  Since Newton, all classical and quantum physics depends upon the "Newtonian
Paradigm". Here the relevant variables of the system are identified. The
boundary conditions creating the phase space of all possible values of the
variables are defined. Then, given any initial condition, the differential
equations of motion are integrated to yield an entailed trajectory in the phase
space. It is fundamental to the Newtonian Paradigm that the set of
possibilities that constitute the phase space is always definable and fixed
ahead of time. All of this fails for the diachronic evolution of ever new
adaptations in any biosphere. The central reason is that living cells achieve
Constraint Closure and construct themselves. Living cells, evolving via
heritable variation and Natural selection, adaptively construct new in the
universe possibilities. The new possibilities are opportunities for new
adaptations thereafter seized by heritable variation and Natural Selection.
Surprisingly, we can neither define nor deduce the evolving phase spaces ahead
of time. We can use no mathematics based on Set Theory to do so. These ever-new
adaptations with ever-new relevant variables constitute the ever-changing phase
space of evolving biospheres. Because of this, evolving biospheres are entirely
outside the Newtonian Paradigm. One consequence is that for any universe such
as ours there can be no Final Theory that entails all that comes to exist. The
implications are large. We face a third major transition in science beyond the
Pythagorean dream that "All is Number". We must give up deducing the diachronic
evolution of the biosphere. All of physics, classical and quantum, however,
apply to the analysis of existing life, a synchronic analysis. We begin to
better understand the emergent creativity of an evolving biosphere. Thus, we
are on the edge of inventing a physics-like new statistical mechanics of
emergence.
