Peter Smith's Blog, page 112

Today wonderful reading: good fun!

If you follow @PeterSmith on Twitter — and why not? — these are apparently the delights that await you …

Logic and Schubert, eh? Can’t be bad.

Added: HT to Rowsety Moid for spotting the tagline I should have used to begin with!

Logic and Schubert

If you follow @PeterSmith — and why not? — these are apparently the delights that await you …

Logic and Schubert, eh? Can’t be bad.

Review: the Pavel Haas Quartet, Schubert ‘Death and the Maiden’ and the String Quintet

Readers of this blog will know how much I have admired the Pavel Haas Quartet for a while. This isn’t me being idiosyncratic: their previous four CDs have been hugely praised, with the most recent Dvorak disk even winning The Gramophone Recording of the Year for 2011. Live, they are the most exciting quartet to watch and hear.

And now, at last, we have a new recording, of the Schubert D minor quartet, “Death and the Maiden”, and the String Quintet.  The Times reviewer wrote “If CDs had grooves I would already have worn out these marvellous recordings  … the perfect fusion of virtuosity and profundity.” Indeed. These performances are of a quite unworldly quality, deeply felt yet utterly thought-through, the most passionate you have heard but with moments of haunting delicacy,  with an overarching architectural vision holding it all together.

The Pavel Haas launch into “Death and the Maiden” with fierce attack and astringent (almost vibrato-less) tone. And they start as they mean to go on. The recent Takacs and the Belcea versions — good though they are — now seem slightly restrained in contrast (this is the still-young Schubert confronting death here, and the still-young Pavel Haas respond with apt intensity). The obvious comparison would be with the Lindsays’ great recording from twenty five years ago, which I would previously have said was the finest post-war version. But the Pavel Haas’s controlled passion, their even more moving account of the variations of the second movement, and their vehement drive to the end of the quartet, makes — I think — for an unparalleled performance.

As for the Quintet, this performance with Danjulo Ishizaka as the second cello is perhaps even finer. For any players, the problem — isn’t it? — is to maintain a shape to the whole piece: a bit too ethereal with the second movement and a bit too cheery with the last movements, and the Quintet is in danger of seeming unsatisfyingly unbalanced. But here, the whole hangs together better than any other interpretation I know. Although the playing is more expansive, within a few bars of the opening, the Pavel Haas have again built a sense of tension — and the underlying tension is then maintained in a quite driven, uncompromising, way to the very end, with the slow movement giving only some partial relief (and there, the central section is played with a yearning fierceness, and the playing when the original theme returns is heart-stopping).  This makes for an extraordinarily intense exploration of the music. Surely, a truly great interpretation.

After a series of changes of second violin over the years, the Pavel Haas have never sounded better. Hopefully they will now stay happily together as they are. Their website has an interesting short video of them in the Supraphon recording studio. Maybe with two of the quartet having a new baby — Veronika Jarůšková was very evidently pregnant in the recordings — for a while they will want to tour a little less and record a little more. That would be wonderful. How about, say, the three Rasumovsky quartets? Please?

Review: the Pavel Haas Quartet, Schubert “Death and the Maiden” and the String Quintet

Readers of this blog will know how much I have admired the Pavel Haas Quartet for a while. This isn’t me being idiosyncratic: their previous four CDs have been hugely praised, with the most recent Dvorak disk even winning The Gramophone Recording of the Year for 2011. Live, they are the most exciting quartet to watch and hear.

And now, at last, we have a new recording, of the Schubert D minor quartet, “Death and the Maiden”, and the String Quintet.  The Times reviewer wrote “If CDs had grooves I would already have worn out these marvellous recordings  … the perfect fusion of virtuosity and profundity.” Indeed. These performances are of a quite unworldly quality, deeply felt yet utterly thought-through, the most passionate you have heard but with moments of haunting delicacy,  with an overarching architectural vision holding it all together.

The Pavel Haas launch into “Death and the Maiden” with fierce attack and astringent tone. And they start as they mean to go on. The recent Takacs and the Belcea versions — good though they are — now seem slightly restrained in contrast (this is the still-young Schubert confronting death here, and the still-young Pavel Haas respond with apt intensity). The obvious comparison would be with the Lindsays’ great recording from twenty five years ago, which I would previously have said was the finest post-war version. But the Pavel Haas’s controlled passion, their even more moving account of the variations of the second movement, and their furious drive to the end of the quartet, makes — I think — for an unparalleled performance.

As for the Quintet, this performance with Danjulo Ishizaka as the second cello is perhaps even finer. For any players, the problem — isn’t it? — is to maintain a shape to the whole piece: a bit too ethereal with the second movement and a bit too cheery with the last movements, and the Quintet is in danger of seeming unsatisfyingly unbalanced. But here, the whole hangs together better than any other interpretation I know. Within a few bars of the opening, the Pavel Haas have built a sense of tension — and the underlying tension is then maintained in a quite driven, uncompromising, way to the very end, with the slow movement giving only some partial relief (and there, the central section is played with a yearning fierceness, and the playing when the original theme returns is heart-stopping).  This makes for an extraordinarily intense exploration of the music. Surely, a truly great interpretation.

After a series of changes of second violin over the years, the Pavel Haas have never sounded better. Hopefully they will now stay happily together as they are. Their website has an interesting short video of them in the Supraphon recording studio. Maybe with two of the quartet having a new baby — Veronika Jarůšková was very evidently pregnant in the recordings — means for a while they will want to tour a little less and record a little more. That would be wonderful. How about, say, the three Rasumovsky quartets? Please?

GWT and TYL on hold …

A few weeks ago, I said I’d this month be starting to post weekly instalments of a new version of Gödel Without (too many) Tears, updating and expanding the previous version to match the new edition of the Gödel book.

Well, things have conspired to prevent this. A temporarily hospitalized very aged mother, lots of visits at some distance, arranging a nursing home, etc., have taken up/will for a while take up a great deal of time and energy, so I just haven’t been able to do the work I’d planned on GWT2. And I don’t want to do a rushed or second-rate job. So I’ll have to delay starting the new sequence of GWT posts until next term/next semester.

For the same reason, it will be a while before I can update the Teach Yourself Logic study guide. I’m planning next a long entry on Peter Hinman’s well-regarded blockbuster Fundamentals of Mathematical Logic, but that too is on hold.

What Frege and Kripke didn’t tell you

Why is Venus star multinominous and called both Phosphorus and Vesper?

Venus is multinominous, to give example to her prostitute disciples who so often, either to renew or refresh themselves towards lovers, or to disguise themselves from magistrates, are to take new names. It may be she takes many names, after her many functions. For as she is supreme monarch of all love at large (which is lust) so is she joined in commission by all mythologists with Juno, Diana, and all others, for marriage. It may be, because of the diverse names of her affections, she assumes diverse names to her self. For her affections have more names then any vice, to wit Pollution, Fornication,

Adultery, … Incest, Rape, Sodomy, Masturbation, and a thousand others. Perchance her diverse names shew her appliableness to diverse men. For Neptune distilled and wept her into Love, the Sun warmed and melted her, Mercury persuaded and swore her; Jupiter’s authority secured, and Vulcan hammered her. As Phosphorus she presents you with her bonum utile, because it is wholesomest in the morning; as Vesper, with her bonum delectabile because it is pleasantest in the evening. And because industrious men rise and endure, with the Sun, their civil business, this star calls them up a little before, and remembers them again a little after for her business.

John Donne, Problem XI, Paradoxes and Problems (c. 1590, published 1633) [Oddly, he in fact has "Hesperus" when he should have written, as here, "Phosphorus"!]

A query about countability

Suppose we are working in an elementary  context where e.g. we don’t want to rush to invoke infinitary choice principles, and want to keep background assumptions modest. What should our attitude be to the idea of countability? Countability is defined by a quantification – X are countable if there is a function f : N → X which enumerates them. But quantification over which functions?

I’m not raising Skolemite concerns here. Even if you fully buy into a rich set-theoretic background, taken at face value, different set theories will supply different enumerating functions. Thus the so-called constructible reals are uncountable according to the theory ‘ZFC + V = L’ but countable according to the theory ‘ZFC + there exists a Ramsey cardinal’. More needs to be said even by the orthodox who identify functions with sets, if it isn’t to be left somewhat indeterminate what objects are countable. But suppose we fall short of  endorsing the orthodoxy because we don’t (in the context, anyway) want definitely to buy into the wildly infinitary assumptions of set theory: we might initially seem to be in danger of making the notion of countability too indeterminate to be comfortable with. For if we are leaving it open just which functions we are prepared to countenance, we leave it correspondingly open which enumerating functions we are aiming to quantify over when we say that some objects are countable.

Yet mathematicians — at least when writing in fairly elementary contexts — cheerfully talk about the countable as if that’s unproblematic. How come? Is that just carelessness?

Well, no. Elementary talk about the countable tends (doesn’t it?) to feature  in three sorts of context:

There are claims that certain objects are indeed countable, defended by showing that the objects in question are unproblematically counted by producing a nice enumerating function. (Consider, for a familiar simple example, how we show that the positive rationals m/n are countable by actually constructing the ‘zig-zag’ enumerating function for ordered pairs m, n, and so counting them.)
There are claims that certain objects are uncountable, defended by reducing the assumption that they can be counted to absurdity. (Consider, for another familiar simple example, the usual diagonal argument that the infinite binary sequences are uncountable.)
There are conditional claims of the kind if X are countable, then …, supported by general arguments that are insensitive to how exactly we delimit (or fail to delimit) the countable.

In none of these kinds of case, at any rate, does such indeterminacy as we might be leaving in the notion of the countable become problematic. So if we proceed with due caution – restrict ourselves to these cases — we can continue to talk about the (un)countable safely enough. And in elementary contexts we do exercise such caution.

Or at least, so it seems. Query: is that a fair description of ‘ordinary’ mathematical practice in elementary, non-set-theoretic, areas? If not, what is going on? While if I’m right, can you think of some texts which overtly ’fess up to the need for this element of caution?

Aldous Huxley being prescient (almost)

Here’s Aldous Huxley writing in 1936:

To a considerable extent browsing has become,  for almost all of us, an addiction, like cigarette-smoking. We browse, most of the time, not because we wish to instruct ourselves, not because we long to have our feelings touched and our imaginations fired, but because browsing is one of our bad habits, because we suffer when we have time to spare and no websites with which to plug the void.

OK, Huxley has “reading/printed matter” rather than “browsing/websites”. But the thought is surely even more true now.

TYL, #17: The Teach Yourself Logic Guide updated

After taking a bit of a rest from it, I’ve been getting back to work on the Teach Yourself Logic Guide. Here then is Version 9.2 of the Guide, newly updated (pp. iii +  62).  Do spread the word to anyone you think might have use for it.

The main new additions are one-page reviews of Dirk van Dalen’s Logic and Structure and Shawn Hedman’s A First Couse in Logic, but there has also been some tinkering throughout.

The previous version from 1 June has been downloaded over 2250 times in three months.  That encourages me to continue putting some time and effort into the project.

The bookshop question: a friendly suggestion?

There are more urgent questions, as the world continues to fall to pieces in depressingly awful ways. But this blog is my distraction from all that, and perhaps in a small way one of your distractions too. So let’s allow ourselves to pause and think about independent bookshops …

Apart from the lovely CUP bookshop in Cambridge, my favourite bookshops these days are Toppings in Ely, the London Review of Books Bookshop (not just for the cakes), and the Oxfam Bookshop in Saffron Walden.

CUP has wonderful lists in maths and philosophy, and their bookshop is a delightful place, not to mention amazingly generous with discounts. While Oxfam bookshops can be very happy sources of serendipitous finds (classical CDs as well as books): the one in Walden which we go to a lot is particularly nice.

The other two shops are just wonderful independent bookshops, that invite endless browsing in calm comfort in quiet corners. Famous for it. Long may they last. But I do have a small problem with them.

I try to resist looking it up, but when I come home with a handful of books, and check what I would have saved if instead I’d noted down the titles I’ve found and ordered them from Amazon instead, it is usually getting on for a third.

That’s a lot.

Especially on some £30 hardbacks.

Especially for someone who buys quite a few books, and whose funds aren’t unlimited these days (no more book grants!).

So what tends to happen is that I buy one or two books (happily paying the extra for the pleasure of the preceding browse) but then when I get home I order one or two more titles from Amazon, or from abebooks if not newly published. I guess quite a few of us do this sort of thing. Which isn’t really the best way to keep these quite splendid places in business, is it?

What would get to me change my behaviour, support the independent bookshops more, and hence keep them going (which is very certainly what I want)? A discount in some form or other. How much? Well, 15% would work for me. Even slightly less. Splitting the difference, as it were, between the cover price and typical Amazon.

Now, this isn’t just a guess. I buy a lot of CDs. And if I buy them from Heffers Sound in town, then I get 15% off using my university card. Which keeps me happy (I don’t worry about saving a bit more via Amazon, as I enjoy using the shop, and of course the instant gratification is worth a little). Again, I guess quite a few of us are like this.

True, 12.5% or 15% off for me is a lot more off a bookshop’s margin. However, with a discount, I’d buy three or four or five times as much in value from the independent shops (it would match my university discount at Blackwells) — I’d buy more books from them, and particularly more of the high-value ones. Over a year I’d be contributing significantly more to their profits. A small-fee discount card you had to apply for in advance would mean that the occasional passing shopper, or the once a year Christmas present shopper, would still be paying as before: while the serious book-buyer would be enticed to spend, in the end, a lot more. What’s not to like?

Something, I suppose, or the shops would be doing it already. Wouldn’t they?

Well, Toppings and the LRB Bookshop  do seem to be surviving, even flourishing (I really hope so): so good luck to them.  Meanwhile I guess that — until they take up my bright suggestion — I’ll just have to carry on visiting them, loving to browse, buying some books there, and then slightly guiltily clicking “Add to basket” for more when I get home.

What do you do?