Turing Computability and Complexity
Ancient documents, like the Rhind Papyrus, dating as far back as 3600 B.C. attest to the fact that men have been performing computations for thousands of years, and for very practical reasons such as farming, land measurements (Egyptian geometry), or simply wishful thinking about the powers of human prediction (astrology). Years later, after Europe surmounted the laggish period of the Middle Ages, a reblooming in the arts during the Renaissance slowly led the way to the dawn of the scientific method, specifically, in the physical- mathematical sciences, with Galileo and the crowning work of Newton on celestial mechanics. In particular, from a modern perspective, their monumental work provides us with algorithms to establish facts about heavenly or earthly objects related to their position and/or their motion. Further research on electricity and magnetism by J.C. Maxwell, and on thermodynamics and heat theory by L. Boltzmann and other 19th century physicists may be regarded in a similar way.
KeywordsEurope Expense Sorting Fermat Alan
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