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In his reply to my letter (Science, 336, .p 1639, 29 June 2012), A. Hodges does not repeat certain exaggerated statements of his original essay on Turing. However, the response still seems to obfuscate certain issues.
Hodges writes: "But Turing successfully addressed Hilbert's question of decidability, a problem that Gödel's work had not settled."
Church published his solution even earlier though. The computational model of Church is equivalent to Turing's (and Post's from the same year). Both Church and Turing built on Gödel's work, of course.
Hodges also writes: "Turing introduced the concept that computation could act on general symbolic, not necessarily arithmetic structures.
In particular, he exploited the fact that a program is itself such a structure." But that's essentially what Gödel did 5 years earlier, using different terminology. In 1931, Gödel showed how to encode axioms and rules of general formal symbolic systems in arithmetics. Internal states of his theorem-proving machine are encoded as integers. His celebrated self-referential statement essentially talks about computations and says: "I am not provable from the axioms by a theorem-proving program."
Hodges also points out that Turing "emphasized that programs could be written in user-friendly form, with the computer itself used to translate them into machine code." In fact, the first higher-level programming language of this kind was Plankalkül, designed by Konrad Zuse, who also built the first working program-controlled (and universal) computer 1935-1941.
Hodges writes: "But Turing had a distinctive place connecting theory to practice and logic to physics." I totally agree. But so did Zuse and others.
Again: Turing was great! But don't attribute to him breakthroughs of others. He certainly doesn't need it. I am sure he would disapprove!
Director of the Swiss AI Lab IDSIA, Lugano
Professor of Artificial Intelligence, Univ. Lugano
Professor SUPSI, Manno-Lugano, Switzerland
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