Arquivo para August 24th, 2017
The problem of consciousness and algorithms
24
Aug
Mathematician and computer scientist Gregory Chaitin, who is Argentinean American and is at the Federal University of Rio de Janeiro, formulated still young from the complexity of Kolmogorov, contributions to the formulation of an algorithmic and meta-mathematical information theory, which was Developed from the formulation of Gödel’s incompleteness theorem, already quoted here in previous posts and its relation with the Turing Machine and Alonzo Church, which gave rise to modern digital computing.
Chaitin defined a constant that bears his name and uses the symbol Ω, a real number whose digits are equidistributed, and which is sometimes informally described as an expression of the probability that a random program will be interrupted.
The constant Ω has the mathematical property of being decidable but computable we can say separates Hilbert-Gödel’s problem from the Turing / Church problem, but more than that, it gives a key to solve problems in the field of biology (obtaining A formal definition of “life,” origin and evolution) and neuroscience (the problem of consciousness and the study of the mind).
In epistemology, Chaitin proposed that both in mathematical logic and in algorithmic theory, “mathematical facts that are true for whatever reason, they are true by accident.these are random mathematical facts.” Chaitin proposes that mathematicians should abandon any hope of proving these mathematical facts and adopting a semi-empirical methodology.
In this sense it creates a metaphysics of mathematics, or a metamathematics one, capable of elaborating algorithms that propose a logic of life and even of the conscience, from there are possible the studies of biology and the mind by formulations of this metamathemamatics one.
Gregory Chaitin will be at USP at the EBICC event in early November this year addressing the issue of awareness from his perspective.
