1,1

Abstract: "I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems."

Tegmark: "This is the 'director's cut' version of the Sep 15 2007 New Scientist cover story. For references, see the 'full strength' version at arXiv:0704.0646. I advocate an extreme 'shut-up-and-calculate' approach to physics, where our external physical reality is assumed to be purely mathematical. This brief essay motivates this 'it's all just equations' assumption and discusses its implications."

Max Tegmark, The Mathematical Universe, 5 Apr 2007, Table 1, p. 3, arXiv:0704.0646

Max Tegmark, Shut up and calculate, arXiv:0709.4024

"Any mathematical structure can be encoded as a finite string of integers..."

a(1) = 100 which encodes the empty set;

a(2) = 105 which encodes the set of 5 elements;

a(3) = 11120000 which encodes the trivial group C_1;

a(4) = 113100120 which encodes the polygon P_3;

a(5) = 11220000110 which encodes the group C_2;

a(6) = 11220001110 which encodes Boolean algebra;

a(7) = 1132000012120201 which encodes the group C_3.

Sequence in context: A094027 A092633 A108343 this_sequence A165406 A135603 A044866

Adjacent sequences: A128815 A128816 A128817 this_sequence A128819 A128820 A128821

nonn,new

Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 10 2007, Oct 01 2007

Replace arXiv URL's by non-cached versions - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009