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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Undecidability, Uncomputability, and Unpredictability (Hardcover, 1st ed. 2021)
Loot Price: R2,200
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Undecidability, Uncomputability, and Unpredictability (Hardcover, 1st ed. 2021)
Series: The Frontiers Collection
Expected to ship within 18 - 22 working days
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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. They could discern what math corresponds
to physical laws, and use those laws to predict anything that
happens before it happens. That time has passed. Goedel'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. While some connections between these results have come
to light, many remain obscure, and the implications are unclear.
Are there, for example, real consequences for physics - including
quantum mechanics - of undecidability and non-computability? Are
there implications for our understanding of the relations between
agency, intelligence, mind, and the physical world? This book,
based on the winning essays from the annual FQXi competition,
contains ten explorations of Undecidability, Uncomputability, and
Unpredictability. The contributions abound with connections,
implications, and speculations while undertaking rigorous but bold
and open-minded investigation of the meaning of these constraints
for the physical world, and for us as humans.
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