  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.
