reductionism and the sum of the parts


Regards the limitations of reductionism, Ludwig von Bertalanffy said
the following sometime prior to 1972, the year he died ....

"... Entities of an essentially new sort are entering the sphere of
scientific thought. Classical science in its diverse disciplines, be it
chemistry, biology, psychology or the social sciences, tried to isolate
the elements of the observed universe - chemical compounds and enzymes,
cells, elementary sensations, freely competing individuals, what not -
expecting that, by putting them back together again, conceptually or
experimentally, the whole or system - cell, mind, society - would
result and be intelligeble. Now we have learned that for an
understanding not only the elements but their interrelations as well
are required ...".

LvB was one of the pioneers of general systems theory, which predated
cybernetics and which LvB considered to be a subtopic of systems
science mainly dealing with feedback.

http://pespmc1.vub.ac.be/SYSTHEOR.html

Basically, LvB was saying there is only so much you can learn via
reductionism, and even if you know the properties of the individual
units, this still doesn't mean you can reassemble them and get the
system working as it was prior to disassembly. This may not be so
obvious with something like a pontiac, but it certainly is with respect
to a dissected cat. Just try and reassemble a living cat from a
chemical soup.

IOW, there are certain relationships and rules or laws that appear when
you have units "interacting together" which aren't necessarily obvious
from knowledge of the components. LvB's systems theory is all about
these interections. I would say getting H2O by assembling O2 and H2 is
one case. Much more complex cases involve anything nonlinear,
especially when feedback is added, and especially when there are
millions or billions of interacting units. Biological organisms are a
clear example of this last situation.

Even so simple a case as the population equation produces unpredictable
outputs, depending upon the parameter K, and the starting x value.

http://en.wikipedia.org/wiki/Logistic_model

x(next) = Kx(1-x) = Kx - K*(x^2)

The reason this simple equation produces chaotic output is due to the
presence of both positive feedback, Kx term, and negative feedback,
-K*(x^2) term, as well as the nonlinearity, (x^2). These are 3 of the
important aspects recognized within mathematical complexity as
necressary for producing so-called "self-organized criticalities".

The whole is more than the simple sum of the parts because of the
nonlinearities. With linear systems, you can predict the outputs when
combining the inputs. With nonlinear systems, this is not the case.


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