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The fundamental issue with mathematics and the notion of truth
Griddle's conclusion is that mathematics may have an inability to describe reality. Philosophers have drawn similar conclusions and believe that understanding mathematics gives them an advantage. However, the solution is to replace traditional mathematics with computation, which allows for the definition of any procedure as long as it converges to a desired value. This means losing the notion that truth is independent of the procedure. Despite this limitation, useful things can still be built. Penrose believes our brain does infinite computations, but in reality, we reason about infinity through finite computations. Infinity cannot be constructed or written down. Penrose's book, The Road to Reality, explores these ideas.