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.

Continue reading

The Physics of Weight Loss

Today I want to talk about weight loss. Or getting into shape. Or both. This is something I’ve been thinking about lately, and while I’m sure probably everyone reading this has had to lose a few pounds at one point or another. Everyone knows the deal: To get in shape you need to watch what you eat, hit the gym, take up running/jogging/biking, so on and so forth.

Time to hit the gym

But why? Why does any of this stuff work? Everyone knows that running can help you lose a few pounds, but most people don’t actually know why, or more importantly where that weight goes. So it’s time for me to do what I do best: overanalyze things with physics.


We often use these two terms interchangeably, but in fact they are completely different—albeit related—things. Your weight is essentially your mass—how much stuff you’re carrying around with you. It’s how hard you’re pulled toward the center of the earth. Every single part of you—fat, muscles, bones, skin, organs, everything—contributes to your weight.

Your shape, on the other hand, is really about how that weight is arranged. In American culture, you’re generally considered to be in shape if you have low amounts of body fat and at least some muscle. Obviously that’s a broad generalization but we have to define our terms somehow.

When talking about either recreational fitness or overall health and wellbeing, your shape is far more important than your weight. Especially since muscle weighs more than fat. It’s not your weight that reduces your lung capacity or puts you at a higher risk of stroke and heart attack, but the amount and distribution of fat in your body. This is why the Body Mass Index (BMI) which compares only your weight to your height, is worse than useless as a measure of health. Just going by their BMIs, most professional football players would be considered obese.

Just look at this fat slob

But there’s another reason for distinguishing between weight and shape, and that’s because the two of them change somewhat independently of each other. Anyone who’s ever started lifting weights to get into shape knows this. As you replace the fat with muscle your shape will improve while your weight increases. And people who starve themselves will see their weight fall while their shape deteriorate as their bodies pack on stores of fat. There is somewhat of a correlation between the two, but what exactly that is differs from person to person depending on body type and genetics.


Physically speaking, losing weight is incredibly easy. One of the most fundamental rules of our universe is the conservation of mass. That is, mass can neither be spontaneously created nor can it spontaneously disappear. And since weight depends on mass, this gives us an equation for the change in a person’s weight:

The amount by which your weight will change over any given time is exactly the difference between how much weight you added to your body (by eating) and how much weight you removed from your body (through various excretions). Notice that this depends only on the amount of food you eat, not the quality of it. In terms of your weight, a pound of celery is just as bad as a pound of birthday cake. Also notice that this does not depend on how much or how little you exercise.  It’s simply the difference between what’s going into your body and what’s coming out.


This is where it gets complicated, and I’ll admit I’m by no means an expert in biochemistry. But I’m not too sure how many people would be interested in those details anyway so I’ll just summarize. Where your weight is all about the mass in your body, your shape is all about energy.

All of our energy comes from what we eat. It’s stored in the chemical bonds of food and we measure it in calories. In our stomachs we use acid to dissolve the food, storing that energy in glucose molecules. That glucose is then either used for energy immediately or stored in the body as glycogen in fat deposits. As our bodies consume energy throughout the day we dip into these fat reserves, so the key to staying shape, or at least the key to not gaining any fat, is to use more energy than you consume.

What makes this difficult is that it’s very hard to measure exactly how much energy your body is using. We are literally using energy all of the time, even when we’re sleeping. It takes energy just to be alive. We’re constantly spending energy to heat ourselves up, and an incredible twenty percent of all of the energy we use throughout the day goes to powering just our brains. We call the amount of energy it takes to sustain your resting body your Resting Metabolic Rate (RMR, although when I learned it we called it the Basal Metabolic Rate), or more commonly known as your metabolism. Since muscle tissue requires more energy to sustain than fat, the more muscles you have the higher your RMR will be. Any extra energy your body uses due to exercise adds to this metabolic rate to determine your body’s total energy output. If you’re consuming less energy than you’re using, your body will naturally take the difference from its stores of fat, leading to you being in better shape.


I’m sure you’ve heard before that you weigh less in the morning than you do at night, and it’s true. It’s not just because of all the food you ate during the day, either. So a big question is: where does that weight go? It’s tempting to say that it’s due to the energy our bodies use while we sleep, as mentioned earlier, but that’s not right. We’re not stars, so we can’t convert mass into energy. Honestly, I think the real answer is even stranger than that.

We breathe all that extra mass away. That might sound ridiculous, but think about it. When we breathe, we inhale air with a density of around 1.2 grams per liter and exhale carbon dioxide which is considerably heavier with a density of 1.977 grams per liter. It’s not enough to notice a difference with a single breath, but multiplied over the course of an entire night it can add up to over a pound. And if this still seems a bit farfetched, consider that the exact opposite process—inhaling carbon dioxide and exhaling lighter oxygen—is where trees get all their mass.


According to everything I’ve said so far, it would seem that there’s no link between exercise and weight loss. But anyone who’s ever exercised knows that isn’t true. I’ve come back from 10 mile rollerblading trips a full three pounds lighter than when I left. So where is that weight going?

As you can probably guess, a significant amount of this is water weight which we lose through sweat, but not all of it can be explained this way. The process of the body using fat to power itself is called ketosis, and through a lengthy series of interactions the glycogen mentioned earlier is converted into ATP, the form of energy which can be used by our cells. The biggest byproducts of this reaction are water and carbon dioxide. So as your body undergoes ketosis, the fat cells shrink as the glycogen is removed from them and you sweat and breathe out the byproducts, causing you to both lose weight and get into better shape.


You’re probably expecting me to have some final wisdom about the best way to get into shape or lose those pesky pounds, and I really wish I did, but ultimately it boils down to knowing your body and using common sense. One of the strangest things working against us in the battle of the bulge is our sense of hunger. Don’t trust it. Studies suggest that for people in developed countries (with ready access to stocked refrigerators and grocery stores) hunger is more of a social and conditioned response than a physiological one. One thing I’ve found lately is that I was just eating way more than I needed to, even though my eating habits before hadn’t been particularly unhealthy. What I’ve come to realize is that what I considered my resting state before was actually my body’s way of saying it was full. I was essentially filling the tank every time it dropped below three-quarters, and in doing so I was keeping my body from using its stored energy. If you find yourself consistently feeling stuffed after meals that might be why. Try to really pay attention to what your stomach is telling you, and just because it’s growling doesn’t necessarily mean it’s empty.

The Problem with Public Education

Wow I’ve been away from here for a long time. But things have been crazy for me. Not that they’ll be getting any simpler in the future (more on that in a second), but going forward I want to make posting on here a much bigger priority than it has been in the past.

Starting next year, in addition to teaching full time, I’m going to be working on a doctorate in science education. After all, who needs sleep anyway? The reason I decided to go back to school was because I, like many people, think the American public education system isn’t doing what it’s supposed to be—what it could be. And, like many people, I see that the current measures proposed to fix it simply won’t work.

Don’t get me wrong. I’m somewhat ambivalent to Common Core, the newest education reform initiative to be unrolled in the States. I think spiritually it’s actually a good idea. Unfortunately, as is often the case when large bureaucracies are involved, many of its fatal flaws are in its execution.

But that’s not even the worst part. Common Core will fail, or at least it won’t accomplish what those who proposed it want it to. And the reason is simple: Common Core is an attempt to fix our education system without addressing any of the things that are actually wrong with it. It’s like trying to treat a cold with a tourniquet.

But I only had a runny nose (Getty images)

Let me start this by saying that I believe in the public education system. If I didn’t then I wouldn’t be a part of it. I wouldn’t be going back to school in the hopes that I can make my voice heard and change it for the better. However, it is clear to anyone watching that we need to do things very differently if we want to get the kind of results we desperately need. And we do need to fix this problem. Toying around with education is gambling with our future and, as anyone who follows the news knows, the need for creative and intelligent thinkers has never been higher.

I’m going to post a lot about what I think we’re doing wrong in public education and what I believe can be done to fix those problems, but here I think I’ll start just by explaining why I think we let things get so bad; why there is such a need for deep, systemic reform. So thanks for sticking with me through the introduction, let’s get to the heart of the matter.




There is only one thing I should have to tell you to make you see that what we’re doing in our schools is wrong, and that is the fact that we haven’t significantly changed the mechanics of our education system since the 1840’s. Yes, we’ve undergone cosmetic changes and many “reforms” since then, but if you ask any modern student what the staples of their education are, you’ll find that the list you get has changed alarmingly little for over 150 years. We may have changed what a classroom looks like by including iPads and SMARTboards, but we haven’t changed what a classroom is, at least as an institution.

But why should we have to change it? As the old adage goes, “if it ain’t broke, don’t fix it.” People could argue that the reason certain elements have persisted in education for so long is because they are fundamentally valuable to the learning experience. But none of them are. I’m sure I’ll go into each of them in more detail in other posts in the future so I’ll leave that alone for now and use a more general argument here.

We most often relate evolution to biological systems, but it is in fact a universal truth. Everything—animals, people, societies, institutions, even ideas—need to adapt and change as the climate around them shifts or risk fading into insignificance. Think about the samurai of Japan, a once dominant class that failed to adapt to the arrival of new technology in the form of western guns. Look at newspapers, which either move more and more into online distribution or fold under the weight of antiquated printing costs when no one (under the age of 30) reads print newspapers anymore. This is just the way of the world: things change; either you change with them or you become irrelevant.

None of this is even to mention the fact that our education system is the spiritual successor of a Prussian model designed not to educate but to instill obedience; made to produce workers, not thinkers. The fact that we haven’t allowed it to change in any significant way is really the least of our worries when the original system was so far off what true education should be.

But why, if as I suggested above institutions must evolve or be left behind, has education almost alone been able to remain fundamentally unchanged for so long? The answer is simple: we need it.

The fact that education in this country has stagnated for so long is a direct result of the way we view education. In America, as in a lot of other places, we see the availability of quality education as a fundamental human right. Education as a resource is something that everyone should have access to.

And don’t get me wrong, I completely agree with that. Education is the strongest weapon against the many inequalities that still plague the modern world. It’s essentially a requirement for social reform.

The problem is exactly that: the institution of public education has become a requirement. And once something is necessary, once its value is determined not by how well it achieves its goals but by the mere fact of its existence, it no longer needs to evolve or change. Because no matter how broken, bloated, or ineffective it becomes, we will still support it because we need it. The exact same thing has happened to our government as a whole, but that’s an issue I really don’t want to touch on here.

Exempting any institution from the need to evolve in order to ensure its survival is the surest way to make it ineffective. If you don’t have to change, why would you? That takes effort. It’s hard and uncomfortable. Other businesses take that risk because if they don’t, if their competitor does first, they lose their customers. But there are no competitors to a public education system, no one to step in and force them to move forward or be left behind.

As only one of many example of this, let’s talk about summer vacation. As much as we love having that solid chunk of time off, any teacher you ask will agree wholeheartedly that having an extended summer vacation the way we do is bad for education as a whole. Kids come back from having that much time out of the classroom with heads full of mush. It’s not their fault. We’re creating an unnecessary and detrimental division between time spent as a student and time spent as a kid. Everyone who has studied this issue agrees that if we took time away from summer vacation and strategically relocated it throughout the year so that the amount of vacation days didn’t change, our educational system would benefit.

Do today’s students even know why summer vacation exists in the first place? So that kids could help out on their parents’ farms during the busy season. That’s it. Does anyone still use it that way? Yes, it is a time for kids to get “summer jobs” and internships, to build work experience and learn some responsibility, but those things could easily be worked into the school year itself if we weren’t so fixed on taking the existence of summer vacation as a given.

So, if summer vacation is so detrimental to our schools, it no longer serves its original purpose, and a solution is readily available, why do we still have it? Because politics. It’s the same reason pennies still exist despite being more than useless. None of the people who are in a position to make this decision feel like it’s in their best interest to change it. No one wants to be that guy who abolished summer vacation, and if he was his odds of being re-elected would probably be pretty slim.

Arguably, summer vacation has taken on a new purpose—to give kids (and teachers) time to recover from the stressful environment of school. But that to me just indicates that we’re doing school wrong. It shouldn’t be some torturous experience that kids have to suffer through until they get their shot at freedom. If schooling were done correctly, kids shouldn’t want to leave. It should be an energizing experience, not a draining one. Yes there should be breaks and times for families to go away together, but if kids really need three months to recover from a year of school, then we are doing things seriously wrong.

In summary, the fundamental problem with public education is that the system has no incentive to improve itself. Public schools will always exist almost regardless of what they do inside their classrooms. Unlike almost any other business or institution, they don’t lose by refusing to adapt to the changing demands of our modern world.

Only we do.

Thanks for reading. Let me know what you think about this issue below.

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):


‘A’ vs. ‘An’–the why and how

It’s been a while since I’ve updated anything at all, and even longer since I’ve posted anything about writing. I’ve taken on a new project which I’ll probably talk about more once I have something to show for it. For now, all you get is a pedantic rant about one of the smallest yet most irksome mistakes I see in writing.

Putting an ‘a’ where there should be an ‘an’ might not seem like such an unforgivable offense at first. It doesn’t obscure the meaning of the sentence as other grammatical mistakes may. But every time I see or hear this mistake it grates on my nerves like nails on a chalkboard.

It’s not just a stylistic or pedantic reason that this particular mistake bothers me. Coming across this mistake robs the entire passage of any narrative momentum it may have had, making you stop dead in your tracks much the same way a misplaced comma does. It’s one of the little things that can suck you right out of whatever you’re reading.

What is the rule?

Most–if not all–of you have probably heard this rule before. If a word begins with a consonant it gets ‘a’ while a word that begins with a vowel gets ‘an.’

However, saying it this way is what leads to some of the confusion. The truth is, whether you use ‘a’ or ‘an’ has nothing to do with how a word is written or spelled. The difference is entirely for spoken English.

Everyone knows the five and a half vowels (a, e, i, o, u, and sometimes y), but how many people are actually taught what makes a vowel a vowel? The difference between a vowel and a consonant is in what you do with your mouth while you pronounce them.

Consonants are closed sounds. While pronouncing a consonant your mouth closes in one way or another, either by touching your lips together or pressing your tongue against the roof of your mouth. In contrast, while pronouncing vowels you keep everything open.

This difference is actually why consonants and vowels combine so well to form syllables, whereas several consonants in a row are hard to pronounce. It’s also why vowels tend to merge together and change their pronunciation when placed side by side.

For most letters you can only say them one way. No matter how it’s stressed you can’t pronounce an ‘a’ without keeping your mouth open and you can’t pronounce a ‘b’ without closing it.

Y is the exception. Sometimes you pronounce ‘y’ by closing your mouth and then opening it, such as in the words yonder or yodel. In this case it’s a consonant. But other times, such as in the word why, you keep your mouth open, making the ‘y’ a vowel. This is why we say that y is only sometimes a vowel.

So the rule ‘a’ if consonant, ‘an’ if vowel, applies only to the sound it makes. If it sounds like it starts with a consonant, whether or not it does when you write it out, you put an ‘a’ in front of it. Two examples of this are “a unit” and “a eukaryotic cell”. Both of these words sound like they begin with a consonant ‘y’, and so they get ‘a’.

Similarly, if it sounds like it starts with a vowel it gets ‘an’. An heir, or an hour are good examples of this, since in both cases the ‘h’ is silent and thus, when spoken, they begin with vowels.

Again, the reason for this rule is to make spoken English clearer and more fluid. Multiple consonants in a row sound slow and sloppy, which is why “an banana” just sounds wrong. Multiple vowels in a row merge together, which is why “a apple” just turns into “apple” with a long ‘a’ in front. The ‘n’ was added to the end in order to keep space between the two vowel sounds, to make it clear where one word ends and the other begins.

What really gets me are the hypercorrections people make, such as putting ‘an’ in front of every word that begins with an ‘h’. This is why you’ll have people talking about “an historic event.” These hypercorrections stem from people knowing the rules but not really understanding why they exist, which is why I went into more detail than you’d ever wanted to know about vowels and consonants.

Hopefully that cleared somethings up for people. If not, at least it let me rant about something that had been bothering me lately. Until next time,


Blue Skies Ahead

Question: Why is the sky blue?


Answer: It isn’t. Not the same way that bluebirds, sapphires, and the members of Blue Man Group are, anyway. To see why, we need to first talk about what exactly we mean when we say that something is ‘blue’ or ‘red’ or any color at all.

To talk about color, we must first talk about light. Light, at the smallest scale, is broken up into photonsindividual particles or pieces of light. Those photons each have a certain amount of energy, and a corresponding frequency, that determines their color. In physics, there are only six colors in the visible spectrum (red, orange, yellow, green, blue, and violet) with many more outside what we humans can see (radio, microwaves, infrared, ultraviolet, x-ray, and gamma). Red light has a lower frequency than yellow light which has a lower frequency than blue light.

So where do the other colors come from? If all we have are those six colors to choose from, how do we get browns and pinks and even white? What may surprise you, especially if you’re artistically inclined, is that you get brighter, lighter colors by adding multiple colors together. White light is light which contains frequencies of all the other colors at once. That is why you can see every color when in a room lit only by white light–the white light contains all the other colors. Notice how this is different than what you get if you add together different pigmentslike paints. If you add pigments together you end up with a dark, blackish color. We’ll talk about why these two are different in a second, but first we must discuss what it means for an object to “be” a certain color.

For the most part, color in the natural world is a reflective property. This is because most objects don’t emit their own light (some things, like butterfly wings, are colored by diffraction but that’s a different story entirely). They only reflect light that hits them, redirecting it into our eyes. However, most objects don’t reflect all of the light that hits them, only certain frequencies or colors.

When you look at an object and see white, it means that object is reflecting all colors of light back at you. Black objects reflect little to no light (this is why wearing a black shirt in summer makes you warm). When you see a blue object, it means only blue light is reflected off of it, with all other colors being absorbed.

When we say an object is blue, we mean that it only reflects blue light. A blue object absorbs every color except for blue. This is why mixing pigments gives you darker colors. Each pigment only reflects certain ranges of colors, and if these ranges don’t overlap, less light will be reflected, giving you a darker, gray or black color.

With all of this said, we can now return to our original question: What color is the sky? To answer this, we need to know what exactly the sky is. And for the most part, it’s air. Mostly nitrogen, about 20% oxygen, some carbon dioxide, and other trace gases. It’s the same stuff that surrounds you all the time. It’s the same air that you’re breathing right now.

So look around. What color is the air around you? What colors of light are being absorbed by the “empty” space in front of you? Unless you’re living in a heavily polluted area, the answer should be clear. Literally.

Air is transparent. And thus, so is the sky.


Revised Question: Why does the sky appear blue?

Answer: You might think that was all a little bit pedantic, but the distinction between the sky looking blue and the sky being blue is crucial to understanding why the sky looks the way it does. The sky isn’t colored by reflection the way most other objects are. It’s a different process entirely, one you may have experienced yourself without realizing.

What lights up the entire sky is the sun. And the sun, despite what you may think from looking up at it here on Earth, is white. Not yellow, not orange, but white.


Courtesy NASA

What you’ll notice in the picture above is that, when viewed from space, the light from the sun doesn’t spread nearly as much as it does here on Earth. In fact, even with the glare, you can see the total blackness of space as little as ten degrees away from the sun.

What allows the sun to color the entire sky is a process known as Rayleigh Scattering, and it’s exactly what it sounds like. If you think of light as a stream of tiny particles (or photons), then you should be able to imagine those particles colliding with things like molecules in our atmosphere. As a result of those many collisions, the light gets scattered, spreading out in all directions so that, no matter where you look, you can see it.

If you have ever played with a laser pointer you’ve experienced this before. Shine a laser pointer at a wall and all you’ll see is a red dot. You won’t be able to see the beam itself. But give the light something thick like smoke or fog or chalk dust, and the beam will scatter off of it, becoming visible to all.

So the scattering of light can explain why the sky has color, why it’s not just pitch black around the sun. But why is it blue?

I will try to stay away from doing too much math (there was enough of that in my last post), but there is an equation which governs the amount of scattering that occurs via this process:


It’s a messy formula, and if you’d like more information about what each variable represents you can check here, but the important part is the dependence on frequency. The higher frequencies of light scatter more than the lower frequencies. This is why you can see blue and violet all over the sky, but red and yellow only when you look directly toward the sun. The lower frequencies don’t scatter as much.

Only a few more questions to clear up. If higher frequencies of light scatter more, why is the sky blue instead of violet? The answer is because the sun emits more blue light than it does violet. The violet does scatter, but it is overwhelmed by all the blue light around it.

Why is the sky red during sunrise/sunset? At these times, when the sun is reaching the horizon, the blue light scatters too much, having to pass through too much of the atmosphere to reach us. Once all of the blue and purple light has been scattered away, all we’re left with are those beautiful red, orange, and golden sunsets.

Well, this was a fun one. What I like about questions like this is how trying to answer one question opens up–and then answers–many more. For example, you may have thought that it would be simple to explain why the sky is blue, but in the process of doing so we got to talk about what color is, how things get their color, and the scattering of light in a medium. These are the kinds of questions I like most, where the answer takes a winding road through different areas and disciplines. It’s because of questions like this that I started teaching. Unfortunately, given our prescriptive and standardized attitude toward education, it’s rare that kids be given the chance to really explore a topic like this in school.

That about wraps it up for this week. If you have any other questions you want answered, let me know.

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.

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.]


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


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.


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.


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.