I teach composition class at the Conservatoire where, for the past forty years, I've spent my time decorticating musical works, trying to figure out what happens in them.
– Olivier Messiaen [i]
The idea of the series was engaging [Messiaen's] maximum attention during these years, and it was probably the influence of this fact that caused him to reflect on the possible strict, and strictly calculated, relationships on which his music might depend; there are many instances in these works of a clear conflict between spontaneity and organization, the one unwilling to abdicate and the other determined to become all powerful. This conflict, or antinomy, is reflected even in the titles of the different pieces written between 1949 and 1951 – Les Yeux dans les roues, Les Mains de l'abíme, Ile de feu.
– Pierre Boulez[ii]
If nature were all lawfulness then every phenomenon would share the full symmetry of the universal laws of nature .... The mere fact that this is not so proves that contingency is an essential feature of the world.
– Herman Weyl[iii]
The main fallacy [of] the reductionist hypothesis [is that it] does not by any means imply a “constructionist” one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. . . . The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. . . . [A]t each level of complexity entirely new properties appear. . . . [T]he whole becomes not only more than the sum of but very different from the sum of the parts. . . . [T]he new symmetry – now called broken symmetry because the original symmetry is no longer evident – may be an entirely unexpected kind and extremely difficult to visualize. ... [T]he whole becomes not only more than but very different from the sum of its parts. . . . At some point we have to stop talking about decreasing symmetry and start calling it increasing complication.
– P.W. Anderson[iv]
A symmetry can be exact, approximate, or broken. Exact means unconditionally valid; approximate means valid under certain conditions; broken can mean different things, depending on the object considered and its context. . . . Generally, the breaking of a certain symmetry does not imply that no symmetry is present, but rather that the situation where this symmetry is broken is characterized by a lower symmetry than the original one.
– Stanford Encyclopedia of Philosophy[v]
Asymmetry is what creates a phenomenon.
– Pierre Curie[vi]
[i] Messiaen, O. ______________
[ii] Pierre Boulez. 'Olivier Messiaen' ('Une classe et ses chimères', tribute to Messiaen on his fiftieth birthday from the programme for the Domaine musical concert of 15 April 1959. Tr. by Martin Cooper, 1986.) In Orientations: collected writings. Faber & Faber, 1990. p.414.
[iii] Hermann Weyl. Symmetry. Princeton UP, 1983. p.26
[iv] P.W. Anderson. 'More Is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science'. Science, New Series, Vol. 177, No. 4047. (Aug. 4, 1972), pp. 393-396. Republished in E:CO 2014 16(3): 117-134 with an introduction by Jeffrey A. Goldstein, 'Reduction, construction, and emergence in P. W. Anderson’s "More is different"' available on-line at https://emergentpublications.com/ECO/ECO_other/Issue_16_3_7_CP.pdf?AspxAutoDetectCookieSupport=1 (accessed 30.11.16)
[v] 'Symmetry and Symmetry Breaking'. Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/symmetry-breaking/#4 (accessed 30.11.16)
[vi] Pierre Curie. 'Sur la symétrie dans les phénomènes physiques.' 1894.