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understanding. These discontinuous and global transformations are the stuff of
miracles, especially for physicists. Even with respect to initial and end-states, rather
than using straight forward phenomenological observation, the mathematical and
physical theories of phase transitions are usually dependent on not necessarily
intuitive, derivative physical quantities. Their verbal representations are often not
concrete but metaphoric. This retreat to derived and abstract, far from the primary
data computables, may be more evidence of man’s many insufficiencies in
understanding of the mysteries that are often placed in the spiritual realm.
Driven by an effect that contributes to cause, like the faith-driven
abandonment to God that generates more faith, a drop of water hanging from a
faucet is pulled down by its own gravitational field as the thinning neck of the drop
facilitates its own further thinning. A gobbet connected by a thick neck to the main
drop begins to separate. The neck between them thins and breaks, and one
becomes suddenly and irreversibly two. A continuous structure has suddenly
become discontinuous in finite time at what is called a singularity. Since the single
measurable feature that dominates the water’s behavior around this singularity is
the diameter of the thinning neck, a derivative physical, one-dimensional
observable, neither the details about where it all began (called the initial conditions)
nor the path it followed to get to the moment of fracture, are predictively relevant
with respect to the sudden transition. Considering this kind of phenomenon going on
in our brains, choosing between theories of behavior that involve changes in brain
cell groups and/or brain chemicals versus those that involve behavioral quantities,
may be neither possible nor necessary. The challenge is to place the problems of
cataclysmic change in brain and behavior in sufficiently abstract and universal terms
that can be represented in some low dimensional, computationally accessible space
of variables.
The simplification and stereotypy of behavior around singularities reduce the
number of features that are required to discuss the dynamics of change in what
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