🚀 go-pugleaf

In article <3806@uceng.UC.EDU> dmocsny@uceng.UC.EDU (daniel mocsny) writes:

   >   Can any phenomenon be so truly uncomputable that no logical process
   >   could behave equivalently (if not exactly)?
   >
   >yes.

   I should expand on my use of "equivalently." While I agree that some
   chaotic systems are probably hopeless to simulate with arbitrary
   precision, certainly that does not prevent an artificial system from
   being equivalently "interesting." I.e., the artificial system may not
   exactly reproduce all the behavior of the chaotic system, but it may
   satisfy some of the same performance measures, it may exhibit behavior
   that appears to be similarly complex, or it may spend roughly the same
   amount of time in the same attractor basins.

indeed it has been shown that while a computed simulation of a chaotic
system will diverge from the `true' trajectory for a particular
initial condition, for many systems it will stay within a small
neighborhood of some trajectory of the system.  thus simulations can
reasonably be used to investigate the behavior of some chaotic systems.

   If we regard the system of (chaotic system + sensor readout) as a
   computer giving the state of the system at time t, the question is:
   "From where does the chaotic system derive its great computing power?"
   For the chaotic system fits quite nicely into the universe, and yet it
   performs the equivalent of a seemingly uncountable number of elementary
   operations.

for that matter, if we posit a RAM machine which can manipulate real
numbers it _can_ solve the halting problem.

real numbwers have strange consequences for the theory of algorithms.
not to mention for the hardware types.

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