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Turing-Church Thesis and Incomputability

Turing-Church Thesis and Incomputability. In which a few things really do not compute. Integer Roots of Polynomials. Turns out x=5, y=3, z=0 works. But integer roots do not always exist. Turing-Church Thesis Is About What Defines a Computation.

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Turing-Church Thesis and Incomputability

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  1. Turing-Church Thesisand Incomputability In which a few things really do not compute

  2. Integer Roots of Polynomials Turns out x=5, y=3, z=0 works. But integer roots do not always exist.

  3. Turing-Church Thesis Is About What Defines a Computation • Several famous math questions were proposed, but there was really no way to answer these questions in the negative • Several models were proposed, two of note were the Turing Machine and the lambda calculus (which is bizarre and awesome BTW) • But, as we’ve seen, a little computation goes a long way and both of these definitions of computation proved to be equivalent

  4. Turing Completeness • Another way to say “equivalent to Turing Machines”. You would say “Turns out 1-dimension cellular automata are Turing-complete” • Way more things are Turing Complete than you’d think. For example, the game of life is Turing complete. There is even a 1-D 2 color cellular automata that is Turing Complete • Often also a feature of excessively featured configuration languages like Postscript (a printer language)

  5. Surely there is nothing our magical machines can’t do?

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