As is the case with many of the important things in the universe, they pass by without due consideration. Today we muse over a funny old thing – symmetry. The feature photograph for this post is a photograph I took in St Isaac’s cathedral, just across from Hotel Astoria in St Petersburg where I had the good fortune of staying for 4 nights. Looking up at that dome really was breath taking and I can promise you I didn’t find Jesus – it is the symmetry that does it.
According to Wikipedia, which on this instance I have no cause to doubt the word itself originates from Greek συμμετρία symmetria “agreement in dimensions, due proportion, arrangement”. When you think about it simply, symmetry is a mirror image – an exact replica of what is on one side on the other. To be honest for most cases this will actually do for understanding. As human beings we are genetically coded to value symmetry – to celebrate it and all it brings us. Have you ever seen someone with an unsymmetrical face? Even I am not cruel enough to post pictures – but type it into Google images. The cold facts of the matter are that the more symmetrical you are, the more attractive you are likely to be perceived.
The human desire for symmetry does not stop at copulation – it extends much further than that. Think of any of the great landmarks that might spring into your head. The Eiffel Tower, the Taj Mahal, the Empire State, The Gherkin and so on – all of these buildings have been celebrated for their architectural brilliance and they are all ever so symmetrical. Take a look at the photo below – it is a great shot illustrating the point.
What is so exciting about symmetry is that it permeates through so much of life. Faces and buildings? Oh we are just getting started. Biology as discussed gives us symmetry and encodes us to value it so it isn’t really that much of a head scratcher that our constructions exhibit the same. Mathematically symmetry isn’t too hard to define – there are just different types of symmetry so it mixes things up a little. But let us not get too bogged down in this, the absolute key take away is that something is symmetrical when it is unchanged under transformation. This could indeed be reflection but it might be rotation; but one might take this even further. A very basic function that maps x to x is symmetric is it not? The input and the output are after all the same which sounds a lot like symmetry. In fact, we don’t need to be that basic – we can spread our wings a little more. In generally we can say that any mathematical operation exhibits symmetry if it preserves some property of the object to which it is applied; it need not be as simple as literally being unchanged.
The end result of all of this was always going to be some science – which is coming up right now. The most important idea here is moving something from one coordinate in space to another the laws of Physics should be the same. That is symmetry – we have performed a translation and preserved a property of the object which has undergone a transformation. Even deeper these laws should not vary with time – the results of an experiment (assuming no statistically driven outputs) should indeed yield the same on Monday and on Wednesday. This is basic physical symmetry.
A Nobel prize was awarded 7 years ago for work on the enticingly titled area of broken symmetry. In other words – things that happen in the world that are not quite symmetrical (don’t panic, they do happen and the Earth stays on its axis). This is yet another area where string theory is the only half respectable means we have of understanding what happens when symmetry breaks – and as we have stated before this is not yet proven. The front running theories say that there is symmetry between the fundamental forces in the universe that was somehow broken early in the universe which is why we see some of the quirks we do today.
With the mention of string theory in an article on symmetry we of course conclude with one of the lynchpins of the theory – supersymmetry ( I know, as if symmetry wasn’t enough for one evening). I do not intend to go into this at great depth namely because it is an area beyond my current full comprehension. In brief elementary classes of particles are related by their spin – and within each of the two sets of elementary particles they can be paired off with a superpartner where everything is more or less the same except for the fact the spin differs by half an integer. This super-symmetry must be proven to be unbroken which it has not yet. Below is a simulation of what we are looking for – coming out of the large hadron collider under which the Higgs Boson is revealed, central to supersymmetry.