The Dream of Oresme 25
the verse from the Psalms seems disingenuous, given his own dismissal of literal appeals
to figurative language in the scriptures. Oresme presents his antigeocentric presentation
as an “ intellectual exercise ” and mere “ diversion, ” hence purely hypothetical and therefore
not subject to the rigorous doctrinal scrutiny he may have anticipated, had he put forward
those views as realistic representations of the cosmos. His allusion to “ those who
would like to impugn our faith by argument ” may refer to long-standing controversies
about the relation of reason to the mysteries of faith; as such, he tacitly seems to indicate
the mathematically simpler motion of the Earth, compared to geocentric cosmology.
His passing comment that the alternative cosmology may violate natural reason as much
as “ the articles of our faith ” could be read as comparing the difficulties of the antigeocen-
tric view with those already surmounted by Christian apologists. His implicit suggestion
may be that heliocentrism strains human credulity no less than do the paradoxes of
Christian doctrine.
But setting aside these more or less speculative possibilities, it is more likely that
Oresme considered the matter finally undecidable, however probable the arguments he
adduced for the Earth ’ s motion and rotation. Likely affected by the wider skeptical and
probabilistic currents in fourteenth-century natural philosophy, Oresme wrote that “ I
indeed know nothing except that I know that I know nothing ” about natural knowledge,
using the famous Socratic formulation to express the inadequacy of human opinion. As
such, he distanced himself from the “ real ” explanations later claimed by Copernicus and
Galileo because of his principled demurral from certainty, which also may have accorded
conveniently with his desire to avoid doctrinal controversy.^10 Even so, we cannot consider
his position merely timorous; he seems quite sincerely to have considered the foundations
of natural philosophy ultimately to lie beyond human certainty — and it remains possible
that he was right.
In trying to assess his real views, however, we should include his treatment of the
musical context of astronomy that immediately precedes his discussion of geocentrism.
His musical considerations provide additional and perhaps decisive evidence against the
diurnal movement of the heavens and hence against geocentrism. Oresme follows Aristotle
in considering that the celestial harmonies are not audible, but he takes the primal musical
proportions quite seriously, arranging the harmonic ratios in a two-dimensional array, a
figure he considers full of “ very great mysteries ” ( figure 2.2, table 2.1 ). Note that the top
row contains the successive powers of 2 (1, 2, 4, 8, 16, 32), while the leftmost column
lists the powers of 3 (1, 3, 9, 27, 81, 243). Then the interior of the array lists the various
products of these outer rows and columns precisely in accord with the modern rule for the
terms of a matrix: the term in the n th row and m th column is given by nm. This may be
the earliest “ matrix ” (though without using that modern term), in which Oresme lists all
the various possible products that appear in musical theory, as he knows it. His diagram
contains many blank cells, in addition to those in which he has noted numbers that appear
explicitly in musical theory. By thus drawing attention to the other, heretofore unnoticed