Yes, the Devil is in the details. It pays to know just how much Devil is in there, and in old school 8 bit BASIC, there is much.
Classical Mechanics gives results that are reversible. So if the model isn't, it's just a numerical flaw, and not a profound fact about physics. Sent from my iPhone. On Feb 19, 2011, at 1:57, Rich Murray <[email protected]> wrote: > 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 > <[email protected]> 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 <[email protected]> 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 [email protected] 505-819-7388 >>> 1943 Otowi Road, Santa Fe, New Mexico 87505 >>> >>> On Fri, Feb 18, 2011 at 4:30 PM, >>> OrionWorks - "Steven V Johnson" <[email protected]> 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 >>> >> >> >
