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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.
Hugh Everett's many-worlds interpretation of quantum physics, "The first and most important of the four strands".; Karl Popper's epistemology, especially its anti-inductivism and its requiring a realist (non-instrumental) interpretation of scientific theories, and its emphasis on taking seriously those bold conjectures that resist being falsified.
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]
Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
The first rigorous and general derivation of the quantum Zeno effect was presented in 1974 by Antonio Degasperis, Luciano Fonda, and Giancarlo Ghirardi, [5] although it had previously been described by Alan Turing. [6] The comparison with Zeno's paradox is due to a 1977 article by Baidyanath Misra & E. C. George Sudarshan.
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.
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 ]