The Mystery of the Murderous Monies

It’s been a long time since I’ve posted anything on here. Life got in the way (as it tends to). One thing I would like to do more of here is explaining things. I am a teacher, after all. So starting today, whenever I get a chance I’m going to answer some common questions or address some misconceptions that are out there. I apologize that this one ended up being a little bit maths-intensive. I’ll try to limit that in the future as much as possible.

 

Question: Can a penny dropped off the roof of a tall building kill someone standing on the street below?

 

Answer: No. Not even if we were to remove the atmosphere. Without the atmosphere, a falling penny would be in a state of free fall in which the only force acting on it is gravity pulling it down toward the ground. A modern penny, with its zinc center and copper core, has a mass of 2.5000 g according to the US mint. Let’s say this penny is dropped from the Empire State Building, specifically from the 102nd floor observatory 1,224 feet (373.0752 meters). A penny dropped from this height in the absence of atmosphere would hit the ground with a speed of just over 120 meters per second (around 265mph).

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Notice that nowhere in this calculation does the mass or weight of the penny appear. That is because the final speed of an object in free fall is independent of how much that object weighs. In perfect free fall, every object dropped from the 102nd floor of the Empire State Building would reach this speed before it hit the ground, regardless of its weight or shape.

But this does not mean that the mass of the penny is irrelevant, even in this atmosphere-less approximation. The mass of the penny may not matter when finding its final speed, but it certainly matters to the person standing underneath it, because the mass of the penny determines how much energy the penny has when it hits the ground. A penny moving at that speed would have around 18 Joules of energy, which is about as much energy as a 60-Watt light bulb uses in twenty seconds.

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Finding an exact number for the amount of energy or pressure required to fracture or break a human skull is difficult (not many people willing to test it out, after all), but the lowest estimate I’ve found is 45 Joules, so even neglecting air resistance the penny just doesn’t have enough mass to kill someone when dropped off the roof of a building.

So let’s go higher. What if we dropped the penny out of an airplane flying at a typical cruising altitude of 30,000 feet (9,144 meters)? I could repeat the calculations, but there is no need to considering the kinetic energy of a falling object increases linearly with its drop height (see the equation below for proof and note you could prove the same thing using conservation of energy).

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Going from 1,224 feet to 30,000 feet is an increase of 24.5 times, meaning the penny would have that much more energy when dropped from the plane than it would when dropped from the building. This would give us an energy of 442.9 Joules, well above our minimum requirement to bust some poor soul’s skull open like a melon.

So does this mean that a penny dropped from a sufficient height can actually kill someone? Alas, no. Keep in mind, we ignored the atmosphere when performing our calculations, and if we were to perform this test in a place without air, suffocation would kill the person long before we could even drop the penny. In order to give an actual answer, we must take into account the effects of air resistance.

You may wonder why exactly it matters whether there is atmosphere or not, and that’s because, for the most part in your life, it doesn’t. We’re so accustomed to being surrounded by atmosphere that most of us tend to think of it as empty space. You can’t see it, and if you reach out your hand you don’t feel it, but that doesn’t mean nothing’s there.

You can feel this for yourself if you swing your hand fast enough—you’ll be able to feel the air being pushed out of the way. A better (although slightly more dangerous example of this) is to stick your hand out of the window of a moving vehicle. If the vehicle is moving fast enough, you can feel the air pushing your hand back. That is the force of air resistance that slows down a falling penny.

Air is a fluid, a term often incorrectly used interchangeably with liquid in daily life (as a side note, it is this misuse of the term that leads to some people believing that glass is a liquid, when it is actually a solid fluid). In physics, a fluid is just anything that flows, and that’s exactly what air does. The space that looks empty to us is filled with air molecules—nitrogen and oxygen and carbon dioxide among many others. In order for an object to move through the air, it must first push these molecules out of its way. Because of Newton’s 3rd Law, the air molecules push back on the moving object with equal force, causing it to slow down.

If you’ve ever tried to wade through water then you’ve felt this force before, known as a drag force. Water is a much denser fluid than air and thus pushes on you much more when you try to displace it. And the faster you try to move, the more force you feel pushing you back because you’re trying to displace more of the fluid at a time.

Applying this back to our murderous penny, the air pushes up on the penny with a resistive force that gets stronger the faster the penny moves. The equation for air resistance, shown below, gives the relationship between the force of drag an object experiences and its speed.

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Plugging in values for the drag coefficient of a flat disk, the density of air, and the dimensions of a penny as given by the US mint, we can calculate that the force of air resistance acting on the penny should be somewhere between the two values shown below (the minimum value assumes the penny fell the whole way with its thin side pointing down while the maximum value assumes it was flat-side down the whole time). Both of these cases are extremely unlikely, but we’ll use the numbers, just to prove our point.

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We now have two forces acting on our penny—gravity pulling it down toward the ground, and air resistance pushing it back up. The gravitational force is constant (the weight of the penny, 0.0245 newtons) while the drag force increases as the penny gains speed. Eventually these two forces will equal each other, and the penny will enter a state of dynamic equilibrium (equilibrium because all of the forces acting on it balance each other out, dynamic because the penny happened to be moving when the forces became equal and thus will continue to move).

Once the penny enters equilibrium, the air will be pushing it up just as hard as gravity is pulling it down. As a result, the penny’s speed will become constant. We have a special name for the speed at which this happens: terminal velocity. Once a falling object reaches its terminal velocity, it stops accelerating and just falls with that speed until it hits the ground. And unlike objects in free fall which we discussed before, the terminal velocity of an object does depend on its weight. A heavier object will fall faster than a lighter one because it has a higher terminal velocity.

Using the two values for the drag force above, we can calculate the range of our penny’s terminal velocity to be between 10 and 85 meters-per-second (21.6 and 190 miles per hour). Notice that the minimum value of the drag force leads to the maximum terminal velocity.

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Given these results, it makes no difference whether the penny is dropped from the top of the Empire State building, from a plane, or even from outer space because in all of these cases the penny will reach its terminal velocity before it hits the ground.

If you would like to look at drag forces for yourself, I’d recommend a simple experiment. All you need are a few clear glasses or bottles and some liquids of different densities (regular water, salt water, mineral oil, vinegar, even clear alcohols can work well for this, and taller glasses will give you a better chance to see what is happening). Drop the same object into each fluid and see which ones slow it down the most. Drop objects of different weights into the fluids and see which ones fall fastest. Change the shape of your weights by using something like aluminum foil and see how the geometry of the object affects how quickly it falls. If you have a tall enough glass or a light enough object, see if you can spot the moment it hits terminal velocity.

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Why Does Helium Make Your Voice Sound Funny?

In my class we just began learning about waves, and so today I figured I’d write about one of my favorite demonstrations. I’m sure you’ve seen this somewhere or another, whether in a classroom or at a party. Someone swallows some helium from a balloon and suddenly they sound like Alvin the Chipmunk.

Have you ever wondered why that is?

Plenty of physics teachers love this demonstration. And why not? It’s eye (or ear) catching, funny, and has a lot of powerful physics behind it. Unfortunately, it’s almost always taught incorrectly, at least from what I’ve seen. Here’s how it’s usually taught, why that’s wrong, and what’s really happening when you swallow a balloon full of helium.

[At this point I should probably include a disclaimer about doing this yourself. Swallowing helium directly from a pressurized tank should never be done by anyone under any circumstances. However, swallowing helium from a balloon is perfectly safe…provided you don’t swallow too much or too quickly. The helium displaces the air in your lungs, which means if you do this too quickly or for too long your body will asphyxiate for lack of oxygen. When this happens you will pass out, and can injure yourself by collapsing. It’s not fatal (helium is so light that it’ll all leave your lungs while you’re unconscious and you’ll be able to breathe again), but can be dangerous if you hit your head on the way down. I recommend you always have someone watching you while you try this.]

HOW IT’S USUALLY TAUGHT

Most teachers use this demonstration to illustrate the fundamental wave equation, the formula shown below (warning: Maths ahead)

(Speed)=(wavelength)x(frequency)

Since helium is less dense than air, the speed of the sound waves produced when you speak is higher with helium in your lungs than with air. Since speed increases, something on the other side of the equation above must also increase. Most teacher will then have their students conclude that when speed increases, frequency increases.

WHY THAT’S WRONG

This is a horrible misconception to be perpetuating in a classroom. The frequency of a wave is like its fingerprint or DNA. Once a wave has been created, nothing can change that frequency. If it did, it would be an entirely different wave. And it’s not the gas in our throat and lungs that is creating the sound of our voice but our vocal chords, which function the same way regardless of what we’ve been breathing. Combining that with the logic and equation above, we see that it’s not the frequency of our voice that changes when we ingest helium but its wavelength.

SO WHY DOES THE PITCH CHANGE?

In order to correctly explain this phenomenon, you need to realize two things:

  1. The human voice is composed of more than one frequency. When we speak, our vocal chords don’t just vibrate in a single mode but in several, creating harmonics of different frequencies all at once. This is why two people singing the same note sound different from one another.
  2. When people speak, our throats function in a very similar way to a pipe organ. The source of the sound is our vocal chords, which transfer their vibrations into the air in our lungs as sound. This is equivalent to the strings hidden within an organ. From there, our throat takes over, which serves the same function as the pipes in an organ: Amplification. Both the organ pipes and our throats accomplish this amplification through resonance. When a sound wave with a wavelength matching the length of the tube/throat passes by, it gets amplified.

Now we can begin to make sense of this. First, the frequencies of sound (the pitches) that we produce are exactly the same regardless of what is filling our lungs at the moment. Those frequencies depend only on how we vibrate our vocal chords. Changing the speed (and thus the wavelengths) of those waves does not change the frequency or pitch we hear.

However, it does change which frequencies get amplified via resonance in our throats (because remember that does depend on wavelength). After swallowing a less dense gas like helium, our throats selectively resonate the higher frequencies among the range that our voice always produces. Similarly, if you were to ingest a denser gas [this is far more dangerous than swallowing helium as denser gases will settle in your lungs, producing a much higher risk of suffocation], your throat would selectively resonate the lower frequencies among that range, making you sound more like Darth Vader.

When Politics get in the way of Education

This is my first post of the new year, and I’m pissed off.

In case you haven’t heard, New York City public schools just lost 250 million dollars in state aid. That’s not what bothers me. What bothers me is why we lost this funding. You’re sure to get a different opinion on this depending on who you ask, with everyone pointing fingers at someone else. But here are the undeniable facts: a school system with around 1.1 million students just lost 250,000,000 dollars of aid because a bunch of politicians couldn’t reach an agreement.

And what exactly was the divisive issue for which we lost all this funding? Was it about what we’re teaching in our classes? About how it’s supposed to be taught? Nope. Those would make too much sense. The issue that just cost our public schools 250 million dollars was how we should evaluate teachers.

Are you freaking kidding me?!

I’m not even going to get into whether the methods we currently have for evaluating teacher effectiveness in the classroom are useless (they are) or whether the proposed methods were better (they were). That’s not the issue here. At this point I don’t even care about that.

What I care about is that 1.1 million students are going to suffer now because the “adults” who are supposed to have their best interests in mind couldn’t get their shit together and think about anyone other than themselves for just a few hours.

The problem is that all of the people making the decisions about education are too far removed from the classroom. Whether they were classroom teachers in the past or not, they’re politicians now. Neither of the parties involved in this negotiation care one bit about the students. The UFT (United Federation of Teachers) only cares about protecting teachers (whether or not they deserve to be protected) and Bloomberg and the DOE only care about the budget. With people like this in charge, is it any wonder that public education is collapsing?

Regardless of who is “responsible” for this monumental failure (both parties share the blame), I have to say I’m disappointed in the Teachers’ Union. I’m disappointed because they’re supposed to represent us teachers, yet I find every single thing they do revolting. How can they possibly represent us when their interests are so drastically different from our own?

If the UFT really wanted to represent teachers, they would do whatever they had to in order to keep this funding. Because if the UFT really wanted to represent teachers, they would care about our students as much as we do.

But the biggest reason I’m disappointed in the UFT is because they’ve betrayed us. By refusing a deal that would make ineffective teachers responsible for their actions, they’ve cost our schools 250 million dollars. And what’s the first thing that’s going to go now that we’ve lost that funding? That’s right, teachers.

Way to protect us, UFT.

About Light Novels and the new Standard of Readability

If you don’t know what a light novel is, it’s a kind of literature pretty much limited to Japan.  They’re written primarily for young-adult audiences, but are distinct from traditional young-adult novels. They’re usually serialized chapter-by-chapter in magazines before being gathered into full-volumes (a topic which I’ll probably discuss later because I love the idea of serialization).

Rental Magica, a Light Novel written by Makoto Sanda

Rental Magica, a light novel written by Makoto Sanda

A lot of people define light novels by the fact that they’re illustrated, which they are (usually in manga-style), but I disagree with that. I think it’s possible to have an illustrated novel that isn’t light and a light novel that isn’t illustrated. To me, the difference is wholly in the style of the writing, and that’s why I’m so interested in them.

The first thing to notice about how light novels are written is that they tend to be…shall we say playful…with the conventions of the language. It’s not uncommon to see musical notes used as punctuation, as well as things like “What???!!?!?!??” and my personal favorite: “…” to indicate a pointed silence. Whether it’s grammatically correct or not to use ellipses that way I think it’s fantastic. And sometimes they go on forever, taking up entire lines so that you can actually feel the awkwardness of it as you read.

But that’s all superficial. The real differences is that they’re very minimalistic in terms of their writing style. They’re generally shorter than regular novels, though not always (and, just as we see in regular novels, they tend to get longer the farther into a series you go). The good ones use their illustrations to make providing descriptions quicker and more fluid (a picture is worth a thousand words, after all), which can be helpful in cutting out some of the bloat. But again, that’s not necessary.

What really makes them faster reading is how their paragraphing is laid out. It’s rare in a light novel to see a paragraph longer than three sentences. This actually makes a huge difference in terms of reading speed. On my best day I can get through a full-length novel in eight hours. I can get through a light novel in three and get just as much out of the experience. The best example I’ve seen in American literature is the Danial X series by James Patterson and various co-authors (no paragraph is longer than three sentences and no chapter is longer than three pages).

This actually brings me to my main point, about what it means for a novel (or anything for that matter) to be “readable.” By definition that would mean if you are capable of reading it, it’s readable. But when we say that, we’re usually only thinking in terms of legibility, of whether or not it can be understood. Yes that’s an important thing to keep in mind, but there’s another question that is equally important that must be kept in mind: Is anyone going to take the time to read this?

There are some people who absolutely love books. For them, reading is its own reward. For them, the time spent reading isn’t a factor. That’s fine, and that’s why books like Ulysses get published despite being hellish verbal bogs through which readers must fight for every step forward. But I would argue that most of the market for novels isn’t made up of this kind of bibliophile. They’re not reading to be reading, they’re reading to be entertained. To hear a story, to see something different or unusual. And for a time, books were the only game in town if you wanted that kind of diversion.

But not anymore. Now books need to compete with movies, TV, video games, and comics to earn the right to entertain us, and just looking at the time commitments involved books don’t look so good. Let’s say it takes an average person ten hours to read a full novel. In that time, they could watch nearly seven movies or an entire 13-episode series of a TV show (I should know, I spent the first part of my winter vacation getting caught back up on How I Met Your Mother when I still have unread books on my shelves).

I believe that each media has some advantages over the others. There are things books can do that movies will never even come close to touching. But are those things really worth a whole 8.5 hours of someone’s life per book? With more things to occupy our time than ever before, now more than ever every moment is valuable and how we choose to spend it matters.

In light of this, I think the traditional ideas of readability, as well as the traditional idea of the novel, may need to change and adapt to the modern marketplace or else face extinction. This is why the style of the light novel interests me so much, because anything we can do to make our writing just that much faster will definitely help it stand out and ultimately survive.

But those are just my thoughts. What are yours?

How much does the Earth Weigh?

I actually heard this question in a smartphone commercial and it bothered me. They were showing off how easy it is to do a Google search from the newest tablet or whatever; just ask your question and it speaks the answer to you. In this case 5.97E24kg.

Only that’s not the answer. That’s what bothered me. And the truth is there’s a lot of interesting physics in that question and a very common misconception. Being a physics teacher, I feel like I should address it. So let’s discuss.

First of all, the question that Google answered isn’t how much the Earth weighs, it’s how massive the Earth is. This is a common misconception, that mass and weight are the same thing. They’re related, but separate, just how you and your parents share some of the same genes yet aren’t the same person. An object’s mass is just a measure of how much stuff it contains, its density multiplied by its volume. An object’s weight is the gravitational force pulling it toward the nearest massive object, usually the Earth. The mass of the Earth isn’t all that interesting to consider, even though it is interesting to think about how exactly we figured it out.

So now that we know 5.97E24kg isn’t how much the Earth weighs, what is? Here’s where things start to get fun. An object’s weight is just the force with which the Earth pulls on that object though gravity. But forces can only exist between two separate objects. By that logic, if we consider the Earth to be a single, solid object, it doesn’t weigh anything.

But that doesn’t really make sense, does it? It can’t weigh nothing. So what if we could take the Earth and put it on top of a big bathroom scale. If we then took the reading on that scale, wouldn’t that tell us how much the Earth weighs?

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Pictured: Science

Believe it or not, you can do this yourself if you have a flat scale. All you need to do is flip it over and put it on the ground. You now have a scale with the world resting on top of it. So what does that scale read? Whatever the scale weighs. So if you’re using a 10 pound scale, the scale would read 10 pounds, a 15 pound scale would read 15 pounds and so on. Scales work by measuring the force used to compress their pressure-sensitive plates. If you flip the scale over, its own weight is the force pressing that plate down, so that’s the force it reads.

So if we take this definition to be our measurement of weight, then the Earth only weighs as much as whatever you’re using to measure it.

But that still can’t be right. Let’s assume we take all of the matter that makes up the Earth, duplicate it, and then put that on a scale. What would be the weight of all that material? Surely we can call this the weight of the world.

Sadly, this also gets us into some trouble, in that we need to consider exactly how big we make our pile of matter. The bigger the pile is, the farther away from the Earth the top of it would be. The farther away the top of the pile is from the Earth, the less it is pulled by the Earth’s gravity. The less gravity it feels, the less it weighs. If we assume our material is molded into a sphere the size of the Earth, then everything halfway up the pile would weight 4 times less than it would if it were at the bottom of the pile (gravity is an Inverse Square Law, so if we double the distance between two objects we reduce the force between them by a factor of 4). The material all the way at the top of the pile weighs 9 times less than it would on the bottom of the pile, since it’s three Earth-radii away from the Earth’s center as opposed to only one. So whatever our scale reads in this case will be much less than the Earth’s true weight.

We can fix this by taking that big ball of matter and compressing it to a size where we can measure it without noticing the changes in the Earth’s own gravitational field–say shrink it down to the size of a baseball (fortunately that’s still big enough that it doesn’t turn into a black hole and doom us all). If we plop this baseball with all the mass of the Earth crammed into it onto our scale, what would it read? What would be the weight of the world?

If you do the math: 5.85E25 Newtons or about 13,000,000,000,000,000,000,000,000 pounds.

With that out of the way, there’s really only one question left: Why am I even bothering to write about this?

The answer is two-fold. First, because this is my blog and I can write about whatever I want. But more importantly because these are the kinds of exercises that make teaching and learning and knowing physics worthwhile. In my opinion this is true physics. Notice I didn’t need to do a single calculation until the very end. Sure there are still equations, but they’re not nearly as important as the relationships they imply between the different variables. And this is what so often gets lost in the increasingly “plug and chug” nature of physics education. With both our kids’ worth as students and ours as teachers determined by the outcome of a single test at the end of the year, fewer and fewer teachers are willing to venture off and teach kids what they should be learning rather than simply what they “need” to know. To me, this is one of the most depressing things to happen to education in recent history.

So I’ll post here whatever I want to. Because no matter how they try, no one can ever stop you from learning.

About Dunbar’s Number and Quality Education

Recently I came across a concept known as Dunbar’s Number that really resonated with me, having just started the school year.

The idea is that based on the size of the human neocortex, there is a limit to the number of people we can “know” at any given time. To know, in this case, means to have a social relationship with, to know not just their name and face, but who they are as a person and how they relate to others. It’s a limit imposed by the brain on the size of our social circles, and estimates (because this is certainly not an exact science) place it somewhere between 100 and 230 people. The most commonly cited number is 150 people.

While this is certainly interesting in its own right when compared to the numbers of “friends” that many people have on sites such as facebook, it really hit home for me when I got my class rosters for the first time last week.

Teaching six classes, each of them at the maximum capacity allowed by law in my city, I see over 200 students every single day.

That’s not just 200 names I need to memorize and papers I need to grade, but two-hundred young individuals with different wants and goals and in the classroom. Two-hundred kids who want and need and deserve to be more than just a name on an attendance sheet.

According to Dunbar’s theories and research, no matter how hard I want to or how hard I try, I can never truly relate with all of my students at a personal level. There are just too many of them. What is so bad about this is that it is precisely that kind of connection that leads to the greatest insight, learning, and growth in students.

Think back to your favorite teachers when you were a student. Were they the ones who didn’t know your name, or the ones who knew and cared what you were doing outside of school? Sure that still happens with plenty of teachers and students, but I think there’s something fundamentally flawed with a schooling system where this physically cannot happen between every student and every teacher.

Teaching isn’t—or shouldn’t—just be about getting through the curriculum. We’re not there just as knowledge dispensers, living encyclopedias. But even if we were, being able to tailor the material and curriculum to the specific needs, interests, and personal histories of our students guarantees that they will learn more and have a better understanding of the material.

I realize that overcrowding in the classroom is a problem precisely because there are too many students and not enough teachers, and I realize there is no simple way to fix this (although affording teachers the respect and professional stature they deserve in an attempt to convince the next generation that teaching is, in fact, a career worth pursuing would certainly be a good start), but I think it needs to be said yet again that the current system is unfair to both the teachers and students who are trapped within it.

It is an unfair expectation that teacher be able to know and interact at the personal level with two-hundred people every day (maybe as many as two-hundred-and-fifty once you include co-workers and other school staff), to place on them such a heavy load and still expect the results and excellence that came from a time when teachers had half as many students to engage and entertain.

But more importantly, it is unfair to the students who must fight for the attention of their teachers, struggling to be known as something more than just a name on a slip of paper. It is unfair to ask them to succeed and excel when their teachers do not have enough time in the day to sit with them as individuals and discuss their personal educations. To me, this is one of the greatest shames of the American education system.

All that said, I love my job and would not give it up for anything, and despite the overwhelming odds I will continue trying to make my classroom a place where all students can be known and all voices heard. Because for now, that’s all we can really do.

About Schools and Being Educated

As the holiday weekend comes to a close, the day that millions across the country dread silently approaches. That’s right. For many, the first day of school approacheth.

The undeniable fact is that far more students dislike school than enjoy it. This is more than just about any fact or statistic depresses me to no end. It shouldn’t be this way. There is no one party responsible for this—neither the ungrateful students nor restrictive schools are entirely to blame. Both sides share responsibility, and both must make concessions to fix this.

First, let’s address the schools.

The concept of fairness and equality in education is a great and noble goal. Unfortunately, the practices associated with that principle often fall far short of their goals. Many policy makers mistake “the same quality of education for all,” with “the same education for all,” which has disastrous effects for everyone involved. This where restrictive and inflexible curricula and standards that favor rote memorization over true and fundamental understanding come from.

Standardization is one of the worst things to happen to education, for the simple reason that only measurable artifacts can be standardized. But learning and understanding often can’t be quantized across a large and diverse population. In today’s environment, schools and teachers are implicitly instructed to favor the product over the process simply because products are easier to measure.

But in education, the process is all that matters.

Especially in the increasingly digital world we live in today, the memorization and regurgitation of facts is becoming an antiquated skill. While I would prefer that students be able to recite from memory Newton’s Second Law or the date Magna Carta was signed (F=ma and 1215, in case you were wondering), today it’s so easy to look things like that up on smart phones that there seems to be no point in even bothering to memorize them. I’ll address the issues with that later, but it’s certain that no one’s life or career will ever depend on their ability to recite trivia from memory any more, if at all they ever did.

Schools should focus not on how much students can memorize, but on how well they can use the resources presented to them. School should be a place for the enrichment of thought and cultivation of understanding, not a place to sit for hours on end and have facts jammed into your head.

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The rigid structures of the school day, the emphasis on shallow assessments, and the passive way in which all too many students are taught to learn are slowly but surely killing education. If we want to thrive as a country and as a culture, they need to change. That said, there’s no simple solution to this problem, no matter which politicians or policy-makers say otherwise.

Now for the students.

You don’t know how lucky you are. That’s not your fault, and I certainly didn’t when I was your age. Given the way things are now, it seems impossible that a little over a hundred years ago there was no mandatory education.

If you go to school, I don’t care what happens in the rest of your life you are privileged. Less than 1% of the human population has ever had access to the kind of education at your fingertips every day. I’m not trying to make you feel guilty, but think about that for a bit. For most of human history, the opportunity to sit in a classroom and do nothing but learn was restricted to only the wealthiest and highest born children. That’s how far we’ve come.

You are privileged because you’re not forced to spend every minute of every day struggling to support yourself and have enough food to make it through the day. Even if you work part-time jobs, the fact remains that five days a week you are given a time and place in which to only think about exploring the world around you and discovering yourself.

Because that’s your primary job as a student. As you are now you’re incomplete. Take the time during the school week to figure out who you are and what you want. Learn to write, learn to think, learn to explore and be self-sufficient.

Yes tests can be tedious and frightening, and sure the rules and regulations can seem restrictive and counterproductive, but that will always be the case, even after you’ve graduated and moved on. Now is your chance to learn how to deal with that pressure while being free from the many responsibilities that will saddle you when you’re older.

If you find yourself wondering when exactly you’ll use the things you’re learning in school, maybe you never will. That doesn’t detract from the value of having learned them. A secondary education is more about learning how to learn than about the particular facts and formulae you end up learning. You’re learning skills, practicing on what might be trivia so that later you can use them on things that will be more directly relevant to your life.

And never forget that your education isn’t free, even if you attend public school. We, the adults of your community, pay through taxes for you to receive the best education possible. This isn’t charity, and it’s not for your benefit. It’s for ours. We are investing in your education so that you can go on to do great things that will make our lives better and longer in the future. We pay for you to be educated so that you can cure the diseases that would otherwise kill us as we age, or clean up the disaster we’ve made of the planet so we don’t choke to death on all the smog, or even so you can invent the device that heats up butter just enough to make it spreadable but not enough to melt it.

No matter who we are, there will inevitably come a day when we need you, and for that reason we want you to be as prepared as possible for when that day comes. Remember that the next time you’re debating the value of the things you’re learning in school.

By all means enjoy yourselves, but also take full advantage of this time in your life where your major responsibility is to learn and grow and develop as a human being. Trust me, it won’t last nearly as long as you think it will.