For Mac geeks …

I’ve just become a real convert to DevonThink, which seems to be by far the best solution for organizing a whole collection of downloaded PDFs of articles, stored emails, lecture notes and the like. I haven’t yet begun to explore its much-praised clever AI engine for e.g. finding other material related to some article. But even while I am just dumbly using it to search through a folder of PDFs and browse the results, I think it is going to earn its keep a dozen times over.

I wish I could find a use too for Scrivener which seems a great concept, beautifully implemented. But it just isn’t suitable for the way I write — everything I do these days seems to be symbol-laden, and is crying out to be done in LaTeX from the start. But if I ever write my great novel of the follies of academic life …

Gentzen, praise and regret

By popular request, I’m continuing an informal lunchtime Mathematical Logic Reading Group with a number of grad students. This term, the plan is to do a ‘slow read’ of Gentzen’s two great papers on the consistency of arithmetic. But we started today with the lecture he wrote between the two papers, ‘The concept of infinity in mathematics’. This is short, very accessible, and gives a great sense of the conceptual problems that Gentzen sees as shaping his work. It is also very clearly sets out the headline news about the structure of his (first) consistency proof and about its supposed finitist/constructivist credentials.

The lecture has its shortcomings — there’s a general murkiness about the notion of a ‘constructivist’ view of infinity (why should a constructivist view of sets in the sense of the paradox-busting idea of a hiearchy in which sets at higher levels are formed from sets already constructed at lower levels go along with a constructivist rejection of excluded middle at the level of classical analysis?). But still it is wonderful, thought-provoking stuff.

I was moved to try editing the piece on Gentzen on Wikipedia in very modest ways (e.g. adding that he was Hilbert’s assistant, which you might have thought was a rather central fact about his intellectual trajectory). But twice my efforts were removed. And I wonder if that was because I’d over-written the claim that he was imprisoned after the war “due to his Nazi loyalties” (I’d put something less specific, but more detailed, i.e. the story as told by Szabo in his introduction to the Collected Papers). Is it true about Gentzen having Nazi sympathies? Regrettably it seems so. Discovering this was really rather depressing, as I’ve belatedly become a great admirer of Gentzen.


One of my Christmas presents was Renée Fleming’s Homage: The Age of the Diva. It is luxurious, wonderful, singing, with some of the arias quite unknown to me (and I’d have thought to many opera fans). A few of Fleming’s interpretations are perhaps a bit over the top — there is a stunningly sustained note near the end of “Vissi d’arte” which is awesome but … Though it certainly does make the hairs stand up on the back of your neck, so let’s not get too purist!

The CD insert booklet has a little about Fleming’s great predecessors in this repertoire. One name stood out for me. For my mother has a copy of Kobbé’s Complete Opera Book, given her as a girl: the evocative black and white photographs include a publicity photo of the Moravian soprano Maria Jeritza in her costume as Turandot. That picture made a deep impression on me when I was small! Jeritza was one of Puccini’s favourite singers; but I’ve only ever heard short clips of her voice. I feel an internet search coming on …

Size matters

One thing that distracted me for a while was getting myself a new laptop, a 17″ MacBook Pro. Simply fantastic, of course. Huge and very bright sharp screen — I got a matte one — and fast. Oh, very fast. On my previous 1.5 Ghz 15″ PowerMac (a thing of beauty too), it took 28 seconds to typeset the Gödel book. Now the same LaTeX processing takes just over four seconds. And no, of course it isn’t that I really need all those saved twenty seconds in a day! But I don’t have to think any more about the business of refreshing the preview of the printed page — you just stop noticing the mechanics, so to speak, of using LaTeX.

I did think long and hard about whether to go for broke and get the big screen version. I’m glad I did. The laptop fits in the same bag I had before, and is not significantly heavier, so I don’t notice any real difference in the bother of carting it around. And after all, neither size MacBook Pro is the sort of thing you’d want to tote if you were really doing a lot of travelling (mmmm, the rumours of a really small laptop for 2008 are promising). So get the bigger one if you can: having the extra real estate again helps to make e.g. working with LaTeX (with TeXShop and BibDesk windows open, etc.) quite a lot more pleasant.

I’ve now just got to write another book to justify the expense …

Spluttering into life again …

I did slightly lose the will to blog, partly through overwork, partly through the blog being spammed, partly through other distractions. But the mood takes me again, so let’s see how things go …

The Gödel book hasn’t left my desk yet, and won’t for another month or so. I’m still waiting to hear back from the CUP proof reader; and meanwhile I’m working through 126(!) comments sent over the holidays with immense kindness by Richard Zach. Thanks Richard! I’ve had to take the book off-line now that it is going through the press, at the reasonable insistence of CUP: but making it available on the web certainly made the whole business of writing it so much more enjoyable, and has made the result much, much better. (More enjoyable, because of encouraging feedback along the way: it can be a pretty lonely and sometimes dispiriting business writing a long book. Nice comments kept me going. And the book might still have its many flaws, but it has certainly been much improved by comments from literally dozens of people. I’m immensely grateful.)

I’m beginning to wonder what to do next. The Preface to the Introduction to Gödel’s Theorems promises a sequel, Incompleteness after Gödel, but that’s going to be a long job, getting really on top of and then organizing the materials. I promised this term to talk about Gentzen’s proof of the completeness of arithmetic to a group of grad students, and have found there isn’t anything treating quite what I had in mind to cover at the level I wanted to cover it. So a tempting smaller project suggests itself, and I’ve even a title: Ordinals, Cuts and Consistency. But we’ll see: watch this space …

On Opera

A number of collections of Bernard Williams’s papers have been put together posthumously. But surely the best has to be the latest, the newly published On Opera which collects together a number of pieces he wrote for various scattered occasions. The four short pieces on Mozart, in particular, are simply wonderful: insightful, subtle, humane, passionate in their commitment to the idea that the best opera is worthy of our fullest engagement and of serious critical response. Read them.

Back to work: SOSOA

I have been mightily distracted from this blog by, first, trying to get the Gödel book into a state where it could go to CUP’s proof-reader and then, second, by the beginning of term. But the book is off, and life is settling into what passes for normality in term-time.

The high point so far is our new Mathematical Logic Reading Group (started by popular request). We are starting by working through the opening chapter of Simpson’s Subsystems of Second Order Arithmetic. The trouble we are having–wearing our philosophical hats–is to get the five key subsystems that Simpson highlights aligned to clear philosophical motivations. We can do that for ACA0; but not, for example, for the base system RCA0 with its curious mismatch between its Delta1 comprehension axiom and Sigma1 induction. And it is worrying–isn’t it?–that the chosen base system resists a clear conceptual defence. I’ll report back if we come to any less inchoate conclusions.

Indexing woes

Indexing a book is no fun. None at all. Yet it can be so annoying when a book has a perfunctory index that I feel compelled to try to do the job decently.

You can only work on so many pages at a stretch. Distractions are needed. One that works for me is opening up sci.logic in Google groups every so often and sounding off. Hence a rash of posts battering away at some of the dafter stuff there. Who knows if anyone appreciates it … but it keeps me amused, and is one of the more harmless ways of wasting time on the web.

Coffee Time in Memphis

Passing the CUP bookshop, I couldn’t resist picking up a copy of Béla Bollobás’ brand new The Art of Mathematics: Coffee Time in Memphis — no less than 157 mathematical problems and their solutions, problems (he says) of the kind that would have delighted Littlewood and Erdös.

Here’s the very first in the book. A lion and a Christian in a closed circular Roman arena have equal maximum speeds. Must the Christian in the end be caught by the lion? Here’s another later one: Is an infinite family of nested subsets of a countable set necessarily countable. (These are fun, because it is difficult to shake off the temptation to say that the answer in each case is “yes” when it is “no”.) Hours of amusement to be had here.

But I suspect that there are two kinds of mathematicians, puzzle-setters and puzzle-solvers on the one hand, and (for want of a better word) more philosophically minded mathematics who want to see the deep interconnections between Big Ideas. Erdös vs. Gödel, perhaps. Once upon a time I used to be fairly good at the puzzling; but these days, it’s Gödel for me.

Passing it on

I’ve just put another full draft of the Gödel book online. There’s an amount of work still to be done (in particular, I’ve yet to take account of some comments I’ve had on the last chapter); but things are progressing towards a terminus. One task now, while I’m thinking about more substantive things as well, is to decide what kind of index or indexes to do. What a thrill.

I’ve been distracting myself a bit by dropping into the newsgroup sci.logic and posting in some of the threads. Which probably shows that I need to get a life. Yet I can’t help finding it irritating (indeed offensive) when loud-mouthed ignorant blockheads are allowed to dominate a public forum which can occasionally can be very useful. So I’ve been diving in and trying to help sort things out here and there.

Two enthusiastic book recommendations, one logic-related, one not. First, I didn’t know Piergorgio Odifreddi’s Classical Recursion Theory before, but I’ve been quickly working through it and it is excellent — I very much like the style and pace. In a way, I’m quite glad that I didn’t read it before or I might have been tempted to follow some of his nice modes of presentation. As it turns out, the treatment in my book is nicely complementary at various points.

The other, my late-night book at the moment, is Alan Bennett’s Untold Stories. Perhaps I should take the words at the end of his Introduction, which he quotes from his own play The History Boys, as the motto for the Gödel book: “Pass it on. Just pass it on.” For that’s exactly what I’m trying to do …

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