⚡ John Conway Research Paper

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John Conway Research Paper

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John Conway - The Game of Life and Set Theory

Conway tried to simplify von Neumann 's ideas and eventually succeeded [ 3 ] Acres of squared paper were covered, and he and his admiring entourage of graduate students shuffled poker chips, foreign coins, cowrie shells, Go stones or whatever came to hand, until there was a viable balance between life and death. Conway showed the game to his friend Martin Gardner who described it in the October column which he wrote in Scientific American.

The game became an instant success and Conway became a household name. It has often been claimed that since more computer time world-wide has been devoted to the Game of Life than any other single activity. Gardner wrote:- The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata. Also in Conway was elected to a fellowship at Gonville and Caius College Cambridge and, three years later, he was promoted from lecturer to reader in Pure Mathematics and Mathematical Statistics at Cambridge. Another topic for which Conway is famous is discovery of surreal numbers, which again dates from around It always comes as a surprise to people that development of the number systems is still going on.

There is a common belief that complex numbers are the end of the road in the development of numbers and Conway's discovery is the perfect illustration of how even the number systems are part of the continually evolving subject. Perhaps the surprising fact is that Conway was not trying to develop number systems, but rather was analysing the game of Go. Conway studied the games of two players of Go at Cambridge who were of international standard. He noticed that near the end of a game it appeared like the sum of a lot of smaller games. Analysing the situation Conway discovered that certain games behaved like numbers and surreal numbers were born.

The name surreal numbers was not invented by Conway, however, but by Donald Knuth who was so impressed with Conway's discovery that he wrote Surreal Numbers in the form of a novelette aimed at introducing the ideas of mathematical research to students. It is impossible in a short article such as this to look at the full range of topics that Conway has studied or even to give an idea of the remarkable originality of his contributions in so many different areas.

Let us mention that, in addition to his innovative contributions to group theory and his creation of surreal numbers mentioned above, he has done leading research in knot theory , number theory, game theory, quadratic forms , coding theory, and tilings. Then, in , he was appointed professor of mathematics at Cambridge. It was around this time that the following picture of Conway was painted by Guy [ 3 ] :- Conway is incredibly untidy. If you can reach the blackboard there is a wide range of coloured chalk, but no space to write. His room in College is in a similar state. In spite of his excellent memory he often fails to find the piece of paper with the important result that he discovered some days before, and which is recorded nowhere else.

In Conway left Cambridge after accepting appointment to the John von Neumann Chair of Mathematics at Princeton in the United States where much of his work has focused on geometry, in particular studying the symmetries of crystal lattices. This Prize is awarded to mathematicians who display outstanding achievement in their discipline by making major contributions to new knowledge. We should mention a few of the books Conway has written, and illustrate their importance and originality with a brief comment from a reviewer.

On numbers and games To really understand and prove everything in the book, not to mention to attempt solutions of the many questions inspired on every page of the book, will engage many people for many years. It is likely to remain an eminent leader in this field for many years to come. Two further volumes of Winning ways for your mathematical plays have since appeared with the second edition of Volume 3 appearing in September and the second edition of Volume 4 appearing in May The book is very "reader friendly". In fairness to any potential readers having even the least interest in the world around them, the publishers should have been required to post a warning label on the front cover indicating that this book contains extremely addictive material.

This slim book is most intriguing to read: it is an excellent exposition of very attractive topics, and it contains several new and significant results. Much of it should be accessible for anyone with an undergraduate-level background in mathematics, and is likely to stimulate further interest. References show. T M Thompson, From error-correcting codes through sphere packings to simple groups Washington, Additional Resources show. Honours show. Cross-references show. Other: Colloquium photo Other: Most popular biographies. Summarizing an example in Conway's paper, Raymond wrote:. If you have four groups working on a compiler, you'll get a 4-pass compiler. Someone in the group has to be the manager. Yourdon and Constantine , in their book on Structured Design , gave a more strongly stated variation of Conway's Law:.

The structure of any system designed by an organization is isomorphic to the structure of the organization. James O. Coplien and Neil B. Harrison stated in a book concerned with organizational patterns of Agile software development :. If the parts of an organization e. Therefore: Make sure the organization is compatible with the product architecture. An example of the impact of Conway's Law can be found in the design of some organization websites. Nigel Bevan stated in a paper, regarding usability issues in websites: "Organisations often produce web sites with a content and structure which mirrors the internal concerns of the organisation rather than the needs of the users of the site.

Evidence in support of Conway's law has been published by a team of Massachusetts Institute of Technology MIT and Harvard Business School researchers who, using "the mirroring hypothesis" as an equivalent term for Conway's law, found "strong evidence to support the mirroring hypothesis", and that the "product developed by the loosely-coupled organization is significantly more modular than the product from the tightly-coupled organization". The authors highlight the impact of "organizational design decisions on the technical structure of the artifacts that these organizations subsequently develop".

Additional and likewise supportive case studies of Conway's law have been conducted by Nagappan, Murphy and Basili at the University of Maryland in collaboration with Microsoft , [10] and by Syeed and Hammouda at Tampere University of Technology in Finland. From Wikipedia, the free encyclopedia. Adage stating that organizations design systems that mirror their own communication structure.

Archived from the original on Retrieved April Datamation : 28— Englewood Cliffs, N. ISBN OCLC Lay summary. Conway's Law: The structure of a system reflects the structure of the organization that built it. Conway's Law has been stated even more strongly: The structure of any system designed by an organization is isomorphic to the structure of the organization.

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