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{"abstracts":[{"sha1":"79671b863d8a2cd888746b3e8c2e6471caec19fd","content":"I explore physics implications of the External Reality Hypothesis (ERH) that\nthere exists an external physical reality completely independent of us humans.\nI argue that with a sufficiently broad definition of mathematics, it implies\nthe Mathematical Universe Hypothesis (MUH) that our physical world is an\nabstract mathematical structure. I discuss various implications of the ERH and\nMUH, ranging from standard physics topics like symmetries, irreducible\nrepresentations, units, free parameters, randomness and initial conditions to\nbroader issues like consciousness, parallel universes and Godel incompleteness.\nI hypothesize that only computable and decidable (in Godel's sense) structures\nexist, which alleviates the cosmological measure problem and help explain why\nour physical laws appear so simple. I also comment on the intimate relation\nbetween mathematical structures, computations, simulations and physical\nsystems.","mimetype":"text/plain","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Max Tegmark","role":"author"}],"language":"en","version":"v1","ext_ids":{"arxiv":"0704.0646v1"},"release_year":2007,"release_date":"2007-04-05","release_stage":"submitted","release_type":"article","work_id":"ftl6xv267vb6xfech3khri3nwa","title":"The Mathematical Universe","state":"active","ident":"ornjo5inebc7nkv6gux3lzdpx4","revision":"0e3a84c8-1955-49e8-be2f-28da1daf727b","extra":{"arxiv":{"base_id":"0704.0646","categories":["gr-qc","astro-ph","hep-th"],"comments":"Replaced to match accepted Found. Phys. version, 31 pages, 5 figs;\n more details at http://space.mit.edu/home/tegmark/toe.html","journal_ref":"Found.Phys.38:101-150,2008"},"superceded":true}}
{"abstracts":[{"sha1":"79671b863d8a2cd888746b3e8c2e6471caec19fd","content":"I explore physics implications of the External Reality Hypothesis (ERH) that\nthere exists an external physical reality completely independent of us humans.\nI argue that with a sufficiently broad definition of mathematics, it implies\nthe Mathematical Universe Hypothesis (MUH) that our physical world is an\nabstract mathematical structure. I discuss various implications of the ERH and\nMUH, ranging from standard physics topics like symmetries, irreducible\nrepresentations, units, free parameters, randomness and initial conditions to\nbroader issues like consciousness, parallel universes and Godel incompleteness.\nI hypothesize that only computable and decidable (in Godel's sense) structures\nexist, which alleviates the cosmological measure problem and help explain why\nour physical laws appear so simple. I also comment on the intimate relation\nbetween mathematical structures, computations, simulations and physical\nsystems.","mimetype":"text/plain","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Max Tegmark","role":"author"}],"language":"en","version":"v2","ext_ids":{"arxiv":"0704.0646v2"},"release_year":2007,"release_date":"2007-10-08","release_stage":"accepted","release_type":"article","work_id":"bbbbbbbb7vb6xfech3khri3nwa","title":"The Mathematical Universe","state":"active","ident":"domerrq5mvdqfdbolkunct3esy","revision":"540ac97b-eb73-43d5-a1da-cfbcf1f50eb2","extra":{"arxiv":{"base_id":"0704.0646","categories":["gr-qc","astro-ph","hep-th"],"comments":"Replaced to match accepted Found. Phys. version, 31 pages, 5 figs;\n more details at http://space.mit.edu/home/tegmark/toe.html","journal_ref":"Found.Phys.38:101-150,2008"}}}
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