Yourgrau P. A world without time.. the forgotten legacy of Goedel and Einstein (Basic Books, 2005)(ISBN 0465092934)(176s)_PPop_

more sympathetic, however, to another of Mach's maxims, against the excessive use of
abstract mathematics in theoretical physics. Mach's preoccupation with the data of sensory
experience made him suspicious of high flights of the mathematical imagination. He
suspected mathematicians of substituting the artful manipulation of symbols for the honest
work of empirical testing and confirmation. Einstein was sympathetic. The mathematics of
his revolutionary paper on special relativity was relatively elementary, and at first he
resisted its reformulation in terms of four-dimensional space-time by his former teacher
Hermann Minkowski, complaining that "since the mathematicians pounced on the relativity
theory I no longer understand it myself." Unlike Mach, however, he quickly came to his
senses, and fortunately so, since the progression from special to general
relativityóEinstein's crowning achievementówould have been impossible without
Minkowski's mathematical reformulation.
Einstein believed that physical reality contained more than what we can derive from the
data of sensory experience. The real world, for him, was what corresponded to physical
theory. It consisted of entities like atoms and force fields, in themselves undetectable by
the senses, but indirectly discernible by their effects on systems that can affect human or
artificial receptors. Mach, in contrast, had no truck with theoretical constructs and
remained skeptical of anything that could not be reduced to a law based on a combination
of sensory experiences. This bias had several consequences, each individually devastating
to
scientific inquiry. First, Mach remained to his final days violently opposed to the new
scientific view that much of the real world consists of entities, like atoms, forever invisible
to the unaided human senses. This stance by such a powerful figure hindered scientists, in
their research and in their careers, who did not share Mach's prejudice, and ensured that
Mach's own scientific worldview would become increasingly irrelevant. As Einstein wrote
later, "the antipathy of these scholars [Oswald, Mach] towards atomic theory can
indubitably be traced back to their positivistic philosophical attitude. This is an interesting
example of the fact that even scholars of audacious spirit and fine instinct can be
obstructed in the interpretation of facts by philosophical prejudices."
Second, Mach, by intention the most empiricist of thinkers, was rendered indistinguishable
from the philosophical "idealists" who believe that the real world is simply a fiction created
by the human mind. The sensations that for Mach formed the very basis of science are
after all individual, private, subjective mental phenomena that cannot be shared, in direct
contrast to the shared, objective, independent physical world that constitutes the
mainstay of the empiricist worldview. Ironically, it is the mathematical Platonist Frege
who turns out to be a greater empirical realist than the supposedly hardnosed Mach. In
"Thought," a late essay, Frege wrote, "We really experience only [our mental] ideas, not
their causes. And if the scientist wants to avoid all mere hypothesis, then he is left just
with ideas; everything dissolves into ideas, even the light rays [and] nerve fibers . . . from
which he started. So he finally undermines the foundations of his own construction." Frege
was not the only prominent figure to be alarmed by Mach's tendency toward idealism. In
Materialism and Empirio-Criticism, in 1909, V. I. Lenin took time out from the revolution to
launch a spirited critique of Mach's idealistic tendencies. That the busy Lenin thought it
necessary to refute him is an indication of Mach's reach.