Year: 2016

The all-you-can-eat book buffet

One of the fixtures of the Cambridge year is the annual Cambridge University Press booksale. It lasts for a week or ten days in January, with the shelves continually being replenished as they empty. The Press sell off oodles of “damaged” books (where, very often, the only damage is caused by a neat red stamp on the verso of the title page, marking the book as “DAMAGED”). The going rate for a few years has been £3 for any paperback, and £7 for a hardback. The range of titles is extraordinary. And you can pick up some delightful bargains — important but inessential work-related books that it would be really rather nice to have but which you would never have forked out the full price for, or interesting finds that are intriguing enough to take a chance on. So far this year, I’ve picked up a few pleasing purchases, including a copy of Linsky’s The Evolution of Principia Mathematica which I’ll want to dip into (but could never have warranted spending £100 on), and a paperback of David Wyn Jones’s The Life of Haydn which is proving to be fascinating and highly readable.

But — O tempora o mores! — truffling through the sale shelves just isn’t the enjoyable experience it used to be. In the past the rule was that you could only buy ten books at a time (or was it a ten a day? I think so). There were busy times, but it was mostly other readers young and old you were bumping into, and you would have occasional friendly book chats to people as you browsed, swapping recommendations, and (by the sad standard of academics) a quietly Fun Time was had by all.

Now the rules have changed. You can buy as many books as you can cart away. So various second-hand booksellers come with bags and bags, boxes and boxes, and stand around like vultures, pouncing as soon as the staff bring out more stock as shelves empty, immediately grabbing great armfuls, not quite coming to blows but certainly jostling for space. And just as, when at a buffet, people heaping enormous stacks of food onto their plates simply puts you right off your lunch, this too is off-putting — the rapaciousness on display by people who want to turn a quick buck rather than find some interesting (and perhaps previously unaffordable) books to read themselves. Greed is never a good look.

I know that the Press want to get rid of a lot of stock in their sale. But it’s rather sad that in the process of increasing the number of books they get rid of (if that’s what’s happening) the genuinely enjoyable atmosphere seems to have gone.

Update Others have expressed disquiet too: new arrangements have been announced, with early morning until 10.30 and afternoons after 3.30 as “quiet times”. Hopefully this will help.

Another update The new arrangements have indeed made for a much more congenial experience, the couple of times I’ve dropped by since.

CD choice #2

51F8TdOZldL I have come very late to appreciate Janáček’s piano music — something I largely owe to two discs by Ivana Gavrić. Her fine first CD, titled after that composer’s In the Mists, was a serendipitous find in an Oxfam shop (it also includes, among other things, an excellent performance of Schubert’s A minor Sonata, D. 784). But her second recording from 2011, From the Street, is even better. If you don’t know Janacek’s sequence of ten pieces On an Overgrown Path, then you have a delight awaiting you. Gavrić’s playing seems exceptional here: the Gramophone reviewer rightly wrote of “the intimacy, finely honed nuance, conversational flow and subtle underlining of the composer’s harmonic surprises that Gavrić brings to each of the short pieces”, and other reviewers were equally enthusiastic. There are, I have since discovered, some other terrific recordings available, including one by Marc-André Hamelin. But this still strikes me as outstanding.

Also on the CD are Janáček’s Sonata 1.X.1905 From the Street, Ravel’s Valses Nobles Et Sentimentalise, and not least a wonderful performance of Prokofiev’s Sonata no. 2. (I’m not usually a great one for mixed recital discs, and I usually listen to these performances separately; but actually the programming works very well). So indeed, all very warmly recommended, especially if the Janáček or Prokofiev isn’t familiar.

Footnote Ivana Gavrić won a BBC Music Magazine Award in 2011 for her first CD. It is now time to vote for this year’s Awards. The Pavel Haas Quartet are shortlisted in the Chamber Music section. So you know what you have to do …

Book Note: Tony Roy, Symbolic Logic, #3

After a longer than intended gap, I return to consider Parts III and IV of Tony Roy’s freely available  Symbolic Logic: An Accessible Introduction to Serious Mathematical LogicThe previous two , rather lukewarm, instalments discussing Parts I and II are here and here (but do please note Roy’s long comment in response).

Part of my beef against this very long text is indeed its length. In teaching maths, often the key task is to engender the kind of understanding that enables the student to see the wood for the trees, to see what are the Big Ideas and what is merely hack-work joining up the dots. The longer you bang on filling in every last detail of a proof, the greater the danger that you will obscure the overall contours of what’s going on (even if you scatter around an amount of signposting). We ask our students in exams to do “bookwork” questions outlining a proof of some major result, and here the name of the game is indeed to highlight the Big Ideas, the key moves, and to confidently know what can be gestured at, or when we can say “rather similarly, we can show …” etc. Where I take issue with Roy’s pedagogic style, then, is in thinking that writing at his length won’t really help foster these skills.

I mention this again because Part III on Classical Metalogic consists mostly of two very dense chapters, one of forty pages, one of fifty pages, going into rather over-the-top detail (by my lights) on relatively few results. So again I wouldn’t recommend these as primary reading for students encountering some metalogic for the first time.

However, on the positive side, the main content of Chapter 9 is unusual in one interesting respect. Roy has earlier introduced both an axiomatic and a natural deduction system for first-order logic. We can of course prove they are equivalent by going via the respective soundness/completeness proofs for the two systems. (That doesn’t really require two lots of proofs as we can point out in particular that what it takes for a Henkin  completeness proof to go through is available in both cases.) But we can also give a syntactic equivalence proof for the two systems by showing how to systematically manipulate in both directions a proof of the one sort into a proof of the other. Now, this tends to be the sort of thing one armwaves about in class, perhaps sketching in a few obvious moves. But I can’t offhand recall any textbook which spells out in any detail, for particular given axiomatic and ND systems, clear routines for moving between proofs in the two systems (any offers here?). Roy however does this at (slightly numbing) length. Good: we can now usefully point any students unsatisfied by classroom armwaving who want to know how such proofs go to Roy’s very careful working-out of detailed routines.

Chapter 10 then tackles soundness and completeness. The completeness proof for the sentential fragment takes eleven pages: another thirty pages labour over the completeness of a first-order calculus with identity. This is, for example, over twice the number of pages needed by the extraordinarily lucid, gently paced, Chiswell and Hodges. I won’t quote chunks, as you can make your own judgement, since the chapter (as with the rest of the Accessible Introduction) is freely available. But I honestly can’t imagine many students finding the extra length going with a doubling in clarity and understanding. Indeed, if a student were stuck on a Henkin completeness proof in one standard text, I’d first suggest looking at another snappy presentation in a different text (before mentioning Roy’s much longer efforts): for the problem would very likely be in seeing the overall strategy, the Big Ideas — and brisker presentations are likely to make those stand out better.

Part III also contains a fragmentary Chapter 11 which belatedly talks about expressive completeness for the sentential connectives, and then says something briefly about compactness and the L-S theorems. But I won’t say anything about this.

To be concluded.

Easing gently into 2016

There is a new version of the Gentle Introduction to Category Theory. There are no new chapters this time, but there are some significant additions (I now prove a result about Cartesian closed categories with natural numbers objects, which previously was only announced, and prove that free monoids can be thought of as initial objects in a certain comma category). And there are many improvements, both in content and presentation. Note in particular, I correct a mistake about the relation between different notions of diagrams, and clear up what was an unnecessarily messy chapter on the existence of limits. I am very grateful indeed to comments/corrections from Paolo G. Giarrusso and Yufei Cai for prompting some of these improvements.

Although now 178pp., this version is still very incomplete: you can find some rough-and-ready follow-up chapters at the categories page here where there is also an alternative link to the Gentle Intro for those without an login.

A cheering start to the logical New Year?

Just before Christmas, I put a copy of Teach Yourself Logic 2016 on my rather sparse page. It has since been browsed there over 45,000 times, and then the whole thing downloaded 2,500 times. I’m not sure how many times TYL has also been downloaded from Logic Matters, as the stats counter here is flakey (though the page it is linked from has been visited over 11,000 times in the last few weeks): but it is hundreds more.

The particular numbers don’t matter. But the trend is good.  At a personal level, this makes the effort I put into TYL continue to seem worthwhile. And more impersonally, this is serious logic we are talking about here: and caring about the future of the subject, it is really  good to find that there is enough interest out there for thousands of people to go to the bother of downloading the Guide, with at least some sense of what they are letting themselves in for. So this is all rather cheering, and puts a spring in my logical step, inspiring me to keep on tinkering with TYL and with related stuff.

But not quite yet! Back to category theory first …

CD choice #1


Those end-of-year lists of recommended books are really rather depressing, aren’t they? Even setting aside the pretentious, the uninviting, the distinctly esoteric, there remain all those novels, all those biographies, all those histories, and much more, books that do sound so enticing, yet which you know — despite your best resolutions to read more, and idle less on the internet — you are never going to have the time to read.

Lists of the best CDs of the year, however, I find much more cheering. And with a subscription to Apple Music or the like, you can quickly sample a fair selection of the recommendations that you’d earlier missed, and then listen to a goodly virtual pile of the discs that grab you the most, all in the time it would take to get through that six hundred page history book you aren’t going to read ….

Well, I’ve missed the appropriate time to give my own recommendations from the new classical CDs released in 2015 — and anyway, to be honest, it wouldn’t have been that exciting, but mostly just a rather predictable subset of the monthly recommendations in the Gramophone (predictable, at any rate, given the sort of CDs and concerts mentioned here over the years). So let me begin the year by starting something hopefully a bit more interesting, namely a fairly regular series of  ‘CD choice’ posts, mentioning a disc that I’ve been listening to with enjoyment over the previous few days, perhaps emphasizing discs not as well known as they might be. I’ll try, by the way, mostly to mention recordings available on Apple Music (and presumably on other subscription services). It could be a new release, or an old disc that I forgotten that I had, a recent charity-shop find, something caught by chance on internet radio … Who knows? We’ll just see how it goes! [I was thinking of posting weekly, hence the initial title ‘CD of the week’, but I quickly thought better of it — not because I couldn’t recommend a  CD every seven days, but because that many posts on music would unbalance what is still supposed to be mainly a logic-related blog!]

First up, then, a delightful disc first released in 2014, the oboist Albrecht Mayer’s “Lost and Found”. This is subtitled “Oboenkonzerte des 18. Jahrhunderts von Hoffmeister, Lebrun, Fiala und Kozeluh”, which sounds potentially worthy but dull; but in fact, this is simply very, very enjoyable.

So these are concertos for oboe and cor anglais from around the 1780s, contemporary with Mozart and Haydn, from four other composers well known in the day (and not entirely “lost” since!). The music is immediately engaging yet certainly stands up to repeated listenings. The playing on the CD is terrific (as the Gramophone agrees). Try it!

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