Gödel's Way
Exploits Into an Undecidable World
by Gregory Chaitin
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Gödel's Way
In the 1930s, Kurt Gödel showed that the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences. This notion of incompleteness and a related property—undecideability, formulated by Alan Turing—are often presented as ideas that are only relevant to mathematical logic and have nothing to do with the real world. However, Gödel’s Way proves the contrary.
Gregory Chaitin, Newton da Costa and Francisco Antonio Doria show that incompleteness and undecidability are everywhere, from mathematics and computer science, to physics and mathematically formulated portions of chemistry, biology, ecology, and economics.
Have you ever wondered why we can’t create an antivirus program for computers that doesn’t require constant updates? Or why so much of the software we use has bugs and needs to be upgraded with patch-up subroutines? Fascinatingly, the reasons involve Gödel’s incompleteness theorems. Nor is astronomy immune from the fun, as the authors show. We can formulate a certain measure of a universe, called a metric tensor, so that it is undecidable whether it is a “Big Bang universe”—with a definite origin in time—or a universe without a global time coordinate. (Interestingly, Gödel himself studied universes of the latter type.)
Undecidability also plays a role in our ability to predict whether the physical phenomenon known as chaos will arise from a given set of equations that describe a dynamical system. This has a number of real-world implications, e.g., determining the stability of bridges. We also see how Gödel’s ideas impact everything from game theory to the P vs. NP problem.
Gödel’s Way proves that the notion of incompleteness arises in a wide range of disciplines outside mathematics.
Softcover : 160 pages
Publisher: CRC Press LLC ( October 13, 2011 )
Item #: 13-569879
ISBN: 9780415690850
Product Dimensions: 6.25 x 9.25 inches
Product Weight: 9.0 ounces (View shipping rates and policies)
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