[FOM] Godel's First Incompleteness Theorem as it possibly relates to Physics

Paul Budnik paul at mtnmath.com
Sun Oct 12 20:54:07 EDT 2008

A physical theory must be at least potentially infinite for Gödel’s 
first Incompleteness Theorem to apply. This means both time and the size 
of structures that can be embedded within it must have no finite bound. 
At the same time Gödel’s proof insures that there is always the 
potential for something new and different in such a universe.

I have long been fascinated by possible connections between Gödel’s 
incompleteness results and biological evolution in a potentially 
infinite universe. For example, the one way around the limitations of 
Gödel’s proof in a deterministic universe is through ever expanding 
diversity where an ever increasing number of alternative paths are 
pursued without selecting which is correct. With such a process, every 
truth of first order arithmetic can be explored by some path. I suspect 
it is not a coincidence that biological evolution, which created the 
mathematically capable human mind, seems to pursue expanding diversity 
whenever resources make this practical.

I created a half hour video "Mathematical Infinity and Human Destiny"
(http://video.google.com/videoplay?docid=-8677521434864225474) that 
offers philosophical speculation about this and related ideas along with 
scenes of nature as metaphors for the philosophy.

Paul Budnik

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