Scribble, scribble, scribble

handel

Radio Three started playing Handel’s My heart is inditing. Child, about 15 seconds in: “Daddy, are they going to play Zadok the Priest now?”.

(This was mostly good luck; she happens to have encountered ZtP recently and doesn’t have a lot of other choral music to compare with. As a measure of how much she doesn’t know, the next thing they played was Holst’s St Paul’s Suite and she asked “Is that by the same person who wrote Zadok the Priest?”.

Speaking of Zadok, in January my choir is organizing a big come-and-sing event in aid of EACH, featuring Zadok, three familiar bits of Parry, and Stanford’s Coronation Gloria. If you sing at all, please come along, have fun, and help a very worthwhile charity!

forty-one

• n²-n+41 is prime for n=1,2,3,...,40.
• 4×41−1 = 163, a Heegner number.
• exp(π√163) = 262537412640768743.999999999999250... = 12³(231²−1)³ + 744 − ε with ε very small.

These facts are not unrelated, but the connection between them is rather too esoteric to go into here. Besides, I don’t really understand it well.

hesperidium

I discovered recently that a fruit with the same sort of structure as, e.g., an orange is called a hesperidium.

Why that curiously beautiful word? Well, you see, Greek mythology features the golden apples of the Hesperides, and oranges look kinda like apples but are kinda-sorta golden in colour.

(The Hesperides are the nymphs of the West, the land of the evening (hesperos); presumably the similarity to the Latin equivalent Vesper is no coincidence, but I know no more.)

nothing

Child: Daddy, better than nothing would be the worst thing in the world.

Daddy: ...

After a moment’s thought, though, I realised that she was exactly right. “x is better than nothing” = “x is not better than anything” = “x is at least as bad as anything else” = “x is the worst thing in the world”.

It’s the same idea as the old joke: A ham sandwich is better than eternal happiness, because nothing is better than eternal happiness and a ham sandwich is better than nothing.

prizes

After we had an appliance serviced, we were sent a survey with a prize draw as incentive. The conditions include the following (emphasis mine).

6. There shall be five winners per draw of this Promotion. The winners will receive Samsung digital still cameras. The model of digital still camera is subject to change and the decision will be made by the Promoter. A total of three prizes per draw.

I wonder what happens to the other two winners. (Maybe each winner gets 3/5 of a camera.)

binomial

The binomial coefficient is the number of ways, if you have n things, of choosing r of them; equivalently, the number of n-digit strings, all digits 0 or 1, with r 1s and the rest 0s; equivalently, the coefficient of x^r when you expand out (1+x)ⁿ.

There’s a nice (and well known) theorem that says: this is odd precisely when subtracting r from n in binary requires no borrowing. (So, e.g., if n is a power of 2, then this happens only when r=0 or r=n.) There’s a very pretty generalization of this which isn’t so well known. (So far as I can remember, I found it myself, but others got there long before me.) Here it is:

Theorem: Suppose you are interested in modulo p, a prime number. (That is, you don’t care if your answer is wrong by a multiple of p.) Then you can compute it as follows. Write down n and r in base p. If r’s base-p representation is shorter than n’s, pad it on the left with zeros to make it the same length. Then

In other words: compute one binomial coefficient for each corresponding pair of digits, and multiply them all together.

You’ll get 0 – i.e., a multiple of p – if and only if one of the factors is a multiple of p, which (it turns out to be easy to prove) happens if and only if for some j, r_j>n_j. In the case p=2 this (it turns out to be easy to prove) is the same as the condition I mentioned earlier about subtracting r from n.

Proof: it’s enough to show that (mod p) since that lets us split off the last base-p digit, and we can then repeat until we’ve done all the digits. So, consider (1+x)^mp+n. This equals ((1+x)^p)^m(1+x)ⁿ. and modulo p this equals (for reasons I’ll explain in a moment) (1+x^p)^m(1+x)ⁿ. Now to get a term containing x^rp+s we need the x^s term from the second factor, and therefore the x^rp=(x^p)^r term from the first. These come with factors of and , respectively, attached. And we’re done ...

... except that I promised to explain why ((1+x)^p)^m and (1+x^p)^m are equal modulo p. Clearly it’s enough if (1+x)^p and 1+x^p are equal modulo p. Well, when you expand out the former, the coefficient in front of each x^r is (by definition) . The coefficients of x⁰ and x^p are both 1, obviously. What about the others? We need to prove that they’re all multiples of p.

Well, remember another definition of : the number of p-bit strings of 0s and 1s containing r 1s. If 0<r<p then a “rotation” of such a string (e.g., 01100 gives 00110, 00011, 10001, 11000) still contains exactly r 1s, and all the p different rotations are different (why?). Hence the number of such strings is a multiple of p, as I claimed.

(You can also prove the theorem more “directly” via a combinatorial argument involving counting the ways of selecting rp+s things from mp+n, and actually that’s how I first proved it. It’s also the proof sketched on the theorem’s Wikipedia page. Maybe there’s an even simpler proof?)

voting

The leaflets put out by the "No2AV" campaign consist almost entirely of outright lies. I'm not talking about mere spin and fuzziness; they say one thing after another that is simply, demonstrably, not true, and that they surely must know are not true. These people are not interested in truth.

One of the more credible-sounding claims they make is this one: AV gives more votes to supporters of minority parties. (Of course they make this claim in a way that is plainly calculated to make you think it amounts to "AV gives lots of power to the BNP". That'll be why the BNP oppose it. But I digress.)

That claim is, of course, false. I've seen it made by at least one extremely intelligent person, so let me show why it's false.

AV is basically equivalent to a series of simpler elections: one with the whole field, then another in which the least popular candidate is removed, then another in which the newly least popular candidate is removed, and so on until someone has all the votes. (AV differs from this in that voters have to decide ahead of time which candidates they prefer to which; hence the alternative name of "instant runoff voting".)

In each of these elections, every voter gets exactly one vote. What's different about the supporters of minority parties is that in some of the elections their less-preferred votes are counted instead of their first-preference votes. This is not an advantage.

Here's a hypothetical election. Three candidates: Left, Right and Crazy. Five voters. Two prefer Left, then Right, then Crazy. Two prefer Right, then Left, then Crazy. One prefers Crazy, then Right, then Left.

So, Crazy gets eliminated and then his second-place vote for Right is counted in the next round (alongside the first-place votes of the other voters). Right wins.

The Right party, although they happen to win this one, are very upset: the Crazy supporter got his second-place vote counted. How very unfair. Very well, gentlemen, we'll count your supporters' second-place votes instead of their first-place votes, shall we? Result: Left wins by a landslide.

Much, much more detailed analysis of the arguments by Tim Gowers: one, two, three. (If you're short on time or patience, read the last one.)

In some situations AV can give really crazy results: see Ka-Ping Yee's simulations and Warren Smith's examples of comprehensively pathological AV results and spoiler effects that may make AV as prone to two-party domination as FPTP.

For the avoidance of doubt, despite those ugly phenomena I think AV is clearly a better system than FPTP.

christmas

Merry Christmas! (Or whatever else you may celebrate at this time of year.)

Perhaps I'll write a bit more in 2011 than I did in 2010.

tests

I ran across this problem elsewhere in the blogosphere, where unfortunately some very clever people are offering a distinctly suboptimal solution.

Suppose you have lots of people, each of whom (independently, with quite low probability) may have a certain disease. There is a perfectly reliable blood test for the disease. You want to identify everyone in your group who has the disease, using as few tests as possible.

We assume that you can pool blood samples, which is why the answer isn't just "one test per person, duh". The test will then tell you whether at least one person in the pool has the disease.

The solution offered on the blogs I linked to above has the following form: divide your group into several roughly equally sized subgroups; test each subgroup; then, for each positive-testing subgroup, test each person in that subgroup. If you do that, then it turns out that you want to use groups of size approximately 1/sqrt(p) where p is the fraction of people who have the disease; the total number of tests you need is then approximately twice the number of groups.

So, for instance, with a group of 1000 people and p=0.000154, you want groups of size 81 and the average number of tests is about 25. That's quite a big improvement on testing everyone.

But you can, and should, do better: when a subgroup tests positive, after all, you don't immediately have to test everyone in it: you can do the same thing to the subgroup as you did to the whole group. (Except that now you know at least one person in the subgroup has the disease, which changes things a bit.) Since you can do this, the cost of processing a subgroup that's tested positive grows more slowly (as a function of subgroup size) than you'd naïvely expect, which means that you typically want to use larger groups.

So far as I can tell, there isn't any simple elegant optimal solution. But one can get a computer to crunch the numbers. It turns out, for instance, that for 1000 people and p=0.000154, you should begin by testing the whole group. (After all, about 86% of the time that test will be negative and you'll be done.) If the test is positive, you should then test a subgroup of 377 people. (Why 377? Search me.)

With optimal choices, the average number of tests you need to do is about 3.2. That's a whole lot better than 25.

You can take a look at my hacked-up code if you like.

In general, it seems (though I haven't tried to prove it) that if your number of people is at most 1/p+1 then you should begin by testing all of them; otherwise you should begin by testing a smaller number, which fluctuates in peculiar ways between about 1/2p and 1/p.

If you have a group of people known to have at least one case, as will happen as soon as you get a positive result, it seems (and again I haven't tried to prove anything) that when the group size is at most about 1/p the optimal size of subgroup to test first is usually a Fibonacci number. More specifically, starting at a group size of F_k+2 there is a long run of values of F_k, followed by a gradual mostly-monotonic transition to the next run of F_k+1 starting at F_k+3.

notes

As I have done for several previous concerts, I've put together some rambling notes on the text for my choir's next concert, in the hope that they'll be useful to other choir members. I'm putting a link here in case anyone else is interested.

cake

My all-purpose chocolate-and-nut cake recipe (which I'm posting because someone asked me for it). It's a slight variation on the one at the end of Nigel Slater's Appetite, which in turn is a slight variation on someone else's.

The recipe is pretty much infinitely malleable; I've never made it quite the same way twice. It's pretty hard to make it not work. The numbers here are what I did the last time I made it.

Toast 200–250g of hazelnuts and almonds (whatever proportion you prefer) lightly; maybe 8 minutes in the oven at 180°C. Let them cool, then chop them up into whatever size bits you prefer along with 250g good dark chocolate.

Soften 250g butter (I just put it in the microwave at very low power for a few minutes) and beat it up with 250g of sugar (some combination of demerara and light or dark brown soft; I usually use more of the former) until pale and fluffy. I'm usually pretty lax about getting it really fluffy, and it works fine.

Add 4 large eggs one by one, beating each one in.

Add 3–4tbsp amaretto and stir in.

Measure out 170g plain flour and 100g ground almonds; add 2tsp (rounded) of baking powder. Sift them into the mixture if you can be bothered; I usually just weigh them out and dump them in. Fold them in.

Stir in most of the chocolate and nuts; leave out 2–3tbsp.

Put it into a lined cake tin of suitable size (say 23cm), preferably one of those with a spring-clip side and a removable base.

Sprinkle the rest of the chocolate and nuts on top, along with another 2tsp demerara sugar.

Bake at 170°C for 70 minutes.

You may need to adjust the cooking temperature and time for your oven. Mine is fan-assisted and runs about 10°C hot, and I more often overdo than underdo this cake.

I usually make this with Green & Black's chocolate: some combination of their 85% dark and their "Maya Gold" (55% or thereabouts; quite orangey).

Slater's recipe has coffee where I have amaretto; his source has milk; I'm sure you could use brandy or Grand Marnier or even water.

cars

Proposition: Cars and similar vehicles should be required by law to have at the rear a prominently-visible digital readout of their current speed.

Advantage 1: it would be that bit easier to match the speed of the car in front, which is generally a Good Thing for efficient traffic flow. (Actually you might want a low-pass-filtered version of the speed of the car two in front, or something; anyway, whatever it is you want, the extra information will do no harm.)

Advantage 2: it would act as a mild deterrent to speeding.

Advantage 3: it would make it slightly easier for police to catch people speeding.

(What's that you say? Sometimes driving faster than the limit is a perfectly reasonable thing to do, and sometimes the police prioritize fundraising over safety when it comes to catching speeders? Quite possibly. In which case, the thing to do is to fix the laws or the speed limits, not to rely on the fact that sometimes it's inconvenient to tell whether someone's speeding or to prove they are.)

It might be difficult to do this visibly enough to be useful without obscuring the view through the rear window; that might be sufficient reason not to do it.

cost

How much does a book cost?

The room I’m in right now contains approximately 1800 books. The shelving on which those books (along with not very much else) are stored cost, I think, about £1500 or so. (You can get bookshelves that cost a lot less, if you don’t mind them sagging and/or looking unsightly. You can get bookshelves that cost a lot more, if you want beauty as well as quality.) So, crudely: shelving a book costs £1.

That room, though. It didn’t come for free, and if we had drastically more books we’d need a bigger house to put them in. (I’m fairly sure that every time we’ve been through the soul-destroying business of buying a house we’ve rejected some houses on the grounds that they didn’t have enough spare wall-space for bookshelves, so this isn’t a purely theoretical concern.) A quick look at house prices in our area suggests that one decent-sized room typically adds something of the order of £40,000 to the price of a house. (Less for smaller houses, more for larger houses; larger houses have larger rooms.) So, crudely: housing a book costs £20.

I’m not sure I wanted to know that.

Of course there’s lots wrong with that analysis. For instance, this room contains not only books but also computers, desk space, etc., and we can fit quite a lot more books into our house before it’s so full we have to buy a new one. Even so, I think it would be quite difficult to justify an estimate of the overhead cost per book that’s below, let’s say, £5. But do I think of that in second-hand bookshops? Why, no, I do not.

There is presumably a broader lesson here.

machine

I just got Knuth’s newly published book of algorithm papers. There are many nice things in it; here’s one. (It’s not actually Knuth’s; it’s due to Larry Stockmeyer.)

Suppose you have a machine whose basic operations are integer addition, subtraction and multiplication, and greater-than-or-equal testing. Theorem: you can’t determine whether a number n is odd faster than some constant times log(n).

Proof: suppose you can; then, in particular, for large enough k your program should be able to determine for any number up to (let’s say) 2^10k whether the number is odd or even, and do something different in each case, using at most k steps. I’ll show that it can’t.

Well, what can the program have done within k steps? It’s done at most k comparisons so there are at most 2^k code paths. Each comparison is testing the sign of some polynomial in n; what polynomial depends on the results of previous comparisons. In any case, the path the program has taken up to this point can depend only on the values of at most 2^k polynomials in n. Oh, and they all have degree at most 2^k.

Well, all these polynomials collectively have at most 2^2k roots. We can therefore find an integer m no bigger than 2^2k+1 such that none of those roots lies between m and m+1 inclusive. (Each root excludes at most two choices of m.) But then our program must produce the same results for m and m+1 since all the comparisons it does produce the same answer for both; since m and m+1 have different parity, it therefore can’t be doing the right thing for both of them.

Knuth’s book contains many clever algorithms. From the cursory reading I’ve given it so far, its contents don’t seem to be “papers on the design of algorithms” any more than the works of Shakespeare constitute “papers on the writing of plays”. So the title’s a bit misleading, which is a pity (it would be very interesting indeed to read Knuth’s thoughts on how to design algorithms) but not a surprise. The book is of course very good anyway.

go

Yesterday, my (3.5-year-old) daughter beat me at go. I am very proud.

Admittedly, that was with a 4-stone handicap on a 7x7 board (which for non-players I should perhaps explain is roughly equivalent to a game of tennis in which one player has a racquet and the other has a wet noodle). And I did give her quite a bit of advice. It'll likely be a while before she really has the least clue what she's doing...

books

One of the drawbacks of having a lot of books is that sometimes my memory isn’t good enough and I end up with duplicates.

If you would like any of the following and can easily collect it, please let me know.

The law of delay, by C Northcote Parkinson

CNP’s second volume of satirical essays on bureaucracy and related matters. Not as funny as his first more famous one, but still amusing.

The Glass Bead Game, by Herman Hesse (translated by Richard and Clara Winston) [taken]

A justly famous novel.

Chamber music, by Alec Robertson

One of those Pelican paperbacks. Chapters on Haydn, Boccherini, Mozart, Beethoven, Schubert, Mendelssohn, Schumann, Brahms, Smetana+Dvořak, Bloch, Bartók; duet sonatas without wind instruments, chamber works with wind instruments; chamber music in America, England, France, 20th century Germany, Russia.

The concerto, by Ralph Hill

Another of those Pelican paperbacks. Chapters on the concerto generally; Bach, Haydn, Mozart, Beethoven, virtuoso violin concertos, Mendelssohn, Chopin, Schumann, Liszt, Brahms, Saint-Saëns, Tchaikovsky, Dvořak, Grieg, Elgar, Delius, Sibelius, Busoni, Rachmaninov+Medtner, Ravel, Bloch, Bartók, Szymanowski, Berg, Prokofiev, Walton, some English concertos, variation forms.

Genius: Richard Feynman and modern physics, by James Gleick

Lengthy biography. Contains some physics. Quite good.

Algebraic topology, by C R F Maunder

Very nice indeed, if you happen to want a textbook on algebraic topology. Fundamental group and classification of 2-manifolds in chapter 3, singular homology in chapter 4, cohomology in chapter 5, more homotopy theory in chapter 6, homotopy groups of CW-complexes in chapter 7, (co)homology calculations on CW-complexes in chapter 8.

Complex analysis, by Lars Ahlfors

Also very nice. Packs a lot into a small space. For an indication of its level, here are a few theorems proved near the end: the Riemann mapping theorem, the Schwartz-Christoffel formula (explicit RMT for polygonal domains), finitely connected domains have kinda-sorta unique conformal mappings to annuli slit along concentric arcs, Picard’s theorem (via the modular function).

A retargetable C compiler: design and implementation, by Christopher Fraser and David Hanson [taken]

A lengthy literate program implementing a complete C compiler. (Not quite all the code is actually printed in the book. There was an accompanying floppy disc, which I don’t have any more, but the code is available on the web.

The armchair economist, by Steven Landsburg

Published years before Freakonomics. Somewhat similar in character, but with a slightly higher proportion of actual economics. You can get a pretty good idea of what sort of book it is from a review written by a friend of mine.

Challenging Chomsky, by Rudolf Botha

Entirely about his linguistic views, not his politics. Might be (but isn’t) subtitled “Brief statements of lots of criticisms of Chomsky’s linguistics, and equally brief statements of why they are all wrong”. Alternates between the sort of academic style you might expect from its subject matter and cutesy introductory material that refers to Chomsky as “The Master” and the enterprise of disagreeing with him as “The Game”. As you may guess, I find the latter annoying. I haven’t read much of this.

Numerical recipes in C, by Press, Flannery, Teukolsky and Vetterling

This is the first edition, from 1988. More recent editions have a lot more material, many bug fixes, and slightly less eyeball-bleedingly-Fortrannish code. The main value of this book lies (I think) not in the code but in the extremely lucid explanations. Tear out the chapter on random numbers and burn it.

JavaScript: the definitive guide, by David Flanagan

This may have been definitive when it was published, in 1998. (Third Edition! Covers JavaScript 1.2!) It’s a long time since I looked at this, but I think it’s pretty good apart from being completely obsolete. This one isn’t exactly a duplicate since my other copy is of a later edition.

The Kraken wakes, by John Wyndham

Ph’nglui mglw’nafh Cthulhu R’lyeh wgah’nagl fhtagn!

The songs of Robert Schumann, by Eric Sams

Translated texts and commentary on all Schumann’s songs, plus a few dozen pages of more general material -- motifs in the songs, Schumann’s health, etc.

Jamie’s Ministry of Food, by Jamie Oliver [taken]

Lots of simple recipes, primarily intended for people not used to cooking. Some better than others. Plenty of pictures. Jamie Oliver evidently wanted to make this the start of a movement, but I just found his sloganmongering in support of that aim tiresome and patronizing. (Actually, I feel that way about a lot of his writing. He knows how to cook, though.)

Updated 2010-01-07: I have a request for three of these now. Updated 2010-01-08: The person who may possibly be the owner of the Ahlfors isn’t sure whether he is or not but says “feel free to find it a good home”, so it’s available.

feast

A very happy feast of (according to preference) Isaac of Woolsthorpe, or Jesus of Nazareth, to anyone reading this!

Also born on the same day of the year: Anwar Sadat, Humphrey Bogart, and (appropriately) Shane MacGowan of The Pogues (co-writer of the best-selling and very miserable “Fairytale of New York”).

Edited to add: oops, I screwed up and this didn't actually appear until 48 hours later than it was meant to. Er, happy new year then.

omission

George Herbert's beautiful poem “Love bade me welcome” has been a favourite of mine for so long that I was very embarrassed to find in a book about something quite different the following observation, which in retrospect is absolutely obvious: it must have originated in a pun on the word “host”, even though that word never appears in the poem.

There's something rather delightful about that. The following joke, which I stole from Math Overflow, has the same feature. My apologies to any readers who happen not to be in the intersection of the two cultures on which it depends. (I worry that part of its appeal lies exactly there; in-group humour.) “Q. What do you call it when you're trying to prove that a map is injective, but you just can't do it? A. Monic fail.”

Any mathematician reading this who happens to have a copy of Littlewood's Miscellany might want to look up Thorin's proof of a theorem of Riesz, in the section entitled “Mathematics with minimum raw material”, where once again the crucial piece of the puzzle is something that isn't there.

(Random geeky note about the Herbert poem: It's frequently titled “Love (III)”, but G.H. never gave it that title. He just called it “Love”, but he also wrote another earlier pair of poems titled “Love” and numbered I,II. So his editor decided to call this later one “Love (III)”. Aren't you glad you know that?)

(Random geeky note about names of things other than poems: So far as I can tell, the fact that in northern Cambridge there are a George Street and a Herbert Street near to one another, and also a Gilbert Road and a Chesterton Road near to one another, is mere coincidence.)

ontological

Consider, if you will, an argument for theism than which no worse can be conceived.

What would such an argument be like? Well, arguments that merely fail to provide any support whatever for their conclusions are two a penny; a worst conceivable argument for any proposition must surely be one that actually conclusively refutes the proposition it's meant to support.

Now, the worst conceivable argument for theism clearly exists in the understanding. But it cannot exist only there, for so bad an argument is of course worse (because more destructive) if it is actually made; so if it existed only in the understanding then a worse would be conceivable, which is a contradiction.

Therefore, there is an argument for theism which is in reality a conclusive refutation of theism.

But a belief that can be conclusively refuted is false. Therefore there is no God.

Note: Yes, of course the above is entirely ridiculous, and in particular I am of course not suggesting that it actually offers the slightest reason for rejecting theism.

refutation

In the wake of the CRU hack, all sorts of allegations are flying around, some more sensible than others. Unsurprisingly, some of what's being said is not merely misinterpretation but outright fabrication. (Oh, the irony.)

Here is an example, excerpted from an email alleged to have been sent from Tom Wigley to Phil Jones on 2009-09-27.

Phil,

Here are some speculations on correcting SSTs to partly explain the 1940s warming blip. If you look at the attached plot you will see that theland also shows the 1940s blip (as I’m sure you know).

[...]

It would be good to remove at least part of the 1940s blip, but we are still left with “why the blip”.

Why is it important? Because over the course of the 20th century the 40's blip leading into the cooling 50's 60's and 70's is a screaming refutation of co2 as a climate driver.

Now, the thing is that that last bit (the only bit that seems to me even slightly incriminating) isn't in the original email. As you can see, e.g.,

• in comment 20 on this RealClimate post (note: I think the discrepancy in date is because the commenter is quoting from a reply to the email in question; see also here), or
• in that email's entry in what seems to be a complete database of the stolen emails.

The real email contains nothing about a "screaming refutation", nor in fact any sort of suggestion that the “blip” is anything other than the sort of measurement anomaly that scientists have to deal with all the time.

Paranoid readers may wish to note that all the sources cited above are hostile witnesses (RealClimate isn't, but the commenter I quoted clearly is), so it is not at all credible that they are covering anything up for the CRU people.

(There is some information about the “1940s blip” on RealClimate.)

Note 1: The fact that this particular allegation is a lie doesn't prove that any other allegation made on the basis of the CRU emails is a lie.

Note 2: Many other allegations made on the basis of the CRU emails do in fact appear to me to be lies.

gramophone

Gramophone, which calls itself "the world's greatest classical music magazine" and can probably make a decent argument in support of that claim, has put a complete archive of its past issues on the web. For everyone. For free.

How, you might ask, will they now persuade anyone to subscribe to their magazine?

The trick may be that their archive is produced by means of OCR software, with the result that what's actually on the web is perhaps better described not as "a complete archive of their past issues" but as "a surrealist composition loosely based on a complete archive of their past issues". Maybe it'll get better; they have a handy button next to each paragraph to let you report errors. Too bad that most paragraphs have errors, often several of them, and that the most entertaining errors are ones where two different articles have been randomly interleaved.

Anyway, good stuff. Here's a random snippet that tickled my fancy, from a review of a recording of the Goldberg Variations.

One recording, by an artist whom gallantry prevents me from naming, would have sent the Count to sleep from sheer boredom; he might well have taken refuge in sleep as a means of escape from another, by a player living further north.

(The story being alluded to here is probably false, but no matter.)

times

This Times article is loathsome. If its loathsomeness isn't obvious on a quick glance, you might like to imagine an article that begins like this:

A Jew man has pleaded guilty to stealing thousands of pounds from a local shop.

Moshe Davidson, who named himself after the Jewish prophet when he converted to the religion, faces up to a year in prison for breaking into the shop and ransacking its supplies of cash.

Davidson, who believes that he is part of God's chosen people, was caught on CCTV smashing down the door and blowing open a large safe.

(Yes, the second word is deliberate; it pretty much parallels the correspondingly barbarous phrasing in the real article. And yes, the transgenderedness of the subject of the real article appears to have precisely as much relevance to her crime as the Jewishness of the subject of my fake one has to his.)

It occurs to me that it's not un-heard-of for newspapers to change their websites, so here for reference is how the article begins at present.

A sex-change woman has pleaded guilty to reckless homicide after her elderly husband was "exercised to death".

Christine Newton-John, 41, who named herself after the singer Olivia Newton-John following her operation, faces up to five years in prison for forcing her exhausted 73-year-old husband to swim in the pool of their apartment complex in Chardon, Ohio.

Newton-John, who was born John Vallandingham, was caught on CCTV dragging James Mason, around the pool by his arms and legs.

clock

I recently read Rhythms of Life, a book about circadian rhythms. I was very struck by (the currently most plausible guess at) the underlying cell-level mechanism.

It's a negative feedback system, like a pendulum (which, as it swings higher, also feels a stronger force pulling it back towards the central position). Startling thing number 1: one crucial step in the feedback loop is DNA transcription. I'd always vaguely assumed that, roughly speaking, the instructions in a cell's DNA determine how the cell is "built" and are more or less passive thereafter (readers who actually know some biology, please feel free to laugh at me at this point), but no.

Here's a simplified description of how it works: there are two proteins (call them A and B), described by genes a and b. Protein B promotes the expression of gene a, but protein A attaches to protein B and stops it doing this. So, the more A we have, the less A gets made; if the details of how this works out are right, we get the sort of negative feedback loop required to produce an oscillation.

Startling thing number 2 is how easily this produces entrainment to the light/dark cycle. It turns out that A is degraded by exposure to light, and this is enough. (Which shouldn't have been surprising, since in general oscillators very easily get entrained to anything in their environment, but it surprised me anyway.)

So: suppose we have a stable 24-hour-ish cycle, and then it becomes light earlier than "expected". Then A gets degraded more rapidly, at around the time when it would have been being degraded anyway, and so the cycle is a bit shorter. Similarly if the onset of light is later than expected. If the light period goes on for longer than expected, then again A gets degraded faster -- but now at a time when its quantity should be beginning to ramp up; so the cycle becomes longer. And so forth.

Three caveats. Firstly, this is all oversimplified; for instance, A and B are actually pairs of proteins that work together, and there are other mechanisms involved in, e.g., arranging for the period of the oscillator not to be much too fast. Secondly, strictly it only applies to fruit flies, and the corresponding systems in other organisms aren't so well understood. Thirdly, lots of important details (for instance, how the period of the clock manages to be largely insensitive to temperature, when chemical reactions consistently run faster at higher termperatures) are still unknown.

birthday

Happy birthday, Schubert!

x-rated

(The following rather dull notes on my recent trials and tribulations with the X Window System are mostly here just in case they help someone else having similar difficulties. If you find such things boring, please just ignore them.)

One · I found that certain web pages would send Firefox into a screaming tizzy, overwriting its window with a random tiling of rectangles grabbed from elsewhere on the screen. (The common denominator appeared to be the use of CSS background images. I don't know why.)

I thought at first that the cause might be some interaction between quirks in Firefox and in my (unorthodox) window manager. It turned out, however, that Firefox misbehaved similarly in ion and KDE's window manager. Time to upgrade some stuff and see if that helps.

Two · After upgrading X to the latest version known to the FreeBSD ports system, namely version 7.4 (server version 1.5.3), X would not start up:

MGA(0): Unable to map BAR 0. Invalid argument (22)

Apparently lots of people have had this problem when trying to run a dual-head setup, but I have only one head. (Er, that is, only one monitor.)

It turns out that this is a bug in x.org's Matrox driver: at various points it maps some memory and unmaps it again, and in one case it's possible for its idea of the size of its framebuffer to change in between the mapping and the unmapping; it gets confused, fails to unmap the memory, and then breaks the next time it tries to map it again. This bug was fixed more than a year ago, but for some doubtless excellent reason the release in the FreeBSD ports system is ancient, and in any case I only discovered that the bug had already been fixed after finding and fixing it myself.

Three · So, then my keyboard and mouse wouldn't work. There appear to have been two separate problems. The first is that they weren't being detected automatically when X thought they should be; adding

Option "AllowEmptyInput" "off"

to the ServerLayout section of my config file fixed that, though I'm sure that's not the right solution. Then it transpired that in the upgrade process the keyboard and mouse drivers (xf86-input-keyboard, xf86-input-mouse) had been built against the old version of the X server code. Forcing those to be rebuilt solved the problem. The FreeBSD ports system, convenient though it is, doesn't appear to have any way to express the fact "Any time you rebuild this port, you must also rebuild these others even if the versions you built before are still the latest versions".

Four · X was refusing to use the 1600x1200 resolution I wanted, preferring 1280x960. Since my monitor is an LCD panel whose native resolution is in fact 1600x1200, this was suboptimal. So, it turns out that if you put

Option "ModeDebug" "true"

into the Device section for your video card, your X log file contains a brief explanation of why each mode got rejected. It turns out that, for reasons I still don't understand, X was setting a maximum width and height for my display, and they were too small. I'm absolutely certain that what I've done to work around this is the wrong solution, but it works OK for me: I've put

Virtual 1600 1200

in each Display subsection of my config file.

Bletch · After 25 years of X, and 22 of X11, surely it should all be easier than this.

Anyway, Firefox no longer garbles those web pages; I don't know whether it's the X upgrade that fixed it, or something else that needed upgrading along the way. Yak successfully shaved.

reviews

Brief reviews of a few books I've read recently but don't feel like taking the time to write up properly:

Nation, by Terry Pratchett  ·  His latest; not a Discworld book. Pratchett was recently diagnosed with a horrible brain disorder. So it's natural (if callous) to ask: Does it show? The answer, I'm glad to say, is that it doesn't, not at all. Nation is a very enjoyable book, and doesn't read at all as if it was written by someone whose mind is going. It's inventive, and fun, and sometimes moving, and sometimes thought-provoking. Don't go expecting it to be like the Discworld books; it isn't. (In particular, it isn't the gag-fest that many of the earlier ones are.)

The myth of the rational voter, by Bryan Caplan  ·  Brief and unfair summary: Voters disagree a lot with economists on matters of economics, in consistent ways. This shows that they are severely irrational, because economists are unlikely to be badly wrong. Therefore, economists working on political issues, who have long consistently assumed that voters are on some level basically rational, are badly wrong.

Seriously, though, Caplan makes a pretty plausible argument that voters are systematically wrong about all sorts of important things; this is hardly surprising, at least not to cynical ol' me. He concludes from this that we need less democracy rather than more, and in particular (e.g.) that we shouldn't try to increase turnout because bothering to vote correlates with some things that correlate with thinking more like an economist. Nor should we worry if much real power is in the hands of businesses rather than politicians, for that effectively gives the power to markets, and markets do better than governments. In general, it seems he thinks that it would be better if richer, better educated, smarter people had more political power. We needn't worry that such people will vote for their own interests and thereby screw the already-underprivileged even worse than they are already screwed, because (he says) there's evidence that people vote for what they think right and not generally in their own selfish interest.

It seems to me that that last bit is absolutely critical; and that its truth is most likely highly dependent on (1) the very idea of democracy, with all the noble and possibly unrealistic sentiments that surround it, and (2) the fact that at present the privileged don't have absolutely all the political power. Therefore, although he may possibly be Repulsive but Right about the shortcomings of democracy and the likely short-term consequences of having a bit less of it, I suspect that in the longer term his faith in the reliability of markets and the virtues of the privileged is Wromantic but Wrong.

Ten moral paradoxes, by Saul Smilansky  ·  Underwhelming; Smilansky is, I think, too ready to call something a paradox when I'd just call it "mildly surprising" or "inconvenient" or "ironic". But aside from Smilansky's tendency to exaggerate the paradoxicality of the things he writes about, there are some nice things to think about here.

Flat Earth News, by Nick Davies  ·  The newspaper industry, says Davies, is hopelessly corrupt: just about all newspapers are now owned by people whose only interest is in maximizing their profits, which means that reporters have no time to research their stories properly and check their facts, and in any case are required to focus on whatever will sell best and cause least trouble; the inevitable result is a press corps easily manipulated by PR firms, governments, and others; so we far too easily see a journalistic consensus that lavishly fails to match reality. This last is what he calls "Flat Earth news". Davies isn't afraid to name names. It all seems pretty convincing, but of course I've got little more reason to trust him than to trust any other journalist on any other occasion...

dangerous

In case anyone was wondering, the Gareth McCaughan who recently killed his friend in a car crash is not me. It seems a fair bet that we're related somehow, but I have no idea how; I don't think I've heard of any other Gareth McCaughan before.

puzzle

In our front garden -- presumably having blown in from someone's rubbish bin -- there is one part of a piece of paper that has been torn in two. On it are the final portions of two words in very large capitals, one immediately above the other. The leftmost letter in each word is only partly present, but in each case there is no doubt what that letter is.

...NCIAL
...ORMA

You'd think the two words might go together somehow, but I'm having trouble thinking of any good candidates. Uncial? Provincial? Norma? Korma? The nearest thing to a sensible combination I can come up with is "financial pro-forma", but that's not terribly impressive.

loop

(Two isn't-my-child-cute entries out of the last three. Sorry. I promise that the next will be something else.)

So, anyway, Heather was counting for some reason or other, and she went: one, two, ..., twelve, thirteen, fourteen, sixteen, sixteen, sixteen, sixteen, sixteen ...

Presumably a broken linked-list pointer triggered by overflowing a 4-bit counter somewhere.

I don't know how you reboot a toddler.

newton

A very happy Feast of St Isaac of Woolsthorpe to you all!

(And also a very happy Christmas, Hanukkah, Kwanzaa, a-few-days-after-the-winter-solstice, Festivus, and Hogswatch.)

pedantry

Child: I want my bunny and Mummy's bear.

Daddy: Do you know where your bunny is?

Child: Yes.

(Pause.)

Daddy: Can you tell me where your bunny is?

Child: Yes.

(Pause.)

Daddy: Please do.

(Pause.)

Child: Bunny is on Daddy's sofa in living room.

Unfortunately Bunny was not on Daddy's sofa in living room, but nobody's perfect.

fraud

Strange.

I got a phone call today from someone purporting to be from the fraud department at Barclays, wanting to talk to Emma. They gave me a number she could call them back at. "And if I check your website, will I find that number there?" "Oh yes. And it'll be on the back of her card, too."

So, I go and check the Barclays website. No sign of that phone number. I look on the back of my bank card (which is the same as Emma's, modulo details). No sign of that number. Uh-oh: phishing?

What saith Google? Well, it found one non-content-free hit for the phone number (since then, writing it in different ways, I've found more; see below): a blog post by Charlie Stross, who as well as being a pretty good science fiction author shows every sign of being sensible and wise. He thinks he was being scammed. The evidence he presents is pretty convincing.

So I called Barclays (not using the number I was given by the Mystery Caller) and after some to-ing and fro-ing got through to their fraud department. And, lo and behold, the person I spoke to there confirmed that they had tried to call me, and that the number I was given was genuine.

On the whole, I'm convinced -- if it's a scam operation then they've successfully subverted either Barclays' website or their phone system, and they've done it in a pretty polished way -- but Barclays do seem to be trying pretty hard to give the impression of being scammers.

Other evidence: 2007-01-10, 2007-09-08, 2007-11..2008-10, 2008-06-05.

The number, mostly so that Google can find it: 0800 389 1652 = 0800 3891652 = 08003891652.

spam

OK, the mystery of the vanishing email is resolved. Speaking of which ...

You can stop BT Yahoo! SpamGuard from automatically sending suspected spam messages to your Bulk folder if you want. It’s hard for us to imagine why you would want to do this, but you’re the boss.

Well, in my case, the fact that (1) I never asked them to turn it on in the first place, (2) if they ever told me they were doing so then I missed it, and most importantly (3) the 25% false positive rate, would be "why I would want to do this". But I can understand that those reasons might be a bit too subtle for the good folks at BT.

Presumably the 25% false positive rate (by which I mean: over 1/4 of the messages in my BT "spam" folder were in fact not spam) is the result of a self-training filter going unstable because, not knowing it was there in the first place, I never went through telling it what messages it had misclassified.

mountain

Good grief.

Then again, if your country's highest mountain is named "Boggy Peak", I can see the appeal of finding an excuse to rename it.

marriage

In the wake of the success of Proposition 8 in California, this has appeared in several blogs (mostly on LiveJournal):

Copy this sentence into your journal if you have ever been in a heterosexual marriage and the idea of same-sex marriage being a threat to your heterosexual marriage is the biggest bunch of shit you ever heard.

I'm not sure I can quite affirm that, just because there's such a tremendous amount of stupidity and silliness out there, but it's certainly a strong contender.

I have long thought that issues like love and sex and religion and fertility are basically none of the state's business, and that its involvement in "marriage" should amount only to having some sort of legally recognized partnership (which might or might not be called "marriage") that people – any people – can enter into, whereby they pool their goods and various other interests. Then those who want the partnership they're entering into to be formally approved by their religion, or marked with special declarations of love and faithfulness, or whatever, can do that in whatever way they find best. (And those who feel that their own marriage is somehow threatened by someone else's can go jump in a lake.)

And, in case it's not obvious, such a partnership needn't have anything to do with love or sex or children, though of course many of them would.

This is a special case of a general principle that seems obvious to me (though I have trouble saying exactly why it should be right, which may be a warning sign): governments shouldn't try to legislate for things they can't reasonably enforce – such as a partnership's really being anything to do with love, sex and children.

(Of course there are all sorts of details that would need to be right, and I'm not going to try to discuss them here.)

mail

Quite a lot of email sent to me (and to Emma) appears to be vanishing without trace. If you've sent anything to either of us and haven't had the reply you expected, please try sending it again. (The problem, whatever it is, appears to strike at random; your next message isn't at extra risk just because your last one got lost.)

Sorry for the inconvenience. I'm looking into the problem urgently and hope it gets fixed soon.

I don't know how long it's been going on, though it seems either to be quite new or to have got worse recently. If you've had suspicions that mail hasn't reached us in the past and haven't already told us, please let me know. Thanks!

Note: The way comments here work is basically that they get mailed to me by the webserver. Therefore, mysteriously unapproved comments should be considered equivalent to mysteriously unanswered emails.

Update, 2008-11-10: evil BT stealth spam filter. Sorted. I've retrieved everything from the last month, but anything before that is lost and gone for ever.

obscure

Memey thing from mathew, Ashley, and Gareth: ten books on my shelves that probably aren't on yours.

1 The elliptic functions as they should be, by A Eagle.

The first chapter is called "Twenty elliptic functions and their forty trig series", and it's all downhill from there. The style is a bit like that of Charles Dodgson's serious writing, earnest italicizations and all.

2 Tuning, timbre, spectrum, scale, by William A Sethares.

Why some notes sound good together and some don't. The answer isn't quite what it's commonly thought to be. See Sethares's website for some more information, including some very interesting bits of music.

3 Told on the air: broadcast stories for children, compiled by Geoffrey Dearmer.

Stories from Children's Hour. Published in 1948.

4 "On", anonymous.

A collection of short articles, mostly on scientific and engineering themes, from "A.E.I. News", the monthly magazine of Allied Electrical Industries Ltd. Published in 1944. The author was, on the whole, wise to remain anonymous.

5 A Christmas Sermon and other essays, by Robert Louis Stephenson.

Just what it says. Actually rather good.

6 Introduction to circle packing, by Kenneth Stephenson.

This is the field in which I did my PhD. I'm cited a couple of times. The book contains some nice mathematics and some nice pictures. Oded Schramm, an absolutely first-rate mathematician who tragically died in September, was a big name in this field before he moved onto other areas of mathematics.

7 Shape, by George Stiny.

Attempts to combine geometry, formal grammars, and aesthetics. I think there's less to it than meets the eye, but maybe I'm just not sophisticated enough.

8 Said or Sung, by Austin Farrar.

A collection of sermons.

9 Universality and the Liar, by Keith Simmons.

"An essay on truth and the diagonal argument". I've had this for years, but either I never got round to reading it or I've now forgotten everything about it.

10 The house that Nino built, by Giovanni Guareschi.

(Actually, this isn't currently on my shelves; I lent it to someone else years ago and haven't chased it up.) Guareschi is better known as the author of the "Don Camillo" books.

I have things on my shelves that are even more deservedly obscure than (e.g.) #1 above, but filling my list with them seemed like it would rather miss the point. I am also not convinced that obscurity and unlikeliness-to-be-on-your-shelves are at all the same thing.

literacy

From an advertisement in the latest TES:

Yup, that fills me with confidence in their ability to assess literacy.

sing

My choir is putting on a "Come and Sing" on the afternoon of Saturday 2008-09-20. Vaughan Williams and (alas) Rutter. Details at the far end of the link in the first sentence. Please come and, er, sing.

While I'm plugging the New Cambridge Singers: we'll be singing Bach's Magnificat in Trinity Chapel on Saturday 2008-11-22. (In the original E-flat version, for those who care.) It'll be good. Please come but preferably don't sing unless you join the choir first.

More consistent notifications of our concerts than you'll get from me are available by email. Let me know if you want to be signed up.

news

I don't normally read the Sunday newspapers, but I was staying with my parents last Sunday and took a look at the papers they'd bought: the Sunday Times and the Sunday Telegraph. Both had about 15 pages of news. The Times had a front-page announcement about Obama/Biden and a short article on some Obama-related subject. Apart from that, every single story in the news section of either paper was UK-specific in some way: mostly things happening in the UK, and a few stories about Brits abroad.

Perhaps there was a separate section called "International News" or something. Even if so: what a parochial notion of "news" these people are working with.

(Probably this is old news to people who read newspapers more than I do. And those wouldn't have been my Sunday papers of choice; maybe some others are different.)