The Function Of Humility

Let $t = 0$ be the start of my life, $t = T$ be the end of my life, and $now()$ be this moment in time.

And let’s define four functions, anxiety ( $a$ ), serenity ( $s$ ), forgiveness ( $f$ ) and laughter ( $l$ ) such that

$a(t) = \left\{ \begin{array}{ll} 1 & \mbox{if I feel anxiety about being in control at time } t \\ 0 & \mbox{otherwise} \end{array} \right. \\ \\ \\ s(t) = \left\{ \begin{array}{ll} 1 & \mbox{if I feel serenity about the illusion of control at time } t \\ 0 & \mbox{otherwise} \end{array} \right. \\ \\ \\ f(g, t) = \left\{ \begin{array}{ll} 0 & t < now() \mbox{ and I can find forgiveness in my heart at time } now() \\ g & \mbox{otherwise} \end{array} \right. \\ \\ \\ l(g, t) = \left\{ \begin{array}{ll} 0 & g < 0 \mbox{ and I allow myself to laugh at time } t \\ g & \mbox{otherwise} \end{array} \right.$

Then, while it is so painfully true that my moments of anxiety far surpass my glimmers of serenity

$\displaystyle \sum_{t=0}^{now()} s(t) - a(t) < 0$

As I write this poem I notice that I feel at peace

$\displaystyle s(now()) - a(now()) = 1$

And if I can allow myself to laugh, then it is provable for any instance of time $t$ I can push anxiety away

$\displaystyle l(s(t) - a(t), t) \geq 0$

Therefore it is technically possible that with laughter the moments of serenity can surpass the moments of pain

$\displaystyle \sum_{t=0}^{T} l(s(t) - a(t), t) > 0$

But if, and only if, I can stay positive for long enough such that the rest of my life I accept there is no such thing as control.

$\displaystyle \sum_{t=now()}^{T} l(s(t) - a(t), t) > \sum_{t=0}^{now()} l(s(t) - a(t), t)$

This gives me hope that if I can find laughter in my heart, it’s possible to live a positive life.

Yet, I am now that at the point in time where in all probability my time remaining on this planet ( $T - now() < now()$ ) is shorter than the time I’ve spent. I am in the back half. Depending on the remaining length of my life $T$ , even if I accept each day I cannot control anything, there is not enough remaining time to balance the scales with laughter alone. Maximizing $\sum_{t=0}^{t=T} l(s(t) - a(t), t)$ is not enough. But then again, perhaps this is the wrong function to optimize. Instead let’s define the function humility ( $h$ ) by combining laughter ( $l$ ) and forgiveness ( $f$ ) such that

$\displaystyle h(t) = f(l(s(t) - a(t), t), t)$

Then if I can find forgiveness in my heart right $now()$

$\displaystyle h(t<now()) = 0 \implies \sum_{t=0}^{T} h(t) = \sum_{t=now()}^{T} h(t)$

We find the past no longer matters, and given in this moment I feel at peace ( $s(now()) - a(now()) = 1$ ) then with laughter and true forgiveness, the future can be shown to be positive.

$\displaystyle \sum_{t=0}^{T} h(t) > 0$

What’s more, if I can laugh in the face of my anxieties, keep forgiveness in my heart, and recognize that control is but an illusion, as I approach the infinite I can become one with the divine.

$\displaystyle \lim_{t\to\infty} \sum_{t=0}^{\infty} h(t) = 1$

The proof is left as the exercise of my life.

A. B. Clarke

The Function Of Humility

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