Many of the most powerful, and to me, most interesting, ideas in science connect two apparently unrelated observations. The breakthrough is to realise that there is a hidden connection between two aspects of the natural world. A simple example is the force one charge exerts on another, that is a distance r away. Coulomb’s Law tells us that this force decreases as 1/r². Now we also know that the area of a sphere centred on the first charge increases as r². You might think that it was a coincidence that in both cases it is r². If you did, you would be wrong.

The force between charges is carried by particles called photons, that go between two charges (these are the same photons that constitute light). So the force the second charge experiences due to the first charge is proportional to the density of photons at the second charge, coming from the first charge. As the distance between the two charges, r, increases, the density drops because the photons are diluted over an area which is increasing as r². Thus the force decreases as one over this area, as 1/r². Coulomb’s Law is just geometry, and as soon as you realise this you know how the charges interact.

But to realise this you need to understand the role of the particles, the photons, so the connection is hidden.

It is perhaps a little ironic that here the connection is photons, which are what light is made of. Truly, here the connection is hidden in plain sight.

This is just one example of many. And hidden connections occur elsewhere. For instance, did you know that the same guy, Mike Batt, wrote both the Wombling Song (from 1970s children’s tv series The Wombles), and the 1998 World Cup anthem of the German team – who had a good run until coming up against Croatia in the quarter finals. Few people watching Berti Vogts rather average German team play would have connected them to the Wombles, but there is a hidden connection.