Any conclusion about information erasure, or entropy, in a given system
seems to depend on the particular meaning assigned to the information.
Note that "assigned" is a verb. What I mean when I say this is that
I'm pointed to the fact that it takes someone to do it.
There's a recurring thought in this thread about information's
dependency on an observer (Russell Standish), a language (Hal Finney).
Bruno suggests entropy is a 1st person phenomenon. In other words, the
assigning of meaning to the information (or "variables", "constraints",
"states") requires a person. From a certain point of view it may look
locally like an increase in information, but do a change of variables
(albeit maybe a horrific one) and viola, information is decreasing.
On the other hand, when we talk about information erasure, it seems
that we are talking about something different from entropy. Saiba
Mitra says that it could be that internal observers can't see
information erasure. Ben Udell appealed to the need for a "meta"
viewpoint. Total information erasure has to be in the global context
of the whole "universe", or Everything. Otherwise you can't be sure
you're dealing with information erasure, or if it's simply negative
entropy. So you have to be omniscient about the whole universe. Hence
my previous reference to the assumption of reductionism and a closed
system, i.e. assume you are God.
Wei Dai's Turing machine, which acts on instructions to erase
information, has to interpret the instructions using a certain
language. The command to erase could be interpreted as having a
different meaning in another language.
Tom Toffoli's paper, "Nothing makes sense in computing except in the
light of evolution", gives support to the idea that there needs to be
some "meta" element to give meaning or design to this whole swirl of
information we see around us. I think this is also why we keep feeling
the need to appeal to anthropic thoughts.
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