The Dream of Oresme 29
controversy) yet still asks “ why did you make the very nature of men such that they desire
to know, and then deceive or frustrate this desire by concealing from us the most important
truths? ” Responding to the intensity of Oresme ’ s pleas, Apollo, “ smiling, ” orders the Arts
and Sciences “ to teach him what he asks. ” Thereupon Arithmetic and Geometry respec-
tively plead their opposing positions before this highest court of knowledge. Apollo then
orders them both “ to defend their cause with reasoned arguments, as if they were litigants
in a lawsuit, ” while Oresme listens “ filled with wonder. ”^11
As Apollo indicated, arithmetic or geometry alone cannot decide such larger issues that
involve all the arts and sciences. Nor does Oresme personify astronomy as a speaker in
the debate, for her status would be dependent on the result of this debate, which concerns
the basis of her science. In the end, both sides invoke music as a deciding factor to break
the mathematical deadlock.
Arithmetic ’ s position is the most straightforward and traditional, as befits her claim to
be “ firstborn ” of the quadrivium, on whose concepts all the others depend. Her biblical
allusion that “ the architect ” built everything according to “ number, weight, and measure ”
still does not quite resolve these more detailed mathematical issues. Arithmetic argues that
“ the greatest prince of all, himself one and three everywhere, ” the triune God, disclosed
the primacy of number when he “ arranged all things pleasantly, that is, harmonically, ”
using rational quantities because each “ irrational proportion is discordant and strange in
harmony, and, consequently, foreign to every consonance, so that it seems more appropri-
ate to the wild lamentations of miserable hell than to celestial motions that unite, with
marvelous control, the musical melodies soothing a great world. ” Arithmetic then cites a
host of ancient authorities from Hermes Trismegistus to Cicero attesting to the sublime
pleasantness of the celestial concords, and hence their consonance. She also notes the
consequent deduction of the Platonic Great Year and other recurrent astronomical cycles
noted by the ancients. But her deepest argument seems to be that irrational proportions
sound terrible and thus cannot be allowed in a harmonious cosmos.^12
In response, Geometry does not deny “ a certain eternal beauty and perfection in her
[sister ’ s] rational ratios ” but wants to subsume them in a larger and less consonant musical
whole. Her argument moves boldly toward a praise of artistic innovation: “ The heavens
would glitter with even greater splendor ” if some motions were incommensurable than if
all were purely commensurable. Though she disputes Arithmetic ’ s claim of precedence as
the “ firstborn, ” Geometry does not try to argue that irrational ratios are more pleasant than
rational ratios. Rather, she considers that Arithmetic ’ s reliance on the criterion of pleasure
is artistically inadequate to grasp the full complexity of cosmic music, for which diversity
is Geometry ’ s touchstone: “ What song would please that is frequently or oft repeated?
Would not such uniformity produce disgust? It surely would, for novelty is more delight-
ful. ” Geometry asserts that purely rational music would be like the sound of a cuckoo,
annoyingly repetitive not only in its uniformity of elements but in its endless
recurrences.^13