# Church Turing thesis [closed]

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?

• In a nutshell, the Church-Turing thesis addresses pencil-and-paper methods. How do you represent real numbers on paper? – dkaeae Jun 21 '19 at 7:35
• The Church–Turing thesis is not a formal statement. It doesn't have an exact statement. – Yuval Filmus Jun 21 '19 at 11:02
• Have you consulted Wikipedia? – Yuval Filmus Jun 21 '19 at 11:02
• – Discrete lizard Jul 18 '19 at 9:17
• Possible duplicate of Is there any data structure that can't be represented or described inside a computer?. Although that question and answer does not mention Church-Turing thesis, it does address the vague questions raise here. – John L. Jul 20 '19 at 2:31

Neither physical computers nor the Turing machine model can exactly represent the value of a continuous quantity or a non-rational transcendental real number. They can, for example, only approximate $$\pi$$ by calculating or storing its value to some finite (but maybe very large) number of decimal places.