> Insofar as what my own Celestial Mechanics research seems to indicate: No elliptical orbits are stable. None. Strictly speaking, and in Neutonian terms, using differential equations and feed-back > algorithms, my research indicates that eventually all elliptical orbits will decay. By "decay" I mean to imply that all elliptical orbits eventually fly apart. The satellite's orbit eventually begins to manifest weird perturbations. It is precisely this manifested "weirdness" that I've have been researching for several years now. The weirdness, the patterns generated, don't seem to follow logical > sequences - thus the term "chaotic." The "breakdown" of stability is certainly not a gradual process either. For example, as instability begins to manifest islands of apparent stability can suddenly > reestablish themselves. Eventually, however, all orbits become chaotic again. This back-and-forth behavior, the tug between stability and chaos, can go on for quite a spell. Eventually the satellite is > completely thrown out of the system. I've been attempting to develop a slew of computer programs and accompanying graphics to help display some of this weird behavior. I hope to better visualize what seems to be going on in ways that help us all acquire a better grasp of the fundamental principles that seem to manifest.
Now I finally understand you clearly, Vincent. What's going on is that your numerical simulations fall short of the complexity you are trying to simulate. Small errors eventually add up, and orbital elements sooner or later escape their orbits. What that means in the end, is that no numerical method, independently of how perfect and precise that it can be, can perfectly simulate the reality of the situation. And it's a fundamental limitation. Because the involved dynamics of the planetary orbits are non mechanicistic, no mathematical method can perfectly reproduce them (i.e. the n-body problem in Classical Mechanics). That was what I intended to mean when I said that the solar system is alive. To say or think that the solar system is completely mechanicistic, would be the same as saying that it is dead. And if that where the case, long ago everything would have escaped the system, or collapsed, i.e. it would have effectively manifested its death, long time ago. And of course, we would not be here. We're here because there's something in the Cosmos that's inherently equal to us, i.e. it's inherently alive. We are no more (and no less) than the most clear, recent, evident manifestation of the living nature of the Universe. > > Mathis's work reminds me of another prominent Pulitzer winning author: Douglas Hofstadter, aka "Godel, Escher, Bach: An Eternal golden > Braid". A more recent publication by Douglas is titled, "I'm a Strange Loop". I enjoyed every line of "Gödel, Escher, Bach". I remember with particular vividness the chapter on Strange Loops and Tangled Hierarchies. I recommend that monumental and beautiful book to anyone with a serious interest in the limits of mathematics and formal systems, and also on how in the end only with the aid of real art and living thought we are able to capture and explain the reality and prodigiousness of the world around us. > > http://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp/0465030793/ref=sr_1_3?s=books&ie=UTF8&qid=1285262229&sr=1-3 > > http://tinyurl.com/2etgl57 > > I suspect there may be tie-ins between what Douglas has been trying to reveal in his impressive body of publications, and the tiny branch of research I've chosen to diddle about in. For example, while my > computer algorithms are based on classic Celestial Mechanical formulas I suspect similar formulas and algorithms could possibly be applied (perhaps in clever ways we have yet to conceive) to the study, oh... say...: Maybe artificial intelligence, the nature of consciousness - how consciousness manifests within our reality, aka: "I'm a Strange Loop". > > -- > Regards > Steven Vincent Johnson > www.OrionWorks.com > www.zazzle.com/orionworks > >
