X-Message-Number: 26052
Date: Mon, 18 Apr 2005 16:02:55 EDT
Subject: Bekenstein cells

Another small amusement about simulations, for those who have time to  waste.
Any computer simulation of a system is guaranteed to miss the mark, for at  
least two separate reasons--even if one were to agree that a description of a  
thing is the thing.
1. We do not have complete or totally accurate knowledge of the laws of  

physics, hence predictions are necessarily approximate at best. How  important 
differences may be is unknown, but we can't assume they are  negligible, as I 
have mentioned before. 
2. What I don't think I have mentioned before is related to the  Bekenstein 
Bound. The uncertainty principle supposedly implies that a "point" in  the 
phase space of a system is really a cell of non-zero volume. What is often  

omitted is that the cell does not have to be the analog of a sphere or a  
could be any shape. 
Now, the computer has only two choices for its calculations--the "center"  of 
the cell, or a randomly chosen point in the cell. In either case, reality  

will be different, because reality is (supposedly) semi-random, and will rarely
(0 % of the time, by measure theory) coincide with the computer result.
In Frank Tipler's world of the Omega Point, there will be so many versions  

of you that some of them will be negligibly different from what you are or hope
 to be. On the other hand, lots of them will be in deep doo-doo.
Robert Ettinger

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