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.
