During the Easter holidays, something happened that will almost certainly have passed most of you by. I was made aware of this by a relatively short article stuck away somewhere in the middle of the Times newspaper, but if you go online, or perhaps ask your maths teacher, you will find some interesting stuff on it. At its heart, it involved the solving of a puzzle which had remained unsolved for the whole of humanity, by a retired printing systems engineer from Yorkshire. This puzzle had stumped everybody. At its essence, it involves patterns. Imagine, if you will, your bathroom tiles at home. The chances are that they form some sort of repeating pattern on the wall, or the floor; in fact, if you imagine almost any set of tiles you can think of – maybe you have visited great mosques or churches or museums with large, tiled, walls and floors – you will recognise what I am saying. The tiles are almost always laid in repeating patterns. According to the Scientific American, “For centuries, experts have been studying the special properties of tile shapes that can cover floors, kitchen backsplashes or infinitely large surfaces without leaving any gaps. Specifically, mathematicians are interested in tile shapes that can cover the whole plane without ever creating a repeating design. In these special cases, (they are called aperiodic tilings), there’s no pattern that you can copy and paste to keep the tiling going. No matter how you chop up the mosaic, each section will be unique.”
In the 1960s, a man called Robert Burger, rather remarkably, found a set of 20,426 differently coloured tiles that can pave a surface without the colour pattern ever repeating itself. This led to a frenzy of activity to see if anybody could find a smaller, more manageable, set of tiles which could be laid in a way that would never repeat a pattern. By 1974, Sir Robert Penrose, who is still alive and who won a Nobel Prize for Physics three years ago, had found a solution using only two tiles. However, almost 50 years later, in the press over Easter, came the announcement that a retired Yorkshireman named Dave Smith, 64 years’ old, and a printing engineer by background, had found a single tile which could be laid ad infinitum without repeating the same shape – and had thus solved an extraordinary mathematical problem which had lasted literally millennia. This single tile problem had been rather beautifully called the Einstein tile, not because it had anything to do with Albert, but because in German, as you linguists will know, “ein stein” means one stone. Dave Smith had found the Einstein tile. And then, mirabile dictu, he found a mathematical formula which showed that his initial find could spawn any number of such tiles.
So what, I hear you all say? Well, quite possibly, so nothing. Sir Robert Penrose’s finding of a two tile solution did lead to one useful invention when Kleenex embossed that two tile pattern onto their toilet roles. There was a particular demand for quilted toilet paper, it seems, which involves bulking up the paper to give an impression and feel of greater softness and mass. Apparently, normal periodic patterns used for embossing suffer from the disadvantage that the toilet paper ‘nests’ on the roll, creating an unattractive appearance, and an aperiodic pattern, such as that belonging to Sir Robert Penrose or Dave Smith, is particularly attractive, since ‘nesting’ is avoided. Weirdly, this led to a lawsuit, because Penrose had patented his discovery and Kleenex had used it without permission. It cost Kleenex an undisclosed amount.
Again, so what, I hear you say! Well, nobody really knows what Smith’s discovery will lead to – Penrose would certainly not have imagined it would have led to more comfortable toilet paper – but of all the newspaper articles I read in the holidays, this was, for me, the one that stood out – and the one I wanted to tell you about. The reasons are several. Firstly, I strongly suspect that a majority of you here are thinking that you really do not care about this – a man with a lifelong interest in shapes, started in primary school, and helped by an online community of shape enthusiasts, solves a longstanding shape problem at home on his kitchen table. “Big deal.” However, to me, this gave great joy and much hope. You see, as a teacher, I genuinely believe that everybody in this room has a talent. Every single person. It may not lead you to a Nobel Prize – few manage that! It may not lead you to an A* or a place in a rugby team or the orchestra. It may be something completely different – it might be a talent for caring, or for thinking in a diverse way, or for networking, or for fixing things, or for reflection, or for argument, or for listening, or even, like Dave Smith’s online community, for shapes. This talent may not even be apparent to you while you are at school; it may come later – but it is there. The Dave Smith story gives us all hope – and for me, personally, it also provided the biggest smile of the holidays. It is great to see this happen to an amateur enthusiast! The other thing it reminds us all is that we must enjoy this story if we are to count ourselves inclusive. It is too easy to say “so what”. It is far harder to say “how wonderful”. We need to enjoy one another’s talents, no matter what they are. We need to believe that everybody has them, no matter how academic you are in the traditional school sense, or how sporty you are and so on. Everybody has talents, big or small, obvious or not. I am often asked by prospective parents when they look around the school for the first time, “What sort of boy are you looking for?” – and my answer is genuine: I am not looking for any sort of boy over any other sort. Life would be incredibly dull if we were all the same. We need to look for, appreciate and celebrate one another’s uniqueness – that is one of the joys of life. Well, this is your duty as well as mine. That does not mean that we do not strive for similarities in terms of basic behaviour – we absolutely should and do – politeness, respect for one another, kindness and the other core values spring to mind (I don’t expect you to express your uniqueness by being rude, for instance) – but it does mean that, by listening, respecting, being polite and kind, we learn to appreciate one another’s unique contribution to the world we live in.
Dave Smith’s own interest in many ways could not be further removed from my own, but what an interesting, creative, searching, thoughtful man he must be.