HI Robert, I hate to get back in the swim with you guys on the subjects of reductionism and emergence and so on, because you all seem to have it well expressed. So let's agree I'm out of that loop.
But I was intrigued by your comments on Barrow's book, which I hadn't heard
about. To summarize what Robert reports on Barrows' book, the physical laws,
satisfy symmetry, but real physical processes break symmetry. The physical
laws necessarily satisfy symmetry, meaning that there are no preferred
observers. (Emmy Noether; continuous symmetries and conservation laws;
symmetrical.)
For more, see my recent book , Hidden Harmony: The Connected Worlds of Physics
and Art (Johns Hopkins University Press, 2008), J. R. Leibowitz. Incidentally,
those interested in art, like Orlando, may find the discussions on formal
analysis in art interesting. (Orlando already is familiar with the book's
discussion on formal analysis in art).
Jack.
----- Original Message -----
From: Robert Cordingley
To: The Friday Morning Applied Complexity Coffee Group
Sent: Monday, September 08, 2008 9:29 AM
Subject: Re: [FRIAM] Reductionism - was: Young but distant gallaxies
I'm reading "The Book of Nothing" by John D. Barrow which begins with a
history of the concepts of zero, nothing, 0 (the place holder) and the void and
moves smoothly on through sets and on to quantum physics. The book raises lots
of questions for me and Ken's post struck a chord. On page 235:
"Yet, despite the symmetry of the laws of Nature, we observe the outcomes of
those symmetrical laws to be asymmetrical states and structures. Each of us is
a complicated asymmetrical outcome of the laws of electromagnetism and gravity.
... One of Nature's deep secrets is the fact that the outcomes of the laws of
Nature do not have to possess the same symmetries as the laws themselves.... it
is possible to have a Universe governed by a very small number of simple
symmetrical laws (perhaps just a single law) yet manifesting a stupendous array
of complex, asymmetrical states and structures that might even be able to think
about themselves."
If physicists find the perhaps one law (the Grand Unified Theory?) isn't that
the ultimate in reductionism? Everything else is just playing in the resulting
stardust.
So is the study of complexity just another way of looking at the asymmetries?
Apparently too Descartes denied that a vacuum could exist (ibid p119), let
alone 0, but now physicists ideas of what a vacuum is seem to make it something
other than a complete void, possessing zero-point energy. So may be D had a
point?
Robert C
Kenneth Lloyd wrote:
Steve,
Good job on the defense of a reductionist position. I utilize a five phase
approach to the study of complex systems.
Definition - Analysis - Normalization - Synthesis - Realization (DANSR)
Reductionism has its place in the analytical phase at equilibrium.
Analysis is normally a study of integrable, often linear systems, but it can be
accomplished on non-linear, feed-forward systems as well. The synthesis phase
puts information re: complex behavior and emergence back into the integrated
mix and may be "analyzed" in non-linear, recurrent networks. This is actually
a probabilistic inversion of analysis as described in Inverse Theory.
Bayesian refinement cycles (forward <-> inverse) are applied to new
information as one progresses through the DANSR cycle. This refines the effect
of new information on prior information - which I hope folks see is not simply
additive - and which may be entirely disruptive (see evolution of science
itself) .
The fact this seems to work for complex systems is philosophically
uninteresting, and may ignored - so the discussion can continue.
Final point: Descartes ultimately rejected the concept of zero because of
historical religious orthodoxy - so he personally never applied it to the
continuum extension of negative numbers. All his original Cartesian coordinates
started with 1 on a finite bottom, left-hand boundary - according to Zero, The
Biography of a Dangerous Idea, by Charles Seife.
Ken
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From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Steve Smith
Sent: Sunday, September 07, 2008 6:42 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Aku
Subject: Re: [FRIAM] Reductionism - was: Young but distant gallaxies
Orlando-
You can find good references in Wikipedia on this topic, including the
Descartes references.
------------------------------------------------------------------------
Reductionism
From Wikipedia, the free encyclopedia
Descartes held that non-human animals could be reductively explained as
automata - De homines 1662.
Reductionism can either mean (a) an approach to understanding the
nature of complex things by reducing them to the interactions of their parts,
or to simpler or more fundamental things or (b) a philosophical position that a
complex system is nothing but the sum of its parts, and that an account of it
can be reduced to accounts of individual constituents.[1] This can be said of
objects, phenomena, explanations, theories, and meanings.
------------------------------------------------------------------------
All -
IMO,
Reductionism(a) is a highly utilitarian approach to understanding complex
problems, but in some important cases insufficient. It applies well to easily
observable systems of distinct elements with obvious relations operating within
the regime they were designed, evolved, or selected for. It applies even
better to engineered systems which were designed, built and tested using
reductionist principles. I'm not sure how useful or apt it is beyond that.
Some might argue, that this covers so much, who cares about what is left
over?... and this might distinguish the rest of us from hard-core
reductionists... we are interested in the phenomena, systems, and regimes where
such does not apply. This is perhaps what defines Complexity Scientists and
Practitioners.
Reductionism(b) is a philosophical extension of (a) which has a nice feel
to it for those who operate in the regime where (a) holds well. To the extent
that most of the (non-social) problems we encounter in our man-made world tend
to lie (by design) in this regime, this is not a bad approach. To the extent
that much of science is done in the service of some kind of engineering
(ultimately to yield a better material, process or product), it also works
well.
Reductionism(b) might be directly confronted by the "Halting Problem" in
computability theory. Reductionism in it's strongest form would suggest that
the behaviour of any given system could ultimately be predicted by studying the
behaviour of it's parts. There are certainly large numbers of examples where
this is at least approximately true (and useful), otherwise we wouldn't have
unit-testing in our software systems, we wouldn't have interchangeable parts,
we wouldn't be able to make any useful predictions whatsoever about anything.
But if it were fully and literally true, it could be applied to programs in
Turing-Complete systems. My own argument here leads me to ponder what (if
any) range of interesting problems lie in the regime between the embarrassingly
reduceable and the (non)-halting program.
But to suggest (insist) that *all* systems and *all* phenomenology can be
understood (and predicted) simply by reductionism seems to have been dismissed
by most serious scientists some while ago. Complexity Science and those who
study Emergent Phenomena implicitly leave Reductionism behind once they get
into "truly" complex systems and emergent phenomena.
I, myself, prefer (simple) reductionistic simplifications over (complex)
handwaving ones (see Occam's Razor) most of the time, but when the going gets
tough (or the systems get complex), reductionism *becomes* nothing more than
handwaving in my experience.
- Steve
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