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Peter Guthrie Tait: a Knot's Tale Transcript Peter Guthrie Tait: A Knot's Tale Transcript Date: Wednesday, 31 October 2012 - 4:30PM Location: Barnard's Inn Hall 31 October 2012 Peter Guthrie Tait: A Knot's Tale Dr Julia Collins Good afternoon, everyone. Thank you very much for the invitation to come and speak at Gresham College. I have never been here before, so it is really exciting to see so many people. Of the three people that we are talking about this afternoon, I think Peter Guthrie Tait is the one who is least well-known. Put your hand up if you knew before today who Peter Guthrie Tait was… Okay, put your hand down if you are a member of the BSHM… [Laughter] I think, of the three, he is certainly the least well-known, so my job today is to tell you a bit about his life story, and in particular the contribution that he made to the mathematical theory of knots. At this point, I want to say, the caveat to that, I am not a historian and I am not a physicist. I do not understand the physics that Tait did, so I will be talking about his mathematics, and we can talk more about other things during the break. I also apologise to any Tait enthusiasts that there will be so many things about his life that I do not have time to fit into 45 minutes, so I apologise for that. I realise that I am the person standing between you and the alcoholic drinks in 45 minutes, so let me motivate this lecture to make you excited about what is coming up in my talk! [Recording plays] I am going to start the story in Edinburgh, but in modern times, with me, the narrator. This is the National Library of Scotland, where I started learning about Peter Guthrie Tait. I was pointed to this repository of knowledge by another historian called Maurice Eppel, and I was told that, in here, there was an envelope that Peter Guthrie Tait had enclosed some of his conjectures and that those conjectures had remained unopened for 100 years, and I wanted to go in there and find this envelope and find what was in there and why it was that no one had opened it, and so part of this lecture is the story of how I found the envelope and what was inside it. At first, I did not find the envelope I was looking for. I found some scribble on the back of a different envelope, which I was really excited by, and we will come back to this again. So it starts off with OT, and I was assuming that you would not know what that meant, but maybe you have got an idea from the previous lecture. More excitingly is this paragraph down here…”Can’t you come on Monday the present at the performance? An elliptical hole gives the rings in a state of vibration.” So, what is this experiment that he has been invited to? Who is it that has been invited whose experiment? That is what we are going to learn about today. Let us go back to 1876, which is the scene of this experiment, and in this lab in Edinburgh, there are two men in this room which is thick with smoke. We may make this room thick with smoke later today, if you are a good audience. The men in question are Peter Guthrie Tait and William Thomson, and what they would do in that room would change mathematical history. Just to set the scene, it is 1876. I do not know how many people were listening carefully to the timeline in the previous talk, but we have got Maxwell, who has been developing, in that decade, his theory of electromagnetism, unifying electricity, magnetism and light, and dealing with kinetic theory of gases. It has been six years since Maxwell developed the first colour photograph. Thomson, just one year before, had been knighted for his laying of the transatlantic telegraph cables on the ship, the Great Eastern, so he is actually called Lord Kelvin. I will interchange William Thomson and Lord Kelvin during the talk, so do not get confused. Darwin has published his Origin of Species only eight years previous, and Tait and Thomson, in that very year, have published their kind of magnum opus, their great textbook, the Treatise on Natural Philosophy, which redefined what physics meant at the time. It is 1867, and it is a really exciting time in science. One of the big questions that are on people’s minds is: what do atoms look like? No one has been able to look at one in a microscope, and there are some people who do not even believe that atoms really exist. There were all sorts of different theories going around at the time. Even for those people that do think atoms exist, there is a conversation about what atoms could look like. Suppose an atom was like a solid, hard ball, like that, what is it about these little balls that would explain the different kinds of matter that we see in the universe? Is it that an oxygen atom would look different from a nitrogen atom or an iron atom? This is the big question that was on people’s minds. During this lecture, I want you to keep that question in your minds. This lecture is going to be the story of the answer to that question of “What do atoms look like?” and the man, Peter Guthrie Tait, who was the catalyst for the discoveries that were made from that point. So, let us go back and start the story as it should have been started, at the beginning, in Dalkeith and Edinburgh, where two boys are born, just a couple of months apart. Dalkeith is just fifteen miles south of Edinburgh. It is a small town. This is its church, and that is where Peter Guthrie Tait was born, in April, and two months later, James Clerk Maxwell was born in India Street in Edinburgh. So they were born very close together. They both had the same kind of tragic childhood. We have already heard, Kelvin lost his mother when he was six years old. Tait last his father when he was six years old, which meant moving to Edinburgh to live with his uncle. Maxwell lost his mother when he was eight years old as well. So they all have this shared tragic childhood, but, in a way, it precipitated them to go and learn science from somebody else. Tait was heavily influenced by his uncle, who inspired in him a real love of natural philosophy and science. Tait and Maxwell both went to the same school, Edinburgh Academy, which still exists in Edinburgh today, and they were in different year groups, despite being pretty much exactly the same age, because Tait’s family enrolled him in school nice and early and so he got into the year group he should have been in, whereas Maxwell’s family were a bit behind, and by the time they tried to enrol Maxwell, the class was already completely full and he had to go into the year above. They were the same age, but they were in different years in school, and despite that, they met each other and they became extremely good friends. They were friendly rivals at the same time, competing to do well in their examinations. When they were sixteen years old, they both went to the University of Edinburgh to study Maths and Natural Philosophy, and their Natural Philosophy professor, as we have heard, was Forbes. In Edinburgh, at that time, the Natural Philosophy class was split into three divisions, so the idea was that you would enter in the third division and, as you became more knowledgeable, you would work your way up to the first division. Maxwell was a confident young man, and he realised he was too good for the third division, so he went straight in at the second division, but Tait had to go one better and he enrolled straight into the first division, despite being told otherwise by Forbes. Forbes said, “This is not a good idea – you should stick with Maxwell,” and he said, “No, I am good enough, I will be in the first division,” and he did well, and after only a year, he decided that he was ready to move to Cambridge and went to Peterhouse College, which is the same place where Kelvin had gone before and where Maxwell would follow him just a few years later. So in 1852, this series of events has meant that Tait has become the youngest ever person to be senior wrangler in the Mathematics Tripos exams, which means that he got top exam marks, and he was only twenty years and eight months old, and the record that he set was not bettered until 1936, when a nineteen year old became senior wrangler. Of the three, he was the only person who was senior wrangler, so both Maxwell and Tait only got second wrangler. This is a picture of Tait here, on the left-hand side. This is Steele, who got second place – he was another great scientist at the time. You can already see this wonderful figure that he cuts: he is a very tall, very imposing young man, and very confident. Based on the strength of his exam results, he became a Fellow of Peterhouse College, and started coaching other students as part of his duties as a Fellow.
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