The Church-Turing thesis has some profound implications for the philosophy of mind. There are also some important open questions which cover the relationship between the Church-Turing thesis and physics, and the possibility of hypercomputation. When applied to physics, the thesis has several possible meanings:
There are actually many technical possibilities which fall outside or between these three categories, but these should serve to illustrate the concept.
- The universe is a Turing machine (and thus, computing non-recursive functions is physically impossible). This has been termed the strong Church-Turing thesis.
- The universe is not a Turing machine (ie, the laws of physics are not Turing-computable), but incomputable physical events are not "harnessable" for the construction of a hypercomputer. For example, a universe in which physics involves real numbers, as opposed to computable realss, might fall into this category.
- The universe is a hypercomputer, and it is possible to build physical devices to harness this property and calculate non-recursive functions. For example, it is an open question as to whether all quantum mechanical events are Turing-computable, although it has been proved that any system built out of qubits is (at best) Turing-complete. John Lucas (and famously, Roger Penrose) have suggested that the human mind might be the result of quantum hypercomputation.
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