Church-Turing thesis

Deutsch [deut85] was the first to point out a possible connection between the C-T Thesis and physics  

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Despite its simplicity, the Turing machine models the computing capability of a general-purpose computer, and since 1936 it has been the standard accepted model of universal computation. The proposition, often called the Church-Turing thesis, says that any process which could naturally be called an effective procedure can be realized by a Turing machine. In other words, this thesis states that no realizable computing device can be more powerful than a Turing machine [150,151]. It is, however, of interest to discuss the... 

In other words, if the brain is constrained by computational tractability, then it limits the possible set of models which could be used when modeling cognition. Van Rooij specifically traces this back to the idea that the Church-Turing thesis is... 

The previous theorem can be generalized to several other paraconsistent logics, that is, to those where a conservatively translation function from CPL can be defined taking into account that such translation function must be effectively calculated. In the other direction, the existence of uniform families of boolean circuits to every uniform family of L-circuits (for any logic L provided with PRC) is guaranteed by the classical computability of roots for polynomials over finite fields. Then, the L-circuits model does not invalidate Church-Turing s thesis. 

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