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My (simpleminded?) view of emergence and nonlinearity is this:
LINEAR: the whole is precisely the sum of it's parts; the parts work
independently, there are no interactions among the parts.
EMERGENCE: arising solely from the nonlinear interactions of the parts; not
available with individual parts; normally unplanned and unanticipated, so a
car, while having many nonlinear parts, is not an emergent property of the
parts (but may be an emergent property of car designers).
Linear math is productive because a family of solutions can be created to
cover an entire solution space, making linear equations soluble. Nonlinear
equations can occasionally be solved, but must more often be simulated,
interacted with, and evolved. General solutions are almost inconceivable.
Can one solve the brain system for all possible thoughts? And yet there is
the promise of gaining insight and power from working with these systems.
-Mike Oliker
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