The limits of mathematics : a course on information theory and the limits of formal reasoning
Abstract: "A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is implemented via software written in Mathematica and C. Using this new software, it is now possible to give a self-contained 'hands on' mini-course presenting very concretely the latest proofs of the fundamental information-theoretic incompleteness theorems."
"Abstract: "A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is implemented via software written in Mathematica and C. Using this new software, it is now possible to give a self-contained 'hands on' mini-course presenting very concretely the latest proofs of the fundamental information-theoretic incompleteness theorems.""@en
"Abstract: "This condensed version of RC 20190 will be the main hand-out for a course on algorithmic information theory to be given 22-29 May 1996 at the Rovaniemi Institute of Technology, Rovaniemi, Finland (see announcement at http://www.rotol.fi).""@en
"This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Godel is much more widespread and serious than hitherto suspected."@en
"Abstract: "The latest in a series of reports presenting the information-theoretic incompleteness theorems of algorithmic information theory via algorithms written in specially designed versions of LISP. Previously in this LISP code only one-character identifiers were allowed, and arithmetic had to be programmed out. Now identifiers can be many characters long, and arithmetic with arbitrarily large unsigned decimal integers is built in. This and many other changes in the software have made this material much easier to understand and to use.""@en
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LISP (Lenguaje de programación para computadores).
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