STRING DIAGRAMS, THE NUMBER 5, AND THE MOONS OF JUPITER ------------------------------------------------------- A tribute to "This Week's Finds" January 26, 2013 Joachim Kock I just learned on the n-Cat Cafe' that John Baez's "This Week's Finds (in Mathematical Physics)" [http://math.ucr.edu/home/baez/TWF.html] turns 20 today (or rather "last week"). I thought I would pay a tribute. I think I have read them all, at least in the same way as I have seen all the James Bond movies -- many of the old ones several times, but possibly missing a few of the newer ones. The TWFs have had a huge impact on my mathematics, and I think on a whole community. As a boy, I would eagerly await Tuesday, where a new issue of "Donald Duck & Co" would come out. Later in my life I would eagerly await the weekly TWF, sometimes waiting a little longer. That was fine -- had it been every week, it would have been a full-time job to read them and to follow the references, and I would have had no time for the less appealing and harder-to-digest math I was supposed to learn. But all those marvelous relationships between many different fascinating topics, all those deep insights into apparently simple things, all those key examples worked out, just immediately illuminating a dense subject. Those beautiful string diagrams and Dynkin quivers in ascii art, the enthusiasm, the relaxed style, and the cool language. (Many locutions have caught on and found their way into research papers, like for example walking structure, being secretly something, or some evil property.) All this was just too attractive reading! But first of all the whole way of thinking mathematics, always trying to look under the surface of things, always coming down to what is really going on, the structure of mathematics. I think it is fair to say that the TWF has shaped a whole generation of abstractly minded mathematicians, helping us all to a broader view on mathematics with a categorical bias. (Speaking of bias, the first time I heard of unbiased monoidal category, perhaps from Tom Leinster, I was sure it was unbaezed.) We are probably many who wondered at some point if John Baez was some sort of Bourbaki: a hand-full of brilliant mathematicians dedicated full-time to scan the internet for interesting mathematics and distilling the key points. Or at least he probably had a high-speed modem (9600 baud) built into his brain. Or maybe he never slept. In the beginning, most of the exposition of the TWF took as starting point some recent preprints. Soon, live blogging from conferences became a standard ingredient. How is it possible to live blog from a conference? When I go to a conference, the 24 hours of a day are very quickly spent: breakfast, talks, lunch, talks, beer, dinner, and then I am exhausted and drop dead in bed. Often I don't even find time to visit the castle on the hill in whatever town the conference takes place. So how can anybody blog in real time? Sitting up all night instead of sleeping? I had the opportunity to spy, once, at a conference in Lisbon 10 years ago: John sat next to me in the computer room after the last lecture, and began to write a blog entry. It took him less than one hour -- a text that it would probably take me longer just to type! Apparently it was just flowing effortlessly, the text coming out perfect in the first go; all the nice explanations, all the didactic sugar, it just came by itself. I reckon this talent is quite important if you want to run a blog for twenty years! (John told me this ability had come with practice.) (Meanwhile at the other computer, perhaps I had managed to put together the words to reply to one email.) * (Partly for the same reason, I have never myself been tempted to blog. Even writing the shortest comment on the nCat Cafe' can take me hours, and sometimes I end up not posting it, and other times I end up regretting I didn't write it differently. The closest I have come to blogging was writing my Frobenius Algebra book, which was deeply influenced by TWF, both in content and in style.) With time, it seems the preprints became less and less prominent on TWF, or became rather an excuse for some more original developments: it became clear that John had more interesting things to explain than what could be read in papers. The tale of n-categories and the tale of groupoidification are perhaps the most prominent examples, together with preliminary analysis of the now famous favorite numbers (whose final version I think was not actually posted on TWF), but also all kinds of introductions to representation theory, number theory, modular forms, exceptional groups, species and q-combinatorics -- and yes, even Mathematical Physics! -- maybe there were preprints lurking in the background, but the impression left was rather just delightful exposition of important mathematics. At some point, perhaps with the passage from ascii to html, the TWF acquired a sort of habit of starting each post with some unrelated astronomy or science story, often with a nice colour photograph. What would we know about Jupiter's moons were it not for TWF? It is a funny feature. Is it just show-off, or is it a piece of pressing information? Well, it has had some effects: it has contributed to the relaxed atmosphere, like a lunch-break conversation, but always containing more than just news stories. But more importantly there has always been a message perceived: that there is more to science than math, that there is a real world out there, possibly just as beautiful as math itself. Perhaps these digressions already pointed towards the radical shift in emphasis that took place a couple of years ago, from mathematical physics to planet- related mathematics, and the creation of Azimuth. I have written most of the above in the past tense, looking back on 20 years of beautiful math exposition. I hope it does not sound like an obituary! I do hope TWF will continue, but it is also fine if its spirit lives on in other incarnations. I am confident John will continue delighting us! Keep cookin', John, and keep relaxin'! Happy Birthday to TWF! ---- *) The story cannot be completely true: I just looked up and found that week197 was posted two weeks after the Lisbon conference, so some stuff was probably added in the interim. Nevertheless, I'll leave the story as it is, to convey the impression I got, which I think is maybe not too far off the point. (Or maybe it was at another conference?)