The only access to "the physics itself" we have with finite nervous systems is by using digital approximations with finite number strings, processed by algorithms of finite instruction size, so there are always round-off errors, which always diverge without limit, even if there are no close encounters. So, it's a huge leap of faith to assume that the "present data" for a certain finite time interval actually allows prediction of a single future path or retrodiction of a single past path -- ie, classical mechanics probably can be proved to be incurably flawed, while allowing a certain amount of qualified estimation of probable paths forward and backward in time for the first 3 "orbits" or so...
I've read that actually the 3-body problem does have exact general solutions, which involve such long, very slowly converging sequences of terms, as to be practically unworkable in practice. Probaby, it can be shown that the energy needed to run an ideal finite digital computer until a certain limit of accuracy is reached (testable by running the same problem in parallel with identical computers, watching to see at what point the results start to scatter) will grow so fast with time and accuracy as to exhaust the energy available in any universe that supports the computer... Probably someone has already studied this... It's not just that shit happens -- "happens" happens... So, in reality, the "present" interval, however brief in time and tiny in space, necessarily in complex interaction with a possibly infinite external universe or hyperverse, must be inexplicable, "causeless", ie, totally "magical"... This has in recent thousands of years been a common insight for advanced explorers of expanded awareness in many traditions. Rich Murray "lookslikeallthoughtiswrong"@godmail.com On Fri, Feb 18, 2011 at 9:50 PM, Charles Hope <lookslikeiwasri...@gmail.com> wrote: > I'm thinking your findings of irreversibility reflected the idiosyncrasies of > floating point math represented in binary numbers, and not the physics itself. > > Sent from my iPhone. > > On Feb 18, 2011, at 22:17, Rich Murray <rmfor...@gmail.com> wrote: > >> does classical mechanics always fail to predict or retrodict for 3 or >> more Newtonian gravity bodies? Rich Murray 2011.02.18 >> >> Hello Steven V Johnson, >> >> Can I have a free copy of the celestial mechanics software to run on >> my Vista 64 bit PC? >> >> In fall, 1982, I wrote a 200-line program in Basic for the >> Timex-Sinclair $100 computer with 20KB RAM that would do up to 4 >> bodies in 3D space or 5 in 2D space, about 1000 steps in an hour, >> saving every 10th position and velocity -- I could set it up to >> reverse the velocities after the orbits became chaotic after 3 1/2 >> orbits from initial perfect symmetry as circles about the common >> center of gravity, finding that they always maintained chaos, never >> returning to the original setup -- doubling the number of steps while >> reducing the time interval by half never slowed the the evolution of >> chaos by 3 1/2 orbits -- so I doubted that there is any mathematical >> basis for the claim that classical mechanics predicts the past or >> future evolution of any system with over 2 bodies, leading to a >> conjecture that no successful algorithm exists, even without any close >> encounters. >> >> Has this been noticed by others? >> >> Rich Murray rmfor...@gmail.com 505-819-7388 >> 1943 Otowi Road, Santa Fe, New Mexico 87505 >> >> On Fri, Feb 18, 2011 at 4:30 PM, >> OrionWorks - "Steven V Johnson" <svj.orionwo...@gmail.com> wrote: >> >>> Just a brief side-comment... >>> >>> Some of this "lingo" is fascinating stuff to me. Having performed a >>> lot of theoretical computer simulation work on my own using good'ol >>> fashion Newtonian based Celestial Mechanics algorithms, where >>> typically I use "a = 1/r^2", I noticed orbital pattern behavior >>> transforms into something RADICALLY different, such as if I were to >>> change the classical algorithm to something like "a = 1/r^3". You can >>> also combine both of them like "a = 1/r^2 +/- 1/r^3" within the same >>> computer algorithm. That produces interesting side effects too. I'm >>> still trying to get a handle on it all. >>> >>> Regards >>> Steven Vincent Johnson >>> www.OrionWorks.com >>> www.zazzle.com/orionworks >> > >
