Max Tegmark
1997 · arXiv
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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Max Tegmark has a larger diagram for math in his paper: Is "the theory of everything'' merely the ultimate ensemble theory? https://arxiv.org/abs/gr-qc/9704009 and a sketchy one for physics in his paper: The Mathematical Universe https://arxiv.org/abs/0704.0646
This reminded me about Tegmark's map of relationships between various basic mathematical structures: https://arxiv.org/pdf/gr-qc/9704009.pdf (on page 2)
> Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds) There are (within academia) alternative views to this one, e.g. Max Tegmark's "Mathematical Universe hypothesis": - http://arxiv.org/abs/gr-qc/9704009 - http://arxiv.org/abs/0704.0646 - wiki: http://en.wikipedia.org/wiki/Mathematical_universe_hypothesi... The basic idea being, all internally consistent (viz., mathematical) structures exist (whatever the notion pertains to), and those containing 'self-aware substructures' are perceived as physical realities by virtue of those SASes being embedded within a particular given consistent…
structure (and hence having a from-within vantage point). Sounds fishy, but it's a hypothesis alright, and there have been (AFAIK) some attempts to provide falsifiability conditions (thus making it a testable scientific hypothesis), but one would first have to address the problem of proper operationalization, i.e. defining the damn concepts at hand; it's probably too all-over-the-place for now - but nevertheless interesting and (heh) internally consistent. Also see (for those interested), e.g. http://plato.stanford.edu/entries/computation-physicalsystem... (nice overview of related problem spaces)
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