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governed by mathematics. String theory and loop quantum gravity are only the latest
“ grand unified theories ” based on the synthetic power of mathematics. Despite the enor-
mous historical changes across this vastly diverse range of time and theories, this cosmic
sense of music and quest for universal harmony remains a recurrent theme. Indeed, con-
temporary theoretical physics at every point takes its bearings from the Pythagorean
project to explain how all is number , so that even “ chaos ” has its mathematical parameters
and universal exponents.
From its beginnings until now, science has followed music, which first connected the
senses to the invisible realm of mathematical theory. In our treatment, even the “ scientific
revolution ” has been an episode in the larger story of how music, mathematics, and experi-
mental natural philosophy decisively came together. Music, after all, first brought forward
experiment as well as the mathematical approach to physics, bridging the ancient divide
between number and magnitude: music harmonized experience with mathematics. Ironi-
cally (or perhaps with poetic justice), the very success of this hybrid enterprise tended to
bury the musical traces under ever denser, more powerful mathematical formalism. One
might legitimately wonder whether the ancient quadrivium gave up the ghost, exhausted
after giving birth to modern science. The language of “ sedimentation ” suggests a decorous
form of burial, with dignified geological overtones; even intentional “ desedimentation ”
suggests exhuming graves, however piously. In contrast, though, the examples considered
in this book show many points at which these ancient musical concepts return to life as
persistent themes and continuing questions. For music, mathematics, and science, the rest
is not silence.