Abstract:

We examine the convergence behavior of an undefined emotional function over discrete moments

of proximity. Through contradiction, we prove that the hypothesized limit—romantic

reciprocity—does not, in fact, exist.

Let:

f(x) = microexpressions I misinterpreted

g(x) = your mixed signals

h(x) = hope, exponentially increasing as x → late-night overthinking

Let x ∈ T, where T = {timestamps of every accidental eye contact}

Define ε > 0 as the threshold of emotional clarity,

δ > 0 as the distance I maintain between delusion and reality.

Assume for contradiction:

limₓ→∞ [f(x) + g(x)] = love

But for all ε > 0,

no δ > 0 satisfies:

  0 < |x − “you said good morning”| < δ

  ⇒ |f(x) + g(x) − love| < ε

Thus, the function diverges—

catastrophically.

Asymptotically approaching something,

yet never converging.

I modeled your attention span as a step function:

discontinuous, piecewise,

defined only on days I looked particularly unbothered.

I Fourier-transformed our last conversation.

The output: only white noise.

I solved our trajectory in polar coordinates.

Your heart: r = undefined

as θ → sincerity.

I ran a Monte Carlo simulation

of “what ifs.”

Probability of mutual feeling:

  P ≈ 0.00001 ± ε(regret)

I even took the Laplace transform

of your absence,

hoping to simplify the pain

into a manageable expression.

No such luck.