dx/dt and dy/dt - partners in crimes against humanity
two coupled equations, that just might be decoupled -
whether partially or completely - equations who beg the question of
their existence, wondering if there is one solution
or three? Will one line answer everything, or will it take
pages and pages of scratch-outs and screw-ups to determine
where at least one equilibrium point lies hidden in the numbers
and variables looking back at us. It’s common to cross your fingers
and hope it isn’t complex. Hope that you won’t have to separate
the imaginary from the real and instead be faced with two
beautiful, real and distinct eigenvalues that have the solution
to all your problems in life. You hope for a problem where you don’t
have to guess - or second guess or even third guess a solution to,
because in the end, it’s very easy to be wrong.
Phase lines on a portrait can tell their own story -
without the numbers. It’s easy to see where a sink lies.
Where everything gets sucked in - sometimes in a counterclockwise spiral
It is not like a saddle, where things go in and things go out, but even ifall the points end up in one place, at least it is constant.