Hi Travis,
I have really enjoyed the challenge of your paper. One difficulty that I
have with it is that the "selection of a gauge" is a highly non-trivial
problem (related to the fine tuning problem!) and thus needs a lot more
attention. More comments soon.
Onward!
Stephen
-----Original Message-----
From: Travis Garrett
Sent: Thursday, January 27, 2011 5:32 PM
To: Everything List
Subject: Re: Observers and Church/Turing
I am somewhat flabbergasted by Russell's response. He says that he is
"completely unimpressed" - uh, ok, fine - but then he completely
ignores entire sections of the paper where I precisely address the
issues he raises. Going back to the abstract I say:
"We then argue that the observers
collectively form the largest class of information
(where, in analogy with the Faddeev Popov procedure,
we only count over ``gauge invariant" forms of
information)."
The stipulation that one only counts over gauge-invariant (i.e.
nontrivial) information structures is absolutely critical! This is a
well known idea in physics (which I am adapting to a new problem) but
it probably isn't well known in general. One can see the core idea
embedded in the wikipedia article:
http://en.wikipedia.org/wiki/Faddeev–Popov_ghost
- or in say "Quantum Field Theory in a Nutshell" by A. Zee, or
"Quantum Field Theory" by L. Ryder which is where I first learned
about it. In general a number of very interesting ideas have been
developed in quantum field theory (also including regularization and
renormalization) to deal with thorny issues involving infinity, and I
think they can be adapted to other problems. In short, all of the
uncountable number of uncomputable reals are just infinitely long
random sequences, and they are all eliminated (along with the
redundant descriptions) by the selection of some gauge. Note also in
the abstract that I am equating the observers with the *nontrivial*
power set of the set of all information - which is absolutely distinct
from the standard power set! I am only counting over nontrivial forms
of information - i.e. that which, say, you'd be interested in paying
for (at least in pre-internet days!).
I am also perfectly well aware that observers are more than just
passive information absorbers. As I say in the paper:
"Observers are included among these complex structures,
and we will grant them the special name $y_j$
(although they are also
another variety of information structure $x_i$).
For instance a young child $y_{c1}$ may know about
$x_{3p}$ and $x_{gh}$:
$x_{3p}, x_{gh} \in y_{c1}$, while having not yet
learned about $x_{eul}$ or $x_{cm}$.
This is the key feature of the observers that we will utilize:
the $y_j$ are entities that can absorb various
$x_i$ from different regions of $\mathcal{U}$."
That is: "this is the key feature of the observers that we will
utilize"
And 4 paragraphs from the 3rd section:
" Consider then the proposed observer $y_{r1}$
(i.e. a direct element of $\mathcal{P}(\mathcal{U})$):
$y_{r1} = \{ x_{tang}, x_3, x_{nept} \}$,
where $x_{tang}$ is a tangerine, $x_{3}$ is the
number 3, and $x_{nept}$ is the planet Neptune.
This random collection of various information structures
from $\mathcal{U}$ is clearly
not an observer, or any other from of nontrivial information:
$y_{r1}$ is redundant to its three elements, and would thus
be cut by the selection of a gauge.
This is the sense in which most of the direct elements of the
power set of $\mathcal{U}$ do not add any new real information.
snip
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