What Will You Learn This Summer?

Reading Time: 2 minutes

two kids in a forest making careful observations about nature

What will you learn this summer?

I’m not talking about academics, though you might choose to do that as well.

I’m talking about learning from the world, from experiences, from nature, and from other people. I’m talking about learning from life.

Perhaps you’ll take up a hobby that requires you to learn something interesting. Gardening? Tennis? Guitar? Foraging? Chess? Cooking? Birding?

Maybe you’ll learn how to run a small business by starting a side hustle. Perhaps you’ll learn a trade through a summer job or internship. The way you earn money this summer might teach you what you don’t want to do with your life.

a fast food worker contemplating their future

Maybe you’ll travel somewhere and learn about another culture or experience natural wonders you can’t find near home. Or maybe you’ll explore the place where you live more deeply, uncovering the stories and hidden gems of your own neighborhood.

Learning can happen by accident, but it’s usually more satisfying when the endeavor is intentional.

But don’t get me wrong; this isn’t homework. It’s life, and summer is a chance to figure out how to make your life more yours. It’s an opportunity to try new things, to explore, to choose your own adventure.

So don’t waste it.

You’ll be back to school sooner than you think.

It Was Never About the Math

Reading Time: 4 minutes

complicated math problems on a blackboard

Most people don’t use math in their careers. Most people rarely use anything other than basic math in their daily lives. So, for most people, learning math is a waste of time, right?

Nope.

Nearly all of the benefits of studying math have nothing to do with math. Math is brain training, pure and simple.

Brain Muscles

The various types of math problems students do are like the various kinds of exercise you do at the gym. Rock climbers, football players, and skiers all lift weights at the gym, not because they do any of the same lifting motions during their sports, but because their athletic performance benefits from having stronger muscles in general.

a cartoon brain lifting weights

As I often say, your brain is like a bunch of muscles that get stronger when you use them. There isn’t a “math muscle” in your brain. Rather, math exercises several important mental muscles that everyone needs.

Logic

Math is sometimes described as “the language of logic” because all math must make sense. Everything in math, from 2+2=4 to the way you calculate a derivative, is something that can be explained and understood logically. None of it is arbitrary.

A common mistake students make is to simply memorize formulas without ever trying to understand them. This might result in a good test score, but it doesn’t give you the benefit of exercising your brain’s logic muscle. Plus, if you focus on understanding the formulas, they’re easier to remember.

Problem-Solving

Another critical skill that math strengthens is problem-solving. Math trains you to wrestle with complicated, multi-step problems where the correct path forward is not obvious. Life is full of problems like that.

an electrician problem-solving

When you solve a word problem in math, you’re forced to do the following:

  • Account for what you know
  • Determine what you don’t know that would be helpful to know
  • Discard useless or distracting information
  • Set aside information that you’ll need later but don’t need right now
  • Assess what resources you have available (formulas, methods, etc.)
  • Sort out how to get where you want to go
  • Adapt that plan of action as you work the problem, if you discover it needs to change

That’s what word problems in math are all about, and it’s also what problem-solving in general is all about. You could be remodeling a kitchen, planning a vacation, or designing a website, and the essential skills of problem-solving would be the same.

Flexibility

a very flexible man with his body contorted

Lastly, math is an excellent way to develop greater mental flexibility.

Many areas of mathematics, such as quadratics or integrals, have numerous methods that you could use for any given problem. As you learn them, you accumulate a toolkit. Your job as a math student is to flexibly switch from one tool to another as needed.

Many students express frustration that there isn’t one way to solve all such problems – one tool that you always use. It would be easier if you always knew which method to use, but that wouldn’t help you learn how to solve problems in the real world.

In just about any career, you’ll be faced with novel challenges every day: new problems to solve with the toolkit you’ve acquired through college, on-the-job training, and experience. If the problems were easy and simple to solve, you wouldn’t be getting paid good money to solve them. The work would be outsourced to a cheaper labor source, an algorithm, or an AI.

Whether you’re an electrician, a doctor, an engineer, a project manager, or a carpenter, your job is to solve hard problems by drawing upon your knowledge and grabbing the right tools at the right times. Many branches of mathematics train your brain to do exactly that.

a bunch of tools on the wall of a workshop

It’s Never Been About the Math

Whenever math students are asked to learn something esoteric, someone will complain, “But when are we ever going to use this?”

The correct answer to this question is, “Probably never. But also, always.”

You’ll most likely never use this specific piece of mathematics for anything practical, but you will certainly use the mental muscles and general skills you’re developing by learning it.

Remember, the point of school is not the specific things you learn, but who you become through the learning.

The Secret Reason We Study History

Reading Time: 4 minutes

A statue depicting historical figures

It is often said that those who do not learn from history are doomed to repeat it.1

On the other hand, Aldous Huxley famously quipped:

“That men do not learn very much from the lessons of history is the most important of all the lessons of history.”2

Furthermore, very few students will find themselves in positions of power from which they can steer humanity away from repeating the mistakes of the past. So this is not the reason we make students study history.

What about citizenship? Doesn’t understanding how we got here make us better citizens?

It does. Or, at least, it can. Demagogues and political charlatans love to tell oversimplifications and outright lies about history, so knowing the truth helps immunize us against them. And knowing that the right to vote is relatively new and hard-earned ought to encourage us to exercise that right.

So that’s certainly a reason we study history, but it’s not really a secret. And it’s also closely tied to what we’re really talking about today.

Perspective

What matters in the study of history is not the endless procession of names and dates; it’s the story. And stories are driven by characters – people with different perspectives and different goals. So our job as students of history is to understand the story and the people in it because, in doing so, we become better at understanding one another.

The primary purpose of studying history is to practice shifting perspective.

When you consider a historical event or time period, you should look at it through the eyes of a variety of people (or groups of people). Consider the varying perspectives of the ruling class and those without political power, landowners and workers, men and women, various religious groups, and so on.3 Understanding their different perspectives and why they hold them not only improves our understanding of the past, it also improves our understanding of humanity in the present, on scales large and small.

a group of diverse people

Progress for Whom?

Consider, for instance, Thomas Jefferson’s famous words in The Declaration of Independence:

“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”4

From the perspective of European men, this was a bold step toward constitutional democracy and away from the tyranny of absolute monarchy. It enshrined the Enlightenment ideal of natural rights into the founding document of a new nation, creating a self-fulfilling prophecy that granted those rights to an ever-growing number of people.

However, from the perspective of other groups of people, Jefferson’s words take on a different meaning. In saying that “all men are created equal,” women would rightly feel left out. Indeed, they would not be granted equal rights for over a century, and only after decades of fighting for them. Jefferson was a slave-owner, so his claim that every man deserves freedom seems deeply hypocritical from the perspective of black Americans. And in making The Louisianna Purchase, Jefferson ensured that native Americans would continue to lose their land – and often their lives – to American settlers.

The point here is not to argue about whether Jefferson was a good man or a bad man, or even to argue about what the words of the Declaration mean. The point here is to practice shifting perspectives. Each of the perspectives described above is valid. There’s value to be found in understanding each of them. And it’s that mindset we need to bring into our personal lives.

a mother and daughter arguing

Perspective-Shifting in Our Daily Lives

Failing to consider the perspectives of other people is the most common source of arguments, misunderstandings, and miscommunications. We can have far more productive and pleasant interactions with others if we practice shifting perspective more often.

This applies to relationships like:

  • Worker-to-boss
  • Coworker-to-coworker
  • Parent-to-child
  • Student-to-teacher
  • Parent-to-teacher
  • Friend-to-friend
  • Partner-to-partner

The practice of perspective-shifting could also improve our ability to have civil political debates, which is something we’re sorely in need of. That’s one of the reasons I read Tangle – a newsletter that gives multiple perspectives from each side of the aisle on every topic they cover. The vast majority of people who vote differently from you are not evil, stupid, or crazy. They just have a different perspective. And if you want to persuade them to vote like you vote, you’ll have to begin by understanding their perspective.

The practice of perspective-shifting can also facilitate greater empathy for people who are different from you. You don’t even have to understand their perspective – you don’t have to get it – you just have to understand that they have a valid perspective that’s different from your own.

Perspective-Shifting About Ourselves

You can even shift perspectives about your own life within your own mind.

If you’re ever feeling morally superior when someone else screws up, the fastest way to get off of your high horse is to ask yourself, “How am I that?” Odds are, you’ve done something similarly foolish or dishonorable.

When you experience a major setback, you can shift your perspective by finding (or creating) the hidden benefits that big problems often bring. Obstacles can be opportunities if you’re able to look at them from the right angle.5

And if you’re faced with a difficult decision, don’t just consider what’s most likely to be the right decision; be sure to think about which version of being wrong you can live with. That way, if you make the wrong decision, it won’t be catastrophic.

This Makes You a Better Person

There are many good reasons to learn about the past, but I think this is the most valuable.

By improving your ability to shift perspectives, studying history can make you a kinder, wiser, and more effective person.

1This is not the exact quote.

2“Aldous Huxley.” The Guardian.

3 John Green does an excellent job of encouraging us to do this in his Crash Course history series. (I’m currently enjoying Crash Course European History.)

4https://www.archives.gov/founding-docs/declaration-transcript

5Holiday, Ryan. The Obstacle Is the Way: The Timeless Art of Turning Trials into Triumph.  Portfolio/Penguin, 2014.