The Derivative Of Hope

The Derivative Of Hope

The Derivative of Hope: What We Get Wrong About Waiting

Here’s what I’ve been thinking about: we talk about “hope” as if it’s a fixed thing—like a stone in our pocket. But the philosophers called this the derivative of hope, and it’s not about hope itself. It’s about how hope changes when we’re in motion.

Commonly, people say, “Just have hope!” as if it’s a switch we flip. But that’s the misunderstanding. Hope isn’t a static object; it’s a rate of change. Think of waiting for a bus. At first, hope is steady: It’ll come soon. Then, as minutes pass, hope accelerates—we check our watch, glance down the street. If the bus still doesn’t come, hope decelerates—we sigh, maybe start walking. The derivative (the speed of hope’s change) is what we actually live in, not the hope itself.

But what does that actually mean for how we live? It means we’re not “waiting for hope” to arrive. We’re navigating its current. When hope feels thin—after a job rejection, a health scare—we mistakenly think we’ve lost it. But the derivative is just slowing down. It’s not gone; it’s shifting. And that’s where action matters. If we sit waiting for hope to feel strong again, we miss the moment to create it. We check the bus app, walk to the next stop, or call a friend. That’s not “hoping”—it’s adjusting the derivative.

This matters because we waste energy fighting the feeling of hope. But the derivative is always moving. It’s not about having hope; it’s about how we respond when it’s rising or falling. A friend recently lost her job. She didn’t say, “I’ll just hope for a new one.” She researched roles, reached out to contacts, and that’s where hope recharged—not in waiting, but in moving with the current.

The derivative of hope isn’t a math problem. It’s the rhythm of our resilience. We don’t need to find hope; we need to listen to how it’s changing, then step into the flow.

— Ray Bates, still asking questions

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Written by Ray Bates — 12:24, 14 January 2026 (CST)