Over the next few weeks I’m going to try out an experimental blogging style, posting a series of rather more technical expository notes than has been my wont in the past.
I’m going to try to keep the tone light, but inevitably these posts will be more technical and demanding than most – though not all – of what I’ve posted in the past. I’ll also continue to post less technical stuff.
I expect it’ll take me a little while to settle into a style that works well. I’m aiming to keep things light and personal, but must admit that after drafting material for the past couple of weeks, I’m finding this more difficult than I imagined it would be.
I don’t think this difficulty is because it’s intrinsically especially difficult to do, but rather a reflection of habit: I’m most used to writing technical material – even expository material – in the impersonal manner common to journals. Getting out of that habit is going to take some work to get right. Feedback will help me figure out what works and what doesn’t, so keep the comments coming!
The initial topics will be: (1) a series on expander graphs, which are one of the most useful and beautiful tools in computer science, and (2) a series on Fermi algebras and the Jordan-Wigner transform, which are extremely useful tools in condensed matter physics.
These are, obviously, pretty specialized topics. I’ve tried to choose topics that are simultaneously: (1) subjects I wish to understand better; and (2) contain deep ideas of reasonably broad and current interest. I don’t expect that they’d be of much interest to, say, philosophers, but expect that the central ideas are of interest to a wide cross-section of physicists, mathematicians, and computer scientists. Furthermore, I’ll try focus on big ideas, and their relationship to the rest of science. Once again, learning to do this well is partially a question of style, and I expect I’ll get better at making these connections as I go along.
Depending on how things go, I may post further expository series in the future. I expect they’ll cover topics in some mixture of physics, computer science, mathematics, and self-development, with occasional digressions into other areas. I expect to range around a lot, through whatever interests me.
On a personal note, I’ve occasionally gotten queries from people about my blog, wondering if it “takes time away from your research”.
With this experiment I’m trying to integrate my blog more thoroughly with my research. Certainly, I find that writing expository notes like these is a good way of building up my own understanding of new subjects, and of preparing the way for new research projects. Indeed, I expect that some of these pieces will be useful warm-ups for some expository journal articles (and possibly books) that I hope to write in the future. I also feel very strongly about the value of synthesis and exposition for Science as a whole, especially the value of trying to explain things as simply as possible.
Finally, I must admit that I’m a little nervous about how this goes. These subjects are more specialized than much of what I’ve posted in the past, and I do enjoy having at least some regular readers! Here’s hoping I don’t drive you all away!