I have found your old post Without models. You work from a very clear understanding of what a model is, and a thermostat doesn’t have it, and with the definition of a model that you seem to use, I agree.
I think people may mean two things when they talk about a “model”:
An abstract representation of something that some entity can reason about. You mention both physical and software structures that are embedded in the larger system and are operated on (interpreted, evaluated, measured) and influence the larger system (to control it).
A part of the system that represents future states. Mathematically speaking, the factorized part of the system’s state space correlates more with future states of the system than current states of the system (over some time intervals of interest).
These overlap. Think of an explicit model component that is fed input from the environment (the controlled process) and outputs predicted future states. This model will have outputs that highly correlate with the component of the state-space of the environment in the future.
More examples:
A model of the Earth, i.e., a globe, is a model in sense 1 but not in sense 2 because it is an abstraction of the real Earth, and you can be reason about it. But no part of it corresponds to the future state of the Earth.
A mathematical model in the head of an engineer is a model in sense 1 but not in sense 2 unless it includes the application of the model to imaginary inputs from the real world. In that latter case, to the degree the outputs correspond to actual future states, it is also a model in sense 2.
A feedforward circuit in a controller that calculates the effect of a disturbance on the output of a process is a model in sense 2 but not in sense 1 because it is not a separate entity that you can reason about, but its output still correlates with the future state of the process.
A beauty contest model might be a model in sense 2 if its look correlates with the looks of other persons in the future.
A thermostat is no model in sense 1 but you will find that its state-space has a component that corresponds to some future states (at least if it is not a simple P-controller).
I have found your old post Without models. You work from a very clear understanding of what a model is, and a thermostat doesn’t have it, and with the definition of a model that you seem to use, I agree.
I think people may mean two things when they talk about a “model”:
An abstract representation of something that some entity can reason about. You mention both physical and software structures that are embedded in the larger system and are operated on (interpreted, evaluated, measured) and influence the larger system (to control it).
A part of the system that represents future states. Mathematically speaking, the factorized part of the system’s state space correlates more with future states of the system than current states of the system (over some time intervals of interest).
These overlap. Think of an explicit model component that is fed input from the environment (the controlled process) and outputs predicted future states. This model will have outputs that highly correlate with the component of the state-space of the environment in the future.
More examples:
A model of the Earth, i.e., a globe, is a model in sense 1 but not in sense 2 because it is an abstraction of the real Earth, and you can be reason about it. But no part of it corresponds to the future state of the Earth.
A mathematical model in the head of an engineer is a model in sense 1 but not in sense 2 unless it includes the application of the model to imaginary inputs from the real world. In that latter case, to the degree the outputs correspond to actual future states, it is also a model in sense 2.
A feedforward circuit in a controller that calculates the effect of a disturbance on the output of a process is a model in sense 2 but not in sense 1 because it is not a separate entity that you can reason about, but its output still correlates with the future state of the process.
A beauty contest model might be a model in sense 2 if its look correlates with the looks of other persons in the future.
A thermostat is no model in sense 1 but you will find that its state-space has a component that corresponds to some future states (at least if it is not a simple P-controller).