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This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The... Read more
This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER
The Unknowable Hardback edition by Gregory J. Chaitin
I. A Hundred Years of Controversy Regarding the Foundations of Mathematics.- II. LISP: A Formalism for Expressing Mathematical Algorithms.- III. Goedel's Proof of his Incompleteness Theorem.- IV. Turing's Proof of the Unsolvability of the Halting Problem.- V. My Proof that You Can Show that a LISP Expression is Elegant.- VI. Information & Randomness: A Survey of Algorithmic Information Theory.- VII. Mathematics in the Third Millennium?- Bibliography.
Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he proved that Einstein's theory allows for time machines....
The author of Meta Math! explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world. 25,000 first printing.
Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras.
This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs.
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Goedel's incompleteness theorem, using an information theoretic approach based on the size of computer programs.
Contains 23 non-technical papers. This book includes essays which summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of Godel and Turing on the limits of mathematical methods, both in logic and in computation.
Discussing the foundations of the theory of distributive lattices and the techniques used in this field, this resource also presents a number of special topics to which the theory is applied. In developing the theory, the authors have made use of the methods and tools of universal algebra and elementary category theory.
Raspberry Pi 2... Master It Today!Programmers may be able to understand how the computer thinks and process their input codes but seldom do programmers realize how the computer accomplish the instructions fed to its system. This is where Raspberry Pi comes in.Learning how software and hardware work hand-in-hand to achieve a desired result will help you develop not only programs but also inventions...
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ShortCuts In MathematicsWhat makes it 'World's first family book of Mathematics" ?It's a family book to be read and used by the whole family. It's a family tonic of Mathematics anyone in the family can have it.It is for the Daughter / Son, Mother / Father and Grand Mother / Father as well ! It's world's first commercial blockbuster of Mathematics full of comedy, emotion and drama. It will...
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Raspberry Pi 3... The Updated 2017 Guide! Programmers may be able to understand how the computer thinks and process their input codes but seldom do programmers realize how the computer accomplish the instructions fed to its system. This is where Raspberry Pi comes in. Learning how software and hardware work hand-in-hand to achieve a desired result will help you develop not only programs but...
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