Have you maxed out?
A re-post of "Making the best of a local maximum"
I’m taking a break from writing this week and getting caught up on a few things. Please enjoy this story, a formerly subscribers-only post from May. ~JRC
Making the best of a local maximum
It's less about where you are and more about what you do while there
First published on May 30th, 2022
Imagine for a moment you are walking in a dense forest. Towering trees obscure the sky, and little light penetrates the woodland floor. Soon, you come to a steep hill and decide to climb it. Up and up you go, weaving through the trees and the brush. Steeper you climb, using both hands and feet to ascend the treacherous terrain.
Finally, you make it to the top, but there is no view. The peak is as forested as the valley below, concealing what undoubtedly is a spectacular view. Still, you feel this must be the highest peak around. But there's only one way to know for sure.
You find the tallest tree and begin to climb even higher.
Hand over hand, you scale through the branches. Finally, emerging from the canopy, the sun hits your face, and for a moment, you rejoice. But elation is short-lived. Looming before you is a mountain much taller than where you are now.
Aggrieved, you gaze out in the distance, wondering if it was all worth it. The climb was so hard, yet you didn't reach the top. Deflated, perhaps even jaded, you begin climbing back down as the realization takes hold.
You, my friend, have reached a local maximum.
"Local maximum" is a concept in math representing the largest value for a function. Think of the above example of a mountainous landscape as a direct simile for a mathematical landscape. Functions are the individual "peaks" on this landscape, and the maximum value for each function is the tippy top solution - a peak - a "local maximum."
The thing is, you can't move from hill to hill, from peak to peak, without changing the function. So in a sense, you are stuck on whatever mountain the function serves; you've climbed a hill but cannot choose another without another function. These "local maxima" may be the best, the "highest" solution for each peak, but there can still be larger peaks, and ultimately there is a largest - the "global maximum."
Outside of math, the concept of local maximum has a lot of parallels, with perhaps life itself being the most poignant.
If our pursuit is to be the best of the best, the highest of all, we'll likely fall way short. There can be only one “richest person in the world” for example. Life is an infinite number of variables all at play that dictate who we are and what we become. Many are chosen for us - our genetics at birth, the family we are born to, and our nationality. Others are decisions we make along the way between life and death. If all goes well, we end up in the vicinity of a local maximum. But there is no guarantee of this. And there is certainly no guarantee that we are on the highest peak of all. So the best we can do is appreciate whatever peak we're on and try to make it work to its fullest extent.
This is a long-winded way of describing "living up to one's potential."
In a far less existential, less philosophical way, a "local maximum" also describes my maker space - my shop.
It's a small, sometimes cramped little room. At 224 sq. ft., it’s flat-out tiny. Still, I've gone a long way toward making my shop as useful as possible. I choose tools wisely, for example, factoring in their size in almost every decision. And lots of things are on wheels so that I can move them around depending on my needs. Often, I make hard decisions on what to keep and dispense with - one can't have it all in a tiny shop.
Sure, I could aspire to get a bigger space. But, technically this is still my local maximum - that’s the trick of it all. We never truly know if we’ve reached it. But still, making it work without working against ourselves is always worth the effort, no matter where we currently reside.
All things being what they are, and what they are right now for me, the soundest thing I can do is make the best of the local maximum I'm on. And making my shop the most useful it can be is working towards reaching the local maximum of my space and my current lot in life.
Am I there? not by far.
Each day I struggle with what works and what does not. I make changes. I experiment. Some of these trials lead me to a better place. And still, others fall short, occasionally making things worse than they were before. Some days I give it my all, and others I almost throw in the towel. But I don’t. I keep at it, hoping to make this space the best it can be.
Okay, so maybe I am still talking about life.
And herein lies the beauty of local maximum. It's about solving the enigmatic function we call living. It's about not settling while not setting unrealistic expectations. Local maximum is about taking stock of where we are and what we can do - without being dejected by all we can never do.
Finding that balance, and making the best of it, is all that any of us can ever hope to achieve. Whether we’ve landed on a global maximum or made the best of a local one, realizing our potential is the gift of a life well-lived.
Until next time.
JRC