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Systems of Logic Based on Ordinals was the PhD dissertation of the mathematician Alan Turing. [1] [2]Turing's thesis is not about a new type of formal logic, nor was he interested in so-called "ranked logic" systems derived from ordinal or relative numbering, in which comparisons can be made between truth-states on the basis of relative veracity.
Alan Turing was driven to a terrible despair and early death by the nation he'd done so much to save. This remains a shame on the British government and British history. A pardon can go some way to healing this damage. It may act as an apology to many of the other gay men, not as well-known as Alan Turing, who were subjected to these laws. [193]
Jack Copeland is the Director of the Turing Archive for the History of Computing, [6] an extensive online archive on the computing pioneer Alan Turing. He has also written and edited books on Turing. He is one of the people responsible for identifying the concept of hypercomputation and machines more capable than Turing machines.
An earlier version of this thesis for classical computers was stated by Alan Turing's friend and student Robin Gandy in 1980. [2] [3] A similar thesis was stated by Michael Freedman in an early review of topological quantum computing with Alexei Kitaev, Michael J. Larsen, and Zhenghan Wang, known as the Freedman-Church-Turing thesis: [4]
The Turing Guide is divided into eight main parts, covering various aspects of Alan Turing's life and work: [3]. Biography: Biographical aspects of Alan Turing.; The Universal Machine and Beyond: Turing's universal machine (now known as a Turing machine), developed while at King's College, Cambridge, which provides a theoretical framework for reasoning about computation, a starting point for ...
Alan Turing, 1938 [1] Alonzo Church (June 14, 1903 – August 11, 1995) was an American computer scientist , mathematician , logician , and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science . [ 2 ]
The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
The Church–Turing Thesis: Stephen Kleene, in Introduction To Metamathematics, finally goes on to formally name "Church's Thesis" and "Turing's Thesis", using his theory of recursive realizability. Kleene having switched from presenting his work in the terminology of Church-Kleene lambda definability, to that of Gödel-Kleene recursiveness ...