>From Robin: > How do you distinguish between the chaos of celestial mechanics, and > the chaos of limited precision mathematics?
You bring up a good point. I need to be more precise in my wording. It would be more accurate to state the fact that I'm investigating the razor's edge between where "mathematical" order and predictability reigns - versus where chaos begins to manifest when one uses the same algorithms to predict the positions of satellites and planets. I used the term, "Celestial Mechanics", loosely here simply because the algorithms used are essentially the same ones used to determine and predict the positions of satellites and planets. In the realm of practical applications, as long as one endeavors to minimize the effects of "limited precision" that these mathematical algorithms can introduce, such as making sure the iterative samples are reasonably minute per-step, their use in predicting orbital positions works pretty well, heuristically speaking. But studying the "predictability" of satellites and planets is not what I'm currently studying. I also did not mean to imply that I'm currently investigating the mysterious characteristics of chaos that have been observed in actual-physical orbital bodies, such as satellites and planets. I meant to imply that I'm currently studying the nature and development of chaos within the actual mathematical algorithms THEMSELVES - the same algorithms which have been used to predict the orbits of satellites and planets. Said differently: I'm deliberately exploring what many call "... the chaos of limited precision mathematics" itself precisely because the patterns I'm seeing fascinate me. I would not have expected some of the patterns and effects my computer simulations have revealed to me. BTW, insofar as the laws of Celestial Mechanics are concerned there may be some debate as to whether the algorithms currently used (such as the use of: F = 1/R^2) truly represents CM phenomenon within the macro world we inhabit. But that is a debate for another time. Miles Mathis has certainly debated this issue, and I suspect he is being routinely ignored by most of "the establishment" for having the audacity of suggesting that so many gods (i.e.: Newton, Einstein) might have gotten certain formulas wrong, or used them incorrectly. A couple of interesting papers to read: http://milesmathis.com/mars.html - "The main cause of all solar system instability" I have not yet read this paper. http://milesmathis.com/cm.html - "Celestial Mechanics, Unanswered Questions" I have read these paper. Miles has introduced some concepts that I'm still pondering the ramifications of. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
