The image shows three light trails held by a single pair of hands: a large orange semicircle, a blue infinity loop, and a jagged purple zigzag. The same hands. Three completely different trajectories. Change never travels in straight lines - but not all non-linear movement is the same.
Look at what the hands are holding.
The same hands. One pair, in the same frame. But three completely different trajectories of light extending from them.
The orange arc overhead is a clean semicircle - a long, high, predictable path from one side to the other. A club arc, or a high ball throw, following gravity’s geometry from peak to landing.
The blue figure-eight in the middle crosses itself. It loops, returns, loops again. It goes somewhere and comes back, then goes somewhere else and comes back from that direction too. It is continuous, closed, and it does not arrive anywhere that is different from where it started.
The purple zigzag at the bottom moves in short, violent angles. It does not arc. It reverses, spikes, drops, reverses again. It is motion without smoothness - the path of something responding to forces rather than following an intention.
The same hands hold all three.
The arc
High, clean, predictable trajectory
The orange semicircle describes a change with a clear peak and a clear landing. High visibility, long duration, landing zone visible from the throw. Everyone can see where it is going.
The loop
Continuous, returns to origin
The blue infinity describes a change that revisits its starting point - a cycle, a feedback loop, a process that returns to reassess before continuing. Not stuck - cycling.
The zigzag
Reactive, angular, turbulent
The purple zigzag describes a change path driven by competing forces: the implementation that reverses course, escalates suddenly, drops into waiting. The motion of something navigating interference.
Why change doesn’t travel in straight lines
The most common representation of a change program in an organisation is a Gantt chart - a series of horizontal bars representing tasks that move left to right from start to completion. The implicit trajectory is linear: work begins, work proceeds, work ends.
This representation is not wrong in the same way that a map is not wrong. It is a useful simplification. But the simplification erases something important: the actual trajectory of change, experienced by the people inside it, is never a horizontal bar.
It looks like one of these three arcs. Or, during complex programmes, it looks like all three at once - different threads of the same change following different trajectories through the same timeframe.
Reading the trajectory you are actually in
The failure mode in most change programs is not that the leaders choose the wrong arc. It is that they plan for the orange semicircle and then, when the change begins following the blue loop or the purple zigzag, they treat the deviation as a problem to be corrected rather than as information to be read.
The change that starts as a high clean arc and then begins to loop is not failing. It is encountering the complexity that was always present in the territory. The loop is the arc saying: there is something here that needs to be revisited before we proceed.
The change that zigzags is not out of control. It is responding to genuine forces in the environment - competing priorities, shifting stakeholder positions, external events. The zigzag is motion in a contested space.
The three arc types and what they indicate about the change environment
The hands that hold all three
The detail that is easy to miss: the same hands hold all three arcs.
This is not three different jugglers illustrating three different change programs. It is one juggler - one practitioner - demonstrating that all three trajectories are available from the same starting position. The arc, the loop, and the zigzag are not assigned to different types of change in advance. They are the actual paths that a change can follow, and the skilled practitioner can read which one they are in and adjust accordingly.
The change that zigzags is not out of control. It is in motion through a contested space. The skill is not in preventing the zigzag but in maintaining enough stability to navigate it without losing direction.
The competency being developed is not “do the arc correctly.” It is “read which arc you are in, and hold steady enough to complete it.”
Read next: When the Light Trails Cross - what happens when multiple arc types run simultaneously without coordination.
