X-Message-Number: 20890
From: 
Date: Thu, 16 Jan 2003 14:30:22 EST
Subject: information conservation again

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Michael Price says there is no evidence for conservation of information. 
Without trying to define "evidence," I can think of several lines of thought 
indicating the possibility or likelihood of information conservation.

1. On a practical and approximate level, there is much more information 
potentially available than most people think. For example, to determine the 
genome of a particular individual to a high degree of accuracy, you don't 
need any part of him--only a few small specimens from some blood relatives. 
Likewise, a tremendous amount of information about a cryopatient's brain can 
be inferred from outside records, including the memories of friends and 
relatives.

2. Cryptology tells us that, while it is easy to degrade information,  it is 
exceedingly hard to conceal it--even when you are really trying, which Nature 
is not.

3. The universe may be deterministic, as many first-rate people have thought. 
In that case--at least in a finite universe--information in principle is 
conserved. 

(It is irrelevant that, in a local region of spacetime, one cannot infer the 
past with complete confidence, since sometimes B would follow from A and also 
from A1 and A2 etc. In any sizable system the possibilities quickly dwindle 
to one. Any guess about the past or present must conform to known records, 
such as written records, fossil records, cloud chamber tracks, etc.) 

(David Deutsch thinks the "multiverse" is deterministic, although a 
particular "universe" is not from the point of view of its inhabitants; but 
he also thinks that, in any universe, the past is fixed. If he is wrong, and 
there are "many histories" instead of many worlds, that's a different kettle 
of fish.)

(The current majority interpretation of the current version of quantum theory 
is not only on shaky ground, but from an historical perspective is almost 
certain to be wrong in fundamental ways. There are wildly divergent views. 
Bart Kosko thinks the current quantum physics is almost certainly wrong 
simply because it is linear, and experience tells us that nature abhors a 
straight line.)

4. Although now more or less outmoded, Einstein's 4 dimensional  block 
universe suggests a "map" of eternity already coexisting--past, present, and 
future equally definite and fixed, the "flow" of time an illusion. In that 
case, everything is conserved--except perhaps human error, which always finds 
more room to grow.

5. It should be noted that "information" means different things to different 
people and in different situations. Shannon's classic work on theory of 
communication made this distinction carefully. A "lot" of information in an 
engineering or communication sense does not necessarily mean a lot of 
information semantically.

Suppose a  zillion monkeys work at a zillion keyboards for a zillion years, 
and finally one of the print-outs is a verbatim copy of the U.S. Declaration 
of Independence. How much information is there in this printout? "None" would 
be a good guess, but it depends on your frame of reference. Key questions 
include the "intent" of the sender (even if the sender is Ma Nature) and the 
"interpretation" of the receiver.

The point is that definitions of "order" or "disorder" are not so simple and 
any one is applicable only in its own appropriate niche. As previously noted, 
we might ask whether being dealt a royal flush in spades at Bridge is a 
common event or an unusual one. Most people at first thought would say 
"unusual," but they have already had their biases built in. After more 
thought, we might ask, "Compared to what?" If you compare a royal flush in 
spades to any other distribution, previously exactly specified, even with 
honor points zero, the probability is precisely the same for any hand.

Furthermore--and this is frequently lost sight of--the effective or semantic 
content of a message or observation need not depend entirely or even 
primarily on its complexity. It also may depend heavily on CONTEXT. For 
example, a Yes or No response to a previous question (e.g. "Is Natasha 
Nogoodnik a spy?) might convey (in one sense) a tremendous amount of 
information, answering many implied questions.

Robert Ettinger

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