What is a metamathematician? Well there is no such person, for a mathematician can DEFINE any number of dimensions that are mutually independent. But the 'meta' or unreality came into the whole of modern physics when more than three dimensions were applied to space resulting in weird mathematics. If one has any three mutually independent perpendicular dimensions one can define any point in space. That is, and always has been, sufficient and real. Modern physics went wrong when physicists became influenced by mathematicians introducing their unreal spaces of more than the three dimensional Cartesian space. Thus when the mathematician Roger Penrose wrote his book The Road to Reality - A Complete Guide to the Laws of the Universe, he was essentially writing popycock. He was not writing about real physics, and this despite having theories that appear to explain some experimental results.
What has been the outcome? Physicists are ruled by the mathematician theorists to whom they bow.
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