Kurt GApdel (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 Einsteinas general relativity, as he proved that Einsteinas theory allows for time machines. The GApdel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitinas groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the GApdel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the GApdel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this bookas writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8And the heada#39;s internal configuration goes to another state, which may be a a shutdowna state that ends the machinea#39;s operation. ... Each line Li can be written in binary code, and we can translate the instructions in any computer program into that kind of Turing ... Suffices to order it to make a never ending calculation, like e.g. the division of, say, 1 by 0, or perhaps constructing a machine that moves to theanbsp;...
|Author||:||Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa|
|Publisher||:||CRC Press - 2011-10-14|