PHQ, congratulations again.

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The Pavel Haas Quartet’s recording of the Dvorak G major and “American” Quartets won the Gramophone Award for Chamber  music for 2011, and not only that, the disc won overall Recording of the Year. Their next disc, Schubert’s “Death and the Maiden”, and the Quintet (with with Danjulo Ishizaka) won the  Gramophone Award for Chamber  music for 2014. And now today it is announced that their follow-up, their recording of the two Smetana Quartets, has won  the  Gramophone Award for Chamber  music for 2015 (here is the Gramophone review of this latest disc).  This surely is the most astonishing achievement: at a time when there are so many really fine quartets playing (not to mention other chamber ensembles), for three recordings in a row to be judged the finest of their year is truly remarkable. But, to my ears, truly deserved.

You can stream all their Supraphon recordings on Apple Music. But the PHQ live can be even better. I count myself fortunate to have been able to hear them in concert now a number of times. And there are tickets in the cupboard for three of their London concerts in the coming months …

Notes on Basic Category Theory, v.9

I have tinkered a little with the previous version of the Notes, removing some fairly obvious typos, adding some remarks or improving a proof here and there, also adding a proof or two. That’s perhaps three or four pages of new material in all. As far as content goes, then, think of this as just a ‘maintenance upgrade’ from v.8b.

However, there is a big change in that the Notes do now look very different. They are now formatted with (more or less) the style-file governing the layout of my Gödel book. There may be a few resulting typographical glitches but the result looks a lot better in a way which should make the Notes more readable. And we all know that fancy typesetting makes what you write much more obviously wise and true  …. So here, for your aesthetic delight,  is version 9! 

Until the lights go out

“If you don’t know the exact moment when the lights will go out, you might as well read until they do.” I think I will adopt that as my motto. It’s from Clive James, in the Introduction to his Latest Readings which comes out next week, a little book that reflects on a delightfully idiosyncratic range of authors and books. James is still reading, and writing too with humanity and wit and insight and, as we say, with undying enthusiasm. Except our author is dying. Though he confesses to feel “the childish urge to understand everything”, an urge which “doesn’t necessarily fade when the time approaches for you to do the most adult thing of all: vanish”.

I’ve been living the last few weeks with Clive James’s previous book, Sentenced to Life. We share the same still-small town-within-a-city, share similarly eclectic tastes (or perhaps not so much eclectic as tastes that place us in the same generation and in somewhat overlapping worlds), and share some favourite authors: we also share rather more that I wish we didn’t. So I have been finding these last poems (if that’s what they prove to be) speaking particularly directly.  Poignant, regretful, looking death in the face without illusion. And very accessible too  – as if, by imposing such clear form, such unabashed rhyming structures, our poet is making his stand against the formlessness to come. There is no false consolation here.  But still (as Blake Morrison puts it in a review) “When in death, we’re in the midst of life – that’s the recurrent, bleakly hopeful theme.”

Not that it is all bleak. Far from it. There is still Jamesian fun to be had: his Compendium Catullianum, for example –

My girlfriend’s sparrow is dead. It is an ex-sparrow.

Though after the jests, we are back to a recurrent thread: “For I …

Miss you the way you miss that stupid bird:
Excruciating. Let’s live and let’s love.
Our brief light spent, night is an endless sleep.

And our poet, before the lights go out, is so vividly aware of the small particulars of his ever-narrowing world:

Once I would not have noticed; nor have known
The name for Japanese anemones,
So pale, so frail. But now I catch the tone
Of leaves. No birds can touch down in the trees
Without my seeing them. I count the bees.

I can recognise that. And so much else here.

I would quote whole poems from Sentenced to Life  if I could. But here is one of the last poems, one of my favourites, first published a year ago in the New Yorker.

Watercolours at the Fitz

John Singer Sargent: Palma, Majorca
John Singer Sargent: Palma, Majorca

There are a couple of particularly good exhibitions on at the Fitzwilliam Museum here in Cambridge at the moment. Treasured Possessions from the Renaissance to the Enlightenment is fascinating, quirky, and full of wonderful exhibits. And now today we went to Watercolour – Elements of nature, a quite beautifully and illuminatingly mounted show of paintings from the Fitz’s own stunning collection — including their iconic Samuel Palmer, ‘The Magic Apple Tree’ which hasn’t been shown for some years, as well as paintings by Cotman and de Wint, Turner and Ruskin, Cezanne and Pissarro. And John Singer Sergeant, as above. The exhibitions are both free too. Very definitely worth a visit to Cambridge in the next month or so to see.

Notes on Basic Category Theory, v.8a/8b

It’s a balancing act. On the one hand, I don’t want to annoy readers with over-frequent announcements of minor revisions. On the other hand, I don’t want to keep propagating flawed versions when I have an improved offering in hand!

Anyway, I’ve been reading through the first 11 chapters of the Notes making some minor corrections and other changes. I’ve also had some much appreciated corrections of a few mistakes in later chapters from Alessandro Stecchina. Since I think there will be something of a pause before I can press on to re-read the rest of the Notes, here’s an interim update, to version 8a version 8b of the Notes.

Three quartets

PHQ in Zagreb

In some sense, the Allegri Quartet have been going for 60 years. But after 30 years, none of the original four were still playing; and now after another 30 years none of those four replacements is still in the quartet … I suppose it is a minor philosophical question, the persistence conditions for string quartets.

But let’s not puzzle about that! The question is: are they still worth listening to? On the evidence of a concert in the chapel of Trinity a couple of nights ago here in Cambridge, very much so. We heard them give a really fine performance of Schubert’s “Rosamunde” Quartet, with nuanced feeling and great togetherness from the four players. Compelling playing.

The second piece in the concert was Dvorak’s “American” Quartet, played by the Wihan Quartet (a new name to me: they are a long-established Czech string quartet currently in residence at the Trinity College of Music, London). This was performed with marked intensity and evident love for the piece, though (we agreed) sometimes there was a very slight sense of rush, particularly in the haunting Lento. The Wihan Quartet CD performance of the Dvorak — available to stream via Apple Music as I discovered afterwards — is extremely good, and the tempi there are a little more spacious. But their live performance was still rather fine.

After the interval, the two quartets combined to play the Mendelssohn Octet, with  verve and much evident enjoyment (and to the huge enjoyment of the audience). A terrific evening.

It is strange, though, that magical alchemy that makes the difference between rather good quartet performances, as these were, and truly great ones. After sampling the Wihan Quartet’s CD performance of the “American” Quartet I listened again to the Pavel Haas Quartet’s CD (which was the overall Recording of the Year for the Gramophone in 2011, and the top recommendation of BBC Radio 3’s “Building a Library”). The playing is just extraordinary in so many ways.  Difficult to listen to entirely dry-eyed.

The same goes for the PHQ’s latest CD, of the Smetana quartets. Again the Gramophone reviewer rightly reached for the superlatives. The second quartet is not so immediately appealing, and I’d never really appreciated it till we heard the PHQ play it at the Wigmore Hall: this recording however is again totally compelling. But it is their performance of the first quartet that I’ve been listening to time and again since it was released three months ago.  Extraordinarily affecting.

But don’t take my word (or the Gramophone‘s) for it: PHQ’s Dvorak and Smetana discs, like their other Supraphon recordings, are all available to stream on Apple Music. Do listen!

Notes on Category Theory, v.8

At long last — more or less exactly nine months since I started intermittently writing them — there is a first complete version of my Notes on Category theory (as they are now called). Or at least, the Notes are complete in the sense that I don’t intend to press on to add further chapters on significant new topics like monads or abelian categories. Rather the current plan is to leave these notes in more or less their present form, for all their shortcomings (and I hope in due course to start writing a differently organized, more discursive, bigger and better version).  Still, I would very much like to hear about errors of one kind or another. And I’ll no doubt issue occasional “maintenance upgrades” when I hear about mistakes or spot passages which really won’t do —  and perhaps I might add more illustrative examples or even new sections here or there to round out the treatment of existing topics where the coverage in retrospect seems too skimpy.

Since the previous version, I have expanded the chapter on some general results about adjunction, and  added a chapter on adjunctions and limits. This has entailed quite a bit of going back to earlier chapters, adding material to smooth the route to later theorems. I finish up by waving my hands at, though not elucidating the content of, the Adjoint Functor Theorems, General and Special.  But it is a non-trivial expositional task to explain these (the technical proofs aren’t hard; what isn’t so easy is to see is the motivation for the various new concepts — like the ‘solution set condition’ — which they involve). I’m not sure I yet have a sufficiently good grip on the place of these theorems in the scheme of things to give an illuminating account of the motivations. So I’m at the moment shirking the task of trying to explain more.

But in any case, the Adjoint Functor Theorems arguably sit on one of the boundaries  between basic category theory and the beginnings of more serious stuff. So given the intended limited remit of the Notes (now highlighted by calling them notes on Basic Category Theory), the Theorems mark a reasonable point at which to stop for now.

So, with that by way of preamble, here is the new version of the Notes (190 pages). [Link updated to version 8a] Enjoy!

Apple Music — some Day One impressions

So here I am, someone who — in phases — has over the years bought a lot of classical music. However, I have never really got into buying the music in the form of digital downloads. Much of the classical back catalogue can be acquired cheaply as second-hand CDs (and there’s fun to be had, searching the charity shops). While the small difference in price between buying a new release as a physical CD and as a digital download is usually balanced by (for me, given our various players) the convenience of the CD — and anyway, it is good to have something of value to pass on to Oxfam if I decide that the recording isn’t one I want to keep.

But storage space has increasingly become an issue. So now, in the nick of time, along comes Apple Music.  This looks very tempting. For the price of one mid-range CD a month, here’s the prospect of  renting access to much of the vast iTunes library. (Yes, yes, of course I know that there were streaming services before! But old dogs, new tricks, etc. )

So today I’ve updated the software on various bits of Apple kit and signed up for the three months free trial.  How does it look on Day One, at least for a classical music listener? For to be frank, the set-up is surely not designed with us much in mind (indeed Apple sometimes don’t really seem to give a fig about us — or else ages ago iTunes would have had the trivial tweak that would tell us that CDs which are assigned the genre “classical” comprise tracks rather than always, idiotically, songs).

  1. The first and crucial question is: what is available to stream via Apple Music? Obviously a huge back catalogue, and many new releases. But there are also significant gaps. For example, you can’t get three of the last six of Gramophone’s ‘Recordings of the Month’ (Rachel Podger’s wonderful L’Estro Armonico, Andras Schiff’s revealing Schubert played on a fortepiano, and Alina Ibragimova’s new Ysaye Sonatas).  And from today’s Gramophone list of ten outstanding Schubert recordings, you can’t currently stream four. Hyperion seems to be one of the labels that has not yet signed up to Apple Music. Which explains not only Ibragimova’s absence, but also some of the other absences and the fact that you also can’t stream two of my other favourite recent buys, Marc-André Hamelin’s Mozart Piano Sonatas  and his Janecek/Schumann disc. And looking back, you can’t yet stream e.g. any of the Hyperion Schubert Edition lieder discs. Now, these are in fact all available on iTunes to buy as digital downloads: so maybe one day … But of course, existing gaps in what you could already purchase on iTunes also carry over to become gaps in what you can stream — so e.g. the coverage of historical recordings can be rather patchy.
  2. What is the user interface like? For basic search-and-play, on any OS X or iOS platform at least, things work pretty well, particularly if you already know what you are looking for. One trouble (as The Daughter pointed out) is that Apple and others didn’t push for the standardization of metadata for classical recordings a million years ago. Presumably the record companies thought that it wasn’t going to be an issue, ‘cos we were all going to be reading CD booklets till the end of time. This means that searching has been a bit of a pain on iTunes and continues to be so now on Apple Music. However, once you’ve found what you want, the information about tracks can be hopelessly inadequate. Here’s an extreme example. There’s a rather splendid L’Oiseau-Lyre 50(!) CD box called The Baroque Era full of interesting stuff. And heavens, you can stream the lot from Apple Music. Great.  So here are the 480 tracks nicely listed, with none of them assigned to their respective composers (even if you control-click to Get Info). Apple have no doubt just used (some of?) the metadata as provided by Decca. But is no one at either end doing any quality control on this sort of thing? Another sign, perhaps, that Apple doesn’t care about the classical listener quite enough to insist that everyone gets their act together.
  3. You might want to ignore the “For You” menu. Otherwise, you have to be prepared to spend time actively rejecting the initially stupid recommendations (even if you’ve told Apple Music that classical music is your thing), in the hope that Apple’s algorithm learns better ! [Added: Though, I can report after a few days, that the algorithm does learn quickly, and is now serving up some sensible and indeed interesting suggestions — so it is seems worth persevering rejecting some suggestions, ‘liking’ others.] Annoyingly, there seems to be e.g. no way of creating a snappy playlist of album titles (as opposed to an unwieldy list of separate tracks — imagine what that can come to with an opera!).
  4. And the listening experience? A minor but irritating glitch (or am I missing something?) is that you can’t adjust the gap between tracks in streaming an album. So, depending on whether tracks have silence at the end, movements of a sonata, say, can follow on each other with without the needed gap. I suppose you could stream one track at a time to avoid this, but this is a (surely avoidable) annoyance.
  5. Sound quality? No complaints at all. No doubt my ears are too old to catch the finest nuances, and so I wouldn’t be able tell the difference anyway between Apple’s encoding and the high quality streaming that is available more expensively from specialist providers. But I guess for most of us, listening on only moderately decent kit, in an averagely auditorily cluttered environment, Apple Music is more than fine.

Not perfect then. But hey, there is a lifetime’s listening of extraordinary recordings old and new available to stream, and a lot of obscure byways to explore, reasonably easy to find if you know what to look for  — and I guess other labels will sign up if Apple Music takes off as you would expect. I’ve already spotted, oh, a dozen recent CDs I had it mind to buy which I can now stream. So at least modified rapture.

And rapture at less than $10/£10 a month seems a bargain to me.

Notes on Category Theory, v.7

Progress seems to have been a bit slow for various reasons, but I have now added two short-ish chapters to the Notes on Category Theory. One is a chapter on Exponentials added between the chapters on limits and the start of the chapters on Galois connections and adjunctions. The other is second chapter on adjunctions, showing how to generalize certain results we saw in the special case of Galois connections to apply to adjunctions more generally.  I have also added some material earlier to make some of the new later proofs work more smoothly.  Here then is the latest version of the Notes, some 170+ pages.

As I have stressed before, I’m myself learning as I go along from the project of writing these Notes. So as more light dawns, I of course can see how I could have arranged/explained earlier material rather better (OK, a LOT better). But for the moment, the plan remains to add a few more chapters, before eventually starting over and trying to get everything into a more ideal shape.

Notes on Category Theory v.6b

Illness (not so great) followed by fortnight’s holiday (really excellent) stopped work on category theory for a while. Very slowly getting back to it. But in the meantime, a number of people have very kindly been sending corrections to the last version of the Notes. I have also tinkered in minor ways, improving the last chapter in particular. There are just about enough changes to warrant another “maintenance upgrade”, making some of the needed repairs and improvements.

I hope to have a couple more chapters on adjoints ready for prime time later in the month — but finding a neat expository path through the material is a challenge, so don’t hold your breath!

The plan at the moment is for another five or six more chapters in total to round off Part I of these Notes, on basic category theory (I’m not sure yet whether I also need to say anything about monads for what is going to follow). And then — having got the bit between my teeth — I’d like to continue, by discussing some logic and set theory in a categorial way in Part II of the Notes. Promises, promises.

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