I got into a long conversation with a friend about asymptotes – how it is probably the saddest mathematical equation. I think the asymptote’s beautiful sadness is necessary. I like its order and chaos, its assurance and uncertainty. I think its own dissonance makes it beautiful.  The equilibrium makes the equation just right.

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Asymptote

Your straight line travels
safely the long distance
as my curve wanders
freely its own orbit
each positioned firmly
traversing its own trajectory.

We journey towards infinity
moving closer
gazing in our remoteness
boundless, endless
in this passage of time.

Our moments forever fleeting
and never meeting.


An asymptote is a straight line continually approaching but never meeting a curve as its distance from its origin increases to infinity, even as their perpendicular distance to each other approaches zero and extended far enough that they would seem to merge, at least as far as the eye could discern.

In mathematics, while they are forever moving closer and interacting, they hold their positions in defining each other and may never converge. If the curve or the line gives up its own trajectory, then this destroys the integrity and intention of the equation.