In the first place we must take into account the musician’s lack of experience in the scientific vocabulary, in the use of which he exhibits neither ease nor skill, invention nor imagination, not to speak of the imprecision of that vocabulary itself or the gaps in his knowledge of it. And even supposing his use of its concepts and terms to be perfectly correct, he does no more than go from one sterile plagiarism to another, impoverishing the language of science without enriching that of music. One can only smile at the diagrams and treatises that consist of a mad collection of permutations totally devoid of interest. Such parallels with scientific procedures remain hopelessly superficial because they do not spring from any musical thought. All reflections on musical technique must be based on sound and duration, the composer’s raw material; and imposing some alien ‘grid’ on these reflections can result only in a caricature. No examination of different forms of permutation will convince us of the quality of the result when these permutations are realized in the substance or the structure of a musical work. What guarantee can there possibly be that a figured scheme, carefully described to the last detail, can—simply as such—support the whole weight of a musical structure? Who can prove to me that numerical laws, however valid in themselves, will remain valid when they are applied to categories that they do not govern? Surely these intricate sophistries are a total absurdity, and indeed almost sublime in their craziness.

Number-fanatics of this kind belong to the same class as those who preach the Golden Number and esoteric ideas about the ‘power’ of numbers. In the last resort they are all concerned with the same thing, finding and deciphering ‘secret affinities’ in the universe. Nowadays magic is out of fashion and would be regarded as a handicap, but in fact such people do assume the ‘mysterious powers of numbers’ in a way that carries little more conviction than that of their medieval predecessors. What is more, this juggling with numbers surely reveals a lack of confidence, an impotence and a lack of imagination. Numbers represent a safe refuge from the undependable, incalculable imagination and provide a form of rational reassurance, a cloak (quite genuinely assumed) for the lack of self-confidence in the much more demanding field of pure invention. In its commonest form this play with numbers is simply a routine that can be carried on without any creative faculty whatever. Given a basic material, I can ‘manipulate’ it straightaway and be sure of obtaining results, thus gaining the impression of having invented something, whereas all that I have been doing is rehearsing a catalogue to the point of exhaustion.

In fact, therefore, the majority of ‘scientific’ minds in music are really hardly more ingenious than Jarry’s Monsieur Achras, who collected polyhedra. It remains to be seen whether the interest of such ‘polyhedra’ is inexhaustible . . . I cannot, for the life of me, see the need for them!

.
.
.

. . . scientific ideas are . . . useless when misapplied. . . . misapplications arise from . . . a weakness of the purely musical imagination aggravated by submitting the data of music to wholly alien systems of ideas and priorities. This amateurish approach therefore gives a kind of legal status to a misapprehension which is both honest and sincere. We must reject, without too much sentiment, these sham solutions whose charm lies in the fact they often present facets of what is undeniably the truth. I believe that music warrants its own individual field of study and must not be submitted to mere arrangements of fundamentally alien methods of thought, which have in fact proved a dangerous threat to the freedom of musical thought.

This does not mean that I am deliberately hostile towards all interference or communication between music and the outside world. Far from being an isolationist of this kind, I recognize that contact with other disciplines can be extremely fruitful, in introducing a different order of vision and providing us with glimpses of what we should never have dreamed, stimulating our inventiveness and forcing our imagination to a higher degree of ‘radioactivity’. But influences of this kind can be only by analogy rather than by any literal application, which has no foundation in fact. As I see it, the most important level at which this fertilizing process takes place is the very deepest, namely that of thought-structures—the imagination adapting outside resources to new purposes in a kind of fertilizing process. There are certain [scientific] discoveries . . . that have first to be transposed before their significance is fully realized, and this transposition cannot be effected by any mere juxtaposition or parallel application. What I am really saying is that in the composer’s imagination these different external ‘acquisitions’ assume an exclusively musical form and become specifically and irreversibly musical concepts.

Pierre Boulez