> I don't beleive there is any way to
> describe a whole without resorting to a reductionist explanation. If
> you can think of an example please let me know.
I believe I have an example: Imagine a circle in XY plan. I can make the
projections of this circle in line X and line Y. But now, when we try to
re-compose the circle, it is not a circle anymore, it is a square. So, a
circle in 2D can not be decomposable into its 1D projections. We have
to use the equation x2 + y2 = r2 as a holistic description, in order to
understand it.
OBSERVATION: This is only a (bad) analogy. To be more correct,
I would have to talk about a function that can not be decomposable
in terms of sums, squares and products. It is interesting as I can't
describe such functions in an algebraic way, as the whole algebra
is based on sums, products and other primitive (holistic) functions. BUT
I can conceive the existence of such functions. A totally random function
would be a function like that. I can imagine also other functions that are
not random, but still are not "realizable" through mathematics. The most
interesting is that they may be realizable through a physical device. For
example: physical lens. With its imperfections and non-linearities. The
input of this "function" would be the angle in which a light bean inputs the
lens, and
the result would be the angle it outputs the lens. Depending on the physical
format of the lens, this function would not be "realizable" through
mathematics.
The maximum that mathematics can gives me is an APPROXIMATION of
such functions. The question here is .... can we live only with an
approximation,
instead the real function ? If there is no chaotic behavior in the system,
it's OK,
but if there is some tendency to chaos, the fact we are using an
approximation
instead the real function would imply in unexpected behavior.
Maybe Don can exemplify other problems that would appear due to the use
of approximations instead of the real functions. This problem with chaos is
one that
occurs now on my mind. Maybe Rosen had catalogued others ?
Best regards,
Ricardo
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