# Alan Turing: His Work and Impact

## S. Barry Cooper

Language: English

Pages: 944

ISBN: 0123869803

Format: PDF / Kindle (mobi) / ePub

In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the *Collected Works of A. M. Turing*. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work.

Offering a more modern perspective than anything currently available, *Alan Turing: His Work and Impact* gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work.

- 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP
- Named a 2013 Notable Computer Book in Computing Milieux by
*Computing Reviews* - Affordable, key collection of the most significant papers by A.M. Turing
- Commentary explaining the significance of each seminal paper by preeminent leaders in the field
- Additional resources available online

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a distinguished cell on the tape called the start cell, and the finite control is in a distinguished state q0. At time 0 all cells contain Bs, except for a contiguous finite sequence of cells, extending from the start cell to the right, which contain 0’s and 1’s. This binary sequence is called the input. The device can perform the following basic operations: (1) It can write an element from A = {0,1, B} in the cell it scans; and (2) it can shift the head one cell left or right. When the

thinking could indeed be the inward manifestation of some kind of nonalgorithmic physical activity.15 3 Turing on physics and uncomputability Turing’s early observation that there might be uncomputable physical processes has not been widely noticed (as witnessed by Penrose’s attribution to him of a thesis equivalent to Wolfram’s, under the name ‘Turing’s Thesis’). Yet Turing was one of the first, perhaps the very first, to raise the question whether there are uncomputable physical

are undifferentiated. More generally, this paper addresses the problem of symmetry breaking. It offers indeed an explanation of how starting with a perfectly symmetric state a system can evolve into differentiated components based on simple and fundamental mechanisms that operate at very basic levels of living systems. This vision is carried through systems of reaction–diffusion equations both in spatial discrete and continuous forms. Along with several other underlying themes, the article

needs of the organism. They do, however, carry out their research as though the variations were completely random. That leaves natural selection as the only non-random effect in evolution and so it is to natural selection alone that we are to look for explanations. Any heritable trait is to be explained by showing how it is or might be useful to the organism and so would have been selected, that is to say by much the same sort of argument that was used by the natural theologians to justify their