Ultimate ensemble

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The Ultimate Ensemble or mathematical universe hypothesis (MUH) is a speculative theory of everything (TOE), suggested by Max Tegmark^[1]. Related to the Anthropic principle and Multiverse theories, the Ultimate Ensemble suggests that not only should worlds corresponding to different sets of initial conditions or different physical constants be considered 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. The Ultimate Ensemble can be considered a physico-mathematical expression of the philosophy known as modal realism, which treats physical reality as indexical, or self-referent rather than absolute.

Tegmark claims that the MUH is a theory with no free parameters, which is not observationally ruled out, and therefore is preferred over all other TOE's by Occam's Razor. He envisages conscious experience as occurring in the form of "self-aware substructures" of mathematical structures, which he claims will subjectively perceive themselves as existing in a physically "real" world, as such characterized by interactions with "physically real" matter and having the experiential illusion of sliding unwaveringly along a timeline.

Contents 1 Criticisms 1.1 Definition of the Ensemble 1.2 Lack of Predictive Power 1.3 Responses 2 See also 3 External links 4 References

[edit] Criticisms

The MUH, like other multiverse theories, has been forcefully criticized by scientists and philosophers.

[edit] Definition of the Ensemble

It has been widely argued that the "set of all mathematical structures" is not even well-defined.

Jürgen Schmidhuber noted that there is no such thing as a uniform prior distribution over infinitely many mathematical structures, as suggested by Tegmark. Schmidhuber's more restricted ensemble admits only universe representations describable by constructive mathematics, that is, computer programs. He explicitly includes universe representations describable by non-halting programs whose output bits converge after finite time, although the convergence time itself may not be predictable by a halting program, due to Kurt Gödel's limitations ^[2][3][4].

This issue is also vigorously discussed in a three-way debate between Tegmark and fellow physicists Piet Hut and Mark Alford ^[5]. Hut and Alford point out that Tegmark offers a formalist (axiomatic) recipe for building his Platonic ensemble, but that it is known from Gödel's theorem that formalism and Platonism are incompatible: the axiomatic method can only encompass the simplest mathematics systems. Issues with Godel's theorem have also been raised by physicist Alexander Vilenkin ^[6].

Don Page has argued that the MUH is self-contradictory because one cannot subsume all possible (partly contradictory) mathematical structures into one structure ^[7].

[edit] Lack of Predictive Power

Since the other "universes" in the ensemble are unobservable, and there is no independent evidence for the scheme that predicts them, many scientists have raised the point that the MUH is not empirically testable, and therefore does not constitute a scientific theory.^{[5] [8]}

[edit] Responses

Tegmark responds to some of these critiques in his The Mathematical Universe^[9], where the Ultimate Ensemble is formalized as the "Level IV Multiverse".

[edit] See also

• String Theory
• Multiverse

[edit] External links

• Which mathematical structure is isomorphic to our Universe?- Max Tegmark's paper published in New Scientist.
• The 'Everything' mailing list (and archives), A "discussion of the idea that all possible universes exist".
• The ensemble of universes describable by constructive mathematics by Jürgen Schmidhuber

[edit] References

1. ^ M. Tegmark, "Is 'the theory of everything' merely the ultimate ensemble theory?" arxiv:gr-qc/9704009
2. ^ J. Schmidhuber (1997): A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science, pp. 201-208, Springer: http://www.idsia.ch/~juergen/everything/
3. ^ J. Schmidhuber (2000): Algorithmic Theories of Everything http://arxiv.org/abs/quant-ph/0011122
4. ^ J. Schmidhuber (2002): Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science 13(4):587-612 http://www.idsia.ch/~juergen/kolmogorov.html
5. ^ ^{a b} P. Hut, M. Alford, M. Tegmark "On Math, Matter and Mind", arxiv:physics/0510188
6. ^ A. Vilenkin "Many Worlds in One: The Search for Other Universes", Hill and Wang, New York 2006
7. ^ D. Page "Predictions and Tests of Multiverse Theories",arxiv:hep-th/0610101
8. ^ W. R. Stoeger, G. F. R. Ellis, U. Kirchner, "Multiverses and Cosmology: Philosophical Issues" arxiv:astro-ph/0407329
9. ^ M. Tegmark, "The Mathematical Universe" arxiv:0704.0646