The Community College Syllabus

This is a pet peeve of mine and nothing more, but I've seen it a lot in similar contexts. Logging in "at least three to five times a week" makes no sense. We can log in at least 3 times a week. If we happen to log in 5 times a week, then that would still be at least 3 times a week.

You could argue that "at least" only applies to the three, but then he's telling us to log in a minimum of 3 times and a maximum of 5 times per week. Who knows, maybe's that the case. Given how often the website goes down, maybe they're trying to limit bandwidth usage.

Or he could be telling us that we must log in a minimum of 3 times per week, but he'd like to see us logging in between 3 and 5 times per week. Clearly, this is what is actually meant, but it is not what is written. Now, I know that no one is going to be confused by this. So it is what's conveyed, even if it is not what's written. So why am I complaining?

My reasons are three. First, he's an English teacher. He's going to be correcting our grammar for the next five weeks with varying degrees of exactitude, so it'd be nice if he showed the same amount of care in his own writing.

Second, this is a course designed for writing in the workplace. Like, if you wanted to be a tech writer, you might start with a course such as this one. Well, I've been a technical writer before. And you know what? Imprecise language like the phrase used above is not cool. It leads to mistakes, complaints, and lawsuits.

(Source)

Third, as a professor of English, he should really care about doing right by the language. Yes, language changes. Yes, the point of a language is communication, and if that's achieved, who cares about anything else.

But here's what gets to me. The English language is a gigantic hodgepodge of words and there are an absolute crap-ton of ways to arrange them meaningfully. So we can communicate precisely if we have sufficient mastery over syntax and vocabulary, but we don't because it's hard. Instead we think whatever we're thinking, vomit out the words we most closely associate with said thoughts, and hope the listener has roughly the same associations for those words, thereby getting the gist of the message across. Blech.

Headlines Funniest Part of Onion Articles, Says Guy on Street

WASHINGTON, D.C.—In a suburb just 20 miles outside Washington, D.C., local man Charles “Chuck” Braxton has recently begun telling coworkers and friends that, “Really, the whole joke is in the headline, if you think about it.”

Chuck, who does banal office work for incompetent middle managers but has always styled himself a comedian, went on to say, “I mean, I could write these articles. The headline is an amusing observation, but the rest of the article just drags out the joke by having imaginary interviews with pedestrians.”

According to Wikipedia, The Onion is a satirical newspaper founded in 1988 by Tim Keck and Christopher Johnson. While originally just a joint project between the two college students with limited circulation on several campuses, The Onion has since flourished into a fully developed satirical news organization featuring a television network, website, and twitter account. But it’s the Facebook posts that really get to Chuck.

“I see the same headline 5 times a day on my timeline,” explained an exasperated Chuck. “And yeah, the jokes are funny, but it’s always the same pattern. I just wish they would spice things up a bit sometimes.”

Sources close to Chuck have indicated that, “If he doesn’t shut up about this ‘Only the headlines are funny’ thing, I’m seriously going to kick his ass.” At press time, The Onion had not responded to requests for comment.

The Community College Website

Human rights, brought to you by your local community college. Did we turn down the first offer?

As far as modern poetry online, I can only assume they're referring to this.

(And don't get me started on the missing apostrophe.)

The Community College Cafeteria

Where timeless wisdom and crass marketing come together.

(I'll probably post something substantive later today.)

Reindeerpower

While watching football today I saw a commercial for the Chevy Silverado featuring the Santa Salesman. Here's a Youtube clip:

Santa is poised to calculate the reindeerpower of the Silverado, but sadly the commercial ends before he can give us an answer. Thus we are left to speculate the magnitude of 1 reindeerpower.

How would we go about doing that? We need to start off by setting a few ground rules. Santa and his reindeer are clearly capable of time travel and/or superluminal speeds, which makes estimating their power output somewhat troublesome from a theoretical perspective. Like good scientists, we have to limit ourselves to the reindeers' documented behavior.

The most authoritative eyewitness account makes the claim that:

More rapid than eagles his coursers they came...

Although the authorship of this account is apparently in dispute, the two possibilities are both American. We can assume that the author was most familiar with the American Bald Eagle, which Wikipedia says can fly at about 17 m/s. Let's estimate that Santa's reindeer can achieve something on the order of 20 m/s.

Now, the record here provides us with another useful tidbit as well:

As dry leaves that before the wild hurricane fly,
When they meet with an obstacle, mount to the sky.
So up to the house-top the coursers they flew,
With the sleigh full of Toys, and St Nicholas too.

We learn from this that the reindeer are ascending while traveling faster than eagles. This gives us a very easy way to calculate their power output.

But before we go any further, we have to figure out just what power is from a physics standpoint. Most of us encounter power in two forms: the horsepower of our cars, and the wattage of our electrical items. Both measure the same thing, just in different units. Power is the rate at which energy is transferred -- the standard unit being Joules/second, the watt. 1 hp is 746 W.

So how do we measure the rate of energy transfer? Well, we know that Santa's reindeer can ascend at 20 m/s, which means they can create 20 meters worth of gravitational potential energy in just 1 second. Gravitational potential energy, as we recall, is mass * gravity's acceleration * height. Gravity's acceleration is a constant and our height is 20 meters, which just leaves us with mass as an unknown.

There are about 2 billion Christians in the world. If every one of them receives an iPad or a Kindle for Christmas, we can estimate that (with packaging) this amounts to 2 billion kg worth of presents. We can safely assume that Santa, the sleigh, and even the reindeer add nothing significant to this estimate. All that's left to do is plug in the numbers, then.

The power output for the entire sleigh comes to about 400 gigawatts. (This is an encouraging result, because it's over 300 times the power needed by the DeLorean to travel through time. And as previously discussed, Santa must rely on time travel to deliver all his presents in a single night.)

If we assume that Santa derives all his motive power from the reindeer, and that there are only 8 reindeer (Rudolph, being a mutant, likely delivers all his power to his red nose and provides no motive contribution), then each reindeer is worth 50 gigawatts. In terms of horsepower, this is 67 megahorsepower. The Chevy Silverado talked about above delivers a pitiful 315 hp, which comes out to 4.8 &#181rp (microreindeerpower).

I must reiterate that this is only an estimate. Santa clearly knows the proper conversion himself, so any confirmation on his part would be swell.

Happy holidays everybody.

Physics of the Apocalypse

Since we all just survived another apocalypse, let's take a look at what could have been. I've always associated impending apocalypses (apocalypsi?) with feline and canine precipitation. A quick googling shows that there isn't any particular reason for me to make this association. I think I'm probably conflating two things: raining animals generally is seen as an apocalyptic portent, and Bill Murray believed dogs and cats living together was a disaster of biblical proportions. I've learned over the years to trust Bill Murray on these sorts of things.

Anywho, just how bad would a rain of cats and dogs be? To answer that, we need to know how much energy a falling animal packs. The basic equation here is U = mgh, where U is the gravitational potential energy of a falling object, m is its mass, g is the acceleration due to gravity at the Earth's surface (~9.8 m/s²), and h is the height of the falling object above the surface. When the object falls, it loses potential energy as its height decreases. But conservation of energy tells us that this energy cannot simply be lost; it is transformed into other forms. Ideally, all of the potential energy has been turned into kinetic energy by the time the helpless animal hits the ground.

So, wikipedia says that cumulonimbus clouds, which are the kind of clouds we often see during thunderstorms, range from 2,000-16,000 meters in elevation. Now, I don't really know what sorts of clouds you'd have during the apocalypse, or what sorts of clouds precipitate animals, but let's just say your dogs and cats are falling from a nice round 10 km up.

If we have a fat cat, or a smaller breed of dog, the animal may have a mass in the neighborhood of 10 kg. This gives us a potential energy of 980,000 J. Let's just call it one megajoule. So, on a perfectly spherical, airless ball resembling the Earth, a falling animal hits you with the kinetic energy of one megajoule. What's that like? Well, that's about the same as getting hit by a car going 70 mph. That is to say, it kills you dead.

But a car is significantly more massive than a dog or cat, which suggests that the falling animal is going much faster than 70 mph when it hits. Indeed, we can calculate the speed of the animal's descent from the energy equation. The kinetic energy of a moving object is the familiar K = &frac12mv². A megajoule of energy and a mass of 10 kg works out to a speed of 450 m/s, or about a thousand miles per hour. That is very, very fast. It's also entirely unrealistic.

(Readers may notice that the initial energy, mgh, is equal to the final energy, &frac12mv². Since both terms contain mass, the mass cancels out. Consequently, the final speed of a falling object turns out to be √2gh, which is independent of mass, just as Galileo and Newton told us.)

We're all familiar with the concept of terminal velocity, and it would seem to play a role here. Objects in an atmosphere can only fall so fast, because there comes a point at which the upward force from air resistance is equal to downward force of the object's weight. At that point, there are no net forces, which means no acceleration according to our good friend Newton. Modeling air resistance turns out to be somewhat hard (and involves differential equations, which your humble physics student hasn't gotten to yet), but one of the interesting things about air resistance is that it increases as the speed of the object increases. In fact, it generally increases with the square of the speed. The upshot here is that falling objects reach their terminal velocity very quickly, so the height from which our animals are falling doesn't really matter all that much.

While figuring out the specifics of air resistance can be difficult, the formula for terminal velocity pops right out if you have a model for air resistance. The basic formula is v = √(2mg)/(&#961AC), where &#961 is the density of air, A is the cross-sectional area of the animal, and C is the drag coefficient, a constant that has to do with the shape of the animal. Working this all out, the terminal velocity for our 10 kg animal is around 25 m/s (56 mph). This is lower than the terminal velocity of a human-like object, and this fact has been put forward as one of the reasons why cats seem particularly capable of surviving falls from great distances.

So, with a maximum speed of 25 m/s, the kinetic energy of our raining animal is a measly 3 kJ, or roughly equivalent to the kinetic energy of a bullet. Getting shot is a bad thing, I'm told, but bullets are much smaller than cats and dogs, which means that the force exerted by the falling animal at any one point is significantly lower than that of the bullet. Getting hit by a falling cat or dog would certainly hurt, but it would be unlikely to kill you. This turns out to be a fairly mild apocalyptic event. The real danger probably arises from the fact that, once the rain has ended, there will be a surprisingly large number of living, and very pissed off, cats and dogs roaming the streets.

The bigger the animal, of course, the more dangerous it gets. Because terminal velocity is dependent on mass, the kinetic energy of a falling animal is proportional to mass^3/2. Cloud-bound elephants would be quite deadly, for example.

Now, some people might be wondering what happened to the other 9,997 kJ our falling furry friend was supposed to have. After all, energy is conserved, right? The answer can be framed a couple different ways. One is to say that the air does negative work on the falling animal. If this negative work is leaving the air, then the air gains energy. While this is a valid interpretation, it leaves one wondering just what negative energy is supposed to mean. The other point of view is that the falling animals push the air out of the way as they fall -- that is, they do work on the air. From this vantage point, the energy isn't lost but transferred to the air. Where it goes from there is beyond the scope of this example, but thanks to Emmy Noether, we know the energy will do just fine on its own.