Category: Psychology of Success

Life’s Asymptotes

Posted on by Chris Loper
Reading Time: 3 minutes

a guitar player practicing

There’s a math concept that I keep seeing in real life. It’s a weird one: the asymptote.

An asymptote is a line that a graph curves towards but never reaches. The graph gets closer and closer, but it can never get there.

a graph with an asymptote

It’s a cool concept in math, to be sure. Well, cool if you’re a math nerd like me. But that’s not the point. And math is never really about math, anyway.

No, asymptotes are interesting because life is full of them. And by understanding asymptotes, we develop a better understanding of how many of the most important things in life actually work.

Mastery

One that I’ve touched on before is that mastery of any skill is an asymptote. As you move along the mastery path, your skills improve. But there’s no point at which you can say you’re “done.” Whether you’re an expert pianist, a brilliant basketball player, or a chess champion, there’s always more room to grow. Complete mastery can never be reached, only approached.

teenagers playing soccer

Knowledge

Knowledge works the same way. It’s impossible to know everything about a subject. Whether you practice medicine, study history, or research physics, there’s no point at which you can say you have total knowledge of your subject. Everything you learn moves you toward completely knowing your subject, but total knowledge is an ideal that can never be reached.

Perfection

The concept of an asymptote is good to keep in mind if you’re struggling with perfectionism. Perfection is an asymptote: it’s an ideal you can move toward, not a destination you can reach. As Tal Ben-Shahar advises, think of perfection like a guiding star rather than an island. It’s a direction to travel, not a place you’ll ever visit.1

a bright star in the night's sky

Health and Fitness

Health and fitness are also asymptotes. No matter how healthy you are, you could always be a little healthier. Mental health works this way, too. No one has perfect mental health. You can approach it incrementally, but the work is never finished.

Thinking of fitness like an asymptote reminds you that you can always benefit from exercise, even if you’re already in great shape. It’s another version of everything counts. But, at the same time, it helps you see that perfect fitness is unattainable, reminding you to be kind to yourself when you fall short of your ideal vision.

a yoga class

The asymptote is both a motivation to keep working on self-improvement and a reminder to give yourself permission to be human.

Love and Kindness

Being kind and loving are asymptotes too. There’s always room for growth in how well you treat others, how you talk to your family, and how you engage with your friends. The same goes for being kind and loving toward yourself.

Wisdom

In Ryan Holiday’s book Wisdom Takes Work, he writes that wisdom is “a kind of asymptote. … There is always more to learn, more to know, more to understand about the world and yourself.”2

Later, he writes that:

“We can get wiser, but never wise.

Smarter but never smart.

Closer but never there.”2

 

1Ben-Shahar, Tal. The Pursuit of Perfect. McGraw Hill, 2023.

2Holiday, Ryan. Wisdom Takes Work. Portfolio, 2025.

 

 

Why Do Students Give Up on STEM?

Posted on by Chris Loper
Reading Time: 3 minutes

a student asleep on their math homework

STEM careers are persistently among the most in-demand and high-paying professions out there, and many children dream of becoming scientists, engineers, or doctors because the jobs sound interesting. But as they go through school, many of these students ultimately give up on STEM.

There are many reasons for this, but the one I’ve never seen discussed is the lack of mastery learning in schools.

The kids who are interested in STEM careers are often the ones seen as smart enough to skip ahead in math. So in middle school, they skip 8th grade math and jump into Algebra 1. Or they skip both 7th and 8th grade math to take Algebra 1 and Geometry. Even for very bright students, this is usually a bad idea. They don’t develop a strong foundation for their math knowledge, and their knowledge gaps come back to haunt them later.

a frustrated student struggling with math homework

Plus, whether or not they skip ahead, the way math classes are taught discourages deep learning. Students are not given enough practice problems to walk the mastery path. Essential learning practices like spaced repetition and interleaving aren’t baked into the curriculum. As a result, most students gain only a shallow understanding of each concept, which they quickly forget.

Furthermore, schools advance students to the next math class as long as they pass this year’s class. But if you earn a 75% in this year’s class, then you’re missing 25% of the knowledge – knowledge that you’ll need to do well in next year’s math class. And, of course, you’ll forget some of what you learned over the summer because hardly anyone practices math on summer vacation, so the amount of missing knowledge is more like 50%.

Eventually, this comes to a head, and students hit a wall. They encounter a math class that they can’t handle. Sometimes it’s Algebra 2. Sometimes it’s Calculus. And the saddest thing is that when they hit that wall, they don’t know the real reasons why, so they conclude that they’re not smart enough.

a student at a desk looking ready to give up

So students often give up on STEM because they mistakenly think that they’re not bright enough to handle the difficult classes, when really the problem is structural. They are smart enough. But schools aren’t teaching STEM strategically, and students aren’t taking matters into their own hands by studying STEM strategically.

So if you’re a student who’s finding your STEM classes too difficult, remember, the problem is not you. These classes are supposed to be hard. And that means you have to engage with them using smart learning strategies and effective study techniques. You’ll probably have to patch the holes in your math knowledge. And you’ll certainly have to do more than they’re asking you to do.

I wish schools would provide you with better structure for success in STEM, but until they do, you’ll have to be proactive and go out of your way to truly, deeply learn the content.

If you’re a parent whose child wants to pursue a STEM career, help guide them. Facilitate summer math practice. Normalize the techniques of mastery learning in your household. (Actively model these strategies with whatever you’re learning.) And don’t push them to skip ahead in math because going far usually requires going slowly.

Getting the Details Right

Posted on by Chris Loper
Reading Time: 2 minutes

the inside of a piano

One of my dad’s favorite sayings is, “It’s not a piano.” He says this when we’re working on a project that doesn’t require a great deal of precision, such as building something that doesn’t need to look good. There’s a threshold of functionality that’s good enough, and once that’s crossed, any extra effort is wasted.

But some things in life are pianos. Okay, very few things are literally pianos, but there are a great deal of situations where the details matter, and there are many careers where precision is important:

  • Law
  • Medicine
  • Architecture
  • Coding
  • Engineering
  • Electrical work
  • The wording of a contract
  • The visuals of a marketing campaign
  • A tax return
  • Painting a cabinet
  • Buying a new fridge that will fit into your kitchen

School (you knew I was going to talk about school, right?) rewards you for being detail-oriented. It demands that you pay close attention to the details, and it punishes you with bad grades if you aren’t precise:

  • Sig figs in chemistry
  • The minutiae of punctuation and grammar
  • Using proper notation to describe the domain of a function
  • The format of a bibliography

When a teacher docks you points for getting these things wrong, they’re not being nitpicky jerks; they’re training you to be detail-oriented. It’s not that the details of this particular problem for this particular class matter (they don’t). It’s that, in the future, you’ll encounter many situations where the details really do matter.

a person filling out a tax form

And since school is all about brain training, one of its jobs is to train your mind to pay attention to details, to be careful, to be precise. So when the time comes to build a piano, whether real or metaphorical, you’ll be ready.

P.S. There’s a fine line between being detail-oriented and being perfectionistic. First, focus on accuracy by getting the big picture right. Then worry about getting the details right. But keep in mind that you’re practicing being detail-oriented, so you probably won’t get all of the details right, and that’s okay.