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 ============================================================ 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
