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pSY, the Copenhagen Interpretation and the Perception of Music

Introduction

To many of you, what I am going to talk to you about will seem completely irrelevant, and maybe it is, at least to you. Over many years, because of inconsistencies I have felt to be present at many levels of discussion about music, I have been found it less and less easy to accept what is often said about the nature of music, and, if I'm honest, about the nature of reality itself. This, I suppose, is inevitable, as since we must accept that music is a part of our reality, then if there are questions about the nature of music, these must at some level at least be questions about the nature of reality. In fact, in my opinion, it's not as simple as this, and inconsistencies and seemingly irreconcilable conflicts concerning many aspects of music are symptomatic of similar difficulties in all areas of reality. As, in the humanities, we are constantly faced with innumerable social, intellectual, political, economic and aesthetic factors which only complicate already complicated questions, one of my first port of calls for help in reconciling these difficulties was within the sciences, and particularly the theoretical sciences of mathematics and physics. There is also the case that within certain areas of these disciplines are theories and commentaries that are, for me at least, awesome, mind-bending and fantastic in their own right, and I suppose at least a part of my interest is achieving a reconciliation of the similar but somehow different sense of wonder I feel when confronted with a colossal work of art and a colossal scientific theory, or an intricate and subtle mathematical argument. Anyone who does not at least in some way share this enthusiasm is likely to find little of interest in what I have to say, and I apologise in advance for imposing this on them. I've tried to make this as short as I can.

So what are the difficulties mentioned above? For a start they're too numerous to mention, but one I can describe, I hope, quite clearly. It was some years ago that I discovered that some of these questions were bothering me. The best example I could think of was an analysis of Mozart's F Major piano sonata. Academically, in my experience, Mozart tends not to be analysed - if he were to be, I suppose, his first movements could be used to demonstrate a reasonably standard sort of sonata form. This is, in itself, a crucial idea, because that's what it would be - a reasonably standard sort. In other words, it's not too difficult to place on the music the abstract form. Certainly, it means analysing the piece and suggesting that here, at bar… we have a typical modulation into the dominant, (or the dominant of the dominant) which almost certainly signals…yes, the beginning of a contrasting episode traditionally called the first subject, and so on…

This is all fine, and it certainly lifts you off ground zero when considering structure, at least in the historical sense. What I found frustrating all those years ago, (though not so much now), it how little this does for the group of material within these traditional terms. So, how does the 'first subject' actually work? Well, a little work on this makes the situation much clearer - the first subject is no such singular thing. There's no problem here, because all we need do is say that we have a first subject group and elevate the form to a more complex level. We can then leave Mozart and go back to conventional Haydn who is far more predictable formally. But giving a thing a name doesn't really help us understand how it works. Twelve years ago, I developed an idea that the music was moving through levels and that the traditional breaks were simply larger levels. The material communicates to us through the interrelationships between these levels. So, clearly, a repeated phrase in the same key is one sort of level. If the phrase then repeats, modulated, it is on a similar, but not identical level. A contrasting phrase, as occurs at the opening of the Mozart is more complex, as it deliberately extends the scope of the first level (if one takes this to be the opening bars), through the contrast. Of course, we could also say that the whole, bifurcated phrase is one level comprising two, contrasting ideas. One or two? This is the start of it.

Either through luck (Dawkins/Darwin), judgement (Plato), or synchronicity (Jung), as I was pondering these ideas, I came across a book called Godel, Escher, Bach by Douglas Hofstadter. It was and is one of the first of series of books that in one sense or another, have attempted to popularise aspects of science. In this case, one of the principal threads of this book, and this description is important, is the nature of mathematics. At the time I didn't really understand much of this, (not that I do now), but one of the many things that I found fascinating and that sounded a chord with me was his description of a derivation made in his own symbolic language, TNT or Typographical Number Theory. Here is the derivation:

Hofstadter, p226

And here is his description of it:

P227

Really, looking back, most of my investigations into the nature of music and the nature of composition have been based on this sort of idea. The definitive score of a piece of notated music can be seen as an abstract from which reality emerges in terms of performance. This relationship in turn can be compared to a mathematical proof or derivation. The latter is itself an abstraction and a common mathematical argument is that, by definition, this is not associated directly with any real, physical process, but in a Platonic way, provides a 'perfect, definitive' form which may then be used, as mathematics and logic have been used constantly, in the 'dirtier' and more real sciences, such as physics. This in itself is controversial in some respects as we shall see, but I suppose of equal importance is another major feature of Hofstadter's book. He is talking as a mathematician with a strong interest in artificial intelligence and is seeking to make very genuine and firm philosophical points using links with, principally, the music of Bach and the graphic art of Escher, and a very fundamental point is the investigation into the nature and validity of these links. Hofstadter feels that they are very much more than just 'analogies' or metaphors, but are perceptual and symptomatic of relationships with the whole area of intelligent thought. I am approaching it from the other direction, but seek to re-evaluate such relationships from the point of view of a musician. In my investigations, involving amongst other areas, number theory, artificial intelligence, Zen Buddhism, evolution, genetics, computation, logic, relativity and on, and on, it seems that not just myself but a number of other people involved in the humanities have been drawn, apparently ineluctably, toward what seems to be accepted with awe or incomprehension throughout the western intelligentsia as being one of the most fundamental and revolutionary theories ever to have been developed within science: the theory of quantum mechanics. This is a theory concerning the behaviour of sub-atomic particles. The 'scientifically accepted' interpretation of the relationship between Quantum Theory and physical reality is called The Copenhagen Interpretation. Coincidentally, some of the fiercest arguments occuring in science and mathematics involve the tension between this, other interpretations, and even the completeness of Quantum Theory itself. So, Einstein disagreed with the Copenhagen Interpretation, suggesting that Quantum Theory was, in fact, incomplete. David Deutcsh, more recently, thinks that quantum theory is complete but disagrees with the Copenhagen Interpretation. His version is called the Many Worlds Interpretation. Roger Penrose feels that Quantum Theory is incomplete and that all current interpretations are incorrect, and so on, and soon. Does this sound familiar?

All, however, do agree that the theory of quantum mechanics is not just one of the most successful experimental theories ever - there has never been a confirmed experiment contradicting it, but that it may well have profound repercussions on the way we relate, at least in philosophical terms, to the world. Most profoundly, there are clear suggestions that it provides experimental evidence for the fact that the symbols we use to communicate with each other, and so, possibly, the way in which we think, do not follow the same rules as reality. This is a fundamental assault on the way not just science, but the way that the majority of people brought up in the west normally think - that is, with a basis in the infallibility of mathematics and logic. I am following up these ideas. As far as music is concerned, one principal one occurs - if, as Penrose (and others) have hypothesised, though itself is a quantum process, (which by definition, at least at some level, it must be), then what effect to quantum processes have on the way we perceive the world. To follow this, how can we properly conceive the world without understanding, at least in part, quantum mechanical processes?

I should like to emphasise, as I do again below, that I do not understand everything about this. But I'm trying. Efforts are not helped by words such as those spoken by Neils Bohr, the founder of quantum mechanics and leading advocate of the Copenhagen Interpretation:

Bohr quote…

1

Okay, so what have music and the theory of quantum mechanics to do with one another? I am extremely guarded in my response to this, for a number of very good reasons.

Not least, in the last thirty years or so there has been considerable speculation, of a more or less founded type, concerning the effects of quantum activity on various areas of human endeavour, or more correctly, I suppose, which attempts to interpret human endeavour in terms of the reality predicted by quantum theory. In 1997 a great swathe of this was attacked in the book Intellectual Impostures by Alan Sokal and Jean Bricmont - the targets of their attack were representatives of the Paris 'postmodern' intelligentsia' - Derrida, Kristeva and Lacan for example who had, in their opinion, both used and abused many aspects of scientific thinking in the service of philosophy, sociology, politics, 'gender' issues, (more correctly sex issues) and psychoanalysis.

Quote

The book is itself based on an 'experiment' performed by Alan Sokal:

The book grew out of the now-famous boax in which one of us published, in the American cultural-studies journal Social Text, a parody article crammed with nonsensical, but unfortunately authentic, quotations about physics and mathematics by prominent French and American intellectuals…We wanted to explain, in non-technical terms, why the quotes are absurd or, in many cases, simply meaningless; and we wanted also to discuss the cultural circumstances that enabled these discourses to achieve such reknown and to remain, thus far, unexposed.

Their main complaint is against intellectuals who use

…scientific ideas totally out of context, without giving the slightest justification…or throwing around scientific jargon in front of their non-scientist readers without any regard for its relevance or even its meaning.

They also attack the one of the main proposals of many 'postmodernists' - that

…modern science is nothing more than a 'myth', a 'narration' or a 'social construction'.

The parody referred to above, (which, incidentally was published with all the fervour which the Trojans viewed their horse, or with which a missionary regards a convert), was called Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity. Once one knows that it is a parody, and apart from the clearly nonsensical and opaque passages, it makes entertaining reading. It quotes Einstein, Godel, Bohr, Heisenberg - the full panoply of stars of the 'new physics', in an argument the true direction of which never becomes entirely clear.

So we must be careful.

On the other hand, and possibly to the immense annoyance of the above authors, the last thiry years has also seen a growing interest on behalf of some members of the scientific community for 'elucidating' ideas concerning the 'new physics', or even just any old physics. For those of us whose principal memory of physics involves amongst other things bunsen burners, boiling water, springs and harsh comments concerning the inadequacy of both my experimental and theoretical methods involving the above, this is now rather frustrating. Why was I not told then about the remarkable, awe-inspiring, mind-warping concepts lying behind relativity and quantum mechanics?

One reason for the outbreak of interest in books concerning such areas recently is probably due to the 'maturing' of the concepts themselves. I find it extremely difficult to come to terms with the majority of these concepts, many of which must inevitably have at least some fundamental effect on the way in which we see ourselves and reality, were in the process of discovery at the beginning of this century. More astounding is that, although the majority of the public is quite aware of the ramifications of the practical effects of these ideas - nuclear bombs, nuclear power, advances in space travel, bubble chambers, black holes, the speed of light, e = mc², etc., very few have any real notion of their physical and, yes, philosophical consequences is less practical areas. Here, I cannot help but make an analogy - is this not comparable to the number of people who still feel that such musical works as The Rite of Spring and Pierrot Lunaire are 'shockingly modern' examples of contemporary music? I received a similar put-down on disclosing, rather proudly, to a friend who is a research physicist that I felt I was finally 'coming to terms with' some of the idea of quantum mechanics - for instance, the idea that sub-atomic particles are not 'pieces of dust' or 'billiard balls' - that our common notions of matter simply do not apply at the sub-atomic level. She replied that this was obvious and found it hard to understand how anyone could think in any other way. I get my own back, though, when she, as a lover of ballet, finds it hard to come to terms with, for instance, The Rite, which, I scoff, is, though a wonderful piece, hardly contemporary.

So I have be careful here, too. I am not, nor have I ever been a physicist. Nor have I ever taken an examination in physics. I did take chemistry O-Level, rather disastrously - one of the experiments we were to undertake reacted in a typically unpredictable way and effervesced, violently, black, bubbling, corrosive fluid over my paper - without really understanding anything. I was more successful at Biology, probably because by that time a great deal of biology seemed to be more concerned with whether things were living, dead, or non-living - a distinction I have never found particularly tricky to deal with - reproduction, or rain forests. Similarly, although at one time I was good at Mathematics, the introduction of the calculus at the time of my discovery of the musical and social benefits of the Youth Orchestra was, in my case, bound to be disastrous, and my failure (in all senses and at every level) in Additional Mathematics was something of which I was particularly proud for some time.

Again, an analogy: I am constantly disconcerted, as are many of us, at how few of our students seem to really understand what we would call musical basics. For instance, how to write a Bach Chorale, or even understanding the point of writing Bach chorales, let alone an understanding that the only way to write them in any way correctly is to achieve an understanding of harmony and part-writing rather than by following a set of rules given to you by your teacher, (who may well not understand them, either!) One of the main things I feel I have learned from teaching is first of all how difficult it is to teach things which you consider to be self-evident, and secondly, trying to understand why you find them self-evident when, in a broader sense, they are quite clearly not - in other words, why is it important that students should learn how to write Bach Chorales?

How can I, then, do the same thing with some of the most subtle and delicate mathematical and physical procedures ever developed, when I have enough difficulty with the most basic forms of algebra, geometry and calculus? I shamefully admit this, and am trying, with what little time I have, to make amends, (although I has to be said as much for practical reasons concerning some of the things I want to do as for sake of my conscience). I can refer to at least one defence - given in the Note of Roger Penrose's mind-warping book, (it warps my mind, anyway), The Emperor's New Mind:

Note to the Reader:

On reading mathematical quotations

At a number of places…

…do not be afraid to leave a formula behind altogether.

In other words, his point is that in his opinion the detail of his own proofs or the proofs of others are not as important as what they indicate about the whole. Clearly, it will not be possible to understand the whole with the same breadth and depth, but there is the clear implication that this should not stop an understanding at some level. There are similar implications behind such famous books as Godel, Escher Bach by Douglas Hofstadter, The Tao of Physics (Fritjof Kapra), The Dancing Wu-Li Masters (Gary Zukav), A Brief History of Time (Stephen Hawking) and The Fabric of Reality (David Deutsch), amongst others. These books principally concern the relationships between physics, mathematics, reality, spirituality, and even music and graphic art and are clearly intended for 'popular' consumption. On the other hand The Unnatural Nature of Science by Lewis Wolpert is less conciliatory, while Richard Dawkins in Unweaving the Rainbow is positively furious that 'artists' as well as the general public pay so little attention to scientific matters, while revelling in such frivolities as astrology, religion, luck and the paranormal.

The reality is, probably, somewhere in the middle. Arguments concerning any subject matter should be discussed in terms of their quality in all the commonly accepted meanings of that term rather than purely on the qualifications of the person that makes them. We can see this in reality when we are sometimes surprised by the wisdom of someone who is 'qualified' in, for instance, biology when speaking about, for example, poetry, and similarly, we may be profoundly disappointed by what we would consider an otherwise 'eminent' person in the field of, for instance, astrophysics choosing what we would consider to be entirely 'inappropriate' music for Desert Island Discs.

In actual fact, as I shall attempt to explain, in my opinion, such phrases as the 'commonly accepted' meaning of the term 'quality'' is, reality, an extremely tricky idea for all sorts of reasons that are to do with physics, rather than postmodernism. And this last comment is, in itself, perhaps an elucidation of the reasons why some postmodernists have chosen on the one hand to adopt certain ideas of the new physics while on the other repudiating the idea of science as an exact form altogether.

This, then, is the backdrop to this discussion, although I think I have yet to make clear how I feel this relates to music. The thing that triggered these thoughts was my programme, pSY. This is a programme for the automatic generation of music, incidentally, via a Yamaha SY synthesiser, although the principal is true for any system. Let me first of all state that this programme does not seek explicitly to emulate any existing form or style of music, although it does, implicitly, make use of some of the 'syntax' that has been accepted in some forms of contemporary music. In creating these sounds automatically, it raises the question - is this actually 'music'?, in the sense that one of the common definitions of a musical performance is that it must be limited in time. Again, by definition, pSY has no such limitation beyond those physically imposed on the hardware. Of course, one could ask the same question of any object which continually creates sound with no 'built in' or 'intentional' form of off switch, and this question has also arisen in the music of Cage and some of the more depressing works of Stockhausen. I can easily, and commonly do, argue that we get around many difficulties concerning the definition of music by suggesting as is implicit in some of the above composers' output, that anything which a composer claims to be music should be granted that status, but that we can immediately qualify that liberality by saying that simply calling something music is meaningless, we do not in doing so grant the work any praise. It is then up to us to decide whether we feel the music is any good or not. In other words, we are back to quality.

I will not make any claims here for the quality of the 'music' that pSY creates. Indeed, there is something of a conundrum behind the whole idea of this, and one that resembles the Turing Test in Artificial Intelligence. I would suggest, though, that the music that pSY creates does contain what might be called a 'creative logic'. By this I mean that, while one knows that the music is automatic, in some people's experience at least, it 'speaks' to them - it doesn't just create, it performs.

The other aspect I find intriguing about pSY is the idea of performance. One of the common complaints held against purely electro-acoustic music is that it has a fundamentally static property to it. The standard 'tape' piece is fixed in the sense that, without re-writing or re-constructing the thing, each 'performance' will be identical, at least in terms of the sound involved. Similarly, there is something rather peculiar and disturbing about live concerts in which one is expected to 'applaud' a tape piece. Presumably one is applauding the work of the composer, (who may or may not be present - rather in the way that cinema audiences used to applaud at the end of films), as there is no 'performance' as such to applaud. The reason for the discomfort is presumably that when we applaud usually, at least a substantial part of that applause is aimed at the performer, rather than the composer. Anyone who has attended both types of 'performance' will be in no doubt as to the value of the former not least because they have interpreted the music rather than simply playing it back, and this is clearly of central importance to the idea of 'western art music'.

This is not the place to go into details concerning the reasons, values and justifications behind the rituals involved in Western Art Music, but the fundamental nature of what we call interpretation is important here.

See Technology and The Nature of Performance

At heart, all of these concepts require one thing, which is the perception of one person's action by another. Traditionally, the humanities have neatly avoided this, preferring to analyse texts in isolation, rather in the manner of a scientific experiment, and indeed many schools of interpretations have grown around this very particular point. Recently, the postmodernists have, as mentioned above, attempted to undermine this method pointing to political, sociological and sex issues as well as scientific issues can be used to undermine the idea that such isolation is possible.

These arguments are useful only in that they can force us to concentrate on what we really mean, and, quite possibly, force us to consider the value of ideas which we consider normally to be 'self-evident'. One of the central ideas that postmodernism has questioned is the nature of reality itself, and, more to the point, the nature of our perception of it. It has tended to suggest that our analysis of reality is faulty due to the presence of ideas which, through political, social, sexual, or even grammatical subtexts, influenced this analysis to the point where it is flawed and prejudiced. Therefore we have the common argument concerning whether a western scientific approach is 'automatically' 'better' than, for instance, the approach to life taken by, for instance, the Australian Aborigines, who place extreme importance on the nature and interpretation of dreams.

In my opinion there is a flaw at the heart of this argument, as there is in many arguments, from whichever source they arise. One of the reasons arguments such as those mentioned above can be so frustrating for all concerned is that, in spite of claims to the contrary, they are both really arguing for the same thing! And this is for a rational, logical analysis of our perceptions of reality. This may seem surprising for each side, because for a 'scientist' there is nothing less rational than, for instance, placing decisions concerning possibly life-changing issues into the hands of an interpretation of a dream. Similarly, there are those who take considerable pride in the importance they place on dreams, (although this could also be how many steps they took to cross the road, whether they have or haven't seen a black cat, whether or not they can bend a spoon without trying, whether they can 'see' something that someone else can't,whether we perceive a star to be here or there at a given point in time, etc.), and would be horrified to think that anyone would consider their point of view to be in any way equivalent to that of science.

In fact, in the fields of both mathematics and logic, the cornerstones of a 'rational' approach to reality, it is becoming increasingly, although still highly arguably, clear that they, too are based on a 'fantasy' of reality. There have been a number of indications of this, most of which have occurred this century. To put this in perspective:

In a speech to the Royal Institution in 1900, Lord Kelvin reflected that there were only two 'clouds' on the horizon of physics, the problem of black-body radiation and the Michelson-Morley experiment. There was no doubt, said Kelvin, that they would soon be gone. He was wrong. Kelvin's two 'clouds' signalled the end of the era that began with Galileo and Newton. The problem of black-body radiation led to Plank's discovery of the quantum of action. Within thirty years the entirety of Newtonian physics became a special limiting case of the newly developing quantum theory. The Michelson-Morley experiment foreshadowed Einstein's famous theories of relativity

Zukav, p328

There have been other symptoms too:

Deutsch p 234

To some extent these have led to the controversy that still rages today concerning the nature of mathematics and logic and their relationship to reality. The poles of this argument can be described by Platonism, where mathematics exists as a perfect reality in our minds at birth, is corrupted by physical reality, and to which we can return only through profound thought and meditation.

Deutsch 227

Penrose 205, 146-151

It seems to me that it is a clear consequence of the Godel argument that the concept of mathematical truth cannot be encapsulated in any formalistic scheme. Mathematical truth is something that goes beyond mere formalism. This is perhaps clear even without Godel's theorem. For how are we to decide what axioms or rules of procedure to adopt in any case when trying to set up a formal system? Our guide in deciding on the rules to adopt must always be our intuitive understanding of what is 'self-evidently true', given the 'meanings' of the symbols of the system.

Penrose 145-146

The opposite is intuitionism, where, for instance, the existence of certain otherwise considered self-evident ideas are questioned. For instance, an intuitionist would deny the exist of the infinite set of natural numbers, that is {1,2,3,4……}, simply because, presumbly, we have no direct evidence through intuition that this sequence will inevitably be completed, (one could argue that, in effect, one could have a computer, a person or any object capable of producing such a sequence until the end of the universe, or until all available matter in the universe (some estimates are that there are 10⁸⁰ atoms present in the visible universe), was consumed with the task. According to our usual thought patterns, we may well argue with equal feelings of intuition that even if this were the case, it would still be possible to imagine that number plus one, and yet if there were no sentient being to imagine it - all energy having been used in the calculation itself, presumably this thought could not occur.

Especially for those of us who have been brought up and educated in certain ways, the very idea of thought is highly based upon what we consider to be fundamentally reliable concepts, and at the root of most, if not all of these concepts is that mathematics and logic are infallible as representations, if abstract representations, of reality. In other words, we assume that if we take a real world situation and manipulate its contents mathematically, that the real world will follow - it will utilise the same rules.

This is an extremely contentious area, and the vast majority of scientists and mathematicians, if questioned would go along with this. Even if there were any question, it would 'theoretical' and they could point, with perfect justification, to the millenia of progress and experiment which has occurred which, even if it doesn't 'prove' the infallibility of mathematics, implies that it is extremely successful. If there is something problematic with the relationship, it only occurs at the quantum or sub-atomic level, and that this has no more relevance to our daily lives and experience than the theory of relativity.

Nevertheless, there are a number of physicists and philosophers who are intrigued by this potential problem, and many who still believe in the platonic view that 'the world is number' are forced to argue their case more strongly than in the past. Incidentally, there tends to be a divergence between mathematicians who believe in this reality, physicists who don't, but who are relatively unconcerned about its ramifications, and physicists who don't but who are concerned. The latter tend to be physicists of a more philosophical bent and/or those whose work involves quanta, (although this is by no means universal - the argument over the Copenhagen Interpretation is in part an argument concerning the necessity of knowing whether quantum theory has any 'real world' significance beyond its ability to predict the outcome of sub-atomic events - Einstein could not accept the latter ideas because it broke the 'one to one' link between a theory of physics and reality and felt that this was a 'problem' that would have to be sorted out. Those who advocated the Copenhagen Interpretation felt that quantum theory would never be explicable in our 'real-world' terms, and that, in any case, it was irrelevant because our only important concern was that its predictions were 'safe'.

David Deutsch has suggested that there is no direct link, and goes as far as to call Plato's ideas a…., but takes the confusion arising over this issue, and more specifically some of the more odd behaviour, in our terms, of quanta as being evidence for the existence of parallel universes. He argues that these anomalies are explained entirely by the existence of many worlds and so sees no need, at least at this point, for any further concern over Plato. As he himself is happy to suggest, however, there is no guarantee that there will not be at some point in the future a better explanation - indeed, he insists that this is inevitable and accepts the necessity for us to be wrong in our explanations as Newton has turned out to be wrong does not invalidate the work that Newton did in explaining the universe.

The relevant rule of inference…

Deutsch 232

Zukav 279

Cf popular scientific catalogue for polarised plastic sheets