X-Message-Number: 9329
Date:  Fri, 20 Mar 98 17:03:38 
From: Mike Perry <>
Subject: digital issues (CryoNet #9323)

Thomas Donaldson writes,

>Furthermore, an argument that we can use digital devices to emulate
>ANYTHING requires more than just the observation that (say) it occurs
>in a discrete set of states.

It seems to me that all that happens can be resolved into "elementary 
events" of which there is at most a denumerable set of different 
types, i.e. the elementary events can be put into one-to-one
correspondence with the integers 1,2, ... . (An example of an 
elementary event is, say, an electron in a hydrogen atom jumping from 
a higher to a lower energy level  and emitting a photon in the 
process.) On the other hand, any finite volume of spacetime 
will contain only a finite number of elementary events--with the 
possible exception of sets (volumes) of measure zero, i.e. isolated 
points and the like, that we should be able to disregard. (One such 
possibility is the collapsing universe model of Tipler--but such 
things do not happen very much if at all.) This is enough, I think, 
to establish a reasonable case for the "digital" paradigm I have been 
urging, which in any case is more general than the CT thesis.

>Digital systems BREED chaos: even if you don't have it when you
>look at the physical system itself, you have to devise your algorithms
>so that the simple inaccuracy of your model will not cause it to blow
>up. In practice, this is done by limiting the time span over which
>your computations are to approximate the phenomena.

You can also use more digits and take more time in the computation. 
In principle, I think this is adequate to achieve an emulation of any 
finite process. Of course we have to take randomness into account 
too. The best we can hope for, as Perry Metzger has pointed out, is 
to do as well with a digital modeling as we would expect to do with 
an analog system that was exactly similar to the original but not the 
same. The two analog systems will also diverge over time, the digital 
should not do significantly worse, if set up properly.

Mike Perry

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