I think your definition of perfect model is a bit off—a circuit diagram of a computer is definitely not a perfect model of the computer! The computer itself has much more state and complexity, such as temperature of the various components, which are relevant to the computer but not the model.
But there is no fundamental law of physics that says that the computer cannot maintain estimates of the temperature of each of its components.
Now it is true that a computer cannot store the exact physical state of every atom that constitutes it, since storing that much information would indeed require the full physical expressivity of every atom that constitutes it, and there would indeed be no room left over to do anything else.
But digital computers are designed precisely so that their behavior can be predicted without needing to track the exact physical state of every atom that constitutes them. Humans are certainly able to reason about computers in quite a bit of detail without tracking the exact physical state of every atom that constitutes them. And there is no reason that a digital computer couldn’t store and use a self-model with at least this level of predictive power.
Containing a copy of your source code is a weird definition of a model. All programs contain their source code, does a program that prints it source code have more of a model of itself than other programs, which are just made of their source code?
Well sure, containing a copy of your own source code on its own is not really a “self-model”, but it does show that there is nothing fundamentally blocking you from analyzing your own source code, including proving things about your own behavior. There is nothing fundamentally paradoxical or recursive about this. The claim was made that things cannot contain perfect models of themselves, but in fact things can contain models of themselves that are sufficiently to reason about.
The key word is “perfect”—to fit a model of a thing inside that thing, the model must contain less information than the thing does.
Well yes, but the autonomous car in the parable didn’t go wrong by having an insufficiently perfect self-model. It had a self-model quite sufficient to make all the predictions it needed to make. If the self-model had been more detailed, the car still would have gone wrong. Even if it had a truly perfect self-model, even though such a thing is not permitted under our laws of physics, it still would have gone wrong. So the problem isn’t about the inability for things to contain models of themselves. It’s about how those self-models are used.
But there is no fundamental law of physics that says that the computer cannot maintain estimates of the temperature of each of its components.
Now it is true that a computer cannot store the exact physical state of every atom that constitutes it, since storing that much information would indeed require the full physical expressivity of every atom that constitutes it, and there would indeed be no room left over to do anything else.
But digital computers are designed precisely so that their behavior can be predicted without needing to track the exact physical state of every atom that constitutes them. Humans are certainly able to reason about computers in quite a bit of detail without tracking the exact physical state of every atom that constitutes them. And there is no reason that a digital computer couldn’t store and use a self-model with at least this level of predictive power.
Well sure, containing a copy of your own source code on its own is not really a “self-model”, but it does show that there is nothing fundamentally blocking you from analyzing your own source code, including proving things about your own behavior. There is nothing fundamentally paradoxical or recursive about this. The claim was made that things cannot contain perfect models of themselves, but in fact things can contain models of themselves that are sufficiently to reason about.
Well yes, but the autonomous car in the parable didn’t go wrong by having an insufficiently perfect self-model. It had a self-model quite sufficient to make all the predictions it needed to make. If the self-model had been more detailed, the car still would have gone wrong. Even if it had a truly perfect self-model, even though such a thing is not permitted under our laws of physics, it still would have gone wrong. So the problem isn’t about the inability for things to contain models of themselves. It’s about how those self-models are used.