Computational Complexity Theory - Revision history

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Tom: Tom moved page Complexity Theory to Computational Complexity Theory: more specificity

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 ==Context==
 * The wiki page on [[Complexity]] begins to address [[Complexity]] from a computation point of view.
-* This page is interesting for the relationship to [https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/ Business]
+* This page is interesting for the relationship to [https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/ Science and its application to Business].
 Between 1500–1700, there was an important and dramatic shift in the way that people in Europe perceived and understood the world. Through the works of thinkers such as Francis Bacon, Galileo Galilei, Johannes Kepler, Rene Descartes, and Isaac Newton, the Western world underwent a scientific revolution. This resulted in a shift from a worldview governed by the Church and Christian theology and ethics, to that of an inanimate, machine-like material world governed by natural forces and exact mathematical rules.<ref>Capra and Luisi, ''The Newtonian world-machine. In The Systems View of Life: A Unifying Vision'' (pp. 19–34). Cambridge: Cambridge University Press. (2014) doi:10.1017/CBO9780511895555.004</ref>

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 * The wiki page on [[Complexity]] begins to address [[Complexity]] from a computation point of view.
 * This page is interesting for the relationship to [https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/ Business]
 Between 1500–1700, there was an important and dramatic shift in the way that people in Europe perceived and understood the world. Through the works of thinkers such as Francis Bacon, Galileo Galilei, Johannes Kepler, Rene Descartes, and Isaac Newton, the Western world underwent a scientific revolution. This resulted in a shift from a worldview governed by the Church and Christian theology and ethics, to that of an inanimate, machine-like material world governed by natural forces and exact mathematical rules.<ref>Capra and Luisi, ''The Newtonian world-machine. In The Systems View of Life: A Unifying Vision'' (pp. 19–34). Cambridge: Cambridge University Press. (2014) doi:10.1017/CBO9780511895555.004</ref>

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-The meta-mathematics of determining how hard it is to solve a problem. This originally was just complexity theory, but that has recently become more complex and includes other specialties/
+The meta-mathematics of determining how hard it is to solve a problem. This originally was just [[Complexity Theory]], but that has recently become more complex and includes other specialties/
 Another major contributor to complexity theory is John Holland, a computer scientist and professor at the University of Michigan. Holland designed the genetic algorithm based on the idea that components of complex systems can be broken down into building blocks, whose characteristics can then be represented in code.

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	David Hilbert proposed in 1900 his challenge #2 to prove the consistency of the axioms of arithmetic for logical problems. Kurt Gödel showed that this was not possible in 1931.<ref>Kurt Gödel, On Formally Undecidable Propositions of Principia Mathematica and Related Systems'' Dover (original in German 1931) ISBN 9780486669809</ref> This discovery was just a few years after Heisenberg showed that the mathematics of [[Quantum Mechanics]] asserted a fundamental limit to the accuracy of any measurements made on an individual quantum particle. Finally in 1996 Ilya Prigogine published a book declaring "The End of Certainty."<ref> Ilya Prigogine, ''The End of Certainty'', Free Press (1996) ISBN 0684837059</ref>		David Hilbert proposed in 1900 his challenge #2 to prove the consistency of the axioms of arithmetic for logical problems. Kurt Gödel showed that this was not possible in 1931.<ref>Kurt Gödel, On Formally Undecidable Propositions of Principia Mathematica and Related Systems'' Dover (original in German 1931) ISBN 9780486669809</ref> This discovery was just a few years after Heisenberg showed that the mathematics of [[Quantum Mechanics]] asserted a fundamental limit to the accuracy of any measurements made on an individual quantum particle. Finally in 1996 Ilya Prigogine published a book declaring "The End of Certainty."<ref> Ilya Prigogine, ''The End of Certainty'', Free Press (1996) ISBN 0684837059</ref>
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		+	Here is just one tip of the iceberg we’ll explore in this book: How much time does it take to find the prime factors of a 1,000-digit integer? The facts are that (1) we can’t even roughly estimate the answer: it could be less than a second or more than a million years, and (2) practically all electronic commerce and Internet security systems in existence today rest on the belief that it takes more than a million years!<ref>Avi Wigderson, ''Mathematics and Computation'' Princeton UP 2019 https://www.math.ias.edu/files/Book-online-Aug0619.pdf#page=1</ref>

	==References==		==References==

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 ==Context==
 * The wiki page on [[Complexity]] begins to address [[Complexity]] from a computation point of view.
-* This page is interesting the the
+* This page is interesting for the relationship to [https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/ Business]

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	[[Category: Physics]]		[[Category: Physics]]
	[[Category: Information]]		[[Category: Information]]
		+	[[Category: Complexity]]

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