Ignore the second part of my initial comment, I was hadn’t read your blog post explaining your idea at that point. I believe your problem can be formulated differently in order to introduce other necessary information to answer it. I appreciate your approach because it is generalized to any case which is why I find it appealing, but I believe it cannot be answered in this fashion because if you examine integrated systems of information by constituent parts in order to access that information you must take a “cruel cut” of the integrated system of information which may result in it becoming differentiable into 2 or more subsystems of information neither of which can contain the integrated information of the initial system.
To be honest I am still in the midst of digesting this and several other ideas relevant to the computability of consciousness/intelligence and my remarks will have to stay brief for now. The first part of my initial comment referred to something similar to the example of a 2D isling model referred to in section C. The information you obtain from a random model of the consistent but incomplete theory will be bounded by other operators on the system from outside which limit the observable state(s) it produces. As for the second perhaps I can rephrase it now.… If viewed in this fashion your initial question becomes one of maximizing the information you get from a physical system however if the operators acting on it evolve in time then the information you receive will not be of T but rather of a set of theories. For example take a box of gas sitting in the open. As the sun rises and sets changing the temperature, the information you get about the gas will be of it operating under different conditions so uppercase phi will be changing in time and you will not be getting information about the same system. However, I do believe you can generalize these systems to a degree and predict how they will operate in a given context while bounded by particular parameters. I am still clarifying my thoughts on this issue.
Ignore the second part of my initial comment, I was hadn’t read your blog post explaining your idea at that point. I believe your problem can be formulated differently in order to introduce other necessary information to answer it. I appreciate your approach because it is generalized to any case which is why I find it appealing, but I believe it cannot be answered in this fashion because if you examine integrated systems of information by constituent parts in order to access that information you must take a “cruel cut” of the integrated system of information which may result in it becoming differentiable into 2 or more subsystems of information neither of which can contain the integrated information of the initial system.
I would recommend reading:
http://arxiv.org/abs/1401.1219
To be honest I am still in the midst of digesting this and several other ideas relevant to the computability of consciousness/intelligence and my remarks will have to stay brief for now. The first part of my initial comment referred to something similar to the example of a 2D isling model referred to in section C. The information you obtain from a random model of the consistent but incomplete theory will be bounded by other operators on the system from outside which limit the observable state(s) it produces. As for the second perhaps I can rephrase it now.… If viewed in this fashion your initial question becomes one of maximizing the information you get from a physical system however if the operators acting on it evolve in time then the information you receive will not be of T but rather of a set of theories. For example take a box of gas sitting in the open. As the sun rises and sets changing the temperature, the information you get about the gas will be of it operating under different conditions so uppercase phi will be changing in time and you will not be getting information about the same system. However, I do believe you can generalize these systems to a degree and predict how they will operate in a given context while bounded by particular parameters. I am still clarifying my thoughts on this issue.