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Is “the theory of everything” merely the ultimate ensemble theory? Export

(1 Dec 1998)

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accessibility all-categorical-structures all-mathematical-structures all-possible-worlds complexity computability computability-theory constructivization control controlability decision-procedure exploitation exploiting exploration exploring extendability extraction formal-interoperability formalization-hypothesis formal-problem-solving formal-science formal-theories goedel-machine hierarchy-of-machines higher-dimensional-category-theory hypercomputability hypercomputing hyperefficiency intelligence-order-relations interconnectivity interoperability mathematical-structures metaevolution metalogical-frameworks metalogics metamathematical-frameworks metamathematics metaphilosophy metascience metaselection philosophy-of-science physical-structures power presentation quantum-computability regularities representation resource-allocation selection specification survivability topos-theory transformation

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We discuss some physical consequences of what might be called “the ultimate ensemble theory”, where not only worlds corresponding to say different sets of initial data or different physical constants are considered equally real, but also worlds ruled by altogether different equations. The only postulate in this theory is that all structures that exist mathematically exist also physically, by which we mean that in those complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically “real” world. We find that it is far from clear that this simple theory, which has no free parameters whatsoever, is observationally ruled out. The predictions of the theory take the form of probability distributions for the outcome of experiments, which makes it testable. In addition, it may be possible to rule it out by comparing its a priori predictions for the observable attributes of nature (the particle masses, the dimensionality of spacetime, etc) with what is observed.


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