Abstract
For reasons both traditional and functional, the academy persists in dividing up its adherents into Bachelors/Masters of Science or Bachelors/Masters of Arts. Only when one reaches the level of ‘Doctor of Philosophy’ does this division apparently break down, but even this is, of course, an illusion. The assumption is that a PhD candidate will now have specialized to such an extent that the sheep-and-goats separation into Arts and Sciences is no longer necessary. The rise in interdisciplinary research, now a requirement of practically every research funding council, is at least in part a consequence of this state of affairs. Despite the prevailing interdisciplinary culture, the academy remains stubbornly resistant to rethinking its medieval-themed divisions. Changing degree titles from BA or BSc to some kind of intermediate qualification, even if it were desirable, is practically impossible because it would involve changing university ordinance itself.
These may seem like arcane matters that are the preserve only of those who delight in such things, but in fact, they have real-world consequences too. In its attempt to prepare students for universities, the education system has to follow a similar path of forcing youngsters to make invidious choices between Arts and Science subjects. As a schoolboy, I had to choose between Music and Chemistry (I chose Music), when I loved them both. Youngsters today are faced with similar choices, that destroy curiosity, confirm bias, and deny the fundamental unity and complexity of the world. Worst of all, ‘creativity’, one of the most highly prized of human attributes, is deemed to belong only to those on the ‘Arts’ side of the divide, at a stroke killing off the very thing that has in the past galvanized our inventiveness and brought about so many advances.
Professor Tom McLeish, in his book The Poetry and Music of Science, takes aim at the beating heart of this ancient culture and with considerable energy and erudition comprehensively demonstrates that the two sides of the supposed divide are in fact exactly the same. He does this through a thorough examination of creativity in a series of what might be called ‘extreme encounters’ between artists and scientists. The conclusion of this exercise is so foregone that it resembles an episode of Columbo in which, as the detective-loving reader will be aware, the identity of the murderer is revealed at the start and the pleasure is in watching the eponymous hero outwit them and deduce the truth. And what a truth it is! Creativity is equally present in both the artistic and scientific imagination.
The model for the methodological approach is provided early on, in the account of the collaboration between the author and the artist Professor Ken Hay on an exhibition of parallel projects. The book makes a clear distinction between this and Sci-Art (in which scientific methods produce artistic outputs and vice-versa), preferring a comparative methodology in which two independently conceived and constructed artefacts are laid alongside one another. The emphasis here is not so much on the understanding of similarities between the outputs themselves, but rather on what was revealed about the processes that led to their creation. These processes are sometimes so similar as to be indistinguishable. If knowledge may be divided up into the propositional (facts), the procedural (processes) and the tacit (indescribable), then what emerges clearly from all of the case studies in the book is that both artists and scientists require a decent mixture of all three types to produce new knowledge.
This comparative, side-by-side, approach has the great strength that it allows both the artistic and scientific works to stand on their own feet, to be excellent examples of research and creativity within their own spheres. The parallels that are drawn are made all the more convincing by this celebration of difference. To be eligible for inclusion in the book, a work of art or a piece of science must first be eminent as art or as science. Only then, can the similarities between the processes that led to its creation be drawn out. However, effective though this method may be, it does also mean that work which inhabits a more ambiguous position, or individuals who cross over from one side to the other, are not so well represented. One thinks, for example, of László Biró, surrealist painter, inventing his eponymous ball-point pen, or Hedy Lamarr and Georges Antheil's player-piano-derived control system for torpedoes, or Marcel Duchamp's precision optics. Here, the creativity itself is transferred into another disciplinary domain intact, regardless of its function within the originating field. There is a danger in insisting on the independence of artistic and scientific creativity that the rule may backfire and consolidate the barriers rather than removing them. The book does avoid this danger for the most part, but the overall impression given is that neither the artists nor the scientists are willing to move much outside their specialisms.
Nor can the comparative method be tested against those who apparently did not have as much creativity as those featured in the book, but who nevertheless succeeded, even unwittingly, in injecting some poetry or music into science or vice-versa. The history of organology, for example, is littered with such cases. The celebrated oboist, Christopher Redgate recounted once how his oboe-maker, taking up the length of wood that would eventually become a new oboe, identified purely by eye where to drill the finger holes. This was virtuosity in an act of creativity founded in scientific knowledge and built upon experience. The oboe-maker would surely not have believed himself to be either an artist or a scientist, but rather a humble craftsman. His contribution was not to the great artistic, scientific or academic traditions, but nevertheless, its creativity was exemplary. This idea comes close to John Dewey's aesthetics, with their emphasis on art as experience and science as a statement about experience. The Poetry and Music of Science takes a different position in its implication that both art and science are experiences. In this book, the processes of artistic and scientific creation are fundamentally the same, and so the experience of a painting or a piece of music has much in common with that of geometry or the motion of waves or particles. As Samuel Beckett, quoting Flaubert, wrote about James Joyce: ‘his writing is not about something, it is that something itself’.
The barrier to fully appreciating the underlying truth of all this lies mainly in the accumulation of technical language or, less politely, jargon, that is necessary but at the same time incomprehensible to anyone other than those working in a given domain. The book mostly manages to overcome this problem by a clear and readable style that sacrifices nothing in terms of disciplinary rigour but nevertheless conveys its meaning in ways which can be understood by non-specialists. The focus is primarily historical, which does much to undermine received wisdom, but does also set up a situation in which the occasional appearance of a living figure seems like a welcome intrusion from another world. So, for example, the brief discussions of two living artists – the composer and music therapist Janet Graham, and the composer Emily Howard – in the chapter on Music and Mathematics provide sudden glimpses of a rather different, more contemporary, mindset than the nineteenth-century perspectives that dominate. Graham's work, for example, is rooted in her lived experience and rather far from the ‘abstract’ structures of mathematics, despite the parallels drawn. Yet, there is clearly a creative relationship between the fuzzy front-end of the design processes that led to her music and the ways in which mathematicians conceive an idea. It would have been interesting to see these two composers given more room in order to develop the discussion of their ideas. It would also have offset the general impression that the scientific contributions are of more recent vintage than the artistic ones.
The most striking omissions in the book are digital technologies. It is very noticeable that this text describes a world without computers, or at least in which computers are merely tools, like pencils or pianos. This world has changed. Forty years ago, to be a composer was a rare thing (I remember being accused of ‘thinking I was Beethoven’). Nowadays, every student on a course entitled ‘Creative Music Technology’, or even just ‘Music’, is a composer and expected to create original work. Similar phenomena apply in other disciplines. What has brought about this change is the explosion in digital technology that is shared across all these subject areas. Everybody uses computers nowadays, which means that there is some kind of underlying commonality of understanding, regardless of disciplinary constraints. The rise of hybrid courses that reflect this disciplinary porosity of boundaries is a feature of the modern university. Transdisciplinary creativity is a real part of this development. The very similarities identified so well by Professor McLeish have made their way into the everyday discourse of students. The process of creation has become algorithmic. To highlight this absence is not to undermine the central argument of the book, because if there is one thing that the pervasiveness of computers has done, it is to confirm the underlying connectedness of everything. However, a consideration of their impact would both strengthen the argument and make it more directly relevant to present-day readers.
It would be tempting to see the ubiquity of computers as a triumph of numbers, but the reality is rather more complicated. Computing has evolved from its initial focus on the survival level of human existence (clothing, eating, housing, travelling etc.) and past the social level (working and contributing to society) evidenced by social media. It is now addressing the spiritual level (being successful, being entertained, thinking philosophically, satisfying curiosity, etc.) and this includes creativity. The transformation that has been brought about by this cannot be underestimated. It is a whole new ecology built on a rhizomatic network through which ideas and applications may be freely shared, not just by humans but also by objects. In this world, computers paint beautiful paintings and make marvellous music, and people must find ways to negotiate relationships with the machines they themselves have created. This has profoundly affected our understanding of creativity, with the result that the traditional boundaries that are ossified into the infrastructure of the academy are dissolving before our eyes. New, hybrid, degree courses are springing up (the BA/BSc in Creative Computing at the University of Leicester, that I founded, is a good example) which inhabit an in-between territory that is part-creative and part-technological and often part-business. Admission to such courses requires a combination of Arts and Science subjects. The creativity they embody is one that has already accepted the conclusion of The Poetry and Music of Science and cheerfully recognizes no sharp delineation between clusters of disciplines.
In this book, the chosen artists (even the living ones) are only the most traditionally painterly of painters, the most literary and writerly of poets, etc. This is apparently a world in which people are moved by string quartets or oil paintings and not by films or computer games. Digital artists, that is to say those whose work is conceived in digital terms, do not appear. Yet the very sciences whose poetry and music are closest to the arts would not even exist without computers. Physics today is almost entirely computational, of necessity, because we have already observed most of what is directly observable by humans. Mathematics could not have reached its current level of sophistication (and poetry) without calculating machines. Engineering relies almost entirely on computer modelling to produce its results. Digital technologies are not just useful tools: they are the means by which we understand the world and ourselves.
To illustrate how this digital absence affects the argument of the book, consider the chapter on Music and Mathematics. This begins with an historical account of the connections between numbers and music, going from ancient Greece through the medieval period to the nineteenth century. This is obviously very Western, and time delimited. The analyses are all based on tonal harmony and make a supposition that the language of music ‘called on notes, bar-lines and staves’. This ignores the fact that the vast majority of the world's music is not notated on a five line staff and is modal rather than tonal. The account works through some familiar tropes: rhythm subdivides time mathematically; the harmonic series is sonified whole-number ratios; perception of loudness is logarithmic; etc. The discussion concludes: ‘whatever element we pick from a close inspection of the musical tapestry: pitch, rhythm, volume, we find numbers … ’. While this is undoubtedly true, what would both clinch the argument and make it even more relevant would be a discussion of part of the ‘tapestry’ that has been overlooked, namely: timbre. Timbre is just as numerical as pitch, rhythm, or volume, and is the parameter that has provided so many examples of groundbreaking musical creativity in the past one hundred years or so. This omission of timbre presumably occurs because of its relative unimportance in the pitch-driven system of Western tonal concert music. It was only in the 20th Century that timbre began to assume equal importance to the other parameters. Edgard Varèse, a mathematical engineer and composer, stood at the threshold of this transition from five line staff notation to a more mathematical approach to notation, performance and sonic manipulations. The titles of his compositions (Ionisation, Hyperprism, Density 21.5, etc.) reflected his scientific conception of organised sound. Most tellingly, the work from 1957 which launched both sound installation and non-linear electronic music, echoed the title of this book in its formulation: Poème Electronique.
The reason that timbre is so important and would definitively clinch the arguments about creativity that Professor McLeish seeks to make, is that the computer has finally enabled us to penetrate the granularity of sound itself. Now, the complex thing called a ‘note’ turns out to be a spectrum, that includes the harmonic series for sure, but also other inharmonics in a shifting kaleidoscope of relationships that define the recognizable character of a sound. Furthermore, sounds that are deemed to be ‘musical’ turn out to have a surprising amount in common with sounds that are called ‘noise’ or, at best, ‘non-musical’. Whole typologies of what Pierre Schaeffer, rather controversially, called ‘sonic objects’ have been created based on their spectral morphology rather than their supposed musical function. From this has emerged a vast amount of composition whose notations are graphical or computer-based and whose understanding of form is derived from the potential for similarity between the waveform of a practically inaudible individual sample lasting 1/44,100th of a second and the shape of a composition lasting perhaps hours. Such electroacoustic music uses mathematics to aid creativity at all its levels and in ways which resemble the working-through of the Fluctuation-Dissipation Theorem. For example: the Nyquist criterion is a standard in digital sampling, where oversampling gives rise to aliasing and consequently unwanted sonic artefacts appearing in the acoustic output; Fast Fourier Transformations provide the building blocks for composition by converting the audio signal into its individual spectral components; and rhythm transforms into pitch as it speeds up beyond the fastest possible iterations that a human could produce. These developments have equally had a transformative influence on music made solely with acoustic instruments. One thinks of Iannis Xenakis, Karlheinz Stockhausen, Gérard Grisey, Jean-Claude Risset, Kaija Saariaho, and many many more.
However, this chapter stops at Schumann, and undertakes instead a close reading of the Konzertstück for Four Horns and Orchestra (1849). The account describes effectively the innovative nature of Schumann's composition in its adoption of an heroic solo quartet of recently invented valve horns. It could go still further in this respect, because the orchestra includes a pair of standard natural or ‘crooked’ horns, contrasting their limited ability to stick within the harmonic series with the chromatic capabilities of the soloists. This combination of old and new technologies is mirrored in the formal construction of the work which, as Professor McLeish observes, is a Romantic reworking of the Baroque ‘Concerto Grosso’. The result is harmonically daring for the time and formally fluid, playing as a continuous piece divided into three distinct movements.
The analysis is written in a style that may best be described as traditional, or even ‘Toveyan’. It follows a narrative account of the piece, punctuating its analytical points with some more personal remarks. The problem with this approach is that it results in the kind of subjective interpretations that would probably leave scientists decrying a lack of rigour. It is not really possible to disagree with such statements such as: ‘a fanfare to wake the dead’ or ‘the mountainous landscape of the first movement and the watery ideas of the second have found a rather terrifying way of combining forces [in the third movement]’, other than to say that, for this listener at least, that is not how this composition comes across at all. It is, to my ears, a rather showy concert piece that is designed to amaze its audience. Its overall character is celebratory, and it aims to demonstrate virtuosity in both performance and composition. Its fleeting moods are rather mannered, even operatic, in contrast to the consistently introspective intensity of Schumann's piano music. Now, it is equally possible to disagree with that description, which shows the problem with subjective interpretations: they tend to say more about the analyst than they do about the object of analysis.
This desire to convey the poetic content of Schumann's music spills over into the more objectively analytical aspects of this chapter too. The opening two chords, for example, are analysed as ‘a bold and accented falling minor third’ which is a ‘statement of ambivalence’. While it is certainly true that the upper voices contain a falling minor third, this could also be read much more straightforwardly as an unresolved ii-V-I cadence in the home key of F major and therefore not ambivalent at all. It simply and quickly sets up an expectation of the tonic that is amply met later on. This is a fairly typical technique of Schumann, and indeed many other Romantic composers. Similarly, the ‘harmonic reversal’ in bar 15 is really quite conventional – just a cadence in the dominant (as a footnote acknowledges) – and not really so ‘unsettling’. The imitative horn entries are described as ‘canons’, but they are not really seen through as such. There are more examples of such slightly overstated points, which seem to arise mainly because of the desire to underline the arguments made earlier about the nature of Schumann's creativity.
The analysis as a whole is difficult to follow, because there are no bar numbers given and, strangely, no clefs on the music examples, which is not such a problem in the horn examples, but confusing when other instruments are added. The most striking comment it contains is an analogy drawn between the formal ambiguity of the end of the development/opening of the recapitulation and ‘the overlapping genes of some viral DNA’ which ‘allows up to a three-fold compression of information’. This idea is not developed any further, which is a shame because it hints at an entirely different analytical approach to the one adopted here. The purpose of all this analysis is to draw parallels between Schumann's thought processes and those of mathematicians like Poincaré. But a piece of music is the outcome of a creative process, rather than the process itself, even when (as sometimes in Beethoven) it dramatizes the act of composition. What would seal the argument in favour of a connection between mathematical and musical creativity would be a genetic analysis of a work by Schumann, or any other composer, rather than merely an analysis of the finished composition. Just as the descriptions in Hadamard's A Mathematician's Mind focus on creative processes rather than the finished products, so an understanding of the technical aspects (rather than the psychology) of the gestation of a composition would tell us a great deal. This could easily be assembled from sketches and would provide a solid basis for the discussion of the preceding section about Schumman's creative life.
This analysis, in turn, leads on to a similarly close reading of the Fluctuation-Dissipation Theorem, and a discussion of the mental processes of Einstein and then those of Harry Nyquist, Herbert Callen and Theodore Welton. Here the account feels much more solid. The parallels drawn between these and the processes of composers such as Schumann are certainly remarkable and the observations that are made are convincing.
The critical reservations expressed above do not seek to undermine the central propositions of The Poetry and Music of Science, but rather to support and develop them. This is a very important book, because its arguments should persuade even the most reluctant academics that the ‘Two Cultures’ model is no longer (if it ever really was) viable. It also provides a valuable corrective to histories of science, by placing the human being at the centre of things. Science, with its desire for ‘objective’ truths, tends to downplay human factors in favour of a Grand Narrative of heroic breakthroughs. In human terms, we may suggest that Science is a useful fiction, whereas Art is a useless fact (even if both make strenuous claims for the opposite position). But The Poetry and Music of Science demonstrates, at least at the level of creativity, both are equally capable of accommodating utility and inutility, imagination and reality. Simple distinctions between the two are inadequate. Art and Science are both as poetic and as musical as Science and Art. What is the knowledge that is conveyed by a work of art? What are the poetics of so-called hard science? These are the real questions that are addressed in this book.