What I Talk About When I Talk About Running – Haruki Murakami

I am a runner.  One of the most frustrating things about lockdown has been the postponement and then cancellation of marathons and half-marathons.  (It’s the ‘not knowing’ that gets you!)

There were cheers in our house when, early in lockdown, the Prime Minister announced that daily outdoor exercise would be permitted (if we had taken an Italian or Spanish approach then I would have had to trot around the edge of the garden, which wouldn’t have been good for the flowers).

I read the brilliant 1Q84 by Murakami several years ago.  I only discovered last week that he was not only a runner but has written about running too.  While we were staying with family I found “What I Talk About When I Talk About Running” on a bookcase and read it in one sitting.  It’s short and easy to read.  The style reminded me of Vonnegut, but without the slightly creepy undertones, the science fiction and the repetition that are a feature of Vonnegut’s work. 

He writes about running, about life, about his life and background and about disappointment and achievement.  This struck lots of chords with me: I don’t run to break records (as if!), but to beat _me_.  I am still improving (having only taken up running four and a half years ago). At some point I will have to come to terms (as Murakami has) with the idea that I will be getting slower as I get older (not yet, though!).

This book works for runners and for non-runners, although those who run will recognise lots of references and things that ring true for them.

The Curious Incident of the Dog in the Night-time – Mark Haddon

Somehow I have never previously read this.  (I lent my copy out before reading it, and only got it back a decade later.)

No spoilers in what follows.  There is lots of maths, explained clearly through the voice of the lead character, 15 year-old Christopher.  The chapter-numbers are prime numbers.  There’s a good explanation (after a complicated one) of the Monty Hall Problem (*).  There can’t be many best-selling young-adult novels that have a mathematical proof question as an appendix. And I spent most time thinking about (and playing in Excel) with a formula for population change which, depending on the value of lambda, becomes chaotic. 

There’s also a story, and it’s a good one too.

So: an easy, quick read, with some interesting maths to think about.

(*) Incidentally, this was referenced in Alex Bellos’ Guardian column yesterday.  He introduces a new variant on the problem.  I spent the whole day thinking about it – and finally got there.  Do have a go: https://www.theguardian.com/science/2020/aug/24/can-you-solve-it-win-the-car-dodge-the-goat

It is possible to get a probability of over 50% !

Music: A mathematical offering – David Benson

This book was a gift from a former student and, to my shame, I hadn’t got round to reading it until this summer.  It took a while (even after I had started!).

It’s a fairly academic book about the maths behind music. 

I was expecting to read about patterns made by sand on drumskins, tuning-systems, Pythagorean commas, etc, and while these did feature, there was so much more too. 

The Musical Offering

To start with, having some musical knowledge was useful.  The title, for example, is a play on the title of an extraordinary work by JS Bach (The Musical Offering).  Frederick the Great, King of Prussia asked Bach to improvise on a melody which the King provided (and perhaps composed).  Bach later wrote a collection of variations on the theme, including pieces where you can play the music forwards and backwards simultaneously, or with one part at half the speed of another, or in mirror image, and culminating in a 6-part fugue.

Pythagorean comma 

The Pythagoreans knew about music and vibrating strings.  They knew that an interval of an octave corresponds to a ratio of 2:1 (nowadays we would say the frequency of the note is doubled) and a perfect fifth is 3:2 (these values can be used to create ‘harmonics’ on a guitar or violin).  On a piano, if you go up in fifths, it takes 12 of them before you arrive back at the same note (seven octaves higher than where you started).  For example:

C – G – D – A – E – B – F# – C# – G# – Eb – Bb – F – C

This should mean that 1.5 (from the ratio 3:2) to the power of 12 is equal to 2 (from the ration 2:1) to the power of 7 (because that final C is 7 octaves higher than the initial one).  Unfortunately it doesn’t:

1.5^12 = 129.746…, while 2^7 = 128

The discrepancy is known as a ‘Pythagorean Comma’. 

This comes about because of the sleight-of hand where G# moved up a fifth to make Eb.  On a keyboard we have to treat G# and Ab as being the same note – whereas in this perfect Pythagorean world they are different notes.  If we continue to go up in fifths, remaining with sharps (rather than switching to flats) we get:

C – G – D – A – E – B – F# – C# – G# – D# – A# – E# – B#

Again, keyboard players would see B# as being identical to C natural, but in fact (as the Pythagorean comma tells us) it is a little higher than the C.

It doesn’t matter if we decide to go down in fifths: the D-double-flat we end up on is lower than the C natural it is deemed to be equivalent to.

And it doesn’t matter if we go up in perfect fourths (ratio 4:3).  12 of them gives 31.569, which is less than the 5 octaves value of 32.

Even a major third is unhelpful.  The ratio is 81:64, and three stacked major thirds ‘should’ make an octave (C – E, E – G#, Ab – C – but there’s the sleight of hand with G#=Ab again).  (81/64)^3 = 2.027…, which is a shade above 2.)

Back to the book!

Lots of cool stuff like this, which I could understand and which taught me lots of new things. 

Some almost incomprehensible (to me) stuff.  I did struggle through the chapter on Fourier Theory, but was relieved the author said this could be skipped!  Here’s a sample:

 

And some lovely stuff about transformations, wall-paper patterns, etc.  See some neat symmetry here:

In summary, if I didn’t have any prior knowledge at all I probably wouldn’t have finished it.  And clearly it is aimed at those in the intersection between maths and music (without one or the other you probably won’t get much out of this).  I did glaze over at the extent of the calculus that was involved.  But I learned some cool new things too. Worthwhile.

The Definitive Biography of P.D.Q. Bach – Peter Schickele

Somehow I managed to miss out on PDQ Bach when younger, but having recently heard his ‘1712 Overture’ and his ‘Unbegun Symphony’, I bought the book.  It’s a very clever biography, a, if will, “baroqueumentary” about the last (“and most definitely the least”) of JS Bach’s 21 children.

No pun is avoided, no potential joke is missed, and it is all put together brilliantly. Even the forced jokes work. (PDQ is apprenticed to a chap who amazed the locals by playing the musical saw while dancing jigs.  When the astonished audience finally worked out how he did it, a newspaper headline followed: “Jig-saw puzzle solved”.  The chap could only play the saw in one key, though.  Obviously it was a ‘C-saw’.)

The musical jokes are clever and most unexplained.  PDQ wrote a harpsichord piece where the stave for the left hand curves up and crosses over the stave for the right hand.  The joke is that this “invertible counterpoint” actually makes no difference at all to the sound of the music.  This is a nod to the ‘Musical Offering’ by JS Bach, where he doesn’t some utterly astounding things with countermelodies to the royal theme provided by Frederick the Great of Prussia.  My favourite is the Crab Canon, where Bach continues and extends the melody.  The melody works when played backwards.  It also works if you play the forward and the backward version simultaneously.  As I say – astounding.  In other movements the melody can be played as normal and at half-speed simultaneously.  This sort of thing possibly influenced PDQ Bach to create a piano sonata which, when turned upside down and reflected in a mirror, is actually a Mozart sonata. 

Piano duets with two performers playing the same instrument are often described as being for “Piano – 4 hands”.  PDQ Bach wrote the only known Sonata for Viola – 4 hands, featuring two people playing the same viola.  Genius!  Other works include Fanfare for the Common Cold, the Toot Suite, and the Canine Cantata: Wachet Arf!.  By far the most excruciating (no mean feat, given some of his other compositions) is the Pervertimento for bagpipes, bicycle and balloons (and string orchestra).

The genius continues into the appendices, where a Two-part Contraption (JS wrote lots of two-part inventions) is given a formal analysis. This is brilliantly done and features utter rubbish presented as if genuine (reminds me of some of my A-level analysis essays).  A phrase lasting a single bar is played in canon and then repeated in different octaves.  When the ‘theme’ is played at the fifth, it is treated as a new theme (because it only features two notes from the original theme), the ‘modulation’ of the piece having occurred during a beat’s rest. 

Genius writing.  Lots of fun to read.  Probably works best if you know a bit about classical music and/or about JS Bach.

(PS the line about the “Baroqueumentary” is mine, not from the book.  Best thing I have ever written, I suspect.)

Enigma – Robert Harris

I hadn’t planned to read another Robert Harris novel, but I found this while tidying up a cupboard in school and re-read it (probably for the third time in the past 20 years) in an evening.  

I had forgotten some of the intricacies of the story.   We usually take Year 7 to Beaumanor Hall in Leicestershire for their activities week at the end of the summer term – and this was one of the intercept stations in the novel.  Jericho and Hester visit it and glean some vital plot-point information.

A number of nice bits of logic in the book – and obviously Turing and the early computers are a key element. 

(p384) “What was it Hardy had written? That a mathematical proof, like a chess problem, to be aesthetically satisfying, must possess three qualities: inevitability, unexpectedness and economy; that it should ‘resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way’.”

I’m sure I’ll read it again in another 5 or 6 years…

Mother Tongue – Bill Bryson

I love Bryson’s books. The ones I have read are entertaining, they wear their author’s erudition lightly, include lots of great anecdotes and deploy well Bryson’s intimate knowledge of the US and the UK.  

It has been years since I last read this one, subtitled: “The Story of the English Language”.  Published in 1990, it hasn’t aged particularly well.  That is perhaps an unfair comment, given that (p136) Bryson quotes someone taking issue with the NY Times’ decision not to switch from the 1934 edition of a dictionary to the then-newly published 1962 version: “Anyone who solemnly announces in the year 1962 that he will be guided in matters of English usage by a dictionary published in 1934 is talking ignorant and pretentious nonsense”.

The time between 1934 and 1962 spans 28 years.  Bryson’s book was published in 1990, which is 30 years ago.  So we would expect the linguistic world to have moved on a little.

It still makes uncomfortable reading to see how Irish words are derided for the lack of sound-writing link, native American words are considered to have far too many syllables and the Chinese and Japanese languages are regarded as incomprehensible.

Then there is the Western-centric nature of some of the writing.  Writing about Australia (p103) Bryson says: “When the first inhabitants of the continent arrived in Botany Bay in 1788 …”.  Presumably these “first inhabitants” were news to the pre-existing aboriginal population, who rate a mention two sentences later: “Among the new words the Australians devised, many of them borrowed from the aborigines, were billabong for a brackish body of water, didgeridoo for a kind of trumpet [...] and of course boomerang, koala, outback and kangaroo.”

So according to page 103, the Aboriginal population were not “the first inhabitants”, were not “Australians” and “lent words” to the European settlers who then “devised” their own “new words”. 

Seen through the prism of 2020, this looks incredibly dated.  And it’s odd for me, because I remember 1990 well!  I don’t recall when I last read this book, but it didn’t strike me as offensive then. 

It is also dated in the lack of usage of computers and the internet.  For example, graduate students were deployed to count occurrences of certain words, and no-one was absolutely sure how many different words were used by Shakespeare.  A computer program would do both of these very straightforwardly today.

The good parts?  Bryson writes very entertainingly: he is happy to go off on an excursus and takes any excuse to deploy an anecdote (which is good news for the reader – they are good value).

He also gives the reader some credit for their intelligence.  He exemplifies Esperanto and earlier versions of English using texts he is sure people will recognise (such as the start of Genesis, or the Gettysburg address).

Bryson seems to me (someone who doesn’t know about linguistics) to be very knowledgeable about related words, pronunciation, spelling, grammar, etc. He pulls some good misspelling-related gags.

His closing thesis that US English and British English will get closer together has, I think, been proved right, largely due to the continuing convergence of culture, prompted by the internet and by the ready availability of music and movies.  (I didn’t consciously choose the word ‘movie’ over ‘film’ here, but I now find myself talking about the “seasons” of a programme on Netflix, rather than its “series” as I would have done 5 years ago.)

Overall, it’s still entertaining, but it would be worth a rewrite to bring it up to date (both in terms of how it views the non-American/Brit and in terms of the language used).  But maybe Bryson has other, interesting things he wants to write about instead.

Prisoners of Geography – by Tim Marshall

This covers politics, history and geography, focusing on the effects on the development of a county of being a continent/island/landlocked/joined/separate/etc. 

There are lots of good stories, lots of interesting ideas and facts and it’s an interesting way to get to know more about some current conflicts in the world.

As with all books about current scenarios, there is a risk it will go out of date.  For example, it is confidently explained that while there are ongoing territorial disputes between China and India, this won’t turn into war largely because of the mountains on their shared border.  I read this only a few weeks after border skirmishes between the two armies were widely reported.

It may seem unbalanced that while Western Europe is the focus of one of the 10 chapters and Africa another, the much smaller area of ‘Korea and Japan’ also have a chapter.  This seems fair enough though, because it is not trying to be comprehensive and is aimed at the non-specialist.

It was interesting to learn more about the struggles of countries that are mentioned rarely in the news (such as Pakistan: with continuing tension with India and the north of the country essentially not under governmental control).  There is also a constant reminder of the mess that colonialism left behind it (in Africa, in Israel/Palestine, in India/Pakistan/Bangladesh).

The only negative for me was an unfortunate over-precision in numbers. We read (p221) of China “supplying 84.12 per cent of North Korea’s imports and buying 84.48 per cent of its exports” in 2014.  While this is referenced, it would seem far more sensible to round these off to 84%.  While a minor quibble, this sort of level of precision is off-putting (particularly given that earlier on the same page it was stated, much more sensibly, that there are “almost 30,000” US troops in South Korea).