4,210 research outputs found
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
A Complete Theory of Everything (will be subjective)
Increasingly encompassing models have been suggested for our world. Theories
range from generally accepted to increasingly speculative to apparently bogus.
The progression of theories from ego- to geo- to helio-centric models to
universe and multiverse theories and beyond was accompanied by a dramatic
increase in the sizes of the postulated worlds, with humans being expelled from
their center to ever more remote and random locations. Rather than leading to a
true theory of everything, this trend faces a turning point after which the
predictive power of such theories decreases (actually to zero). Incorporating
the location and other capacities of the observer into such theories avoids
this problem and allows to distinguish meaningful from predictively meaningless
theories. This also leads to a truly complete theory of everything consisting
of a (conventional objective) theory of everything plus a (novel subjective)
observer process. The observer localization is neither based on the
controversial anthropic principle, nor has it anything to do with the
quantum-mechanical observation process. The suggested principle is extended to
more practical (partial, approximate, probabilistic, parametric) world models
(rather than theories of everything). Finally, I provide a justification of
Ockham's razor, and criticize the anthropic principle, the doomsday argument,
the no free lunch theorem, and the falsifiability dogma.Comment: 26 LaTeX page
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