28 Chapter 2
associated with a high pitch. Moving inward from it, the planets closer to Earth should
then have successively lower pitches, until we reach the unmoving (and hence presumably
silent) Earth itself. But this seems to him problematic, for those most exalted stellar spheres
would seem more suitably associated with deep, solemn tones, not high-pitched squeaks.
These musical considerations concern a cosmological decision of considerable importance,
undecided on purely astronomical grounds. One wonders, too, whether he was troubled
by the correlate arguments implied for the “ music ” of the Earth, in each case. On the
contrary supposition, the Earth ’ s immobility would be associated with the highest pitch,
which also seems problematic: how can an immobile body be associated with a high degree
of vibration?
Oresme does not comment on these incongruities, so it is not finally possible to assess
their significance for him. If we were to take them most seriously, they would seem to
impeach the geocentric view on musical grounds. As such, they might be read as forming
an implicit extension of his antigeocentric arguments, amassed above, perhaps indicating
to discerning readers a hidden heliocentric drift in Oresme ’ s argument, his disclaimer
notwithstanding. But nothing in the text authorizes us to take this rather conspiratorial
reading as anything more than speculation. What is clear is that, for Oresme, musical
arguments can address otherwise undecidable astronomical questions.
In his Livre du ciel , Oresme brings this approach to bear on his own inquiry into the
relative status of incommensurable versus commensurable celestial movements. Here
again he faces issues that are not decidable from within astronomy alone; he reminds us
that nothing tells us a priori whether any given celestial sphere is or is not commensurable
with another, though far more likely to be incommensurable. In his earlier Tractatus de
commensurabilitate vel incommensurabilitate motuum celi ( Treatise on the Commensura-
bility or Incommensurability of the Celestial Motions , written sometime during 1340 –
1377), Oresme staged this problem in the form of a debate between personified figures of
Arithmetic and Geometry, enacted at the command of Apollo himself. The whole dramatic
scene is unique among his works, which he generally phrased in the traditional Euclidean
style of geometrical propositions.
Appearing as a character in his own drama, Oresme expresses his perplexity whether
incommensurability is actually present in astronomy or only a purely theoretical possibil-
ity. Then Apollo, accompanied by the Muses, Arts, and Sciences, appears to Oresme “ as
if in a dream. ” Apollo rebukes him for being “ ignorant of the ratios relating the things of
this world ” and hence subject to “ affliction of the spirit and an unending labor. ” Apollo
phrases the problem trenchantly; “ an imperceptible excess — even a part smaller than a
thousandth — could destroy an equality and alter a ratio from rational to irrational. ” Citing
the authority of al-Battani ( “ if you have read him ” ), Apollo concludes that “ the ratios of
these motions is unknown, and neither arithmetic nor geometry can lead you to a knowl-
edge of it. ” Addressing Apollo as his “ dear father, ” Oresme reiterates “ that it is not given
to human powers to discover such things ” (his stated position on the geocentric