The mathematical symbol for change is a neat little triangle Δ.

I can remember drawing it on my notebook with a pencil. The teacher told us what it meant, and we took her work for it, but I wondered why, if we were describing change, did my pencil end up back where it started. There has to be something better.

And yet, I have to admit that the clean little package contains an uncomfortable reminder that most attempts to change actually don’t result in much of anything new at all. How many times does a person have to quit something before they actually quit it? For every last cigarette, every I-mean-it-this-time break-up, every “give it over to god”, there are 500 re-runs of the old bad habits. The truth is that most attempts to change revert back to uncomfortably familiar territory. I recognize in that pretty shape the shorthand of futility. But while the triangle does a great job capturing the impotence of so many attempts to change, it still doesn’t convey the power of actual change with actual results. So what instead could we use?

The first best alternative that comes to mind is an arrow →. It’s an obvious choice because it so clearly embarks into new territory. This symbol is used in chemistry equations to show how the raw ingredients of a reaction come together to make something else, often irreversibly so. Is this how we change? With brute force? With grand gestures? Our backs to the cliff? A person desperate enough for change may take on these methods, but they tend to change the scenery more than the substance. This symbol goes too far, heading straight out into infinity with no trace of its origins other than as an impact on trajectory. It is entropic– unidirectional and endless, almost fatalistic. Maybe this symbol could hold for metamorphosis but not change as we know it.

Perhaps then, the symbol for change should be a gentle aside, a parenthesis ( ). Many change occurs independently from effort of any real magnitude, maybe it just takes time. Cells die and regenerate, we age, hair grows. I certainly don’t put sweat into growing my fingernails, and yet there they are, diligently inching into the world beyond week after week. Like a pot of water or a skittish rabbit, real change rewards patience, bursting forth only when one stops looking for it. Maybe it is these subtle, gradual changes of nature that we should model our own personal growth after.

But no! We can’t just resign ourselves to wait to outgrow our problems. How could a person do something so difficult as to really change without continuous deliberate effort? A person who merely sits and waits for change to happen will produce very long hair and very little else. This symbol is just too passive to be worthy of a concept as powerful as change.

Staring at the keyboard, I finally found the answer. Change is a spiral: @. Even when we make the same mistakes, we aren’t truly back where we started because time has passed, the pencil has shifted, effort has been expended. With each attempt to change, we pass back over ourselves and yet make gradual progress- the same, and yet different.

It’s no use to wallow in the futility of your efforts, better to take each pass as an opportunity to enjoy the old vantage point plus perspective. If you’re paying attention, you might notice the old scenery before it traps you, you might be a little more humble but also a little wiser than the last time around.

And so we slowly edge along with our fingernails, those agents of slow change within us. We have no choice to carry on, we don’t even choose to change, but to improve with each passing is entirely up to us.