Self-Improvement Is An Asymptote

October 31, 2019

Everyone has a pretty good idea of what the phrase “self-improvement” is supposed to mean: it’s the process of getting better at a skill. Most people are more concerned with what to improve on and less so about what it actually means, because the definition is in the phrase itself, staring back at you—it’s improvement of the self.

However, when you take a moment to try and fully grasp the concept of self-improvement, you might find yourself stumbling across some tough questions:

  • What actually is self improvement?
  • What does self-improvement look like?
  • Does self-improvement have an observable end?

Soon, that initially straightforward definition begins to unravel. So, we’re going to grapple with a few of these questions and figure out what’s going on with self-improvement.

What actually is self-improvement?

At its core, self-improvement is the pursuit of perfection.

What I mean by perfection is pretty much what’d you expect: it’s reaching that point where you can carry out the skill at hand without a single flaw. For example, every time you shoot a basketball, your mechanics are so good that you never miss a shot. Or your time management skills are so good that you literally never waste a second when you divvy up your schedule for the day. You get the idea.

Of course, not only are these goals highly unrealistic, but no sane human being ever goes onto the road of self-improvement aiming for utter perfection; in the end, though, perfection is exactly what we’re all working towards.

We just like to word it more conservatively:

perfectguy perfectguy2 perfectguy3 perfectguy4

What does self-improvement actually look like?

There are two main aspects of self-improvement.

1. The actual process

Conventional wisdom tells us that self-improvement, if it were to be represented graphically, would look like this:


We’re told that the harder you work and the more energy you pour into your craft, the better you’ll get at it, and the longer you continue to improve, the sooner you’ll get really good at it. And maybe, just maybe, if you work extremely hard and get good enough, you’ll become, like…a professional, or something.

And while that’s great content for vague motivational posters, I think most of us have found that this general advice, though not necessarily wrong, is certainly incomplete.

The most obvious problem with this graphical representation is that it implies that the rate of improvement remains constant throughout. The issue with this is that while progress in the beginning stages of improvement may be linear, it gets increasingly harder to find more ways to further optimize performance the better one gets.

After fully understanding the basics, which constitute the most difficult parts of learning a skill, improvement then boils down to the fine-tuning of details; after all, at a certain point, what separates the good from the great no longer is the mastery of the underlying fundamentals, but instead, one’s proficiency of the often overlooked and underappreciated details.

The better one gets, the harder it gets to improve because they’ve already exhausted all the obvious paths to get better.

With this in mind, we can create a much more accurate representation of self-improvement:


For those of you who didn’t recognize what this was a graph of, it’s one end of an asymptote.

For those of you who read that and still don’t know or remember what an asymptote is, I don’t blame you; essentially, an asymptote is a mathematical term that describes a line that gets closer and closer to a certain value, but never actually reaches that value in a finite plane.

Right off the bat, you’re probably noticing two main differences between the graphs: the asymptote’s slope (steepness) doesn’t remain constant, and there is a defined “end” just outside the asymptote’s reach, which is perfection.

The gradually decreasing slope (steepness) of the line goes back to what we discussed about the rate of self-improvement: it’s probable for one to make leaps and bounds in their initial improvement of a certain skill, but the longer one goes at it, the more difficult it is to find ways to get better.

As for the rest of the graph, we can see that the more effort you put in does tend to increase your overall skill level at any particular thing, but complete mastery of any skill is simply unattainable: just like how that asymptote will perpetually get closer to a certain value but never reach it, you can get really close to perfecting a certain skill but never quite get there—after all, there’s always something more you could improve on.

2. Our constantly shifting standards

If I asked you to solve the following equation, you’d probably be able to do it pretty quickly:

5x+4=60. Find x.

But there was a point in time where you weren’t able to do this problem in your head quite as easily.

What changed?

The answer is simple: your math skills and your standards. You’ve probably practiced that sort of problem many, many times, and nowadays you expect yourself to be able to solve equations like that with ease; if you somehow missed a problem like that on a test, you’d probably be pretty mad at yourself.

As it turns out, there is a linear relationship between our standards and our mastery of a certain skill.


For a concrete example, let’s go a little bit more in depth on this math problem. Assuming that you were able to figure it out with ease, then your mathematical standards, at the very least, would be somewhere around here:

math graph

Compare that to a 3rd grader’s mathematical standards. They’re all the way down at the basic arithmetic level; their innocent little brains probably haven’t even heard of concept of letters in math. But over time, as they get more familiarized with algebra, their skills, and subsequently, their standards, will slowly rise through the ranks and they’ll end up where you are right now—solving primitive algebraic equations without batting an eyelash.

The overarching point here is this: every time you improve, all you’re doing is adjusting your standards to match that level of improvement; consequently, you’re never fully satisfied with your improvement because now you expect that level of skill from yourself.

While others who’ve observed you go through this process might have congratulated you for making it all the way to where you currently stand, in your mind, you were still more concerned with what’s ahead of you.

algebra geo at geo precalc

Sure, you might look back and appreciate the progress you’ve made thus far.

look back

But not for too long…

look back2 look back3 look back4

Does self-improvement have an observable end?

So, if the actual end goal of self-improvement, perfection, is completely unattainable, and if our standards are constantly shifting every time we improve, and then how do we ever conquer self-improvement? When does the grind end?

Can it ever end?

Well yes, but actually no.

Before we get into the thick of things, however, I have a confession: up to now, I’ve talked about what self-improvement is, what it looks like, and the inherent difficulty of improving (in both a technical and mental sense), but I’ve been avoiding the question of why we do it. Why do we have to keep improving? Why can’t we just be happy with where we are now?

Well, let me address it now. The reason why we choose to improve on a skill is simple: we care about that skill.

But there’s an important distinction to be drawn here: you can care about that skill for a short period of time—improving on that skill up to a certain point—or you can care about that skill for a long period of time—improving on that skill without an end goal in sight.

And it’s this distinction that determines whether or not the improvement of a certain skill can ever have an end, because self-improvement can end if you are happy with your current skill level; but if it’s a skill that you really care about, then you probably aren’t ever going to be satisfied with where you are now.

Some examples of short term skills: if you couldn’t already tell, basketball is something that I hold dear to my heart. 3 And naturally, I’m always looking to improve my ball handling, passing, and shooting skills when I can. But at the same time, I’m fully aware that my basketball career isn’t exactly going to blossom into anything realistically significant (unless I grow eight inches within the next two years). So while I am trying to get better, it’s only up to a certain point that I’m happy with.

screw perfection

But, hell, writing? That’s a skill that I never want to stop improving on, because it’s something I find super enjoyable (if not stressful at times). So, while I can be content with my basketball or STEM based subject skills, since I place less emphasis on them, I’m never ready to just settle with my writing skills.

Self-improvement ends when you want it to end. And that end is different for everyone.