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There’s a Twitter account called Richard Feynman, after the American theoretical physicist and Nobel prizewinner. He was also a renowned pedagogue and many of the tweets from this account are quotes from Feynman on teaching and learning. While his speciality may have been physics, his approach to teaching and learning is universal. For those of us who teach and study music, there are some wonderful Feynman nuggets to inspire and motivate. Here are just a selection:

As you would expect from someone with a mind like Feynman’s, he advocated curiosity and questioning, challenging perceived norms and standard ways of doing things. I particularly like this rejection of rote learning:

And this, which I feel is an excellent manifesto for musicians:

And finally this one, which for me really sums up how, as musicians, we should practice our craft on a daily basis (for “Mathematics” substitute Music):

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Guest post by Rolf Dragstra

The name that can be named

Is not the right name

The way that can be told

Is not the right way.

Laozi

My older son must have been about five years old, when we were riding on a 43 double-decker bus from Highgate Station down the Archway Road. Its sides appeared to be rigidly converging towards the bridge still far below, whose high arch, once having given the road its name, now looked like a tiny loophole hovering over it in the distance. “That’s where we’re going, through there”, I pointed out. “But the bus can’t through there”, he exclaimed, “it’s too small!” Luckily, another red double-decker, the 134, was just overtaking us at the bus stop, and I said: “Watch that one, Adam, it may well go through down there before we do!” And his eyes followed the bus now quickly diminishing in size while descending – eventually slipping way below through the arch, to complete the experiment…

Our bus, taking in lots of passengers, had just about stopped long enough to make this observation possible. By that time, at least subconsciously, my son must have already started to register the shrinking size of a person or a ball or a car moving away from him. But I had alerted his consciousness by pointing towards the tiny arch below, made him aware of a peculiar situation. He was about to become more aware of something he had learnt already. And it wasn’t me explaining it all to him that raised his awareness – it was Adam looking again: his eyes following the dramatically shrinking size of the bus ahead of us, guided by the converging size of the road, the “bridle and rudder” (1) of this experiment in perspective diminution. Looking afresh enabled my son to create a better balance between what he had seen and was seeing now: that apparent sizes continuously shrink and expand very much when things, including ourselves, are on the move.

For all animals, including ourselves, learning is a subconscious process. It starts long before we become aware of it, before we learn to speak, let alone explain things. And becoming aware of ourselves, learning to think things through, does not put an end to it. It’s a lifelong process. Even the eureka moments of our conscious discoveries, often inspired by a gulf of common sense emerging from our memories, have to sink in, as we say. This process of embedding takes time – especially if academically acquired knowledge appears to contradict common sense and past experience…

At any point in our lifetime, the part of our knowledge, which we are, have been, and will become aware of, only forms the tip of an iceberg, or better: a huge mountain forest… First of all, we should become aware of, and respect, that giant mountain on whose shoulders we are standing. And the roots of all its trees are out there. The information is out there. Information is a natural phenomenon. Both the natural and the fabricated world pervade us through perception, through the use of all our limbs and senses. As the pioneer of perceptive psychology J.J. Gibson put it: “Ask not what’s inside your head, ask what’s your head inside of” (2) : the natural world.

Learning is always based on creating a balance between what we do or observe, and what we make of it. A balance between all forces involved: inside out, and outside in. It’s physical, not just about thinking straight, but finding out whether it works, doing it. Il faut le faire, as the French say.

Nature isn’t just the “environment”, as our eyes would have it, and as everyone seems to call it these days. We’re part of it: grew up in it. And our brain is part of it: a muscular organ, physically rooted in all corners of our body, like the crown of a tree. Thus we would appear to be walking trees, whose limbs and organs, like branches and leaves, are reaching out to as much as taking in what’s happening.

I am aware that the tree is only a metaphor. But I’m suggesting it might be a more appropriate one than that of a machine, or a computer.

There always was, and is, one way or another, a lot of computation going on inside the brain. Each time we cross a busy road, we have to estimate the acceleration of an approaching car; the better we get at it, the better we’ve learnt it – and the more casual we go on about it… But we’re not aware of these processes; and do not yet know how we perform all these computations: many ways lead to Rome…(3)

And let’s not talk about virtual worlds either; let’s stick to the real world, for once – not talk about artificial intelligence, but stick to natural intelligence, natural learning:

How do we learn to walk? How the cat, to pounce? How do we learn to swim, or a bird to fly? How does the child’s mouth learn to speak? How does the hand find the right measure of force? How did that girl learn to always put her fingers in the right place while bowing her violin with the other hand? How did I learn to tune pianos?

I had two parallel educations, as an academic, and as a craftsman. I studied philosophy and physics, history of science and the arts – while practicing the skill of tuning and maintaining pianos which my father had passed on to me. Trying to find a balance of touch and tone on those instruments, while trying to maintain a balance of the two strands of my education, wasn’t always easy, but personally rewarding.

At the time of the Archway Road bus ride with my son, when my third education into becoming a father was already in full swing, I was doing research on Renaissance perspective, and was therefore intrigued by Adam’s initial rejection of what linear perspective was all about. Shortly after I got involved with this subject, pondering over Leonardo da Vinci’s Last Supper, I had realised that there was an analogy between scaling and creating the geometry of a visual space, as surveyors and painters were doing, and scaling an acoustic space, as I was doing every time I tuned a piano.

My academic qualification hasn’t made much of an impact on my professional career: bringing up my sons, and, much more so, curing all those ill-maintained pianos in this country, hasn’t left much time for research, writing or publishing. But more recently, a customer of mine whose old Schiedmayer upright piano is in my care, gave me an article published in the Journal of Neuroscience, 29/8/2012.

Julija herself is working in the field, and she told me it contained the first piece of pioneering neuroscientific research on piano tuners.(4)

The research, based on acoustic experiments comparing the performance of piano tuners – differing in years of experience – “with controls matched for age and musical ability” demonstrates that particular parts of the brain are activated, moulded and enlarged during and in relation to years of tuning practice: The “psychophysical task” of piano tuning results in the creation of “precise sound templates”, “encoded and consolidated into memory over time in an experience-dependent manner.” (5) This process of learning is compared to that of taxi-drivers, who, while obtaining and consolidating their spatial knowledge in years of driving, create templates of maps shaping regions of the brain very close by. (6)

Acoustic navigation of tuners within an octave, memorising and comparing the speed of harmonic vibratos created by different musical intervals, is compared to spatial navigation in a jungle of roads. In both cases, the memory bank built up over the years appears to be located in the hippocampus. This comparison of spatial and acoustic navigation took me back to my realization of the analogy between perspective and tuning: scaling the visual, and scaling the acoustic reality. (7)

The result of this research confirms the physical and largely subconscious nature of learning. Although piano tuning seems to be a rather quaint and highly specialised activity, it is, like any other art, definitely embedded in the roots of natural learning. Experience remains the ultimate judge of your work, the routine completion of which does not ask for conscious intervention, unless a problem arises. Empty that head: let ears, hands and memory do the talking. Most communication is still non-verbal…

But the article in the Journal of Neuroscience only looks at what’s inside the head, not what the head’s inside of. There is no mentioning of the cooperation, the creation of a balance: between the ears; the hand of the tuner turning that crank firmly, but very slightly; and the located parts of the brain involved in the process. Only practice makes perfect – but the practice is not investigated here. It’s not about the process, but about its results. But, as Bertolt Brecht’s reading working man asks:

“Caesar beat the gauls…

  Did he not at least have a cook with him?” (8)

The limitation to evidence that can be located in the brain may come with the territory. Yet for the sake of future research and our underlying understanding of reality, it may be wise to look for, and question its philosophical premises – especially if they turn out to be not part of the solution, but part of the problems and traps that are being created. What if Descartes’ dictum: “I think therefore I am” will neither allow us to understand the nature of our existence, nor the process of learning? What if the true nature of the beast cannot be merely understood as a cognitive process?

What if the balance of all agents involved was at the root of natural selection itself?

The agents here not understood – as in Peter Kropotkin’s somewhat romantic theory of “mutual aid” (9) – as creatures or persons working together; but as perceptive organs, or even tiny integral parts of these, cooperating with their natural surroundings: obtaining, processing and exchanging information. It’s out there: it’s not all happening inside heads… Nature produced an ecological niche filled by the brain. And nobody, no brain, nothing became what it is on its own, not even a “selfish” gene.(10) As everyone else, as George Bernard Shaw and H.G. Wells, Charles Darwin was a child of his age. He was well aware of the difference between his concept of “natural selection” – in the context of aeons of evolutionary change; and its ideological misunderstanding – in the context of socialisation and economic competition. “Survival of the fittest” became the metaphor for individual and social success, a principle of education, a philosophical principle: “the way of the world”… Darwin himself did not escape the influence of this abuse of his concept – nor do we, still tied up in the same rat race, long after the decline of the British Empire. (11)

To sum it up: at some point “competition” was identified as the engine of natural selection. Yet any working engine is based on a well-balanced interplay of all its vital parts. Competition itself is, on a deeper level, always based on cooperation…

Metaphor and formula: no scientist, let alone the rest of us, can do without either of them. And when there are not many estimates, rules, equations, there will be all the more metaphors… We need them both, balanced; and apply them both in the right way…(12)

The clockwork was once what the computer is today: they tried to apply it to everything. It was the pinnacle of mechanical engineering in the Middle Ages, and was soon to be used to simulate all sorts of physical activities and operations: by breaking them up into little segments of linear and circular movements. The piano action, for example, is a set of 88 clockworks in a row, simulating the action of hitting the strings of a harp with hand-held little mallets.

Classical mechanics with its mathematical framework laid foundation to physics as a science. The planetary movements were to be described as those of a clockwork wound up by its creator, and eventually, even human perception and thought processes were described in a mechanical fashion. (13) When we get too good at something, we keep using the same recipe, the same metaphors: it’s like a progress trap…(14)

But our brain isn’t a calculating machine – it’s a living organ. And nature isn’t a factory, nor is a hospital a business, or a university a chicken farm, producing degrees like eggs: all these understandings, or misunderstandings, of reality are based on ridiculously false premises. But beware: the ridiculous will become the dangerous, once we stop laughing, and the money is allocated to put the wheels in motion…(15)

“Cogito, ergo sum”? I can feel my heart beat; I sing, I dance, I tune a piano: that’s also how I know I’m around. And all the while, Nature still makes a lot of common sense – probably most of it; and animals and children, from a very early age, are partaking in it…

As a piano tuner, I am inclined to use the term of resonance to describe the balance created in the learning process: all agents involved acting in resonance – not necessarily an acoustic resonance, for that matter.

Something comparable to the power of resonance could strengthen, shape and mould particular parts of our body, when learning a skill: muscles, organs, nerves, the “medial temporal lobe” or the hippocampus.(16) Or even much smaller vital parts…

I am a biased layman, of course – but I will throw my hat into the ring, anyway.

And it wouldn’t make me wonder if this did not just apply to the navigational skill of taxi-drivers and piano tuners – but to all skills we, like all other creatures, pursue with a vengeance. They have been, are and will be shaping our mind and body.

Like the tune played on a fiddle, or a temperament put on the scale of a piano:

We are making ourselves up as we go along, always have been, and always will be.

And what the scientists investigating my skill have impressively demonstrated is that we have to give ourselves time, allow for the information we process – including all we learn academically, I would add – to sink in: take root in the backhand of our memories; memories also of all the mistakes we made, without whom we would not learn anything. It all happens over time, “in an experience-dependent manner”. “Experience is the mother of wisdom”, says Leonardo. (17)

With so much useless or misleading information bombarding us these days, whether “science, non-science or nonsense” (18), we can’t be mindful enough. My father’s soft-spoken warning is still ringing in my ears: “Some never learn, others later still”…

Notes:

1) Leonardo da Vinci, Treatise on Painting:

“Perspective is the bridle and rudder of painting.”

2) James J. Gibson, The Senses Considered as Perceptual Systems, Boston 1966, p. 21; and W.M. Mace, James J. Gibson’s strategy for perceiving: Ask not what’s inside your head, but what your head’s inside of, in: R. E. Shaw & J. Bransford (Eds.), Perceiving, acting, and knowing, Hillsdale, New Jersey, 1977.

3) And Neuroscience has taken the lead in exploring them: Stephen Pinkers How the Mind Works, 1997, was and still is a revelation.

4) Sundeep Teki et al., Navigating the Auditory Scene: An Expert Role for the Hippocampus, in: Journal of Neuroscience, 29/8/1912, pp. 12251-12257.

5) Ibidem, p.12251

6) Maguire et al., Navigation-related structural change in the hippocampi of taxi-drivers, Proclamations of the National Academy of Science, vol. 97, USA 2000, pp. 4398-4403.

7) It was the late Prof. E.H. Gombrich who pointed out the limits of this analogy to me: “There are no octaves in optics”…

8) Bertolt Brecht, Fragen eines lesenden Arbeiters, Moscow 1936. Brecht is in exile in Denmark at the time.

9) Peter Kropotkin, Mutual Aid: A Factor of Evolution, London 1902

10) Again, a metaphor introduced in 1976 by the young Richard Dawkins, which may not have been the best choice for what he was trying to say. Or, as Andrew Brown, The Science of Selfishness, 22/12/98 (Salon, book review) puts it: “Selfish”, when applied to genes, doesn’t mean “selfish” at all. It means, instead, an extremely important quality for which there is no good word in the English language: “the quality of being copied by a Darwinian selection process.” This is a complicated mouthful. There ought to be a better, shorter word—but “selfish” isn’t it.”

11) Less than the first two, Darwin also shows a certain affinity to the ideas of eugenics, which were quite popular in Britain and other parts of Europe and the United States at the time…

12) Around 1800, when the triumphs of experimental physics are popularizing the scientific endeavour around Europe, the German writer, playwright and publicist Heinrich von Kleist put it this way:

“Metaphor and formula: those who understand both of them are small in number – they don’t make up a class.” In a distich, musing about gravity, he observes the stability of a stone arch standing the test of time: “because all stones want to fall together”… Poetry – of the romantic period! – isn’t always “romantic”: the metaphors of poets observing nature are often much more precise than those chosen by scientists themselves…

13) The mathematical framework of Classical Mechanics is Analysis, as devised by Isaac Newton and Gottfried Wilhelm Leibniz; the eminent French mathematician, physicist and astronomer Pierre-Simon Laplace imagines God as the great clockwork custodian, and the German philosopher Immanuel Kant, in his Critique of pure Reason, analyses the cognitive processing of perceptions in metaphors borrowed from his thorough understanding of Newtonian mechanics and its mathematical foundation: the result almost reads like the action of a film camera at work – long before the actual existence of such a device…

14) Ronald Wright, A Short History of Progress, Edinburgh 2006.

15 E.H. Gombrich, On General Knowledge, in: Ideas and Idols, Oxford 1979.

16) Sundeep Teki et al., p. 12256

17) Leonardo da Vinci, Treatise on Painting

18) Martin Kemp, Science, Non-Science and Nonsense: the Interpretation of Brunelleschi’s Perspective, in: Art History 1, 1978, pp. 134-61

Rolf Dragstra was born in 1952 in Germany. His father was a piano master builder, with a workshop in which he overhauled and restored pianos and other keyboard instruments. That is how and where Rolf picked up his first tools and tricks of the trade, alongside academic studies in physics, philosophy, history of science and the arts. During the 1980s he worked in Berlin as a piano tuner and technician, and author of radio dialogues. In the 1990s he undertook post-graduate studies on Leonardo da Vinci at the Warburg Institute, University of London. From 2000 to 2010 he worked as head piano technician in London’s oldest music shop (Yamaha Music, formerly Chappell of Bond Street). Now self-employed as a busy piano tuner and technician, he has also started writing again.

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Some years ago, before I resumed playing the piano seriously and started taking lessons again, I would open a score, look at the forest of notes and think “I’ll never be able to play that!”. I’d visit my friend Michael, who owns a beautiful Steinway B (purchased when he retired, instead of the clichéd sports car), see Schumann’s Kreisleriana open on the music rack, and my heart would sink. “I’ll never be able to play that!”.

There are certain pieces which represent the high Himalayan peaks of the piano repertoire: the Rach 3, Liszt’s Transcendental Etudes, Ravel’s Gaspard de la Nuit, Balakirev’s Islamey, Chopin’s two sets of Etudes, to name but a few. Pieces which have become the preserve of the virtuoso pianist to showcase technical prowess and extreme pianism. We probably have Franz Liszt – he of the famously difficult Transcendental Etudes – to thank for the elevation of the pianist from salon ivory-tinkler, providing a pleasing accompaniment to drinks, supper and chat, to onstage superstar whose pianistic pyrotechnics caused ladies to faint and piano strings to break

About 18 months into my study with my current teacher, I heard Chopin’s Etude in C sharp minor, no. 7 from the Opus 25, on Radio Three’s Breakfast show, and was instantly entranced by its melancholic tone, the singing left hand cello-like melody (this Etude is nicknamed “the cello”), the floating chords in the right hand, in which the simplest secondary melody is embedded. I downloaded the score from Pianostreet and started to learn it. Eventually I performed it at a concert at my teacher’s house last year, and also on a 1920s Bluthner owned by Sir Alfred Beit, at Russborough in County Wicklow. “I can play a Chopin Etude” I told myself, when my confidence needed a boost. I felt I had at last entered that exclusive Himalayan club.

Playing the Russborough Bluthner

My teacher then suggested another Etude, this time the E major from the Opus 10, a piece I had always wanted to be able to play. This is one of the most famous of Chopin’s Etudes (along with the ‘Winter Wind’, the ‘Revolutionary’, the ‘Black Key’, the ‘Aeolian Harp’ and the ‘Butterfly’), which adds an extra degree of difficulty in the learning process. As my teacher said, “It’s so famous, and you want to play it well”. Aside from the dread sixths in the middle section (which, once analysed, unpicked, and put back together again, are not so fearsome – there is a pattern, yes, really!), it’s not as hard as it looks. Oh, all right, it is pretty difficult – allowing the right hand melody to sing above the accompaniment and achieving balance between the hands being the chief issues of this piece – but it is certainly not insurmountable, and my teacher would not have suggested I learn it if she did not think I could cope with it. This massive boost to my confidence has enabled me to go on to learn one of Chopin’s Ballades (the first, in G minor), some pieces by Liszt from the Années, and one of Messiaen’s Vingt Regards. Waiting patiently in my score library is Chopin’s Polonaise-Fantasie Opus 61, one or more of the Scherzi, more Liszt, Hindemith, more Messiaen…. Now, when I open a score, I do not immediately react negatively: “I’ll never be able to play that!” has been replaced with “OK, where do I start?”.

Analaysing the score, going through it with a pencil, looking for patterns and sequences, listening to other people playing it, and general familiarity with what the printed page looks like before you all assist in learning. There is also a physical-versus-mental aspect: convince yourself on first sight of a new piece that you can’t play it, and you probably won’t. But sit down and sight read through it, get your fingers round the notes, enjoy the architecture and melody of the piece, spend time with the music, inhabit it, and quite soon it will become familiar; eventually it will be like an old friend (which is how I feel about the Messiaen now, despite finding it utterly terrifying for the first few months of learning it!).

There are other practical considerations, of course. Some music is physically very difficult or tiring to play, although I dispute the claim that you need big hands to play Liszt or Rachmaninov. You don’t; just a strategy for getting around the music efficiently and comfortably. Some pieces do not lie comfortably under the hand; others are simply exhausting to play and sometimes one is practising only to improve stamina.

Young students often lack the confidence to pick up music on their own, without a teacher’s help to guide them through the score. When I start a student on a new piece, we go through it together. I ask the student to highlight any signs or terms they don’t understand, to mark patterns and sequences, and to generally take the music apart and separate it into manageable chunks. Thus, a page of score which at first appeared daunting can be quickly simplified, making the learning process easier. Of course, many young students want to be able to play the piece straight through, preferably loud and fast (!), and find the crucial detailed study dull and arduous. But working in this way reaps huge rewards: I find I can learn – and retain – music much more quickly now, and “tricks” learnt from, say, a Chopin Etude, can be applied to other music. The “dread sixths” passage of the Opus 10, No. 3 enabled me to devise a simple strategy for a similar section in Liszt’s Sonetto 123 del Petrarca. A case of “Well, hello! I’ve seen this before!”.

The piano repertoire is vast, hugely varied, and wonderful: don’t discount certain pieces because you think you’ll never be able to play them – but remember: sometimes the simplest pieces are the hardest!

Chopin, Etude Opus 25, No. 7 – Murray Perahia

Liszt, ‘La Campanella’ – Jorge Bolet

Mozart, Adagio for Glass Harmonica

Berezovsky plays ‘Islamey’

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“Practise a tricky section five times. If you make a mistake, go back and start again. Play it perfectly five times, and you can consider it “done” and then move onto the next thing….”

This is a mantra oft-repeated to my students, most of whom greet such useful, teacherly advice with much shrugging of shoulders and rolling of eyes. One or two remember it, and so when I ask them how they intend to practise a problem area, they will repeat my mantra back to me. I assure them that I also use the same dictum when I am practising, but they don’t always look convinced!

In reality, I probably practise a tricky section many more than five times at one sitting, but the “five times rule” is helpful in keeping me focussed when a problematic passage is beginning to frustrate. “One more go and you can move on…” I mutter to myself as I repeat that same passage for the nth time and wonder if I will ever permit myself to move on to another section. Sometimes, when I’ve been practising the nasty bits of the Chopin Op 10 no 3 Etude over and over again for nearly an hour, I treat myself – and my neighbours who are probably forced to listen to the tedious repetitions – to a complete play-through of the piece. This is not just self-indulgent wish-fulfilment, where I hope that everything will fall into the right place at the right time; it also serves a practical purpose – to check that what I have been practising really has been taken in by head and hands.

Repetitive practise breeds familiarity, not just with the music open on the rack in front of you, annotated with all sorts of very personal markings, fingerings, reminders and hints which become crucial signposts on the map (pink dots to highlight to remind me to pedal carefully, the words “WATCH IT!!” in bold, gestural strokes, exhorting me to keep focussed in a passage where my attention is liable to wander to check what my hands are doing, causing me to lose my place in the score), but also with the landscape of the keyboard and the physical sensation of the notes under the fingers. Repetition informs muscular memory, enabling the fingers to fall in the right place more often than not, and, eventually, one hopes, every time. Learning the patterns, the feel of a particular passage as well as the sound, all contribute to the overall process. In time, all these ‘learning components” come together, and one can enjoy that special moment when everything seems to slot into place and you play as if standing back from the music momentarily, playing at arm’s length, as it were. I love this sense of disengagement, of watching myself play. I feel it sometimes when I’m swimming, or running – a rare, special synergy. Yet, as my teacher pointed out when we were discussing it once, it is at this point that the mind and body are fully engaged, concentrating fiercely.

Even though I tend to employ the same strategies for learning new work, it never fails to amaze me how an hour of going over the same passage again and again can result in noticeable progress along the sometimes steep learning curve. There are times too, though, when a passage repeated again and again just fails to “go in”. I remember feeling this with a short piece by Delius I tried to learn last winter. It was a gorgeous piece, but full of bear traps to trip up the unwary, and it always felt awkward under my hands. However hard I tried with it, it never felt comfortable, and in the end, I reluctantly had to admit defeat and set it aside. It is rare, these days, for me to give up on a piece of music, but sometimes even the “five times rule” fails to achieve the desired outcome.