Hiding in the Mirror Read Free

theories unique—do they represent some fundamental
underlying reality about nature—or have we just chosen one of many
different, possibly equally viable, mathematical frameworks within
which to pose our questions? In this latter case, would the
apparent underlying physical pictures corresponding to these other
mathematical descriptions each be totally different?
    Because we have made huge strides in our
understanding of the nature of scientific theories in the
intervening forty years since Wigner penned his essay, I believe we
can safely say that the question he poses is no longer of any great
concern to scientists. We understand precisely how different
mathematical theories can lead to equivalent predictions of
physical phenomena, because some aspects of the theory will be
mathematically irrelevant at some physical scales and not at
others. Moreover, we now tend to think in terms of “symmetries” of
nature, what are reflected in the underlying mathematics. While this
once again argues for the importance of mathematics in our
understanding of nature, these symmetries themselves seem so
fundamental that we expect that any theory that can produce correct
predictions must reflect them. Thus, seemingly different
mathematical formulations can really be understood to reflect
identical underlying physical pictures. There is also a flip side to
the discussion regarding the unusual effectiveness of mathematics
in describing nature. Not all novel mathematical notions that open
new horizons for our imagination have correlatives in the natural
world. If that were the case, science would be no more than
searching for new mathematics.
    The power of mathematics will play a large role
in what follows, but when it comes to the relationship between our
scientific imagination and reality, elegance or mathematical beauty
is by itself not sufficient to generate fruitful science. What
matters are results. That is why science isn’t philosophy, and why
nature holds the upper hand. As Richard Feynman once put it,
science is “imagination in a strait-jacket.” In the end our
theories rise and fall based on their successful ability to
quantitatively predict the future. Imagination truly rises to the
level of beauty in science when it allows one to make predictions
about things that one may never have thought were predictable.
    To return to Plato’s cave, Socrates pointed out
that the unfortunate soul who had literally seen the light would,
when dragged back in the cave, appear at first to his former
compatriots to be a lunatic. This does not, however, mean that all
lunatics have seen the light. Every religious prophet in history,
for example, from Moses to Jesus, from Mohammed to Joseph Smith has
cloaked his or her revelations in language similar to Plato’s. They
all suggest that to see the true nature of the world, we merely
have to remove the curtains in front of our eyes. But they cannot all be correct. There are different worlds
behind each of their curtains. Which brings us inevitably to
another complementary aspect of the human experience that literally
depends on the existence of another world: religion. It is perhaps
not surprising that one of the most popular Christian writers of
the the twentieth century, C. S. Lewis, produced a profoundly
successful children’s series, The Chronicles of
Narnia, which literally exploited a whole new world hidden just
under our noses in order to relay its highly allegorical epic saga.
Lewis’s Narnia was not like Tolkien’s Middle Earth, located far,
far away and long, long ago. Rather, it could be accessed simply by
entering an old wardrobe located in a professor’s cluttered house
in the country. This was supposed to be some kind of magic, but it
is in a fundamental sense not too different from Bill’s portal
through the fourth dimension that aired less than a decade later on
the Twilight Zone . Lewis’s fantasy stems
from a long tradition that indeed lies in that dimension that