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Theories as Models Isomorphic to Reality

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The aim of a theory in any field is essentially to build a model that is isomorphic to reality, so that its behavior will mimic exactly the behavior of the physical or other system that it tries to describe.

Let us see how this works for physical systems. We have the space of all possible states of the system we study. This is usually called phase space, but it would be more exact to call states space. Each point of this space represents a state of the system. Physical laws determine the movement of the system along these points. When the system is at a specific state-point, in the next time step it could conceivably pass to any other state-point, or at least to any other "neighbouring" state-point. Physical laws determine to which of all the possible state-points it will pass. (So if we hold an apple and release it, the apple will move in a specific direction with a specific speed.)

Here there is an interesting parallel with information. When we do not know the state of a system, information restricts the possible alternative states the system could be in. In the evolution of a system, physical laws restrict the possible alternative states that the system can pass to.