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Math is about abstraction. It's OK to describe elementary maths and calculus with water-filling bottles, but it ends there, because the higher order abstract structures of mathematics have no real-world equivalent. If we start teaching people with Flash simulations, we 'll have to forget about the Standard model, relativity, electromagnetism, Symmetry, string theory etc. Sure, visual representations make some subjects more accessible, but they can also be terribly misleading and limiting. (Just imagine how much bias our 3-dimensional world experience imposes to our visual thinking). If anything, abstract (written) math allows us to escape the confines of perceived reality.

Math and language are 2 faces of the same ability we have to model the world in arbitrary symbols. Just like math, language has symbols and syntax, that have meaning to us regardless of representation (spoken, written or digital).

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