### The Baywatch principle

Science isn't always great at naming things. For every photon there are plenty of clunky names that don't do a lot for you. Take, for instance,  the 'principle of least action', which sounds like a description of the lives of teenagers. This is a shame because it is really interesting. For reasons that will become clear I like to think of it as 'the Baywatch Principle.' And what it says, in essence, is that nature is lazy.

French mathematician Pierre de Fermat used the principle of least action to explain why light bends as it moves from a thinner to a thicker substance (from air to glass, for instance) – and Richard Feynman made it a fundamental part of quantum electrodynamics.

The principle of least action describes why a basketball follows a particular route through space on its way to the basket. It rises and falls along the path that keeps the difference between the ball’s kinetic energy (the energy that makes it move) and potential energy (the energy that gravity gives it by pulling it downwards) to a minimum. Kinetic energy increases as the ball goes faster and decreases as it slows. Potential energy goes up as the ball gets higher in the air and reduces as it falls. The principle of least action establishes a balance between the two.

This principle is applied to light by considering time. The principle of least time says that light takes the quickest route. Fermat had to make two assumptions – that light’s speed isn’t infinite (the speed of light was yet to be measured in 1661 when Fermat produced this result), and that light moves slower in a dense material like glass than it does in air. We are used to straight lines being the quickest route between any two points – but that assumes that everything remains the same on the journey. In the case of light going from air to glass, bending is the quickest route. To see why this is the case, compare the light’s journey to a lifeguard, rescuing someone drowning in the sea. The obvious route is to head straight for the drowning person. But the lifeguard can run much faster on the beach than in the water. By heading away from the victim, taking a longer path on the sand, then bending inwards and taking a more direct path in the water, the lifeguard gets there quicker.

Similarly, a light ray can reduce its journey time by spending longer in air and less time in glass. The angle that minimizes the journey time is the one that actually occurs.

When Richard Feynman was inspired by the principle of least action to come up with quantum electrodynamics, the theory that describes the interaction of light and matter so brilliantly, he imagined not just the one “best” path but every single possible path a particle could take in getting from A to B. At the heart of QED is the idea that you can identify the particles behaviour by taking a sum of every single possible path combined with the probability of that path occurring.

### Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's recent gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some ex

### Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

### Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope