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Do you think, that it would be possible to run a infinite and recursive simulation of the universe on an turing machine?

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The concept of the Turing machine is a mathematical concept representing exactly that which can be computed (is 'decidable'). Therefore, the answer to that question depends on your worldview.

In a strict scientific-deterministic worldview, the world could ultimately be modeled in a mathematical model, and iterations of that model would be well-defined. Therefore, by definition, a Turing machine could implement that model.

Other worldviews may not accommodate for such possibilities. Hume comes to mind, claiming causation cannot be proven to exist.

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