Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Conceptual reduction and emergence paper
Marco Giunti is giving a conference paper entitled -
Emulation, Reduction, and Emergence in Dynamical Systems
- at a Systems Science conference in Paris this week. He distinguishes reduction and emergence as separable, independent relations between systems rather than opposites. The paper gives useful and intuitive definitions of dynamical systems and emulation for them, and essentially proposes meanings for "reduction" and "emergence" based on those definitions.
Here is his abstract -
The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamical systems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical system DS2 when DS1 exactly reproduces the whole dynamics of DS2). This representational view of reduction, contrary to the standard deductivist one, is compatible with the existence of structural properties of the reduced system that are not also properties of the reducing one. Therefore, under this view, by no means are reduction and emergence incompatible categories but, rather, complementary ones.
This and other recent papers can be found on his website, here -
I note he is not explicit in the body of his paper about the point, an emulation may in general involve a different number of steps than the original, to mimic a given portion of the evolution of the emulated system. It is enough if every actually occurring sequence of states in the emulated system can be built in the emulating one, from a sequence of updates in the emulating one. Some emulated (single step) h(x1)'s may be emulated by a g(y1) transformation, others by g(g(y2)), others g(g(g(y5))), etc.
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