In Search of Certainty - The Science of Our Information Infrastructure by Mark Burgess

Author:Mark Burgess [Burgess, Mark]
Language: por
Format: mobi, epub, azw3
Publisher: XtAxis Press
Published: 2013-11-25T04:00:00+00:00

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The effect of Gödel’s theorem was something akin to the shock of quantum theory and the uncertainty it introduced. Gödel cemented the 20th century’s position in history as the number one undoer of certainty, and put the final nail in the coffin for determinism. Indeed, quantum mechanics offered actual proof that the world can, in fact, does exist in states that are neither true nor false, at least within the framework of our own understanding of it. Both states do occur at the same time in physics, proving that nature does not respect Hilbert’s second challenge (ironically the way one shows this in quantum mechanics is with a Hilbert space).

Alan Turing went on to use his work on computation to prove his own version of the theorem, using his prototype computer, the Turing machine. He considering the so-called Entscheidungsproblem or halting problem for a machine to answer a question. The idea here was to know whether every problem fed into a computer could be resolved with a true or a false answer. Are there results that are not computable at all? Turing showed that it was possible to construct problems that could neither proved true nor false. By assuming the discreteness of time and state, and the sequence of cause and effect as in logic, he showed that there were problems that were undecidable. Far from being a disaster, however, this realization opened the door to entire new fields of mathematical understanding, like algorithmic complexity theory, which I return to at the end of this chapter.

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