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/Faddeevâ€“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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