What is the exact statement of the Church Turing thesis?
Is it fair to say anything computable in the physical world can be computed by a Turing machine? If so, how does a Turing machine handle continuous variable computations (for example, computing solutions to differential equations or storing/computing any real number)? It will take infinitely many tape squares to specify anything continuous. If the input itself is infinite, what does it even mean to compute based on the infinite input?