What Shows, the Brachistochrone curve, and Life Have in Common

The unexpected truth about the path that doesn’t look like progress

This article is also featured on Substack & Medium

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What Shows, the Brachistochrone curve, and Life Have in Common

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The Comfort We Carry With Us

I have always been drawn to shows like The Durrells in Corfu, All Creatures Great and Small, and Call the Midwife, but I think my love for them started long before I even understood why.

When I was younger, I remember staying up late watching Masterpiece Classic on PBS. I can’t even express how much joy it brings me to see and hear the same intro all these years later. There’s something about it that feels different from everything else on TV. it just feels slower, softer, and more intentional. It feels like stepping into another world. One where people talked things through, where connection mattered, and where even the quiet moments carried weight.

That feeling has never really left me.

Now, when I watch these kinds of historical dramas, it is not just the storylines that pull me in. It is the way they capture humanity, the landscapes, the small interactions, the tension and tenderness between people trying to understand one another. Even when there is conflict, there are still conversations; even when there are differences, there is still an attempt, however imperfect, to try and bridge them.

I understand these are stories. I know real life is often messier, more complicated, and not nearly as neatly resolved, but there is something undeniably beautiful about being reminded of what is possible.

These shows hold onto the parts of life that feel easy to lose sight of, the connection, the resilience, the way people come together and move through things, even when they don’t have all the answers. They reflect something true: that life is not static. It shifts, it stretches, and it ebbs and flows.

Recently, I also came across a simple video that stuck with me and kind of inspired this article. It showed two balls on two tracks. One track was straight, and the other dipped, curved, then rose again.

At first glance, the outcome felt obvious. The straight path should win. It is shorter, more direct, more efficient, but it did not.

The curved path, the one that dipped down first, reached the end faster. I could feel the meaning behind it immediately. It felt like a reflection of life itself.

Still, I found myself wanting to understand more than just the symbolism. I wanted to know why. What was happening beneath the surface? What did physics say about it, and, maybe just as importantly, why does it resonate so deeply with how we experience growth, struggle, and change?

Section 1: The Curve That Wins

After seeing that video, I couldn’t stop thinking about it. It felt so obvious at first, two paths, one straight and one curved. The straight one should win. It’s shorter, more direct. That’s just how we tend to think about things, that the quickest way from one point to another is the most efficient, the most logical.

But that’s not what happened.

For some reason, that stuck with me enough that I ended up going down a bit of a rabbit hole last night trying to understand it. Not in a super technical way, I’m definitely not an expert in physics or anything, but I like figuring things out when something catches my attention like that. It felt like one of those small things that probably meant something bigger, even if I couldn’t fully explain why yet.

That’s when I came across something called the Brachistochrone curve. I had never even heard of it before. It’s the shape of the fastest path between two points, not the shortest, but the fastest. Which, even just reading that, felt a little backwards from the way we’re used to thinking about progress.

What surprised me most was how simple it actually was once I understood it. The curved path dips down first, and that drop is what changes everything. It’s not a mistake or a detour, it’s what gives the ball speed right away. Gravity pulls it down more directly, so it builds momentum early on. By the time it starts coming back up, it’s already moving faster than the ball on the straight path, which never got that same push at the beginning.

So even though the curved path is longer, it still gets there first.

There was something about that that just stayed with me. That first dip, the part that looks like it’s going the wrong direction, is actually the reason it wins. If you just looked at the starting point and the ending point, you would never choose that path. It doesn’t look efficient. It doesn’t look like progress. It looks like extra, like something unnecessary.

But underneath that, something is happening that you can’t see right away. Something is building, gaining, shifting in a way that only makes sense once you see the whole picture, and I think that’s what caught my attention the most, not just the physics of it, but how easily it mirrors the way we experience things in our own lives.

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Section 2: When It Feels Like You’re Falling Behind

I think the reason that the curved path stayed with me had less to do with physics and more to do with how familiar it feels. There are so many moments in life where it feels like you’re doing everything right, trying to move forward, trying to grow, and somehow, it still feels like you’ve fallen behind, like everyone else is on that straight path, moving steadily forward, checking boxes, and making progress that’s easy to see. Then there’s you, somewhere in the dip, wondering how the hell you got there.

That space can feel so confusing and frustrating, and sometimes even a little defeating, especially when you’re in the middle of healing. Healing doesn’t move in a straight line. It doesn’t follow a clean, predictable path where things just get better over time. It dips, it circles back, it brings things up you thought you had already worked through. There are days where you feel strong and clear, and others where it feels like you’ve undone all of that progress without even meaning to.

It can feel like you’re going backward.

But what if that feeling isn’t actually backward at all? What if it’s part of the same kind of movement as that curve? That dip, the hard conversations, the emotions that resurface, the moments where you feel unsure or stuck, might actually be where something is building. Not in a way that’s obvious or visible, but in a way that creates depth, awareness, and eventually, momentum.

We’re so used to measuring progress by what we can see, by how quickly things improve, how steady things feel, or how closely our lives match the timeline we thought we’d follow, and when it doesn’t look like that, it’s easy to assume something is wrong. That we’re behind, that we’ve missed something, and that we should be further along by now.

But life doesn’t really work like that.

The parts that feel like pauses or setbacks are often the same moments that shape us the most. They slow us down enough to notice things we would have missed and they ask us to sit with ourselves in ways that aren’t always comfortable. They shift something internally, even when nothing on the outside seems to be changing.

Then, just like the curve, the movement is still happening, even when it doesn’t look like it. It might not feel like progress while you’re in it, and it might not make sense until much later, but that doesn’t mean it’s not carrying you somewhere. Sometimes the path that feels the most uncertain is the one quietly building the most momentum in our lives.

Section 3: The Parts We Don’t See Building

Not everything that matters looks like progress.

Some of the most important shifts happen quietly, in moments that don’t feel significant at all. The in-between spaces where things feel slow, unclear, or even a little stuck. Those times when nothing obvious is changing, and because of that, it’s easy to assume nothing is happening.

Those are usually the moments we question the most. We wonder if we’re wasting time, if we’ve lost momentum, if we should be doing more or moving faster. There’s this pressure to keep moving forward in a way that’s visible and measurable, as if growth only counts when we can point to it, explain it, or prove it to someone else.

But a lot of growth doesn’t work like that.

Some things build underneath the surface long before we ever see the results of them. Awareness, boundaries, and the ability to pause instead of react. The ability to notice patterns we didn’t see before, the ability to choose differently, even if it’s just in small, quiet ways.

Sometimes it looks like saying less instead of more, or walking away instead of staying, sitting with a feeling instead of pushing it down, or distracting yourself from it. Choosing rest when everything in you feels like you should be doing something more productive. These shifts don’t always feel like progress in the moment, but they are often the foundation for something deeper.

Often, we fail to recognize the changes happening within us until we find ourselves on the other side. A situation occurs, and we respond in a way that is different from how we would have reacted before. We notice that something that once overwhelmed us doesn’t affect us the same way anymore. We come to realize that we have been changing gradually, in ways we weren’t fully aware of.

From the outside, it can look like a pause, a delay, or something that’s taking longer than it should. It can look like a season where nothing is moving, where things feel uncertain or unfinished, but underneath that, something is already in motion. Something is building, gaining strength in a way that isn’t loud or immediate, but steady in its own way, and maybe that’s part of what makes it so easy to miss.

Because we’re looking for movement in the wrong places. We’re often looking for straight lines, clear direction, and visible results. When in reality, a lot of what changes us happens in the quieter, less obvious moments.

Section 4: Not Everyone Starts at the Same Line

Not everyone is starting from the same place.

Have you seen those videos where a group of people stands in a line, and someone begins asking questions? If you had this growing up, take a step forward. If you experienced that, take a step back. One by one, people move, and slowly the line that started even begins to shift.

By the end of it, it’s no longer a line at all.

Some people are far ahead. Some are still near the beginning. Some have taken steps back they never asked to take, and what stands out isn’t just the distance between them, it’s how invisible those differences are until something brings them into the light.

From the outside, it’s easy to assume everyone had the same starting point, that everyone had access to the same support, the same stability, the same opportunities. It’s easy to look at where someone is now and measure it against where you are, without ever seeing what came before it.

But those starting lines matter.

They shape how fast someone can move, how much they have to carry, and how many obstacles they have to navigate just to reach the same place someone else started from. For some people, the path was relatively straight. For others, it dipped early and deeply, long before they even knew what direction they were trying to go, and that changes things in a significant way.

It changes how progress looks; it changes how long things take. It changes what it even means to be ahead or behind. Because if someone starts further back, or carries more weight along the way, the distance they travel holds a different kind of meaning.

It also makes comparison a little less useful.

Because when you only look at where someone ends up, you miss the shape of the path that got them there. You miss the dips, the detours, the parts that required more effort than anyone else could see. You miss the strength it took just to keep moving at all, and maybe that’s another piece of this.

Not just that life doesn’t move in a straight line, but that we’re not all walking the same path to begin with.

Section 5: What Can Grow From the Dip

Some dips in life are small. Others change everything.

There are experiences people carry that were never chosen, never deserved, and never something that can be simplified into a lesson or a reason. The impact of those things is real. The way they shape the body, the mind, and the way someone moves through the world, it stays. It shows up in ways that aren’t always visible, and it doesn’t just disappear because time passes or because someone tries to move on. That part matters.

At the same time, there’s something else that can exist alongside it, not instead of it, not to cancel it out, but alongside it. There’s a term for it called Post-traumatic growth, and it describes the ways people can develop new strengths, awareness, and depth after going through something difficult. Not because they should have had to, but because they did.

Sometimes it shows up as a deeper understanding of people, a heightened awareness of emotions, both your own and others. It can look like the ability to read situations more clearly, to sense what’s unspoken, to navigate complexity in ways that aren’t always taught but are learned through experience. Sometimes it looks like resilience, or the ability to keep going even when things feel heavy. Sometimes it’s boundaries, realizing what you will and won’t tolerate, and learning how to hold that line.

These aren’t things anyone would choose to gain the way they had to be learned, and yet they are the very same kinds of skills people spend years trying to develop. People read books, take courses, go to therapy, and search for ways to understand themselves and others more deeply. They invest time, energy, and sometimes thousands of dollars trying to build awareness, emotional intelligence, and resilience, and in a complicated way, many of those same qualities already exist in people who had to learn them through lived experience.

That doesn’t make what happened okay, and it doesn’t mean it was worth it. But it does mean those skills are real, and they are invaluable.

I think that’s where this idea of the curve becomes something deeper. Because trauma can feel like that kind of dip, the kind that doesn’t just slow you down, but changes the shape of your entire path. It can feel like something that pulls you away from where you thought you were going, something that makes everything harder, heavier, and less certain, and in many ways, it does.

But it can also be a place where something begins to build underneath the surface, not in a way that erases what happened, and not in a way that makes it okay, but in a way that creates depth, awareness, and strength that didn’t exist in the same way before. It’s complicated to hold both of those things at once, to acknowledge the pain without trying to make it meaningful in a way that dismisses it, to recognize growth without suggesting it was worth the cost, to see that something developed without saying it had to happen that way.

But both can be true.

Perhaps that’s what this whole idea suggests: not that every setback has a purpose or that every challenge is meant to teach us something, but rather that even in the moments of life that feel the most stagnant, something can still be developing. Over time, these experiences contribute to how we navigate the world, not because we consciously chose that path, but because we persevered despite the ups and downs.

Closing: Where You Are Still Counts

The dips, the pauses, the moments that feel uncertain aren’t always interruptions; they’re just part of the path, part of what shapes it and moves it forward, even when it doesn’t feel like it.

It’s easy to look around and feel behind, to compare your path to something that looks more steady or certain. But what we don’t see are the curves beneath the surface, the starting points, the weight people carry, and the unseen ways they’ve had to grow. Your path has its own shape, and just because it doesn’t look how you expected doesn’t mean it isn’t working or that its wrong.

There is movement, even when it feels still. There is growth, even when it feels slow. You are not behind, you are in motion.

If you’re feeling overwhelmed or just need a place to land, start here:
https://hellbloomhaven.com/lets-ground-and-breathe/

Thank you for taking the time to read this and sit with it for a moment.

The path that dips isn’t the one that fails, it’s often the one that carries you further.

Have a beautiful day lovely souls

Wendi Kehn