About Suspensions of Disbelief and American Horror Story

Happy new year everyone!

I know I’ve been excessively absent for a while, but one of my resolutions is to post at least one thing every week, even if its small. Maybe that will involve more reviews of books, movies, and TV shows and the narrative elements which work in them or the ones that fall apart.

Like many people over the winter holidays, freed from the requirements of work and school, I’ve taken to binge-watching TV series’ on Netflix. That phenomenon, and how it has changed the way TV shows are written and produced, could very well be the topic of another post. Today, however, I want to talk about the show I watched: American Horror Story. Specifically, I want to talk about season two: Aslyum and why it felt weaker to me than seasons one and three.

Small Spoiler Warning

While I won’t be talking about specific plot points in this post, I will be discussing the premise of each season, which may necessarily reveal some of the plot. If you haven’t seen the show yet and want to watch it completely unspoiled, I recommend it. If you’ve already seen it, or want to take the risk of a big plot element being revealed, then read more to hear my take on it.

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The Dangers of Oversimplified Narratives: The Story of Galileo

Though it might seem like it would be from the title, this is not a post about writing. It’s a post about history and science and religion and some of the dangers of the way news is reported nowadays.

The story of Galileo Galilei and his famous beef with the church is one that most people think they know. However, as with any story that has been told and retold numerous times, what we’ve heard is only a fraction of the truth.

The Story:


Galileo Galilei (1564-1642)

Galileo was, among other things, a scientist and astronomer. He improved upon the design of the telescope, allowing him to make extremely accurate observations of the night sky.

He was also a strong believer in the Copernican Model of the universe. He supported the idea of heliocentrism, where the Earth moves around the sun rather than the other way around.

This put him at odds with the ruling power of the time: the Catholic church. Because it says several times in the bible (e.g. Psalms 93:1, 96:10, 104:5) that the Earth is immovable, Galileo was branded as a heretic for suggesting that it was the sun, not the Earth, that was immobile.

Galileo stood in gallant defiance to the tyranny of the church and declared the truth as he saw it.

Galileo was tried for heresy, convicted, forced to recant his view of heliocentrism, and placed under house arrest for the rest of his life, during which time he went blind.

The Narrative:

This story is technically true (the worst kind of truth), and it’s easy to see why it has been told this way for so long. The story, as presented above, has a clear and simplistic narrative that is easy to follow and makes the story compelling.

Galileo is clearly the protagonist of the story, a straight-forward intellectual interested only in advancing the scientific truth of the universe.

The villain of the story is, of course, the Catholic church; the evil empire which seeks to suppress any deviation or originality in favor of mindless dogmatic adherence.

The story of Galileo as it is usually told is the classic tale of an underdog beaten down for being a thorn in the side of an oppressive establishment, only to be vindicated after his death.

This is a good story. It’s concise, uncomplicated, and satisfying. We know who to root for and who to boo.

Unfortunately, the truth is rarely uncomplicated, like a coast line which looks straight from far away but twists and turns as you get closer.

The Whole Story:

Like I said before, the classic story is technically true, but it’s a drastic oversimplification of a complex and interesting story.

Galileo was a proponent of Copernican heliocentrism and did go to the Vatican in 1616 to defend Copernicus and his ideas from an injunction passed by the Catholic church.

For this, he was admonished. There was no punishment, just a kindly “please stop,” to which Galileo said, “OK.” He continued his work on heliocentrism, but labeled it as a purely mathematical concept so as not to defy the church.

Then, in 1623, Cardinal Maffeo Barberini was appointed Pope Urban VIII. Barberini was an admirer of Galileo’s work, and Galileo hoped that under his leadership the church might just lessen its opposition to Copernican heliocentrism.

Despite the 1616 admonishment, Pope Urban VIII received Galileo personally six times in 1623, during which time the two discussed arguments for and against heliocentrism, and allowed him to publish a book on the topic provided it discussed both sides of the issue and did not paint either in a favorable light.

Galileo then wrote his Dialogue Concerning the Two Chief World Systems (as it is now known. The title at the time of publishing was simply Dialogue with a long subtitle from which the rest of the current title was extracted) in 1632.

Dialogue was written, unsurprisingly, in the form of a dialogue between three men. Two of them, Salviadi and Sagredo (both named after friends of Galileo), were intelligent philosophers. The third, Simplicio (supposedly named after Simplicius of Cicilia but also meaning something along the lines of simpleton), was a layman who was less eloquently spoken than the other two.

In this dialogue, Salviadi represented the view of heliocentrism, Sagredo was initially neutral, but ultimately sided with Salviadi, and Simplicio represented the view of geocentrism (or the church’s view). Over the course of the debate, Simplicio is often caught up and generally portrayed as a fool.

As if this were not insulting enough, Galileo had Simplicio recite many of the arguments the pope had made in their 1623 meetings.

Naturally, Pope Urban felt betrayed by Galileo’s portrayal of him in Dialogue. And the man already had more than enough problems on his plate. He was racking up a large debt using military might to expand the papal dominions, and at times he actually feared for his life. His betrayal by Galileo was the straw that broke the camel’s back.

Interestingly enough, most historians think Galileo was unaware of how Dialogue both insulted Pope Urban and advocated heliocentrism, meaning he thought he was staying within the church’s mandate.

Galileo was called to defend his writings and stand trial. Technically this was for disobeying his 1616 admonishment, but in truth it was both a vindictive and calculated move by Pope Urban to appear strong and save face.

Had Galileo written his Dialogue with just a little more tact, it is entirely possible that he never would have been persecuted by the church.

Why any of This Matters:

Just as it’s clear why the common version of the story is the one that gets passed on, it’s equally clear why the full version usually gets overlooked. First of all, it’s TL;DR, but most importantly it’s no longer an easy-to-digest narrative.

Galileo is no longer the flawless protagonist who shoulders no blame for his persecution. The church is no longer a monolithic oppressor. It’s much harder to find someone to root for in this version. Everyone involved is only human, for better or worse.

Does this mean the church was correct to act as it did? Absolutely not, but the story lacks the potency it had when the church was merely trying to suppress a dissident.

That’s why stories don’t usually get told this way. We as readers/listeners/viewers actually  prefer the simple narratives. We like having our heroes and villains clearly marked and knowing who to root for. We like conflicts that are purely good vs. evil, right vs. wrong.

But again, that’s almost never how it happens. The real world is messy and conflicted. No one is the villain of their own story. Everyone has their own justifications. There’s always more than one side to any story.

In order to fit a story into a simple narrative, you need to trim the edges so that the square peg can fit in the round hole. When you do that, important details are inevitably lost and even the whole meaning of the story can change. In the case of the Galileo story, it goes from being mostly about politics and ego to a conflict between enlightenment and dogmatic oppression. That’s a pretty big jump.

And the most frightening part is that we don’t just do this to the past. I generally try to avoid watching the news as much as possible (here is a good explanation of why), but if you watch for just ten minutes, you’ll see that every story is spun and contorted until it fits a simple narrative, no matter how complex the issue really is. At best it’s misleading. At worst, it’s manipulative.

Just keep that in mind the next time you see something on the news…there’s usually more there than what they’re showing you.

Everything in its Place: Managing Modifiers to Improve your Writing

Let me start this with a few disclaimers.

Disclaimer #1: I have not formally studied writing since high school. I am not a syntactician nor am I a grammarian of any sort. I am a physicist and a teacher by training and a writer only by preference, someone who loves to read and write and observe. I will be avoiding using technical syntactic vocabulary because 1) that is not my area of expertise, and 2) who really cares about that shit anyway (side note: I apologize if you do in fact care about that shit, but if you do you can find many far more knowledgeable sources on those topics than myself). Basically, this is just my opinion and I welcome you to share your own so that we all (myself included) might improve ourselves.

Disclaimer #2: My view of the goal and purpose of writing no doubt colors my thinking of structure and style to a large extent. For that reason, I feel I should briefly describe where I’m coming from before diving in to the subject at hand. I view writing from the aspect of storytelling. I judge almost everything about a book by how well it sucks me into its world and carries the forward momentum of the story along. I love phrases and sentences for the payload they carry, the effect they have on me, and not for their grammatical or syntactic perfection or elegance. A beautifully-crafted sentence that cannot translate into a tangible image or emotion when I read it (if such a sentence is possible) just doesn’t do it for me. I’m a pragmatist when it comes to writing; good writing is writing that works, not necessarily writing that is most technically correct.

Disclaimer #3: This may get a little bit long. I apologize for that. I’ll try to make it worth your while.

What are modifiers?

Disclaimers out of the way, let’s briefly review what a modifier is so that we’re all on the same page. If you’re confident you already know what a modifier is and there’s nothing I might cover you haven’t heard before, feel free to skip down to the next section.

Modifiers are, brace yourself, words or phrases that modify other components of a sentence. I’ll try not to get too technical (because, again, who cares?) but the very foundation of your sentence is called the base clause. This is the meat and potatoes of your sentence, the essential information that it must relay to your reader. It doesn’t have to be neat or pretty, just (technically) complete: subject and verb, all that stuff you learned back in elementary school. For the purposes of this section I’ll use as my base clause: He sat in the chair.

A modifier is anything you add to your sentence to give new meaning to your base clause. The first kind of modifier that will immediately come to mind is the one-word modifier: adjectives and adverbs. He anxiously sat in the chair. He sat in the green chair. Or, if we’re being truly bold: He anxiously sat in the green chair. Notice how each has expanded on the meaning of the base clause (though not by much, admittedly)

Adjectives and adverbs are the easiest modifiers to make and use in a sentence, so of course we won’t talk about them much. Actually, we’ll neglect them because 1) modifying phrases usually do a better, more descriptive job of conveying the same information; and more importantly 2) the main point of this post is to talk about the placement of modifiers in a sentence and there really isn’t anything to say about the placement of adjectives or adverbs. They can either precede or follow whatever they modify, and picking one of the other doesn’t much change the flow of the sentence. Case and point: He anxiously sat in the chair vs. He sat anxiously in the chair. Any difference in those two sentences are entirely rhythmic or stylistic, two things that are so individualized trying to tackle them would be pointless.

The same is true of adjectives. He sat in the green chair vs. He sat in the chair, which was green. Here the difference is a little bit pronounced and in this example one seems stuffy if not downright ridiculous. Adding so many extra words just for a single adjective is wasted space which dries out your sentence and decreases its impact and fluidity.

The other type of modifier, the type which will be the focus of this post, is the modifying clause or modifying phrase. These are any phrases which cannot themselves stand as full sentences that modify any part of the base clause of your sentence. For reference, each of the last two sentences contained modifying phrases (the type which will be the focus of this post, and which cannot themselves stand as full sentences). These are, usually, far more powerful than one-word modifiers because you can use them to evoke specific details or add new actions altogether, giving you much more freedom than simple adjectives or adverbs ever could.

Notice how He sat, hands trembling and sweat forming on his brow, in the chair gives you a much more visceral sensation than does the simple adverb anxiously. It also, I would argue, changes the feel of the sentence. By deliberately spending more time and space emphasizing his reaction, the simple words the chair gain almost an ominous portent that was nowhere to be found before. Or, as another example: He sat in the chair, green although the dye had long since started to fade to a dreary and depressing white. Notice that, while before putting the modifier after the noun felt clunky, here it fits because the modifier adds enough extra information to warrant the extra space and word count afforded to it.

And keep in mind that the most famous modifying clauses of all are the sibling Metaphor and Simile.

Where to place your modifiers

Grammatically, modifiers are very easy to place. The can go before whatever they modify or after it. You can even jam them all the way to the front or back of your sentence, although doing so opens you up for the dreaded misplaced modifier (Green although the dye had long since started to fade to a dreary and depressing white, he sat in the chair is an example of the misplaced modifier because the modifier, which is intended to modify the chair, seems to want to modify the person sitting in the chair, which makes no sense).

As long as it’s clear what they are intended to modify, you can place your modifiers wherever you want.

But where should you place your modifiers? Finally we reach the main point of this post!

While to some extent the choice of where modifiers are placed is one of the things that gives each writer their own personal style, there are some concrete advantages and disadvantages to each. Knowing these can help you decide if you’ve placed your modifier in the most effective position.

Putting modifiers in front

In most cases, I would advise putting your modifiers in front of whatever they modify. This is certainly the case for descriptive modifiers.

The thing to keep in mind is that as a writer it is your job to determine three things:

  1. What information is given to the reader (plot, details)
  2. How that information is presented (word choice, foreshadowing)
  3. In what order that information is presented (sentence structure)

The point I’m going to be talking about is #3. Most people remember this on a large scale (You don’t put the conclusion to the story in the first chapter), but tend not to think about it on the small scale.

You have to remember that people read one word at a time in the order you’ve put them, and that as they do they form mental images of what is happening. Most readers don’t, or at the very least I certainly don’t, wait until they reach the end of a sentence or paragraph to begin processing the information it contains. It’s a brick-by-brick process, so putting your descriptive modifiers after whatever they are intended to modify can actually cause the reader to misinterpret the scene, then have to stop and go back over it.

This has happened to me a lot. I read a line of dialogue, imagining it said in a certain way only to get to the end to see “she shouted, tears in her eyes” when I thought she was happy. This is a sign of sloppy writing, and a betrayal of the reader-writer contract of “I’ll tell you what you need to know, when you need to know it.” If it matters that the character is shouting, you need to find a way to convey that information before I read the dialogue.

The same is true for modifiers. In some cases the difference is negligible, for example knees cracking, he sat down and he sat down, knees cracking have no real significant different between them in terms of the pacing of the sentence, but only because the modifier is so short.

As an example of where it would matter, take the following two sentences:

“I don’t think I’ve done anything wrong,” the man added without a hint of regret.

“I don’t think I’ve done anything wrong,” the man added, his eyes looking anywhere but at mine.

Those two sentences are identical up until the modifier at the end, but that modifier colors everything that came before them including the tone in which the dialogue should be read. If your modifier completely changes the tone of the sentence, it needs to be in front.

This is the case with most adverbial modifiers. You need to tell me how something is done before it happens so that I can picture it the way you want me to. Otherwise you’re just hoping that we both picture the same thing and slapping me in the face if I’m wrong.

That said, you can also do the reverse by intentionally misleading your reader using modifiers before whatever they modify. For example: Huffing and puffing, sweat pouring from every part of his body, looking like he had just ten rounds with a champion boxer, he finally made it up the first flight of stairs.

Putting your modifiers at the front of your sentence allows you to set your readers expectations. Whether you fulfill or dash them is up to you.

Putting modifiers in back

All that said, there are times when the modifiers should go behind whatever it is they modify.

Adjectival modifiers generally fit into this category, and for exactly the same reason adverbial modifiers should go in front: It allows the reader to process the information in the proper order.

Take for example: Once white, now speckled with the grime and wear of neglect, the walls needed a new coat of paint.

That sentence works, but only if the subject of a walls was brought up previously. If this is the first we’re hearing of the walls, we just have no idea what this phrase is modifying and thus cannot establish a mental image of it until we finally reach the end of the sentence. That modifier could just as easily be describing a floor, a sink, a bathtub, or a toilet.

The same way you wouldn’t start painting without first laying down your canvas, you don’t start describing something you haven’t first introduced to the reader. That’s just wasting your words.

Another reason to put modifiers after whatever they modify is to imply order, especially chronological order. He took his stance, his gloves shaking slightly in front of his face, his footsteps heavier than they had been just one round earlier, but his gaze unwavering. Here the choice of putting the modifiers after the base clause seems to give the sentence a sense of motion through time. It progresses the story.

Note that the same thing can also be done with the modifiers in front (e.g. Not even having time to toast it, he shoveled some bread into his mouth as he sprinted for the bus) depending on the situation.

Yet another use for putting the modifier at the end is if it adds new information that isn’t directly related to the action of the base clause. He reached down a grabbed the fish, the very one which had swallowed his wedding ring all those years ago. Adding too much new information in the middle of a sentence can cause your reader to lose interest, while putting it at the end makes a nice segue between the two ideas.

You can also use this to surprise or shock your readers. He howled with delight tainted to no small extent with madness, the severed hang hanging by its hair from his bloodied hand.

Final thoughts

There really aren’t any hard and fast rules for when to put your modifier before or after the clause it modifies. These are only some of the many things to keep in mind. Just remember when writing to think about how the information you present will hit the reader and go with whatever sounds right. Maybe try it both ways and see which one strikes the chord you’re looking for.

And for sticking with me through such a long, possibly-boring post, here’s a picture of a smiling puppy (note: this puppy is, sadly, not mine):


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).


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.


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).


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.


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.


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.


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.

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?


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.


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.