Undecidability, Uncomputability, and Unpredictability Aguirre Anthony
Undecidability, Uncomputability, and Unpredictability Aguirre Anthony For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and…
Specifikacia Undecidability, Uncomputability, and Unpredictability Aguirre Anthony
Undecidability, Uncomputability, and Unpredictability Aguirre Anthony
For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. That time has passed. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens.
While some connections between these results have come to light, many remain obscure, and the implications are unclear. G del's undecidability results (the incompleteness theorems), Turing's proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. Are there, for example, real consequences for physics -- including quantum mechanics -- of undecidability and
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