Mastering maths monsters

‘Partial differentiation’ is an important mathematical technique which, although I have used it for decades, always confused me until a few years ago. When I finally had the blinding insight that de-confused me, I vowed to share that insight so that others could be spared the same trouble (or was it just me that was confused?). It took a while to get around to it, but here it is:

My daughter Eleanor make a drawing for it, of a maths monster (or partial differentiation monster, to be specific) terrorising a hapless student. The picture only displays in a small frame at the linked site, so I’m reproducing it in all its glory here.

Andrew Kirk

Bondi Junction, October 2016

Let’s all use the word ‘Interlocutor’ more often

Today is international polysyllablitis awareness day. I hope you can spread the word so that people will better understand this debilitating condition and try to support those that suffer from it.

Polysyllablitis is a communication disability that primarily affects people that read too many fancy books. The main symptom is a swollen vocabulary, leading to frequent difficulty in finding an acceptable word to express a concept they are trying to convey. Such difficulty typically manifests in uncomfortably long pauses mid-sentence, because the speaker was about to say that the proposed expedition to a nightclub would be ‘inimical to his health‘, but didn’t want people to think him a ponce for saying a fancy word like ‘inimical‘, yet the alternatives ‘it would make me feel bad‘ or ‘I’m tired‘ (average syllable count per word = 1.0) refused to present themselves to his desperately searching mind.

For this to happen just occasionally – say every couple of months – is manageable. Many people have such experiences. But people with really serious polysyllablitis (known as PSI to health and remedial vocabulary professionals) can suffer such attacks as often as several times a day. At such frequencies it can become terribly debilitating. Sorry, I mean it makes the person feel really bad.

Chronic sufferers have complained of persistent diffidence (meaning they often feel shy), disorientation (they feel dumb or lost), isolation (they feel lonely) and melancholy (they feel sad).

I have studied this phenomenon (sorry, I mean thing) for many years now. I think there is hope for the sufferers, as long as they don’t get excluded (shut out) from society. That’s why we need this awareness day. If people can keep a look out for others that may be suffering this malady (it makes them ill) they will be able to find ways to help them, reassure them (make them feel good) and put them on the road to rehabilitation (get better).

The best way to help these unfortunates (poor guys) is to include them in your conversations. When they say an unnecessarily fancy word, or get stuck mid-sentence with that look on their face that says they can’t remember the normal-people’s word for ‘lugubrious’*, the best thing to do is to gently correct them, remind them of the normal-person word while making clear that we still love and accept them. (*it’s ‘sad’). Studies have shown that these inclusionary strategies (being nice to them) are in most cases highly efficacious (they work).

However, in my years of study, there is one word for which I have simply never found a way of translating it into normal person speech, and that is the word ‘interlocutor‘ – being ‘the person with whom one is having a conversation‘. I have searched in vain for a simple alternative. The closest I’ve seen is ‘discussant’ but that has the dual problems that (1) it’s ugly and (2) I suspect it’s not a real word.

The next most reasonable alternative seems to be to replace the word with its definition ‘the person with whom one is having a conversation’. But that doesn’t really help much, as that ‘whom’ is bound to raise eyebrows, not to mention the monarchical ‘one’ (sorry – I mean like how the queen would speak). Plus inserting that long string of words into a sentence raises the risk of apparent poseur-ness because of the length of one’s sentences.

‘He’s always interrupting those with whom he is having conversation‘ just doesn’t have the pizazz of ‘He’s always interrupting his interlocutors‘.

I doubt Hemingway would approve.

It wouldn’t matter if it was a useless word, like that silly old ‘antidisestablishmentarianism’ that schoolboys used to quiz each other on, but nobody ever used in a genuine sentence. That was, until the Guinness Book of Records people wanted to get in on the act and invented ‘floccipausinihilipilification’, just so that people would buy their book to find out about the new record-breaking word.

Of course if you want a long word that’s actually used by proper people, it’s supercalifragilisticexpialidocious, which at 34 letters is longer than either of those non-words to boot. Plus it’s used by Mary Poppins, who is cool and not anything like a social reject that got her head stuck in a dictionary, so it must be OK.

But, unlike antidisestablishmentarianism, interlocutor is not a useless word. How can one talk about conversations one had yesterday without using it? More importantly, how can one give counselling and therapy to PSI sufferers if one cannot tell them useful things like ‘try to use the same words that your interlocutors use‘? The word is simply too useful to discard. I find myself needing to use it at least seven times per day on average. I’d be lost without it.

I can only see one way out of this conundrum (tricky thing). That is to make interlocutor an honorary normal person’s word. We could do that by all making an effort to use it at least once a day. Then before long it would seem as normal as ‘but’. There are precedents for this. Normal people use the pentasyllabic ‘qualification’ when talking about who might get into the finals in the footy, and the quadrasyllabic ‘ceremony’ when talking about who earns the right to humiliate themselves in the next round of a reality TV show. So I think, If we all make an effort, we can create some space for ‘interlocutor’ in normal people’s language.

I leave you today with these two requests:

  1. Please keep an eye out for PSI sufferers, and try to be kind to them (and help them to get better); and
  2. Try to use interlocutor as often as is consistent with common decency.

Just remember, no matter how strange and scary they seem, every PSI sufferer is somebody’s son or daughter.

Andrew Kirk

Bondi Junction, October 2016

About smiling

George Orwell said ‘At the age of fifty, everyone has the face s/he deserves’.

I first heard that saying decades ago and for some unknown reason remembered it. I was never very confident about exactly what Orwell meant by it, but I have always interpreted it to mean that if you spend your life being cross you will end up looking like a cranky old wo/man. But if you spend your life smiling kindly, you will look like a kind old person. It goes along with that other old saying, that your face will get stuck with whatever expression you are wearing when the wind changes (or does that rule only apply if you are making a face at somebody?).

If it were true, it’s bad luck for those that suffer a lot of pain or grief in their first few decades. They would end up looking permanently in pain or sad.

There’s not much we can do to avoid pain or grief, but we have at least some control over whether we scowl or smile on those around us.

Orwell’s saying came back to me at around the age of forty. I didn’t remember what the cutoff age was but I remembered that you had to watch out if you didn’t want to end up like Mr Wintergarten or any other fictional old person the neighbourhood children avoided in fear.

I started paying occasional attention to my facial expressions, noting when I smiled. I was somewhat relieved to find that I smiled quite often, partly because my children, who were all below ten years old at the time, often made me laugh or smile at their antics. ‘Thank goodness!’ I thought. I would be safe from ogredom and the neighbourhood children would be free from my future reign of terror.

There are two special occasions when I do my best to smile – they are when riding my bicycle on public roads, and when jogging.

The reason for the jogging smile is that I heard that a famous American public intellectual and wit said something like ‘If I ever see a jogger smiling I might try it‘. For a long time I thought Gertrude Stein said that but now the internet tells me it was actually the comedian Joan Rivers in 1982. I don’t know if others would count Joan Rivers as a public intellectual, but I like to think of Public Intellectuality as a broad church. Anyway, I resented the implication that joggers were a miserable bunch that hated jogging and did it either because, like banging your head against a wall, it feels so good when you stop, or because like an Opus Dei monk wearing a cicatrice, they felt that the pain they were suffering was somehow accumulating points for them in their heavenly bank account.

Fie on you Ms Steinem (yes I know, I get Gertrude Stein and Gloria Steinem mixed up – pathetic isn’t it) I admonished her inside my head. I don’t suffer when I jog. I quite enjoy it most of the time, and sometimes I even love it. But I had to admit she had a point about the smiling. Joggers didn’t tend to smile, perhaps because they were too busy trying to breathe.

So I determined to set the world to rights. I became possibly the world’s first ever smiling jogger. I didn’t smile all the time. It is quite tiring on the facial muscles to maintain a smile for minutes at a time, as any games show barrel girl will attest (some people think that catwalk models look so sulky these days because they are perpetually hungry, but I think it may also be because it is more relaxing to maintain a vacant gaze than a beaming smile). But as soon as a passer-by hove into sight, I lit my face up like a Christmas tree, so they could see just how much fun I was having.

This led to some peculiar looks, and mothers shepherding their children anxiously away from me with worried expressions on their faces.

My campaign of smiling on a bicycle was for a different reason, and met with rather more success. There are a bunch of nasty ‘shock jocks’ in my city that anathematise anybody that expresses any concern for the environment as a Luddite, anti-democratic communist. They save their most virulent hatred for refugees and bicycle riders, in both cases, apparently because they clog up the roads and thereby interfere with the God-given right of every right-thinking person to drive their Land Cruiser down any street at 60km/h plus, unimpeded.

While most people, fortunately, are not influenced by this outpouring of bile, it does have some spillover effects and it did tend to generally increase the degree of hostility between cyclists and motor-car drivers. I thought that if I smiled at motorists that I encountered (or, at least, at the ones that hadn’t just nearly killed me by turning in front of me, cutting me off, passing too close and fast or just blaring their horn at me so close as to make me nearly fall off in fright) I would be doing my little bit to rebuild cordial relations.

I am pleased to report that this little strategy, unlike campaign Joggers-Can-Smile-Too, met with unexpected success. I received plenty of return smiles, waves and other gracious, heart-warming gestures. So, take that, Alan Jones!

For some reason it is also easier, and feels more natural, to smile when riding than when jogging. It might be because riding is after all more intrinsically fun than jogging, because of the whizzing. We all love to whizz after all, and not many of us are capable of jogging at whizzing speed. I used to be able to, but have not been able to for a long time now. Plus, every time one’s foot hits the ground (which is about eight-three times a minute, in case you were wondering), one’s facial muscles all get wobbled about by the shock-wave, making it more than usually hard work to maintain a smile. If you don’t believe me, look at a slow-motion replay of the 100m race in the Olympics and watch what the faces do. Ignore that famous sideways smile photo of Usain Bolt at the Rio Olympics. That was in a semi-final, so he wasn’t really running very fast (for him).

There’s also the fact that, because the air is rushing towards you quite fast on a bike, you don’t need to open your mouth into a big fat O shape to get enough air in. A sweet smile leaves more than enough opening for enough of the rearward rushing air to find its way to the lungs.

After a while, it just became a habit to smile when I was riding my bicycle, at least, when I wasn’t climbing a difficult hill or negotiating a particularly dangerous traffic situation.

So, in between the child-induced smile, the jogging smile and the bicycling smile, it seemed that my face was probably doing what was necessary in order to meet Mr Orwell’s challenge.

Now I am well past fifty, so I suppose I am out of danger. My face has, I suppose, become set in whatever configuration it is to maintain from here on in. The only expected future changes are ever-increasing numbers of wrinkles, perhaps sun-spots and scars from removed skin lesions and a gradual loss of teeth and hair. But can I be sure of that? After all, while Mr Orwell’s skill as an author is beyond question, his expertise as a gerontologist is comparatively unknown. Could he have been mistaken? What if it is sixty, seventy, or even eighty? One cannot be too careful. Perhaps it is too early to stop smiling.

Which brings me to the topic of this essay (better late than never): adolescent and young-adult offspring just don’t seem to compel beaming, helpless smiles from adults in the same way that two year olds do. Of the positive emotions that adolescents can generate (we’ll not dwell on the negative ones), there are affection, pride, sympathy and a number of others but “Oh my goodness that’s so adorable!” is not usually one of them. I presume this has something to do with evolution. We are programmed to find almost every utterance and action of a two-year old adorable, because they cannot fend for themselves and, if we didn’t find them adorable, we might not be inclined to fend for them – which wouldn’t do at all, not if we want them to grow up to be Prime Ministers. But above the age of about sixteen, the fending skills of the human species appear to be adequate, so evolution decided to ease off on the adorability spell. That may be all very well – after all, many adolescents prefer to spend time in any company other than that of their parents, and parents are easier to shake off if they are not following you around with adoring grins on their faces. But how are we to meet our smiling quota in the absence of such an influence? I have a feeling that now I may spend less than half the amount of time smiling that I did ten years ago. I can put some of that down to my mid-life crisis, but I think the partial maturation of my children has to bear some of the responsibility.

What, then, is to be done? One has to find other things to make one smile. But what? That will have to be the topic of another essay.

Ian Dury knew though. He made a list, in his song Reasons to be Cheerful (Part 3).

Ian Dury
Here’s a picture of Ian Dury showing he had not much to smile about, with his grim environment and the after-effects of his childhood polio on display. And yet…….

Dury smiling






Acoustic ‘beats’ from mismatched frequencies

Here’s a piece I wrote explaining the mathematics behind the peculiar phenomenon of acoustic ‘beats’.

It’s a bit maths-y. But for those that don’t love maths quite as much as I do, it also has some interesting graphics and a few rather strange sound clips.

Andrew Kirk

Bondi Junction, August 2016

I think my spaceship knows which way to go

Miss Honeychurch piano

I am re-committing to memory my old piano repertoire which, 25 years ago, comprised somewhat over an hour of music.

Playing complex piano pieces from memory amazes me. Any form of memorised material is impressive, but piano seems weirdest because one doesn’t have to just memorise a melody, but all the chords and counterpointal parts as well. There are usually three to eight notes being played at once, so superficially it sounds as though one has to memorise three to eight separate parts and play them simultaneously. It’s not really that hard (unless it’s a five-part fugue by JS Bach, and I haven’t memorised any fugues yet) because while there may be three notes in an A major triad in second inversion, they are not just any old three notes. They are three notes that nearly always go together. So one can just remember that there’s a triad there, rather than remembering three separate notes.

But still, there’s an awful lot of stuff to remember. I think concert pianists and Shakespearean actors are the most impressive to me in terms of memory feats.

I find it astounding to what extent the fingers – after a fair bit of effort at memorising – just know which notes to play. If you asked me what the next chord was, I could play it, but I couldn’t tell you beforehand what it was. I might even need a run-up to play it, because it seems that playing the chords leading up to it set the context that enables my fingers to ‘know’ what comes next. I know this because if I get lost and have to get re-started, there are only certain points in the piece from which I can start cold.

I have read that it’s really the Cerebellum that ‘remembers’ what to play, not the fingers. But it feels like it’s the fingers.

One can commit a piece to memory either consciously, so that one can say out loud what comes next – what chord it is, which notes and perhaps which of passages A, B, C or D it is in a Rondo structure – or unconsciously, by just playing it over and over from sheet music until it gets programmed into one’s subconscious.

I think it is safest to learn both ways.

Committing the piece to conscious memory is a safeguard against a crisis of faith or a sudden disorientation. Playing unconsciously relies on context to know what comes next and it needs faith so that one trusts one’s fingers to do the right thing. As soon as one loses context or faith – easy to do when under pressure in a performance – one can lose the ability to let one’s fingers do the work.

It is like the art of flying in the fourth HitchHiker book (‘So long and thanks for all the fish‘) or a Roadrunner cartoon where Wile E Coyote accidentally runs over a cliff but only falls when he looks down and realises where he is. You only lose the ability to fly when you remember that it is impossible. Then you suddenly plummet.

There is a very long trill in a Chopin Nocturne that mixes me up because it covers three notes and is more complex than an ordinary trill. I can play it fine, and very fast, as long as I don’t think about it. But because it’s long, I usually end up inadvertently thinking about what my fingers are doing about halfway through and then getting muddled. The last few times I have succeeded in playing it right through without mistake by looking around the room as I play it, focusing on things I see – keeping my mind occupied by anything except what my fingers are doing.

My fingers playing music are like me doing maths. They are very good at it as long as nobody is watching. But as soon as somebody is watching it turns to mud. Young children enjoy tormenting me by sidling up to me and asking me something embarrassingly easy like ‘differentiate x squared!‘ and then staring at me intently so that my brain won’t work (like a watched pot).

But if one also knows consciously what comes next, one can silently tell oneself to play an E flat diminished chord in the second inversion, or to reprise theme B, one octave higher. One knows how to do that, so one does it – no faith required. The conscious brain acts as scab labour to supplant the striking union of the unconscious fingers.

Although both conscious and unconscious memory always have a role to play, I feel that this time I am learning a lot more unconsciously than I did 25 years ago. I can see how much conscious involvement there was in 1991 because some of the scores still have the pencilled notes I wrote on them to help me categorise and memorise the thematic and harmonic structure of each piece. It’s more enjoyable learning subconsciously. But it’s higher risk to do only that, if one has to perform.

I have been finding that, once one has committed a piece thoroughly to memory, it is quite peaceful and meditative to play without thinking about the notes one is playing. One thinks about the music, because one puts the feeling into the piece by variations in loudness and pace, but not about the microstructure of the notes. That is beyond one’s gaze, being taken care of by the fingers/cerebellum.

It is important to keep one’s mind on the music though, otherwise the relentless, angst-ridden chatter of the modern monkey mind comes in to disturb the peace. I can remember occasions of playing pieces in the past, whether from sheet music or from memory, with my mind completely oblivious to the music and instead working philistinically though every grievance, anxiety and obsession it could find, re-running past conversations and projecting future ones at a rate that would make a Boddhisattva wince and that could generate material for at least three psychology PhD theses.

I wonder what concert performers do – whether they do both, or just one and if so which one? Or does it vary between performers?

In case anyone is interested, here are the pieces from the 1991 repertoire, showing which ones have so far been re-learned:

  • Beethoven Pathetique Sonata, all three movements (2nd and 3rd re-learned so far)
  • Mozart C major sonata, all three movements
  • Beethoven Moonlight Sonata First movement (the famous one)
  • Beethoven Fur Elise (re-learned)
  • Debussy First Arabesque (re-learned)
  • Debussy Clair de Lune
  • Chopin Nocturne in E flat major (re-learned)

Mr Beebe would say ‘Too much Beethoven‘.

Mr Beebe3.jpeg

But I will never be able to competently play the fiendishly difficult Opus 111 sonata whose crashing rendition by the troubled Miss Honeychurch prompted those immortal words.

I have vague aspirations to extend the list if I manage to re-learn all of it. I have in mind to do one of Faure’s three lovely impromptus. Given my comment above, I am tempted to also take up the challenge of attempting to memorise a Bach fugue. I probably shall. Sadly, nobody in my circle of friends and family seems to really like Bach fugues. Perhaps he really wrote them for the enjoyment of the performer rather than for the listener.

Andrew Kirk

Bondi Junction, July 2016

Miss Honeychurch piano 2


The Joys of VERY Amateur Music


Although this third movement is less “pathetic” than the preceding ones, the player alone will be to blame should the Pathetic Sonata end apathetically.

Thus writes the author of Schirmer’s Library of Musical Classics, at the foot of the first page of the score of the last movement of Beethoven’s Sonata Pathetique (That’s ‘Pathetic’ as in pathos, ie emotionally moving, not as in contemptible, in case you were wondering). The bold font emphasis was added by me, by the way – it’s not in the original.

Many were the admonitions of this type that one used to encounter in learning, performing and reading about music. I don’t know if such admonitions still abound, but I used to take them very much to heart.

Here’s another gem from the last page of the same movement:

In proportion to the greater or lesser degree of passion put forth by the player before the calando, this latter is to be conceived as a diminuendo and ritardando. Excess in either direction is, of course, reprehensible.

A piano teacher once told me that, while Mozart piano sonatas seemed easy to play, especially the slow movements, they were actually especially difficult because their smooth lightness and sustained notes would ‘expose’ the inadequacy of any player whose touch upon the keys was not delicate and even. I interpreted this as meaning that only an impostor would attempt to play a Mozart Sonata without first obtaining the very highest degree of musical performance qualification possible. Their crime of trying to hide their lack of skill behind the apparent simplicity of the score would be exposed by the very first unplanned variation in pressure ( a ‘plonk’ in lay terms) leading to their justly deserved shame and humiliation and, it is to be hoped, excommunication from any future association with decent, honest, genuine music lovers.

Although I did take this sort of sermon to heart, I nevertheless dared to play sonatas by Mozart. I enjoyed it. But I just had to secretly hope that no true music connoisseurs would ever hear me, perhaps as they walked past the open window of the room in which I was playing, and be goaded into a rage by my lack of finesse – not to mention the unmitigated temerity of presuming to play Mozart. I imagined they would feel it were as though I had reanimated the corpse of Wolfgang Amadeus himself, just so I could slap him in the face and jeer at him.

I don’t think that any more. In fact, I may have swung so far to the opposite extreme that I have to remind myself not to be too intolerant of those poor souls that do happen to be internationally renowned piano virtuosi.

In short, I love amateur music. There is a point at which it may become difficult to listen to, as with a tone deaf singer or the tuneless screeching of a child unwillingly doing their ten minutes a day practice on the clarinet or violin. But short of that (and even that isn’t too bad, but that’s another essay) I find that musical flaws enhance rather than detract from the performance, as long as the player’s heart is in it. Sincerity and enthusiasm is all that’s needed to make a performance truly marvellous.

My youngest daughter will graduate this year from high school, after which I will no longer have a socially acceptable reason to attend performances of school musical ensembles, whose enthusiasm is often in inverse proportion to their skill. What a pity! Like a Persian carpet, where (it is said) the maker always includes a deliberate flaw because only Allah is allowed to be perfect, the flaws in an amateur musical performance are an essential ingredient, without which the performance would lack – I don’t know, maybe ‘soul’?

For ensembles of young children, the many mistakes, constantly varying level of pitch accuracy and plodding pace are, of course, adorable. But my liking for amateur music is not limited to a sentimental fondness for kitsch cuteness. I feel just as warmly about performances by tall, spotty adolescents in rock bands – as long as they have not been stage managed by Simon Cowell and do not have PR agents in tow. What is important is sincerity and enthusiasm. The occasional (or frequent) mistake emphasises the humanity of the performer.

And in any case, a liking of cuteness could not explain my recently acquired toleration of my own mistakes since, if I recall correctly, some biologist or other (was it Richard Dawkins? Or perhaps Francis Collins? I get them mixed up. Goodness knows they have so much in common) has proven conclusively that it is impossible for any individual member of any mammalian species to find itself cute. I’m not talking about pretending to be cute. All humans seem to do that at a certain age. But pretending to be cute is not the same as finding oneself cute. Indeed, it requires a healthy dose of cynicism to pretend to be naively clumsy and inarticulate just to manipulate the emotions of those around you. It must be done with a cold, clear, calculating mind and a total awareness of what one is doing, and leaves no possibility open for being taken in by one’s own deception. Or so I imagine. It is many years since I discarded any hope of garnering positive attention by feigning sweet ingenuity.

I digress. Refocussing: I think perhaps it is the humanity revealed through their imperfections that make amateur performances so valuable. We have had flawless performances available ever since the piano roll was invented. No doubt it is now possible for a computer to produce a virtuoso performance of a piece of music direct from the written score. I’m not knocking that. Even when that is done, we still have the human element provided by the composer. I doubt the day will ever come when a computer can write something like Beethoven’s fifth symphony. And if it does, I may find myself believing that the computer has attained consciousness.

But music is an activity for participation, not passive observation. Even apparently passive listening often involves participation of some sort. If one taps one’s foot, sways a little to the rhythm, or hums along, maybe out loud or maybe silently inside one’s head, one is participating. If that mild level of participation is enjoyable and life-affirming, how much more so when one is fully involved in producing the music? Churches seem to have understood this for a long time, with hymns that all the congregation participates in singing. I also think of the wonderful chants that some African villagers do, and of Australian Aboriginal corroborrees. As I understand it, these are social activities, in which all tribe members participate, rather than demonstrations of skill.

When one is learning to play an instrument or, having learned the instrument, trying to master a difficult new piece on the instrument, it can be disheartening to think that, however much effort one might put in, one will never be able to perform the piece as well as a computer program programmed by a mildly competent computer nerd, regardless of whether they have any musical ability. It is a little sad to think that the role of musical performance could be supplanted by instruments played by computers. My response to such negative thoughts is to remind myself that a critical part of any performance is the personal experience of the performer. It will be many centuries before they can program a computer to not only perform Scott Joplin’s ‘The Entertainer’, but to enjoy playing it as well.

That experience of playing multiplies when one is part of an ensemble. It is especially so in a choir, when one can feel the harmonies with the other singers resonating throughout one’s body.

I think the knowledge that there is an important experience of the performer is part of the experience of the listener too. If we reflect on it, we can feel that the performer is feeling the music and, in a way, communicating to us through the music. It would be different, a less complete experience, if the music were being performed by a (non-sentient) computer and we knew that to be the case.

And that’s why I think international piano competitions are bad! Does that opinion follow smoothly enough from the previous paragraph? No? Well, never mind, that’s how I feel. Like many of my opinions, that particular one (which is only a minor aspect of my overall preference for amateur music) was planted in my head by another. It was a talk given by an Australian that was an internationally renowned concert pianist – I forget their name – about how damaging the world of international piano competitions is to musical appreciation, as well as to the lives that compete in them. Most of the contestants are virtuosos, whose difference in skill can only be discerned by the most experienced of connoisseurs. Yet one person will win and be declared ‘better’ than the others. What nonsense. Perhaps the problem is that there are too many virtuoso pianists and not enough paid jobs for them.

The Berlin Philharmonic is an amazing orchestra and tremendous to listen to. But I wonder whether my daughter’s high school orchestra sounds more like the orchestras that premiered works by Beethoven, Mozart, Haydn or Schubert, than the Berlin Phil. From what I have read, the musicians of late eighteenth century Vienna were poorly paid, possibly ill and malnourished and distracted by the worldly cares that beset the financially insecure. They frequently had insufficient opportunity to learn and practice a new piece – sometimes with score changes occurring mid-rehearsal – and the halls in which they performed were irregularly heated, which would have driven constant variations in tuning. My brother and sister-in-law married in a small, freezing stone church in the midst of a dark Oxford winter. I remember the sounds of the string quartet drifting in and out of tune as they played ‘Jesu Joy of Man’s Desiring’. The pitch went up when an eddy blew warm air from the bar heater towards them, and down when the warmth moved away. When I think about it, I realise that that is probably the way the piece was meant to be played. From what we know of JS Bach, the Leipzig churches in which his pieces were performed were probably even colder and draftier than the one in Oxford. There were no electric bar heaters in 1725.

And yet, even though the premier performances of those works may have been riddled with faults, the audiences still responded with adulation and rapturous applause. They could see past the occasional wrong note, loss of synchronisation and variation in pitch, to the underlying genius and emotional power of the composition, and the sincerity of the performers.

I don’t want to sound critical of virtuoso performers and ensembles. They are valuable too and have a key role to play in the world of music. I have no reason to doubt their dedication and sincerity or their enjoyment of the music they play. It is marvellous to hear every now and then a highly skilled performance of some challenging orchestral work. There are some, like Mahler’s second symphony (‘Resurrection’), that are so gargantuan – in both length and number of musicians and different instruments required – that it’s just not feasible to perform it with anything other than a top-level, fully professional orchestra. But they are not what music is about, just as teams like the All Blacks or Manchester United are not what sport is about. Attending an FA Cup Final or a Super Bowl would be a great experience but, given a choice between never being able to watch professional sport again and never being able to watch my children play sport, or play sport myself, I would give up watching professional sport in an instant. And it’s the same with music.

sbhs music


Standing on one leg. Number One in a series of Adult Amusements

Have you ever been in a meeting or other group activity that was just dragging along, keeping you teetering interminably on the edge of profound boredom? It happens to me quite often.

When children are caught in this sort of situation – such as in church or on a long car journey – they can relieve their feelings by complaining to their responsible adult ‘I’M BORED’ or ‘Are we there yet?

But we poor adults do not have that excellent outlet available to us. Partly because we have no responsible adult to complain to, and partly because people would judge us if we were to blurt out such phrases.

So I thought it was time that somebody came to the rescue of the wretched responsible adults that have to endure these situations. To that end, I am starting a series devoted to equipping adults with the tools to amuse themselves and stave off boredom, when caught in unexciting, unavoidable group activities.

I don’t know how long the series will be – perhaps not long at all. It is, after all, so much harder for adults to amuse themselves than it is for children, to whom everything is new and exciting (until they reach adolescence, when suddenly everything becomes old and beneath contempt).

Here, then, is my first piece of Useful Advice For Bored Adults.

Stand on one leg!

Start by lifting one foot just a little off the floor, and see how long you can keep it off. If you only lift it a tiny bit, nobody will notice, and it may not affect your balance much. You may find you can do it for ages.

Once you’ve mastered that, which might be straightaway, or might take a little while, start increasing the height to which you raise the foot. The higher it goes, the higher one’s centre of gravity is and the easier it is to overbalance.

Don’t overdo it with the high foot. If you raise your foot above your waist, people might start to look at you funny. But kudos to you if you can do that and remain balanced though. I couldn’t do it to save my life.

I recommend that, once you can sustain the foot at near knee level, you move to the next phase, which I think of as the Aboriginal pose. I think that name springs up in my mind because when I was a wee lad, for some reason the pictures we were shown of traditionally-living Australian Aborigines in the outback often showed them standing like this. I am a little nervous of calling it that in a public blog, lest anybody think it disrespectful. That is certainly not my intent. And, since the ability to sustain the pose is an admirable skill, I am hoping that it is not considered disrespectful. It certainly seems no worse, and probably much better, than saying that somebody gave a ‘Gallic shrug’, which seems a fairly accepted (if somewhat dated) turn of phrase that is by no means complementary to our French cousins.

Here’s what that pose consists of: you lift one leg and bring the foot of that leg to rest with the sole against the side of the knee of the other leg. More advanced practitioners may even rest the foot on the thigh above the knee. Rookies may content themselves with resting the foot against the upper part of the calf.

I can do this pose a bit. I find that I can rest motionless for a while like that – maybe up to twenty seconds – then I start having to make lots of little adjustments with my planted foot to try to remain in balance. These adjustments increase in frequency and amplitude until either I overbalance and have to put the foot down, or – magical relief – I re-attain a stable body position. The latter doesn’t happen very often, but when it does, it’s like winning gold at the Olympics! One looks around in triumph, just a little puzzled as to why the others in the group activity haven’t broken out in rapturous applause.

While engaged in this entertainment, I often overhear myself telling myself that not only am I staving off boredom, but I am burning calories, toning my leg muscles, getting closer to nature (really?) and building a much-needed sense of balance. This is based on a total number of scientific studies that was, at last count, approximately none. But I still feel good about it.

Plus, you get to feel like a four-year old for a while.

That’s all for now. Stay tuned for the next instalment – ‘drawing stars’.

By the way, could it be that the reason for standing on one foot in the outback is to minimise the amount of heat soaked in from the hot sand? If so, that sounds like a very sensible arrangement. But whatever the reason, I remember always thinking that traditionally-living aborigines must have a much better sense of balance than we clumsy Europeans.

Oh, and one last thing. Remember to switch feet from time to time. Otherwise you’ll end up getting all asymmetric, like Arnold Schwarzenegger on one side of your body and Woody Allen on the other.

Which would make it hard to find clothes that fit.

Andrew Kirk

Bondi Junction, April 2016