Some of the background appeared in the previous points so I was too lazy to repeat it here, which might have been a mistake.
To recap what I’m doing here, regardless of how I do it:
Legg and Hutter defined an intelligence metric for agents which are input-output mappings. I.e., each input-output map gets a number which says how intelligent it is. AIXI is the maximally intelligent agent by this definition. Of course this intelligence metric is completely Cartesian in nature.
The Legg-Hutter metric is defined for any mapping, regardless of the computing resources needed to evaluate it or even if it is uncomputable (like AIXI). Of course there is nothing stopping us from restricting to mappings that can be realized by a given computing model. For example, we can assume the agent to be a universal Turing machine augmented by special “input” registers and map some bits from the tape to the output. This way we get an intelligence number for every program that we can write into the universal Turing machine.
I define a different way to assign “intelligence numbers” to such programs which is physicalist. The construction is inspired by UDT. Indeed, most of the ideas already exist in UDT however UDT is a different type of mathematical object. UDT speaks of decision algorithms and/or values of decisions by an algorithm, whereas I speak of quantifying the intelligence of a program for a fixed “robot” (abstract computing device with input/output channels).
Maybe you can ask a few specific questions?
Some of the background appeared in the previous points so I was too lazy to repeat it here, which might have been a mistake.
To recap what I’m doing here, regardless of how I do it:
Legg and Hutter defined an intelligence metric for agents which are input-output mappings. I.e., each input-output map gets a number which says how intelligent it is. AIXI is the maximally intelligent agent by this definition. Of course this intelligence metric is completely Cartesian in nature.
The Legg-Hutter metric is defined for any mapping, regardless of the computing resources needed to evaluate it or even if it is uncomputable (like AIXI). Of course there is nothing stopping us from restricting to mappings that can be realized by a given computing model. For example, we can assume the agent to be a universal Turing machine augmented by special “input” registers and map some bits from the tape to the output. This way we get an intelligence number for every program that we can write into the universal Turing machine.
I define a different way to assign “intelligence numbers” to such programs which is physicalist. The construction is inspired by UDT. Indeed, most of the ideas already exist in UDT however UDT is a different type of mathematical object. UDT speaks of decision algorithms and/or values of decisions by an algorithm, whereas I speak of quantifying the intelligence of a program for a fixed “robot” (abstract computing device with input/output channels).