OnTeaching the Unteachable
p 1 initial problem → ts trial solution(s)
→ e e process of error elimination applied to the attempted solution(s) → p 2 and resulting problem(s)
Bryan Magee, Popper (Glasgow: Collins, 1973; Fontana Modern Masters), p 20. It is said that one of Popper’s greatest achievements was to offer an acceptable solution to this problem. Strikingly, some of Popper’s seminal ideas (such as those about dogmatic and critical thinking) were an outgrowth of his interest in music. His bold ‘Speculations about the Rise of Polyphonic Music’ are remark-
able, regardless of whether or not they are historically correct. For him, polyphony is ‘possibly the most unprecedented, original, indeed miraculous achievement of Western civilisation, not excluding
science’. Unended Quest, pp 55–60.
The same could be said about practically any other aspect of musical interpretation, so long as we approach it from a strictly rational standpoint, that is.
Even after trying many ideas (including imagery), I still found the first burst of fast notes (and the ensuing analogous one) next to impossible with the printed fingering (upper stave), until a somewhat unusual option (the ‘delayed’ action of a left-hand slur along the fourth string, with 3 on the C slurring down to pro- duce the B
b
) crossed my mind and surprisingly turned out to be a highly effec- tive and reliable alternative (lower stave).In the light of such experiences, in which we find ourselves refuting our own conjectures or ‘breaking the rules’ (by using an atypical slur, for example), Pop- per’s path-breaking idea of falsifiability – instead of verifiability – clearly sets it- self as the only logical criterion of demarcation between science and non-science:
Once we realise that all scientific statements are…conjectures, and that the vast majority of these conjectures (including Bacon’s own) have turned out to be false, the Baconian myth becomes irrele- vant…we question nature…and try to elicit from her negative an- swers concerning the truth of our theories: we do not try to prove or
verify them, but we test them by trying to disprove or to falsify them,
to refute them…Nature very often resists quite successfully, forcing us to discard our laws as refuted; but if we live we may try again.
Now while nature’s unequivocal no is discernible to the intellect, only our intu- ition can hear its imperceptible yes. Indeed, as creative musicians we sometimes reach a point where it is no longer possible to say about our fingerings that they are mere approximations to truth. Nor could anyone claim (as Popper so fit- tingly did about our positivist beliefs in natural laws) that they ‘cannot have a safer basis than our unsuccessful critical attempts to refute them’. The reason is that an artist’s best doings stem from the surest basis imaginable, namely, his po-
etic wisdom, which allows no room for uncertainty. Popper himself admitted the
possibility of arriving at absolute knowledge, even if he regards such certainty as metaphysical, hence untestable and non-scientific, but not necessarily untrue, meaningless or useless, as positivists would contend. So what real musicians are after is creative (rather than unquestionable) fingerings – and by extension, cre-
ative hand movements, creative methods of tone production, creative phrasings:
in short, creative musical interpretations.
Explaining the Inexplicable
When beginners are first introduced to the basic notions about source, quality and quantity of physical motion, or when they come to refine that knowledge at any later stage, it becomes evident, as F.E. Sparshott points out, that if we merely show the appropriate movements and say, ‘Do it like this’, they must grasp what- ever it is about our movements that makes them like this. And in the vast ma-
V V F 24 i œ cresc. m œ 4 i œ b bœ1´ IV Uneasy (slow q ) 4 3 p œ i œ 3 1 m œ b bœ´ ‰ Œ œ œ œb œ ÿ ‰ œ œ œ œ ÿ
‰ Britten, Nocturnal, ‘Uneasy’, bar 1.
Popper, Conjectures and Refutations, pp 138, 192 & 48.
This example is a good instance of the point I tried to make earlier about solving musical and technical problems together. Indeed, it is irrelevant whether you start from one end or the other, as long as we solve the one and only problem. In this case, it was a fingering that triggered the solution.
Ibid. p 57.
‘Only in our subjective experiences of con- viction, in our subjective faith, can we be “absolutely certain”.’ Popper, The Logic of
Scientific Discovery, p 280.
F.E. Sparshott, ‘Education in Music’, section vii, in The New Grove Dictionary of
Music and Musicians, ed. Stanley Sadie
(London: Macmillan, 6th edn, 1980), vol. 6, p 55.
jority of cases, students will require a minimum of explanation. But can we ac- tually rationalise and elucidate what it is that makes our movements like this – especially if they have taken several decades of playing to become what they are? Of course, there can be little point in trying to explain more than a problem de- mands, and the attempt may even end up in a ‘paralysis of analysis’. On the other hand, the reality of how we play is always richer than the ideas we have about it. What is more, we can so easily mistake what we do for what we think we do, or falsify by contaminating our hands with the self-conscious look of move- ments that are being looked at. But let’s imagine we are dealing with an eager, advanced, and highly rational student who demands an unequivocal account of, say, how left-hand shifting works. Perhaps we could try yet another exercise of rationalism and see how far we get. In the sequence below, a is a cause that leads to an effect b, and the arrow represents their physical and tangible connection in time and space:
For example, if you have a billiard ball and you want it to hit another ball, the trajectory of the first ball and the effect of hitting a second ball is an observable and, to a considerable degree, predictable event, because the motion of a can be accounted for in terms of Newton’s mechanical laws and our ordinary sen- sory experience. And when it comes to shifting, the situation might be seen as essentially the same: one’s left hand is in one place, and it has to move to an- other. As long as we observe what we believe are nature’s laws, all that is needed is a straight command sent from the mind instructing the hand to move. Heinrich Neuhaus thought that all the technical problems in the piano repertoire had a common denominator which he described as the ‘fundamental nucleus’. Neuhaus explained it by borrowing concepts from physics (F = force;
m = mass; v = velocity and h = height) in a manner that seems clear and per-
suasive, yet guarding his back by saying that ‘The mystery of art remains unfath- omed, retaining all its force and scope…but one should not see the “unfathom- able” where common sense, against which…all of us sin so much, can perfectly well understand all there is to understand.’
It seems to me that this kind of appeal to common sense epitomises a gener- alised symptom of pseudoscience, for it implies that our reasonableness should be capable of arriving at ultimate explanations, that it can unequivocally distin- guish the fathomable from the unfathomable, and that everybody’s common sense can grasp – and agree about – ‘all there is to understand’. If that were so, then further explanation would not only be unnecessary but impossible, and one would justifiably wonder how is it that everyone else could have failed to re- alise the simple truth. The fact is, for all we know, that such ‘fathomable’ knowl- edge is pretty hard to come by. What is common sense, anyway? I believe it is a hazy and fleeting thing; namely, the often satisfactory and true, but just as often inadequate and mistaken, intuitions or opinions of many – though never all – men; which is why it seems more sensible to think like Einstein did:
The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy.
Popper recalls the case of his friend, the violinist Adolph Busch (member of the famous Busch Quartet): ‘He told me that he once played Beethoven’s Violin Concerto in Zurich, and afterwards the violinist Huberman came and asked him how he played a certain passage. Busch said it was quite simple – and then found he could no longer play the passage.’ Karl Popper, Knowledge and the Body–Mind
Problem: in defence of interaction (London:
Routledge & Kegan Paul, 1994), p 116.
Heinrich Neuhaus, The Art of Piano
Playing (London: Barrie & Jenkins, 1973),
p 113. Neuhaus was the legendary Rus- sian teacher of such artists as Sviatoslav Richter, Emil Gilels and Radu Lupu.
Ibid. p 87. Neuhaus lists eight basic elements of technique (i.e. the playing
of one note, trills, scales, arpeggios, two-note intervals, chords, shifts and polyphony) of which he believes ‘the great edifice of piano playing as a whole is made up’ (see pp 114ff).
Albert Einstein, The Meaning of Relativity (London: Methuen, 1922), p 2.
A B
I should clarify that my criticism is not aimed so much at Neuhaus as towards the positivist teaching itself, for I believe that he was a great teacher and that this is the case of a dubious idea becoming profitable in the hands of a master teach- ing talented students. Before the relativity theory, many people’s common sense assumed that time and space were absolute, measurable constants. If I follow Einstein’s ‘common sense’ I may no longer take it for granted that my perception of gravity, speed, time and space is necessarily the same as yours and everybody else’s. Doesn’t it then seem odd to represent a left-hand shift by reducing it to the concept of a body with a certain weight which has to follow a predictable and desirable trajectory within ascertainable intervals of time and space, when our experience tells us – mine, for sure – that every successful shift takes place in the realm of weightlessness, timelessness, spacelessness and purposelessness? If anything, such a notion seems ideal to warrant unsuccessful shifts. Besides, can we treat our hand as if it were an inanimate object, rather than an organic part of a living human being? The plain fact is that shifting, like every aspect of tech- nique, involves a task of mind and body coordination. Considering that a is a left hand to be activated by a thought – say, ‘I now want my hand to shift from here to there’ – and b is the effect of arriving there, the above sequence (a leads to b) is inadequate to trace a logical connection between something as intangi- ble as a thought and the motion of a concrete object such as one’s hand. Re- search tells us that the mind makes an amazing use of certain chemicals called
neuro-transmitters. As the name implies, they transmit nerve impulses:
Mind, by any definition, is nonmaterial, yet it has devised a way to work in close partnership with these complicated communicator molecules. Their association is so close…that mind cannot be pro- jected into the body without such chemicals. Yet these chemicals are not mind. Or are they?
This turns our attention to the so called body–mind problem: how can we ra- tionally explain the relation between the states and processes of our bodies and those of our minds? In the case of left-hand shifting, this connection may be represented by means of the following diagram, in which the horizontal line separates the physical and metaphysical worlds:
The u-shaped detour suggests that an unobserved – and probably unobservable – process must take place which transforms our thoughts into physical move- ment, and that such a process is not accountable by, say, Newton’s rational laws,
physical
metaphysical
?
A B
‘If…teachers are enlightened, their teach- ing may effectively take any form. If they are not enlightened, whatever form their teaching may take, it will actually blind their students.’ Muso Kokushi, Dream
Conversations, pp 50–51.
See Albert Einstein, Relativity, the Special
and the General Theory: a popular exposition (London: Methuen, 1920),
especially sections iii, viii, ix and x (‘Space and Time in Classical Mechanics’, ‘On the Idea of Time in Physics’, ‘The Relativity of Simultaneity’ and ‘On the Relativity of the Conception of Distance’, respectively).
Deepak Chopra, Quantum Healing:
exploring the frontiers of mind/body medicine (New York: Bantam Books,
1989), pp 64–65.
This problem occupied much of Popper’s attention and he published two fascinat- ing books on the subject: The Self and Its
Brain (London: Routledge & Kegan Paul,
1977; with neurologist John Eccles), and
Knowledge and the Body–Mind Problem
(London: Routledge & Kegan Paul, 1994 ).
This diagram has been borrowed from Chopra’s Quantum Healing, p 97.
because it takes place in a ‘hidden’ zone, below the line. The neuro-transmitters behave like messengers running to and from the brain telling the whole body of our desires, emotions, memories, concepts, images, etc, and generating a myr- iad of physiological changes and physical responses:
It is quite astonishing that with every thought, the mind manages to move the atoms of hydrogen, carbon, oxygen, and the other particles in the brain cells. It would appear that nothing is further apart than an insubstantial thought and the solid grey matter of the brain.
Miraculous as this fact indeed is, I wonder why are we not as impressed by it as by watching someone like David Blaine perform his feats of psychokinesis. So what happens in the ‘?’ zone? What is it? Surely not a place we can visit in the realms of time and space, but one which stands for wherever it is we arrive when our thoughts turn into physical motion. It seems to be nowhere – and yet everywhere. This whole issue boils down to a vindication of how complex our ordinary experience of life actually is, and how incomplete a thought-adventure of the kind we call science is when it tries to explain it. Rather than a thing, as Gerald Edelman explains, our brain is more like an ever-evolving process. And considering that every brain has unique neuronal connections and is unend- ingly growing new ones from the moment of our birth (thereby creating all the memories that give each one of us a sense of personal identity), is it reasonable to prescribe universally valid rules about physical motion, and to pretend to be in conscious control of everything we do when we make music?
It often seems to me that our predicament is a much too wilful will coupled with the mistaken belief that what we do not purposefully do ourselves cannot happen. The point can be made that we are not meant to deliberately control everything while we play, but that we nevertheless need purposeful, conscious programming when we practise, so that our mechanical skills can become sec- ond nature. Neuro-Linguistic Programming (nlp), for example, envisions four stages of learning: (1) unconscious incompetence, (2) conscious incompetence, (3) conscious competence and (4) unconscious competence. While this seems a valid idea, it is doubtful that real-life learning takes place in as clear cut a way as that. One is inclined to share Chopra’s argument that a computer can be ‘taught’ to perform specific tasks, like adding 2 + 2, for example, and it will invariably yield the right answer – unless a computer error occurs. A young child asked to do the same operation may answer correctly; but he might just as well say ‘I want to go to the park.’ Are we entitled to consider the child’s answer ‘wrong’? Perhaps we should interpret it simply as a disclosure of our inability to predict and rationalise all the possible ways in which we respond to the world as we in- teract with it. Even when we recall or play a very familiar piece of music, some- thing will seem different about it – for remembering is a creative activity. Our mind is constantly generating new images, new brain, and unlike a computer, we forget and recall, we like and dislike, we reconsider and change our minds. In fact, we are recreating ourselves every time we think. It then looks like our in- quiry didn’t take us very far; nor does it seem to lead to any explanation that may satisfy our rational student – which is why Lao-Tzu’s aphorism remains as enlightening as ever:
He who knows it, tells it not. He who tells it, knows it not. Part of an explanation given by
neurologist and Nobel Prize winner Sir John Eccles at a conference of
parapsychologists. See Chopra,
Quantum Healing, p 65.
Edelman is a Nobel Prize-winning neuro-scientist (ibid. p 153).
‘Only when he no longer knows what he is doing does the painter do good things’ – a remark from Edgar Degas’s notebooks.
See J. O’Connor & J. Seymour, Introducing
Neuro-Linguistic Programming (London:
Harper Collins, 1990), p 8.
Chopra, Quantum Healing, pp 152–153.
The Limits of Language
That everything which makes our movements like this can be spelt out is defi- nitely a naive pretence, especially when one considers that the most complex of human movements are possibly those used in the performance of instrumental music. But leaving aside how much we can and need to explain, I would think that what makes the teacher’s task particularly demanding – apart from the in- herent complexity and elusiveness of the knowledge involved – is its stubborn resistance to being rationally formulated in language. Of course, the prevailing conception of teaching is based on the premise that ‘training cannot be achieved and is not attempted without a lot of explaining why one does what one is doing’. Thus, the challenge of having to explain what appears to be inexplicable remains, and in order to explore this idea further I would like to touch on some provocative issues raised by Martin Esslin in his fascinating book about Antonin Artaud (1896–1948), that most enigmatic and heroic cult-figure of twentieth- century theatre:
All thought…it could be argued, is verbal, is language; a thought that is incapable of being formulated in words, therefore, by definition would not be a thought, would not exist at all.
Nevertheless, Esslin asks:
To what extent can thought exist that is not formulated in words, that stubbornly resists being put into words at all? Are thought and language necessarily co-terminous?
Artaud knew himself to be suffering from a mental disease to which he partly attributed his extreme difficulty in expressing his innermost feelings and emo- tions by means of words. In his desperate attempts to bridge the gap between his inner world – which he envisioned as thought in a pre-verbal, unformulated state – and its expression in language, Artaud became increasingly contemptu- ous of other artists (particularly writers) who seemed to be free of his predica- ment, for he felt – rightly or wrongly – that they indulged in a facile and insin- cere use of language based on the arrogant observance of rules of grammar and of elegance of literary style, as well as on the ideals of rationality, self-control, moderation and bienséance. In any case, you don’t have to be mentally ill to ex- perience difficulty in converting such an intangible thing as an image or emo- tion into verbal language, for even great writers have to wrestle with words and