An elaboration of some points of “K. Ammon. An Effective Procedure for Computing “Uncomputable” Functions, 2013” (http://arxiv.org/pdf/1302.1155v1.pdf). on Kurt’s Blog. To start to understand this, it is necessary to read that article first… Admittedly dense thoughts that require some background in theoretical computer science, but I hope that Kurt’s Blog and my own, and the dialog between the two, plus your comments, will lead to the development of formulations of these thoughts that are more accessible for non-experts. This is a first step in that direction.

Turing ^{[1]} discusses the development of intelligence in man and in machines:

*If the untrained infant’s mind is to become an intelligent one,** it must acquire both discipline and initiative. So far we have** been considering only discipline. To convert a brain or machine** into a universal machine is the extremest form of discipline. But** discipline is certainly not enough in itself to produce intelligence.** That which is required in addition we call initiative. … Our task** is to discover the nature of this residue as it occurs in man, and** to try and copy it in machines.*

Thus, Turing’s discipline is the execution of a universal [Turing] machine, that is, the execution of an ordinary computer program. He writes: “*That which is required in addition [to produce intelligence] we call initiative.” *This means that Turing assumes that intelligence cannot completely be represented by any Turing machine, that is…

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[…] can, in mathematical terms, be modelled as “Turing machines”. This provides a connection to the article of Kurt Ammon I reblogged recently: mathematically, programs can be modeled by “Turing machines”. Technically, the formalism of […]