There was an article in the Guardian a few days ago on Why does music give us chills? (shivers down the spine, goosebumps…). This has been the subject of  some interesting neuropsychological investigations; there are a few links in the article. I was surprised to learn that such chills are only experienced by about half the population — and even more surprised (to put it mildly) by what some of those interviewed at the end of the article reported as giving them the sensations. Still, here for your delight, I hope, is something that works for me. I wasn’t quite sure what performance to link to: dramatically, perhaps this is better. But while it may be a little hard to believe in Anna Netrebko here as a Gilda (such is her undimmable megawattage as a diva), she and Elina Garanca, Ramon Vargas and Ludovic Tézier, certainly deliver the chills:

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Tony Roy: Symbolic Logic

Tony Roy has kindly alerted me to the existence of his freely available Symbolic Logic: An Accessible Introduction to Serious Mathematical Logic.

It is now in version 7.1, so I guess I should have discovered this before! It looks, at a quick first glance, a remarkable resource; still work in progress but looking very polished. There are no less than 746 pages together with another almost 200 pages of answers to exercises. It goes from an introduction to sentential logic, through the usual topics in first order logic (presented both axiomatically and in a natural deduction system) getting as far as e.g. a discussion of compactness and the downward L-S theorem, and then moving on to some quite detailed work on Gödel’s incompleteness theorems. And Tony writes that “it’s aimed especially at accessibility and so builds in a level of explanation and detail that may be missing from other sources.” So I’ll certainly be taking a look at this for TYL2016, and probably commenting there. In the meantime you can take a look yourself on the book’s website here.

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One future for journal publishing

On his blog, Tim Gowers has announced a new journal, Discrete Analysis for which he is to be the managing editor. The content of the journal probably won’t be of much interest to most readers of Logic Matters. It will cover topics in additive combinatorics and other topics which have a suitable family relationship. But the form of the journal is fascinating, and will surely come to be emulated by other editorial groups for other areas of mathematics. It is to be an arXiv overlay journal. What this means, in Tim Gowers’s words, is that

rather than publishing, or even electronically hosting, papers, it will consist of a list of links to arXiv preprints. Other than that, the journal will be entirely conventional: authors will submit links to arXiv preprints, and then the editors of the journal will find referees, using their quick opinions and more detailed reports in the usual way in order to decide which papers will be accepted. … [So] The articles will be peer-reviewed in the traditional way. There will also be a numbering system for the articles, so that when they are cited, they look like journal articles rather than “mere” arXiv preprints. They will be exclusive to Discrete Analysis.

There’s much more in the very lucid and persuasive blog post, about both principles and practicalities.  Plainly this is one way forward for journal publishing, one way to push back against the stranglehold of commercial publishers extorting funds from hard-pressed university libraries.

One issue I noted. Tim Gowers  only expects Discrete Analysis to get in the order of 50 submissions per year (less to start with). So — after the kerfuffle of setting up the systems and working through teething problems — this promises to be a relatively small commitment for the editorial board to keep running. However, the arrangements won’t so easily scale up: there is nothing in the funding model, as I understand it, to pay a managing editor of a bigger project an honorarium for a more substantial time commitment. But maybe keeping things small is no bad thing. I’m all for well-focused, relatively niche, journals. A more distributed network of small-ish arXiv overlay journals could well be the way to go (so long as, like Discrete Analysis, they don’t aim to set stern boundaries, so that interesting papers that break new ground sitting between familiar clusters of topics can still find a home).

I wonder if any logicians out there are thinking of starting such a journal?

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Procrastinating, but in a good way …

When the thinking or writing has got stuck, and work on the next book (if that’s what it ever becomes) is stalled for a while, one entirely harmless diversion on the internet is to go along to to see if I can usefully answer any logic questions. If you don’t know the site, it is the junior partner of the stunningly useful research-level which operates mostly beyond my pay grade.

Some of the questions on are pretty confused stuff, or are from students trying their luck in getting others to do their homework for them. But such questions usually get closed down quickly. And there are enough questions which — even if hardly novel — are interesting enough to keep me going back to the site and having a shot at answering them. For some recent efforts with an unusually philosophical flavour, see this (on whether we can prove  mathematical induction is sound), or this (on defining functions in set theory) or this (on whether there currently exists a set of Olympics 2016 winners). Or if you want something more techie (and don’t know the footnotes in my Gödel book!) you might like this proof from Rosza Péter that there are recursive but not primitive recursive functions which aren’t fast growing.

It might be fun to contribute, but is it worth the small-but-not-neglible effort? I’ve just checked my “profile” on as you do: the whole enterprise is gamified, there are reputation points to be accrued, badges to be won, … sad eh? (Well, no, not sad — the whole point is that the voting up and down of answers for accuracy, clarity, helpfulness is what makes the site reliably useful).  And what’s just really struck me is the Impact score. That’s the number of times people have read answers of mine that got positive votes (I think that’s how it basically works — though obviously no one is counting the quality of the reading!). The score is ~352K.

That’s a lot of readings. But it is not a wildly exceptional total (there are some very impressive expositors who contribute frequently to and whose impact score is in the millions). So I’ve nothing especial to boast about here. Rather, it just brings home how very heavily used a site like is. I imagine that this is very much on the basis of student-to-student recommendation, as in my experience lecturers can be distinctly sniffy about this sort of thing. But quite wrongly, I think. As a reader I’ve certainly learnt a lot of fiddly points of category theory there by searching around when stuck. Grad students and beyond can learn from the exercise of writing crisp cogent solutions to problems (and should surely be encouraged to do so, within reason). And old hands in their retirement, with little taste for golf or gardening, can continue to satisfy their pedagogic urges and find a grateful audience out there (much larger than any audience they were ever paid to teach!). What’s not to like?


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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 …

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Teach Yourself Logic — suggestions?

I haven’t looked at all at the Teach Yourself Logic Study Guide since the 2015 version came out on January 1st. I earlier had it in mind to do a mid-year update in time for the new (northern hemisphere) academic year: but that bird has flown. The main Guide continues to be downloaded eighty or more times a month. It certainly seems to serve some need, and I get appreciative emails.  So I will put time aside over the coming months to get a 2016 version ready for next January 1st.

So now’s the time for feedback on both style and content. As far as style goes, while keeping to the spirit of the present Guide, what would make it more user-friendly? Should I keep the one-big-PDF format, or go over to a suite of webpages? (I still incline to the PDF format — easier to maintain, but also easier to read off line, and for students to work with by highlighting, commenting, etc. onscreen.)

As to content, any suggestions for additions, improvements? One thing I’ll want to say something about is The Open Logic project. But are there more conventional new publications that could definitely rate a recommendation for student use?

Feedback from logicians at any stage of their career, whether taking first steps or on their zimmer frame, will be most welcome — either in the comments below, or by email (address at the bottom of my “about” page here).

Posted in Logic, TYL | 9 Comments

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! 

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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.

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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.

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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.

Posted in Category theory | 5 Comments