Jürgen Schmidhuber argues that 'Although Tegmark suggests that '. Although he 'wouldn't dare' go so far as to say he believes it, he noted that 'it's actually quite difficult to construct a theory where everything we see is all there is'. This categorization posits a nested hierarchy of increasing diversity, with worlds corresponding to different sets of initial conditions (level 1), physical constants (level 2), quantum branches (level 3), and altogether different equations or mathematical structures (level 4).Īndreas Albrecht of Imperial College in London called it a 'provocative' solution to one of the central problems facing physics. The MUH is related to Tegmark's categorization of four levels of the multiverse. Tegmark also considers augmenting the MUH with a second assumption, the computable universe hypothesis ( CUH), which says that the mathematical structure that is our external physical reality is defined by computable functions. Thus, he reasons, it is preferred over other theories-of-everything by Occam's Razor. Tegmark claims that the hypothesis has no free parameters and is not observationally ruled out. The theory can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical entities a form of mathematicism in that it denies that anything exists except mathematical objects and a formal expression of ontic structural realism. In any mathematical structure complex enough to contain such substructures, they 'will subjectively perceive themselves as existing in a physically 'real' world'.

Observers, including humans, are 'self-aware substructures (SASs)'. Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). Tegmark's MUH is: Our external physical reality is a mathematical structure. In physics and cosmology, the mathematical universe hypothesis ( MUH), also known as the ultimate ensemble theory and struogony (from mathematical structure, Latin: struō), is a speculative ' theory of everything' (TOE) proposed by cosmologist Max Tegmark.

Our mathematical universe