George E. P. Box is famous for the quote: “all models are wrong, but some are useful.” […]

In my experience, most models outside of physics are heuristic models. The models are designed as caricatures of reality, and built to be wrong while emphasizing or communicating some interesting point. Nobody intends these models to be better and better approximations of reality, but a toolbox of ideas. Although sometimes people fall for their favorite heuristic models, and start to talk about them as if they are reflecting reality, I think this is usually just a short lived egomania. As such, pointing out that these models are wrong is an obvious statement: nobody intended them to be not wrong. Usually, when somebody actually calls such a model “wrong” they actually mean “it does not properly highlight the point it intended to” or “the point it is highlighting is not of interest to reality”. As such, if somebody says that your heuristic model is wrong, they usually mean that it’s not useful and Box’s defense is of no help.

On the opposite end of the spectrum are abstractions, these sort of models are rigorous mathematical statements about specific types of structures. These models are right and true of their subjects in any reasonable definition of the words. They are as right or true as the statement that there are infinite number of primes; or that in Euclidean geometry, the tree angles of a triangle sum to two right angles. When somebody says that an abstraction is wrong, they mean one of two things:

1. It is mathematically false. […]

2. Or, the structure you are applying it to does not meet the requirements of the abstraction. For example, in general relativity, space is non-Euclidean, so triangles don’t sum to 180 degrees.

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I think you are missing out on some ideas on complexity. […] What makes you think that something mathematical is comprehensible? You already invoked one simple form of incomprehension: undecidability in computing. […] As to a belief that the universe is not “mathematical”: well, what else could it possibly be? Many mathematicians define mathematics as the sum-total of all possibility; to say that something isn’t mathematical is tantamount to saying it isn’t possible. Since there is nothing else that it could be, by law of excluded middle, it must be.

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Hmmm, no edit-button to correct my post. Some footnotes, then: […]

Box’s quote is kind-of the mirror image of Kolmogorov complexity, which states that a model is useful only if it is smaller than the thing being modelled, and, what’s more, that there are things that cannot be modeled.

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