David Deutsch's claim about "mathematicians' misconception" (Jose M.)

[Yu Li]

Dear FOM members,

I would like to share my opinions about the topic of  mathematicians’ misconception due to David Deutsch.

David Deutsch made this claim in his paper The Philosophy of Constructor Theory  when he talked about the computability (chapiter 2.8) [1], he said : 
- The principle of the computability of nature must be that a computer capable of simulating any physical system is physically possible.

So a possible interpretation of his claim is that, by mathematicians’ misconception David Deutsch perhaps refers to phenomena in the current computability theory where theory and practice are out of touch, that is, a computable function is not necessarily physically possible, that is, physically computable.

Let me quote a similar commentary from the wiki in French [2] :
- A computable function (or recursive function) is one computed by a Turing machine that halts .
- A computable function is not necessarily physically computable, for example, if its execution time exceeds billions of years.

Jose M. asked : what could be the status of what David Deutsch calls the mathematicians’ misconception in the framework of foundations of mathematics? 

Let us go back to Turing’s 1936 paper that laid the foundation for the theory of computability (On Computable Numbers, with an Application to the Entscheidungsproblem) to recall how Turing established the concept of computability. 

I wonder to know if you have noticed that :
1, The computable number (sequence), a concept throughout Turing's paper and even as a key word in the title of paper, has disappeared from the current computational theory;
2, There are some subtle differences between the current Turing machine and Turing's computing machine : the current Turing machine finishes the computation of an instance of a problem and then halts , where the infinite tape is interpreted as unlimited memory for computing an instance; while Turing's computing machine finishes the computation of an instance, returns to the initial state, and continues to compute the next instance without halting.

Best regards

Yu Li

Reference:
[1] https://arxiv.org/pdf/1210.7439.pdf <https://arxiv.org/pdf/1210.7439.pdf>
[2] https://fr.wikipedia.org/wiki/Fonction_calculable <https://fr.wikipedia.org/wiki/Fonction_calculable>
[3] https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf <https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf>

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