Actually I think the thread is heading into some interesting and (for me) useful directions. Several contributors (Eric, Glen, Russell et al.) are explicitly filling in the blank in the sentence "if a phenomenon is identified as emergent then <blank>" (and thanks to Doug for the clear statement of my question). As to the math, I'm absolutely not against developing a theoretical grounding for emergence but (IMHO) it needs to inform the "if" clause of Doug's statement AND the "then" clause. I think that our discussions over the past months have tended to focus on the former rather than the latter: my question was just an attempt to correct the balance.
-- Robert P.S. Does it help if I know whether my simulation will display chaotic behavior? You betcha: if I know the shape of the attractor in phase space I know which states of the system are impossible and which are possible and I can calculate the probability of finding the system in those possible states. So that means (for example) that I can apply error bars to my prediction of next week's weather or properly price the financial derivative that I am selling. On Mon, Oct 12, 2009 at 12:13 PM, Owen Densmore <o...@backspaces.net> wrote: > Robert: Just to help untangle the discussion: Are you saying a theoretical > grounding for Complexity .. or even just Modeling .. appears to have no > concrete use for you? > > To be even more specific: Chaos has at least one definition: divergence. > It uses the Lyapunov exponent to define chaotic systems. > > Thus would it be useful for you in a calculation to know whether it was > inherently chaotic? > > -- Owen > > >
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