Elementary Catastrophe Theory

Elementary catastrophe theory


Let us suppose that a is alone, at equilibrium,
making coffee perhaps, or gazing idly at the garden,
considering the hydrangea.  Tiny perturbations
can reset parameters.  Imagine a scenario
where a picks up the letter, lights a match,
drops the burning remnants in the fireplace.
Or envisage, instead, her reading, then regard the way
she wraps her arms around her, unexpectedly cold.
Observe while a hits zero, the tipping point:
things can go either way.

Let us now have b enter the equation, walk
down the path, ring the bell.  We’re on the cusp
of a catastrophe.   Our stable outcome
can leap in an unexpected direction.
a opens the door, stares at b, but b is intractable,
his face shaded by the trailing clematis.
a does not know where she stands; vary b, and the system
oscillates, attracting and repelling. 
She brings hand to mouth, remembers
sometimes the lilies, soft as fingertips, sometimes
the rough concrete grazing her face.

The future is unpredictable
where the exact state of a is unknown.
It may be that a will ponder past experience,
find it in herself to call the Alsatian to her side,
possess the gumption to slam the door. 
One can consider what happens if b holds constant
and a vacillates.  Observes a pitchfork bifurcation,
a choice of solution, neither of them good for a.
b will rip out the hydrangea, buy only herbal teabags,
chop down the clematis.  a will exist only
as a derivative of b, a reflection, scraping thick mud
from her shoes, pockets full of seeds
she will never plant.

(first published in Matter 10, October 2010)