GWT2, Category theory, and other delights …

A last call for comments/corrections (please!!) for the draft second edition of Gödel Without Tears — I plan to finalize and publish a paperback version around the end of the month. You can download the draft here (though I imagine that anyone interested will have done so by now).

I’ve mentioned before that my three hundred pages of introductory notes on category theory are downloaded surprisingly often — frequently enough for it to be rather embarrassing, given their current ramshackle state. So, with GWT2 simmering on the back burner while I wait to see if there are any last minute suggestions to deal with, I’m getting back to thinking a bit about categories.

I was, for a while, stumbling over two things when thinking about how to revise/develop the notes. Firstly, I didn’t have a clear enough conception of where I wanted to get to.  Secondly, I’ve become increasingly unhappy with the way the very opening chapters are handled (with those distracting sermons about set theory!). But I think that things are now falling into place rather better.

On the question of scope, of where to finish, I’m lowering my sights a bit. I had occasion, the other day, to be looking at the classic book on topos theory by Mac Lane and Moerdijk. It starts with a scene-setting fourteen pages of “Categorical Preliminaries” — a glorified checklist of what you need to bring to the party if you are planning to dive into the book. And that checklist more or less exactly corresponds to the topics sort-of covered (in rushed way towards the end) in the existing notes. So that’s persuaded me that maybe, after all, the notes do get to a sensible enough stopping point (and perhaps only need be rounded out with some brief pointers to routes onwards).

And on the question of how to start, I’ve decided that fussing at the outset about such issues as whether we should identify functions with their graphs just doesn’t make for a happy beginning. That’s largely got to go! But this makes for quite a bit of fiddly re-writing over the initial chapters.

I’m having a family break for a couple of weeks, so the new version of the first seventeen chapters or so won’t be ready for a few weeks. But I’m feeling decidedly cheerier about the project of improving those notes, at least enough for me to rest fairly content with the unambitious result.

The wider world continues to go mad and/or bad in various depressing ways. The most distractingly enjoyable novel I have read just recently? Perhaps Elspeth Barker’s atmospherically gothic O Caledonia. I dived in because of an enthusiastic recommendation by Maggie O’Farrell. I enthusiastically pass on the recommendation!

I have also been much distracted by Edmund de Waal’s The White Road, swept along by his obsession with porcelain and its origins (with walk on parts for Spinoza and Leibniz by the way). Strangely gripping I find!

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