Saul, On first glance it appears that Noether's theorem is quite similar to mine, but just does not take it to the next level. My similar theorem starts from extrapolating the three conservation laws for energy flow as a hierarchy applying to all derivative levels, apparently like Noether seems to do. Taking that another step finds that the whole hierarchy of separate laws becomes one unified law of continuity in energy flows. The particular usefulness of that is to then work backwards from the n'th derivative to observe that the form of equation for the beginning or ending of any energy flow is a developmental sequence which has all derivatives real and of the same sign for a finite period as a necessity for avoiding infinite accelerations and energy densities.
So, finding rates of change that are all of the same sign then indicates where one might find a conserved process that is beginning or ending. What I find most useful is the unprovable extension of the principle, that anything displaying continuity of change is a conserved process, and measures of it may have useful conservation laws of their own at least temporarily. For example, a complex system's total mass (however estimated) often behaves as if a strictly conserved quantity, changing only by smoothly differentiable progressions of change. That's basically how business development or the health of newborn infants is gauged, using stable rates of changing scale as a stand-in for complex system developmental health. Sometimes the conserved properties of systems display emergent or transient derivative continuities, ones that weren't there before. One well documented example is in my plankton punctuated equilibrium study, where the speciation event was shown to be comprised of a series of emerging eruptions of developmental change in the organism's profile area. Yes, it may well be true that being able to classify things need not be particularly informative. As you say, Nothier's theorem only holds for certain classes of problems, but I think that suggestion is that that class may be most generally for the class of problems that involve continuity. It's just a guess, but maybe the way the Wikipedia entry states the restrictions of Nothier's theorem to systems following Lagrangian dynamics and so excludes dissipative processes indicates that the theorem might have been developed with unnecessary shortcuts that reduce its generality. Theorem http://www.synapse9.com/drtheo.pdf Background an applying to physical systems http://www.synapse9.com/physicsofchange.htm Best, Phil Henshaw NY NY www.synapse9.com From: Saul Caganoff [mailto:scagan...@gmail.com] Sent: Tuesday, January 06, 2009 6:44 AM To: s...@synapse9.com; The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Classification of ABM's Phil, your statement in bold below peaked my interest because there seems to be a tenuous analogy with symmetry or conservation laws as described by Noether's theorem <http://en.wikipedia.org/wiki/Noether%27s_theorem> . This theorem relates symmetries in a physical system to conservation laws. E.g. rotational symmetry in space is related to conservation of angular momentum. So does your observation relating energy transfer to derivative continuity have a deeper basis behind it? Also with respect to ABM classification, Noether's theorem only holds for certain classes of physical problem and hence could form a basis for classification. Similarly for your observation? After all, there are two classes of <insert phenomenon here> - those that fall into two classes and those that don't :-) Regards, Saul Caganoff On Tue, Jan 6, 2009 at 9:38 AM, Phil Henshaw <s...@synapse9.com> wrote: Steve, Well,. there are rather practical sides to some kinds of top level views. You might notice, possibly, that wherever energy transfer is involved derivative continuity in developmental processes will be too. That tells you nothing at all bye itself, but might give you a great observation tool. I use it something like a change process magnifying glass. Where a natural system subject of interest displays continuities of energy flow, or any other similarly conserved property only changed by addition or subtraction, it may give you a clear view of the sequence of assembly (adding and subtracting steps) for the complex systems involved. Seeing how it's done naturally might give you ideas, or even help you replicate things of similar kinds. Phil Henshaw NY NY www.synapse9.com From: friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] On Behalf Of Steve Smith Sent: Sunday, January 04, 2009 10:44 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Classification of ABM's Doug - On the other hand, top (top, top, top) level views which result in such profound observations such as * Order matters, or * Complexity is, or * Taxonomies exist rarely hold much interest for me, unless they make the job of designing functional complex systems easier. Which is why I give you high marks for pragmatism! clip. ============================================================ 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 -- Saul Caganoff Enterprise IT Architect LinkedIn: http://www.linkedin.com/in/scaganoff
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