  The probability distribution P from which the history of our universe is
sampled represents a theory of everything or TOE. We assume P is formally
describable. Since most (uncountably many) distributions are not, this imposes
a strong inductive bias. We show that P(x) is small for any universe x lacking
a short description, and study the spectrum of TOEs spanned by two Ps, one
reflecting the most compact constructive descriptions, the other the fastest
way of computing everything. The former derives from generalizations of
traditional computability, Solomonoff's algorithmic probability, Kolmogorov
complexity, and objects more random than Chaitin's Omega, the latter from
Levin's universal search and a natural resource-oriented postulate: the
cumulative prior probability of all x incomputable within time t by this
optimal algorithm should be 1/t. Between both Ps we find a universal
cumulatively enumerable measure that dominates traditional enumerable measures;
any such CEM must assign low probability to any universe lacking a short
enumerating program. We derive P-specific consequences for evolving observers,
inductive reasoning, quantum physics, philosophy, and the expected duration of
our universe.
