpredictable too. We do, however, retain our knowledge that when we have just one thing to look at, it behaves in a nice, orderly manner.

Quantum Mechanics

Or so we thought. Quantum mechanics, in contrast to Einstein's relativity, was developed by a committee, and hence is messy, awkward, and still argued about now, 70 years since its conception. The serious sandal wearers frequently get excited about different 'interpretations' of the theory; for example the idea that perhaps there are loads of possible different universes, and that the universe splits in some way whenever a choice is made. In spite of not being all that popular among the elbow-patched, this idea has been pushed into the popular world by various sci-fi writers. One thing which is agreed on, however, is that our little single object is now not so well-behaved. Heisenberg formulated this very neatly in his 'uncertainty relation', the gist of which is that we really know nothing at all about anything. The only saving grace is that if we have a system with nothing in it at all, we could be pretty certain what was going on.

Quantum Field Theory

But not for long. A bunch of people decided that ignorance had just not gone far enough, and set about inventing quantum field theory. The most famous of these was perhaps Richard Feynmann, who was really astoundingly clever, and wore sandals². They reasoned that, just as you can make up zero by adding one and minus one, so you can have nothing made up of things and anti-things. So instead of just a vacuum with nothing in it, there can be particles popping into existence along with anti-particles, floating round a bit, annoying physicists, and meeting up again to disappear. Thus we are now really not sure of what is going on when we have nothing.

It remains to be seen what sort of ignorance the future holds. Perhaps if we ever manage to come up with a quantum theory of gravity, our ignorance may reach levels hitherto only dreamed about, with potentially far-reaching effects on our view of the universe.