I have a puzzle that sounds simple, but baffles me. We can call it the pieces/relations problem or, to go in reverse direction, the issue of interactive/self-organizing systems {ISO}. Two examples: 1.NEUROSCIENCE: Modularity is a major issue in neuroscience (and behavioral science). Without modules ("pieces") there is no order, just mush. However, if the modules do not speak to one another ("relations") one has neurobehavioral anarchy. But its more: if the pieces modify one another's properties through interactions, then they become in some sense interdependent. If they are interdependent, then the very distinction between "pieces" and "relations" becomes hard to maintain. There is a lot of evidence that neurobehavioral systems are indeed both "interactive" and "self-organizing", but I see very little on an attempt to think about the deeper meanings of this duality (or better, polarity). I suspect systems are relatively isolated, and change their rules of relative isolation (vs. communication) in time, but this makes the story even more difficult. Anyone got ideas?
2.DEVELOPMENTAL BIOLOGY: Cells (etc.) become more specialized (differentiated) in time. Blobs become replaced by pieces, but as development proceeds the pieces interact and again change each other's properties. Differentiation becomes supplemented by integration. And so on.
This may sound either esoteric or so simple that its not a problem. However, we have been trying to model the dynamics of the "pieces/relations" problem in a way that might work for both integrative and developing systems, at both behavioral and neural levels. I won't bore folks with too many details here. Suffice it to say that the model is based upon a central "excitatory" core and surround "inhibition", where the relative balance between excitation and inhibition shifts with the dynamics of the system. It would take a long time to scribble details here (though we have published some).
The point is that I am not very satisfied by the way I, or others, think about this. Neither homogeneity (entropy) nor anarchy work. Throw away phrases such as "interactions among separate systems" are oxymorons when thought about more deeply, and so on. I'll stop here. If no response, I'll pout my way along in silence for a while.
Thanks for any inputs.
John F.