A tribute from Emma Montagu.

I’ve always loved Windmills. I remember the Thornton windmill, near Blackpool, from when I was 3 or 4. It sat back from the high street unloved, dirty and forgotten about. Fenced off. When we went back last year it had been ‘restored’ by building a shopping centre round it and scrubbing all the charm away from it.

I’m a terrible romantic and I think they appeal to my imagination of what the country was like before the industrial revolution. You know, when skill and craft actually meant something. Or maybe it’s from watching too many episodes of Trumpton and Windy Miller. I don’t know.

I first came across George Green when I was a maths undergraduate. He was an 18th century miller from Nottingham and in his spare time did mathematics. He gave his name to something called a Green’s function. They seemed very odd and esoteric and I could never quite get the hang of them. Later on when I did my PhD I studied them further and as I started to understand them I started to appreciate the beauty of them. I also read about the life of George Green and very quickly he became my hero and to this day remains my hero.

He did his maths by sitting on the top floor of his windmill in quite moments. I have this romantic picture of him in his windmill late at night in the midst of a storm. The windmill and sails have been shut-up tight to protect them from the storm and he’s sitting on the grain strewn floor writing out his calculation by candlelight.

It is a mystery how he learnt all this. There was no one in Nottingham who knew any real maths, let alone maths at the high level George was doing it. It would take years and years of careful self-study to reach the level of mathematical knowledge required to do the cutting-edge work that George did. He was a member of ‘Nottingham Subscription Library’ – an institution that still exists – so maybe the books came from there. We don’t know.

In 1828 he printed a pamphlet containing what is now regarded as one of the fundamental results in physics. It was mostly bought by his friends in Nottingham out of kindness. It’s unlikely anyone understood it.

One of the areas he looked at was waves in canals. So how does that tie in with Quantum Physics? Well the physics is different but the underlying maths is the same. Instead of looking at water waves in a canal you consider the ‘wavefunction’ of sub-atomic particles.

I’ll let you into a little secret you don’t actually need to know any physics to do quantum physics. Indeed the pioneers of quantum physics in the 1900’s didn’t actually know how to physically interpret the wavefunction. It was 20 years before anyone realised that the wavefunction represents the probability of finding the particle at a given place at a given time.

Going back to the canal: suppose you consider a canal boat and you want to find out the wake it produces in the canal. You could just observe a canal boat and see what happens. But suppose you can’t or you don’t want to. Maybe you’re trying to design a new type of canal boat or a new type of canal. Or suppose you’re not actually looking at waves in canals but wavefunctions of sub-atomic particles. In either case you need an abstract model of the physics involved.

Metaphorically you can think of the abstract model as being like a “black box”. You guess at what the wave produced by the canal boat looks like and you feed this guess into the “black box”. If you guessed right a little flag pops up. Unfortunately, the chances are you guessed wrong. You could just keep going by trial and error hoping to find the right answer.

What George Green did wave to have a brilliant flash of insight and realise that all the waves have a certain underlying structure. The number of possible waves you have to look at is then dramatically reduced. What’s more he also devised a systematic way of calculating which one of the remaining possible wave is the right one. This might not sound that impressive until you remember that one way or another all known matter in the universe is made up of wave-like entities.

For all this work George Green only started to get any recognition towards the very end of his life. He died in 1841 and it was a further 10 years before the magnitude of his discoveries was recognised. The only obituary he received was a brief mention in a Nottingham newspaper.

A plaque is dedicated to him in Westminster abbey in the nave between the graves of Issac Newton and Lord Kelvin. His windmill still stands and was restored in 1986.