Posted by
Phil Henshaw-2 on
URL: http://friam.383.s1.nabble.com/Seminal-Papers-in-Complexity-tp524047p524106.html
Mike,
Non-linear does not need to be defined with equations. Non-linear can
be a process having continuity. Any process that begins and ends with
continuity (i.e. w/o discontinuity) is inherently non-linear because it
requires finite periods of that have all derivatives all of the same
sign. It 'only' requires is developing a calculus for physical system
rates. Search for 'continuity' on my site for some things. It's a
new non-linear kind of math.
Phil Henshaw ????.?? ? `?.????
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-----Original Message-----
From:
[hidden email] [mailto:
[hidden email]] On
Behalf Of Michael Agar
Sent: Tuesday, June 19, 2007 10:41 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Seminal Papers in Complexity
This thread is sliding around some, but still I?d like to add this
overlong comment in case it?s useful. The emails have been good brain
food. The problem I keep worrying about in my own work is, I use many
core concepts metaphorically because they work at the human
organizational scale in powerful and useful ways that I believe respect
their scientific origins but at the same time allow the human/social
world to see and understand and act differently. But I also want to be
clear on those origins, to know and describe when and where and how I?m
stretching the concepts. The problem I have is, up close the conceptual
basis of ?complexity? more often than not turns to mush. Mea culpa much
of the time, I?m sure, but look what happened to reductionism in this
thread. Even Wikipedia has several entries. I don?t know how much
credence to give them, but here they are:
0. <
http://en.wikipedia.org/wiki/Reductionism#Varieties_of_reductionism>
1 Varieties of reductionism
0. <
http://en.wikipedia.org/wiki/Reductionism#Ontological_reductionism>
1.1 Ontological reductionism
0.
<
http://en.wikipedia.org/wiki/Reductionism#Methodological_reductionism>
1.2 Methodological reductionism
0.
<
http://en.wikipedia.org/wiki/Reductionism#Methodological_individualism>
1.3 Methodological individualism
0. <
http://en.wikipedia.org/wiki/Reductionism#Theoretical_reductionism>
1.4 Theoretical reductionism
0. <
http://en.wikipedia.org/wiki/Reductionism#Scientific_reductionism>
1.5 Scientific reductionism
0.
<
http://en.wikipedia.org/wiki/Reductionism#Set-Theoretic_Reductionism>
1.6 Set-Theoretic Reductionism
0. <
http://en.wikipedia.org/wiki/Reductionism#Linguistic_reductionism>
1.7 Linguistic reductionism
0. <
http://en.wikipedia.org/wiki/Reductionism#Greedy_reductionism> 1.8
Greedy reductionism
0. <
http://en.wikipedia.org/wiki/Reductionism#Eliminativism> 1.9
Eliminativism
And now emergence. I?ve heard it used in several ways. Way back when, we
used it in anthropology as a form of methodological defense against the
usual social science model of everything planned in a modular way before
the research started. Emergence was shorthand for ?I can?t tell you
what I?m going to do until I get there and learn what?s worth learning
and how to learn it.? Then it?s also used more generally as shorthand
for ?surprise,? the presence and nature of which depends on perspective
and prior knowledge of observer. Then it?s used for the end result of a
deterministic process that has characteristics unlike the elements of
that process, like water out of hydrogen and oxygen. Then it?s used for
the need for different concepts and methods for different levels of a
phenomenon, like phonology, morphology and syntax in linguistics. Then
it?s used for unexpected evolutionary and historical transitions, like
the Cambrian explosion. Probably many other uses if we sampled a lot of
texts and conversations. Probably some of the sources cited already in
the thread help with the problem. I need to read them.
Maybe the field has outgrown the concepts that got it started. If true,
that?s probably a good sign.
So I think I?ll work on nonlinearity for awhile. Russell writes: ?most
of my readers understand perfectly well what a linear function is: one
that obeys f(a*x+b*y) = a*f(x)+b*f(y).? That?s clear, resembles the
definition in the Wikipedia entry. But then he writes : ?If neither * or
+ are defined for your objects of discussion, you cannot talk about
(non-)linearity.? That won?t do. I have to be able to talk about
nonlinear effects of, say, mental health policy on local programs in a
qualitative way. I know it makes sense to do so from experience. Problem
is to make it clear what the term means in that context. If the math
won?t do it, something else has to. I?ll puzzle over the NECSI
definition and the opening pages of Strogatz? book for awhile. So maybe
nonlinearity won?t be so easy either. There?s the famous Einstein quote
for inspiration: As far as the laws of mathematics refer to reality,
they are not certain; and as far as they are certain, they do not refer
to reality. Maybe we need a new nonlinear kind of math. Maybe it exists.
Enough already.
Mike
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