It does seem a little confusing how to quantify information when the universe itself is regarded as a computation.
Some flies buzzing around the horses may make a difference in the horse race. If the flies are "erased," then that issue is settled, which seems to count as a decrease of uncertainty and therefore as an _increase_ of info. How does one arrive at a result for net change of info?
The settlement of questions by imaginary erasure of all 'extraneous' factors, elimination of 'details,' "reductive" abstraction, etc., seems to be a basic working step for treating a scenario under a probability-theoretic viewpoint. Would the "real" erasure of those factors count in the same way as an increase of information? It seems like an increase of info at least in the case where we do remember the real things that we've erased or annihilated. Anyway, trying to arrive at a result for net change of information seems to require adopting some "meta" viewpoint, though I don't know, I'm not well versed in information theory.
On the other hand, when we treat things as being samples & surfaces of more opaque things even when we do know somewhat about what is or isn't under those surfaces, then factors/details which have been settled tend to get put into question or "veiled" such that it's uncertain what difference they make, and that's a decrease in info which seems to be a basic working step for treating a scenario under a statistical-theoretic viewpoint. When we feign ignorance about how things will be affected, that's an imaginary addition possible factors. Would a real adding of possible factors, uncertainty, count as a decrease in info? It seems like a decrease of info at least in the case where we do remember that those factors weren't previously there.
Are these problems real? Maybe a universe doesn't allow for change of information that requires some sort of "meta" viewpoint to calculate. On the other hand, maybe I just don't know what I'm talking about.
Best regards, Ben Udell
----- Original Message -----
From: "Wei Dai" <weidai.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Sunday, April 09, 2006 3:11 AM
Subject: why can't we erase information?
If we consider our observable universe as a computation, it's rather
atypical in that it doesn't seem to make use of the erase operation (or
other any operation that irreversibly erases information). The second law of
thermodynamics is a consequence of this. In order to forget anything
(decrease entropy), we have to put the information somewhere else (increase
entropy of the environment), instead of just making it disappear. If this
doesn't make sense to you, see Seth Lloyd's new book "Programming the
Universe : A Quantum Computer Scientist Takes On the Cosmos" for a good
explanation of the relationship between entropy, computation, and
information.
Has anyone thought about why this is the case? One possible answer is that
if it were possible to erase information, life organisms would be able to
construct internal perpetual motion machines to power their metabolism,
instead of competing with each other for sources of negentropy, and perhaps
intelligence would not be able to evolve in this kind of environment. If
this is the case, perhaps there is reason to hope that our universe does
contain mechanisms to erase information, but they are not easily accessible
to life before the evolution of intelligence. It may be a good idea to look
out for such mechanisms, for example in high energy particle reactions.
However I'm not sure this answer is correct because there would still be
competition for raw material (matter and energy) where intelligence can
still be an advantage. Anyone have other ideas?
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Received on Sun Apr 09 2006 - 13:55:19 PDT