According to Wikipedia:
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae
(the law of parsimony, economy or succinctness), is a principle that generally recommends from among competing hypotheses
selecting the one that makes the fewest new assumptions.
Occam's Razor is used by scientists to browbeat other scientists and lay people. In general, Occam's Razor is a
sideways method of saying what would be perverse in mathematics: "It's obvious."
The average human being knows to be on the lookout any time he or she hears that something is obvious, yet every
scientist needs a way to add weight to his or her theory and accomplishes this by invoking Occam's Razor.
Consider the example in Wikipedia: The idea that the planets revolve around the sun as opposed
to the sun and other planets revolving around Earth is proven by the invocation of Occam's Razor.
What exactly is simpler about the first theory than the second one? The math is simpler.
The math involved in explaining the rotation of the planets about the sun is simpler than the math involved in having the
Earth as the center of the Universe. In fact, we would probably have problems with Einsteinian equations were to pursue
this latter idea.
So the simpler mathematics (and more rational physics) is the "proof" that the Earth is neither the
center of our solar system or of the Universe.
There you have it: Earth loses, Sun wins.
Well, not quite.
Actually, any equations that place the Sun at the center of the solar system will be dubious.
The problem here is that while the gravitational field of the sun has the greatest impact of the various bodies in our solar
system, the other bodies (from asteroids to planets) all that their own gravitational pull, and everyone of them are all pulling
and jerking at every other one.
And while all that motion is trying to achieve some kind of equilibrium, it is all happening as the
entire solar system is itself in motion about ... well, about something. Probably.
As arrogant as it was to assume the Earth was the center of the universe, it is no less arrogant
assuming our Solar System is -- the math is just as complicated.
The fault here was directly from the invocation of Occam's Razor. It seemed obvious that all
planetary motion could be related to our sun more easily than to any other planet; but ultimately that failed, too.
In truth, no process is simple. Biological processes are so complex that, were Occam's Razor to be invoked, it
is most likely that fairies rule the world of living things.
The assumptions behind fairies are much less complex and demanding than those behind Solartropism and DNA and RNA and
self-replicating viruses and species' variations and ...
Of course, that isn't really how Occam's Razor is wielded. The heart of Occam's Razor lies in the imposition of
mathematics on the world being described. If math can be imposed on one explanation and not fitted to the other, then
the latter is considered too complex and the former to have the better chance of being right.
Unfortunately, math fails to perfectly fit any physical process.