On Tue, Sep 22, 2009 at 05:37:00PM -0700, glen e. p. ropella wrote: > Thus spake russell standish circa 09-09-22 05:06 PM: > > I still don't follow why circular causality is required, although it > > is an interesting class of systems. So long as > > the two languages are lexically mismatched, that suffices, as there > > are behaviours (eg flocking) inexpressible in the reduced language. > > Well, remember that this is all speculation on my part. I could easily > be wrong about all this. However, the reason I think circular causality > is necessary is because if the construction is built up from a single, > consistent language, then all one need do is show that the other > language is isomorphic to the first (or find a new language where that's > the case) and any apparent "complexity" is proven illusory. However, if > the system is constructed with mismatched languages, in the first place, > then it's no simple task to find a 3rd language that is isomorphic to > the composition of the languages from which the system is constructed. > > I.e. for "strong" or "real" complexity, we need something that is > _constructed_ with mismatched languages, not merely constructed with a > single coherent one and operated on by another. > > And the only way to construct a system with mismatched languages is to > embed one (different, mismatched) language inside another ... i.e. for > one part of the system to use the results of an (inaccurate) operator as > part of its mechanism. > > All this boils down to is that circular systems are not reducible beyond > the elements of the circle. And if the circle is expressed in a single, > consistent language, then the circle can be formulated nicely and isn't > complex, which is why we need the language mismatch. >
Its sometimes worth discussing examples. A thermodynamic system is described by its therodynamic state, which has amongst its properties entropy. Entropy has the peculiar property of almost always increasing in time, name the second law of thermodynamics governs it evolution. Thermodynamic language is obviously lexically mismatched with the Newtonian language of particles, positions and momenta, which describe a time reversible system. How do I create a language that can embed both thermodynamics and newtonian mechanics? It seems impossible to me, given their incommensurability. Second, where are there causal loops in this example? I can't see any. Therefore, is a thermodynamic system complex according to GEPR? -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [email protected] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ 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
