Based on this, we defend the thesis that comprehension is compression, i. The limits of mathematics, a course on information theory and limits of formal reasoning, by gregory j. Much of the value of this book comes from the terse lisp proofs, which can be. Gregory john chaitin is an argentineamerican mathematician and computer scientist. Having published four books on this subject, why a fifth because there s something new. Chaitins three books are based on his popular lectures and must be taken together in order to assess his ideas.
Of particular interest is the halting probability omega, whose bits are irreducible, i. In addition, rather than succumb to the ready pleasures of polemic in carrying out these aims, he carefully provides, in his own writing, an example of intellectual scrupulousness so striking as to inspire the improbable hope that the knowable and the unknowable might set a discursive benchmark to which less circumspect commentators may one day. I compare and contrast godel s, turing s and my work in a very simple and straightforward manner using lisp. It is pretty much a standard topic for a first lecture, leading in to a standard reductionist sequence of biological topics that builds upon the studentsa. In the unknowable he compares his work on incompleteness to. The unknowable by gregory chaitin the unknowable by gregory chaitin mackay, robert s.
First, it presents the fundamental ideas and results of the metabiology created by gregory chaitin. The unknowable is a readable and concrete introduction to chaitins ideas, and it includes a detailed explanation of the programming language used by. Abstract we discuss views about whether the universe can be rationally comprehended, starting with plato, then leibniz, and then the views of some distinguished scientists of the previous century. What links here related changes upload file special pages permanent link page. Up to now i never wanted to examine godel s and turing s work. In the early twentieth century two extremely in fluential research programs aimed to establish solid foundations for mathematics with the help of new formal logic. On the intelligibility of the universe and the notions of simplicity. Chaitin, the unknowable, springer, singapore, 1999. Chaitin 2012, 42 thus for chaitin the bb f unction serv es as a kind of an engine, necessary to start and then to drive the ev olutionary process of abstract organisms. A course on information theory and limits of formal reasoning, springer new york, ny, 1998. Chaitin this essential companion volume to chaitin s highly successful the limits of mathematics, also published by springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant.
Discrete mathematics and theoretical computer science. Springerverlag series in discrete mathematics and theoretical computer science. In the unknowable i use lisp to compare my work on incompleteness with that of. Contribute to melvinzhangaitlisp development by creating an account on github. The unknowable discrete mathematics and theoretical computer. It is, by far, the most polished and most readable of chaitins publications. To make the discussion more concrete we will formulate all.