1 The Birth of Science - MSRI

11.11 Recovery and Crisis of Scientific Methodology 351
theories, a culture that still confused theoretical entities with real objects
found it normal to attribute to nature the inconsistency of science itself.
Not surprisingly, an intellectual edifice built on the laying aside of the
non-contradiction principle must claim citizenship in a country quite distant
from mathematics. Thus de Broglie writes:
In explaining scientific theories the “axiomatic” method is the most
pleasing to reason, but in practice the least fruitful, except perhaps
in the field of pure mathematics. 191
We must conclude that for the creator of particle-wave duality, pleasing
reason is a dangerous obstacle to the advance of science. De Broglie’s ideas
are deeply rooted in old traditions, also prized by Niels Bohr. This author,
in his book The unity of human knowledge, illustrates his complementarity
principle with the following comments, among others:
Indeed, in renouncing logical analysis to an increasing degree and
in turn allowing the play on all string of emotion, poetry, painting
and music contain possibilities of bridging between extreme modes
as those characterized as pragmatic and mystic. Conversely, already
ancient Indian thinkers understood the logical difficulties in giving
exhaustive expression for such wholeness. . . .
[I]t is equally clear that compassion can bring everyone in conflict
with any concisely formulated idea of justice. We are here confronted
with complementary relationships inherent in the human position,
and unforgettably expressed in old Chinese philosophy, reminding
us that in the great drama of existence we are ourselves both actors
and spectators. 192
And perhaps, too, when the Pythagorean school ran into an impasse in
classifying the diagonal of the square, someone resorted to Eastern teachings
and the inherently contradictory nature of the world, and proposed a
solution: to declare the diagonal a profoundly ambiguous entity featuring
a duality or complementarity between even and odd.
191 [de Broglie], p. ??
192 [Bohr], at 72% and 81%.
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