Posted by
David Breecker on
URL: http://friam.383.s1.nabble.com/Seminal-Papers-in-Complexity-tp524047p524080.html
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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