At risk of sounding soft-brained, I'd recommend considering other domains as a
source of inspiration for a new non-linear kind of math. Music in particular,
and other so-called "creative" forms, offer insight into different kinds of
problem-solving approaches, and quasi-logical expression.
And besides, Einstein liked playing his violin more than just about anything ;-)
db
----- Original Message -----
From: Michael Agar
To: The Friday Morning Applied Complexity Coffee Group
Sent: Tuesday, June 19, 2007 7:41 AM
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:
0.1 Varieties of reductionism
0.1.1 Ontological reductionism
0.1.2 Methodological reductionism
0.1.3 Methodological individualism
0.1.4 Theoretical reductionism
0.1.5 Scientific reductionism
0.1.6 Set-Theoretic Reductionism
0.1.7 Linguistic reductionism
0.1.8 Greedy reductionism
0.1.9 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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FRIAM Applied Complexity Group listserv
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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
