I was really trying to stay out of this thread, but NOW you've done it.
Pythagoras -- not only one of history's greatest mathematicians,
but the
experimental physicist who first put music and harmony
on a firm, solid and
permanent mathematical foundation -- believed that Number
(more specifically,
the Whole Numbers or positive integers) is the Ultimate
Reality.
Everything else we experience -- people on the subway,
air, the stars and planets,
grape jelly, sounds, smells -- are just sort of fuzzy,
hazy reflections of this
ultimate numerical reality filtered through our very
imperfect and myopic
perceptions.
If this sounds flakey to you, remember whom you're calling
a flake. Also, most
practicing mathematicians tend privately and personally
to hold some form of the
Pythagorean belief.
As Pythagoreanism made its way through 2500 years of mathematicians
and
philosophers (P's chief advocate and disciple was Plato),
a very widespread
modern belief is that mathematics is entirely independent
of human thought or
human existence -- that, indeed, Number Exists eternally
and incorruptibly in
some Locus independent of time and space, whether we're
here thinking about
mathematics or not. We can have contact with and experience
of these "Platonic
Objects" (perfectly straight lines, perfectly flat planes,
dimensionless points,
perfect circles) never through our senses, but only through
the intellect.
One implication of this is that no one ever Invents new
mathematics; rather, the
best you can do is Discover some previously unknown aspect
of mathematics that
was already eternally in existence in the eternal Locus.
Bach Invents. Shakespeare
Invents; had they not written their compositions and
plays, no one would ever
have subsequently done so. But Newton and Leibniz only
Discover; had they not
lived or died young, inevitably someone would have come
along and Discovered
precisely the same Calculus.
Back to Pythagoras' original flakey contention. While
he lived, he showed that
music, including its emotional effects on the human heart,
was entirely numerical.
Long after his death, an obscure monk and gardener in
Moravia discovered that
the fundamental basis of all living heredity is based
entirely on Whole Numbers, in
the famous and previously discovered pattern known as
Pascal's Triangle. Earlier,
a vast collection of natural phenomena (foliation of
leaves, population growth of
rabbits) was shown to obey the simple integer pattern
known as Fibonacci's
Series: 0, 1, 1, 2, 3, 5, 8, 13 ...
In the 18th century, the Quaker schoolteacher Dalton discovered
that chemistry --
the elements and molecules -- are also entirely a function
of Whole Numbers. In
fact the history of the sciences is largely a history
of discovery that -- as
Pythagoras stated bluntly -- physical Reality, whatever
it may or may not be, is
entirely constructed around a numerical design.
The best (prose, don't be frightened) introduction to
this notion is The Character
of Physical Law by the Nobel physicist
Richard Feynman. Why is physical law so
inherently, consistently and inescapably mathematical?
he asks. "I haven't the
slightest idea," he replies. But it is.
Numbers exist. Get with that.
Bob Merkin