🚀 go-pugleaf

In article <3750@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.

   The presence of such phenomena would seem to imply a universe where
   theory is of no value at all.

no.



virtually all chaotic dynamical systems have the characteristic of a
computational horizon beyond which any particular computer cannot keep
up with the physical system in doing the simulation.  

================
Sorry I don't have the commentator's name here.  There was no signature at
the bottom and the header has scrolled off my finite screen.  But...

The problem is not whether a process is computable, or if computable is
chaotic, but that there is no way that the *actual* behaviour of any
small part of the universe can be described by deterministic laws, even
though the entire universe may be.  For the behaviour of a part of the
universe to be detemined, that part would have to be isolated from the
rest of the universe, and thus be unobservable.  If it were not isolated,
the part whose behaviour is supposedly described would be affected by
"surprising" events (events from other parts of the universe not subsumed
in the description of the boundary conditions and/or descriptive laws.
Often, these outside influences do not matter, because the observed system
is in a dynamic state near an attractor, or some similar insensitive
condition.  But it might be near a repellor across which the unexpected
event pushes it, into a quite different basin of attraction.  I don't
think it much matters about the system being chaotic, provided that the
chaos is expressed in the form of a strange attractor, because it is
likely that most of th trajectories in the attractor have behaviourally
similar consequences.

What this points out is that there is *NO* physical system that can
be guaranteed to compute according to any algorithm.  If the algorithmic
nature of computation is what causes Penrose to require new physics,
he need not bother.  All he needs is to note that brains and computers
are sub-parts of the universe, and therefor are non-deterministic.
-- 
Martin Taylor (mmt@zorac.dciem.dnd.ca ...!uunet!dciem!mmt) (416) 635-2048
"Viola, the man in the room
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