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. However, one could have a real observer $y_{\alpha}$ whose main interests happened to include types of fruit, the integers, and the planets of the solar system and so forth. The 3 elements of $y_{r1}$ exist as a simple list, with no overarching structure actually uniting them. A physically realized computer, with some finite amount of memory and a capacity to receive input, resolves this by providing a unified architecture for the nontrivial embedding of various forms of information. A physical computer thus provides the glue to combine, say, $x_{tang}$, $x_{3}$, and $x_{nept}$ and form a new nontrivial structure in $\mathcal{U}$. It is possible to also consider the existence of ``randomly organized computers" which indiscriminately embed arbitrary elements of $\mathcal{U}$ -- these too would conform to no real $x_i$. This leads to the specification of ``physically realized" computers, as the restrictions that arise from existing within a mathematical structure like $\Psi$ results in computers that process information in nontrivial ways. Furthermore, a structure like $\Psi$ allows for these physical computers to spontaneously arise as it evolves forward from an initial state of low entropy. Namely it is possible for replicating molecular structures to emerge, and Darwinian evolution can then drive to them to higher levels of complexity as they compete for limited resources. A fundamental type of evolutionary adaptation then becomes possible: the ability to extract pertinent information from one's environment so that it can be acted upon to one's advantage. The requirement that one extracts useful information is thus one of the key constraints that has guided the evolution of the sensory organs and nervous systems of the species in the animal kingdom. This evolutionary process has reached its current apogee with our species, as our brains are capable of extracting information not just from our immediate surroundings, but also from more abstract sources such as $\mathcal{X}_{Riem}$, $\mathcal{X}_{prot}$, or $\mathcal{X}_{elec}$. We can absorb the thoughts of others on wide ranging subjects, from Socrates' ethics, to Newton's System of the World. Observers can also create structure, from individual works like van Gogh's paintings, to collective entities like the global financial system. The combinatorics that arise from the expansive scope of sources that Homo Sapiens can extract information from thus explains why we are currently the typical observers. " Anyways, the idea I am proposing is not really that complex, although it is somewhat nonintuitive. It does, however, take more than a cursory glance to understand. It may not be correct, but it is most certainly not obviously wrong. Sincerely, Travis > I finally got around to reading. I am completely unimpressed. Two > points: > > 1) His use of Physical Church-Turing Thesis is rather > unconventional. Normally, this means that the physical universe is > Turing simulable, but he uses it to mean something like COMP or > Tegmarks MUH. Note that by Bruno's UDA, the physical universe is no > longer simulable if COMP is true! > > 2) More seriously, I don't buy his Observer Class Hypothesis > (OCH). Observers do not just "absorb" information, they model > it. In one way, they could be said to search for short algorithms that > predict/reproduce the information at hand. So there will only ever be > a countable number of observers. They cannot be power sets of the set > of information strings. This becomes most absurd when talking about > observers observing themselves. Yet the number of information strings > in the plenitude will be uncountable (2^\aleph_0). There is an analogous > relationship with the concept of computable numbers versus all real > numbers. > > Cheers > > -- > > --------------------------------------------------------------------------- - > Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 [email protected] > Australia http://www.hpcoders.com.au > --------------------------------------------------------------------------- - -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
