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SilasBarta comments on Without models - Less Wrong
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This post is an example of how words can go wrong. Richard hasn't clearly specified what this 'model' or 'implicit model' stuff is, yet for the whole post he repeats again and again that it's not in control systems. What is the content of this assertion? If I accept it, or if I reject it, how is this belief going to pay its rent? What do I anticipate differently?
Can anything be 'model'? How do I know that there is a model somewhere?
The word itself is so loaded that without additionally specifying what you mean, it can be used only to weakly suggest, not strongly assert a property.
Any property you see in a system is actually in your interpretation of the system, in its semantics (you see a map, not the territory, this is not a pipe). Interpretation and the procedure of establishing it given a system are sometimes called a 'model' of the system, this is a general theme in what is usually meant by a model. Interpretation doesn't need to happen in anyone's head, it may exist in another system, for example in a computer program, or it can be purely mathematical, arising formally from the procedure that specifies how to build it.
In this sense, to call something a model is to interpret it as an interpretation of something else. Even a rock may be said to be a model of the universe, under the right interpretation, albeit a very abstract model, not useful at all. Of course, you can narrow down this general theme to assert that rocks can't model the universe, in particular because they can't simulate certain properties, or because your interpretation procedure breaks down when you present it with a rock. But you actually have to state the meaning of your terms in the cases like this, hopefully with a definition-independent goal to accomplish by finally getting the message through.
This is exactly why I tried to restate the situation in terms of the more precise concept of "mutual information" in Richard's last topic, although I guess I was a bit vague at points as to how it works.
So in the context of Bayesian inference, and rationality in general, we should start with:
"A controller has a model (explicit or implicit) of it's environment iff there is mutual information between the controller and the environment."
This statement is equivalent to:
"A controller has a model (explicit or implicit) of its environment iff, given the controller, you require a shorter message to describe its environment (than if you could not reference the controller)."
From that starting point, the question is easier to answer. Take the case of the thermostat. If the temperature sensor is considered part of this controller, then yes, it has a model of its environment. Why? Because if you are given the sensor reading, you can more concisely describe the environment: "That reading, plus a time/amplitude shift."
Richard puts a lot of emphasis on how cool it is that the thermostat doesn't need to know if the sun is shining. This point can be rephrased as:
"A controller does not need to have mutual information with all of its environment to work." Or,
"Learning a controller, and the fact that it works, does not suffice to tell you everything about its environment."
I think that statement sums up what Richard is trying to say here.
And of course you can take this method further and discuss the mutual information between a) the controller, b) the output, c) the environment. That is, do a) and b) together suffice to tell you c)?
EDIT: Some goofs