The intelligence of a physicalist agent is defined to be the UDT-value of the “decision” to create the agent by the process creating the agent. The process is selected randomly from a Solomonoff measure conditional on obeying the laws of the hardware on which the agent is implemented. The “decision” is made in an “ideal” universe in which the agent is Cartesian, but the utility function is evaluated on the real universe (raw Solomonoff measure). The interaction between the two “universes” is purely via logical conditional probabilities (acausal).
If we want to discuss intelligence without specifying a utility function up front, we allow the “ideal” agent to read a program describing the utility function from a special storage immediately after “booting up”.
Utility functions in the Tegmark level IV multiverse are defined by specifying a “reference universe”, specifying an encoding of the reference universe and extending a utility function defined on the reference universe to encodings which violate the reference laws by summing the utility of the portion of the universe which obeys the reference laws with some function of the space-time shape of the violation.
For what it’s worth, even though you reference some of my work, I’ve been procrastinating on reading your post for several days now because it seems so difficult. It feels like I need to memorize an alphabet’s worth of abbreviations to figure out what’s going on and what’s actually new. The tl;dr helps a little, but I’m still mostly lost. Since there might be valuable stuff in there, maybe you could try to reformulate parts of it, using more standard terminology from logic or CS, or even just more standard LW jargon? Maybe then more people would be able to participate.
I’ve written down the next version of the formalism without introducing any notations until the very last moment when I must do it to write the result in the form of a formula. I would be extremely grateful if you read it and tell me what you think.
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).
tl;dr?
The intelligence of a physicalist agent is defined to be the UDT-value of the “decision” to create the agent by the process creating the agent. The process is selected randomly from a Solomonoff measure conditional on obeying the laws of the hardware on which the agent is implemented. The “decision” is made in an “ideal” universe in which the agent is Cartesian, but the utility function is evaluated on the real universe (raw Solomonoff measure). The interaction between the two “universes” is purely via logical conditional probabilities (acausal).
If we want to discuss intelligence without specifying a utility function up front, we allow the “ideal” agent to read a program describing the utility function from a special storage immediately after “booting up”.
Utility functions in the Tegmark level IV multiverse are defined by specifying a “reference universe”, specifying an encoding of the reference universe and extending a utility function defined on the reference universe to encodings which violate the reference laws by summing the utility of the portion of the universe which obeys the reference laws with some function of the space-time shape of the violation.
For what it’s worth, even though you reference some of my work, I’ve been procrastinating on reading your post for several days now because it seems so difficult. It feels like I need to memorize an alphabet’s worth of abbreviations to figure out what’s going on and what’s actually new. The tl;dr helps a little, but I’m still mostly lost. Since there might be valuable stuff in there, maybe you could try to reformulate parts of it, using more standard terminology from logic or CS, or even just more standard LW jargon? Maybe then more people would be able to participate.
I’ve written down the next version of the formalism without introducing any notations until the very last moment when I must do it to write the result in the form of a formula. I would be extremely grateful if you read it and tell me what you think.
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).